Supplement No.6, dated May 19, 2026toProspectus, dated October 29, 2024 andProspectus Supplement, dated October 30, 2024 This supplement amends, supplements or modifies certain information contained in the prospectus supplement, dated October 30, 2024 (the“ATM Prospectus Supplement”), and the accompanying prospectus, dated October 29, 2024 (the “Base Prospectus,” and together with theATM Prospectus Supplement and the documents deemed incorporated by reference in each, the “Prospectus”), which relate to the sale ofshares of common stock of Capital Southwest Corporation in an “at-the-market” offering (the “ATM Program”) pursuant to certain equitydistribution agreements (as described below). The terms the “Company,” “CSWC,” “we,” “us,” and “our” refer to Capital SouthwestCorporation and its subsidiaries, unless indicated otherwise. Capitalized terms used but not defined herein shall have the same meaninggiven them in the ATM Prospectus Supplement. You should carefully read the entire Prospectus and this supplement before investing in our common stock. This supplement should be readin conjunction with the Prospectus.You should also carefully consider the information set forth under the sections entitled “Risk Factors”on page S-9 of the ATM Prospectus Supplement, page 10 of the Base Prospectus and in our Annual Report on Form 10-K for the fiscalyear ended March 31, 2026, which is incorporated by reference into the Prospectus, as well as in our subsequent filings with theSecurities and Exchange Commission that are incorporated into the Prospectus, before investing in our common stock. This supplement is being filed to reflect that, on May 19, 2026, we increased the maximum amount of shares of our common stock to be soldthrough the ATM Program to $2,000,000,000 from $1,000,000,000. In connection with the upsize of the ATM Program to $2,000,000,000,on May 19, 2026, we entered into those certain (i) sixth amendments to the third amended and restated equity distribution agreements, eachdated May 26, 2021 and as amended from time to time, with each of Jefferies LLC (“Jefferies”) and Raymond James & Associates, Inc.(“Raymond James”), and (ii) sixth amendments to the amended and restated equity distribution agreements, each dated May 26, 2021 and asamended from time to time, with each of Citizens JMP Securities, LLC (“Citizens Capital Markets”) and B. Riley Securities, Inc. (“B.Riley” and, together with Jefferies, Raymond James and Citizens Capital Markets, the “Sales Agents”). The Company’s equity distributionagreements with each of the Sales Agents are on substantially the same terms and conditions as one another. STATUS OF THE "AT-THE-MARKET" OFFERING From March 4, 2019 to March 31, 2026, we sold a total of 40,437,289 shares of our common stock under the ATM Program for grossproceeds of approximately $870.1 million and net proceeds of approximately $854.7 million, after deducting commissions to the SalesAgents on shares sold and offering expenses. As a result and as of the date hereof, after giving effect to the sixth amendments to the equitydistribution agreements with each of the Sales Agents referenced above, up to approximately $1.1 billion in aggregate amount of ourcommon stock remains available for sale under the ATM Program. FEES AND EXPENSES The following table is intended to assist you in understanding the costs and expenses you will bear directly or indirectly. We cautionyou that some of the percentages indicated in the table below are estimates and may vary. Except where the context suggests otherwise,whenever there is a reference to fees or expenses paid by “you,” “us” or “CSWC,” or that “we” will pay fees or expenses, you will indirectlybear such fees or expenses as investors in us. Shareholder Transaction Expenses:Sales load (as a percentage of offering price) (1)Represents the Sales Agents’ commission with respect to the shares of common stock being sold in this offering. There is no guarantee that there will be anyadditional sales of our common stock pursuant to the Prospectus.(2)The percentage reflects estimated offering expenses for this offering of approximately $4,100,000, of which we have incurred $2,180,000 as of May 15, 2026, and (3)The expenses of administering our dividend reinvestment plan (“DRIP”) are included in operating expenses. The DRIP does not allow shareholders to sell sharesthrough the DRIP. If a shareholder wishes to sell shares they would be required to select a broker of their choice and pay any fees or other costs associated with thesale.(4)Operating expenses in this table represent the estimated annual operating expenses of CSWC and its consolidated subsidiaries based on actual operating expenses for the year ended March 31, 2026. We do not have an investment adviser and are internally managed by our executive officers under the supervision of our board ofdirectors. As a result, we do not pay investment advisory fees, but instead we pay the operating costs associate