<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-23</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000793547</issuerCik>
        <issuerName>NAVIGATORS GROUP INC</issuerName>
        <issuerTradingSymbol>NAVG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001523819</rptOwnerCik>
            <rptOwnerName>Johnson Geoffrey</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O THE NAVIGATORS GROUP, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>400 ATLANTIC STREET, 8TH FLOOR</rptOwnerStreet2>
            <rptOwnerCity>STAMFORD</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06901</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2019-05-23</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10829</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>70.00</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">On May 23,  2019, The Hartford Financial Services Group, Inc. (&quot;The Hartford&quot;) acquired the Issuer pursuant to the Agreement and Plan of Merger (the &quot;Merger Agreement&quot;), dated as of August 22, 2018, by and among the Issuer, The Hartford and Renato Acquisition Co., a wholly owned subsidiary of The Hartford (the &quot;Merger&quot;).</footnote>
        <footnote id="F2">Pursuant to the Merger Agreement, at the effective time of the Merger (the &quot;Effective Time&quot;), each share of common stock of the Issuer, par value $0.10 per share (&quot;Issuer Common Stock&quot;) issued and outstanding immediately prior to the Effective Time was converted into the right to receive $70.00 in cash, without interest.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Deepa R. Nayini, attorney-in-fact</signatureName>
        <signatureDate>2019-05-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
