The Goldman Sachs Group, Inc. (GS) 8-K Material Modifications to Rights of Security Holders

Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

January 28, 2020

The Goldman Sachs Group, Inc.,

200 West Street,

New York, New York 10282.

Ladies and Gentlemen:

We are acting as counsel to The Goldman Sachs Group, Inc., a Delaware corporation (the “Company”), in connection with the registration under the Securities Act of 1933 (the “Act”) of 350,000 depositary shares (the “Depositary Shares”), each representing aone-twenty-fifth (1/25^th) interest in a share of the Company’s 4.40% Fixed-Rate ResetNon-Cumulative Preferred Stock, Series S, par value $0.01 per share and a liquidation preference of $25,000 per share (the “Preferred Shares”). The Company filed with the Securities and Exchange Commission, on July 10, 2017, a registration statement onForm S-3ASR (FileNo. 333-219206) (the “Registration Statement”) under the Act relating to the proposed offer and sale of an unspecified principal amount of the Company’s preferred stock in the form of depositary shares, including the Preferred Shares and the Depositary Shares. The Depositary Shares are being issued pursuant to the Deposit Agreement, dated as of October 21, 2005, between the Company and The Bank of New York Mellon (as successor to JPMorgan Chase Bank, N.A.), as Depositary (the “Depositary”), and the related Letter Agreement, dated as of October 18, 2012, between the Company and the Depositary, as amended by Amendment No. 1, dated as of June 17, 2019, between the Company and the Depositary (such Deposit Agreement, Letter Agreement and Amendment No. 1 to the Deposit Agreement, collectively, the “Deposit Agreement”). The Depositary Shares are evidenced by depositary receipts (“Depositary Receipts”) issued pursuant to the Deposit Agreement.

In rendering this opinion, we have examined the following documents:

1. The Restated Certificate of Incorporation and the Amended and RestatedBy-Laws of the Company.

2. The Deposit Agreement.

3. The Certificate of Designations of the Company, as filed with the Secretary of State of Delaware on January 27, 2020.

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4. Certificates of officers of the Company with respect to the authorization of the Preferred Shares and the Depositary Shares, the determination of the terms of the Preferred Shares and the Depositary Shares and related matters.

5. Specimens of the certificates evidencing the Preferred Shares and the Depositary Receipt.

We also have examined such questions of law as we have considered necessary or appropriate for the purposes of this opinion. Upon the basis of such examination, it is our opinion that the Preferred Shares have been validly issued and are fully paid andnon-assessable, and that the Depositary Receipts evidencing the Depositary Shares have been validly issued and entitle the holders thereof to the rights specified in the Depositary Shares and the Deposit Agreement, in each case subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

The foregoing opinion is limited to the Federal laws of the United States, the laws of the State of New York and the General Corporation Law of the State of Delaware, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in the Registration Statement or any related prospectus or other offering material regarding the Company or the Preferred Shares or the Depositary Shares or their offering and sale.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible, and we have assumed, without independent verification, that the Deposit Agreement has been duly authorized, executed and delivered by the Depositary, that the certificate evidencing the Preferred Shares has been deposited with the Depositary in accordance with the Deposit Agreement, that the certificates evidencing the Preferred Shares and the Depositary Receipt conform to the forms thereof examined by us, that the certificate evidencing the Depositary Receipt has been duly executed and delivered by one of the Depositary’s authorized officers, that the certificate evidencing the Preferred Shares has been duly countersigned by a transfer agent and duly registered by a registrar of the Preferred Shares, that the certificate evidencing the Depositary Receipt has been duly recorded by the Depositary and that the signatures on all documents examined by us are genuine.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.

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Very truly yours,

/s/ Sullivan & Cromwell LLP