<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>2120100 - Disclosure - Significant Subsidiaries</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000722833</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>crpiii_EquityMethodInvestmentsSummarizedFinancialInformationAbstract</ElementName><ElementPrefix>crpiii_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Equity Method Investments, Summarized Financial Information [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>crpiii_EquityMethodInvestmentsSummarizedFinancialInformationTextBlock</ElementName><ElementPrefix>crpiii_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;SIGNIFICANT SUBSIDIARIES&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The following Local Partnership invested in by the Partnership represents more than &lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;color:#000000;text-decoration:none;"&gt;20%&lt;/font&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt; of the Partnership's total assets or equity as of June 30, 2013 and 2012 or net income (loss) for the three-month periods then ended. The following financial information represents the performance of this Local Partnership for the six-month periods ended June 30, 2013 and 2012. The financial information consists of estimates based on the audited financial statements of the Local Partnerships at December 31, 2012 and these estimates are unaudited. &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:center;font-size:10pt;"&gt;&lt;div style="padding-left:0px;text-indent:0px;line-height:normal;padding-top:10px;"&gt;&lt;table cellpadding="0" cellspacing="0" style="font-family:Times New Roman;font-size:10pt;margin-left:auto;margin-right:auto;width:56.0546875%;border-collapse:collapse;text-align:left;"&gt;&lt;tr&gt;&lt;td colspan="3" rowspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td width="34%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td width="33%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;td width="33%" rowspan="1" colspan="1"&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:middle;border-bottom:1px solid #000000;background-color:#bfbfbf;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;Meadow Lanes&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:middle;border-bottom:1px solid #000000;background-color:#bfbfbf;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;2013&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:middle;border-bottom:1px solid #000000;background-color:#bfbfbf;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:center;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;"&gt;2012&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Total Assets&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$3,888,464&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;$3,574,383&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Total Liabilities&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;262,557&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;433,329&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Revenue&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;412,667&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;253,636&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;Net Income&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:left;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;52,292&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;td style="vertical-align:bottom;border-bottom:1px solid #000000;padding-left:2px;padding-top:2px;padding-bottom:2px;padding-right:2px;border-left:1px solid #000000;border-right:1px solid #000000;border-top:1px solid #000000;" rowspan="1" colspan="1"&gt;&lt;div style="text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;51,518&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>Equity Method Investments, Summarized Financial Information [Text 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