WASHINGTON  Goldman Sachs has agreed to pay $550 million to settle federal claims that it misled investors in a subprime mortgage product as the housing market began to collapse, officials said Thursday.

If approved by a federal judge in Manhattan, the settlement would rank among the largest in the 76-year history of the Securities and Exchange Commission, but it would represent only a small financial dent for Goldman, which reported $13.39 billion in profit last year.

News of the settlement sent Goldman’s shares 5 percent higher in after-hours trading, adding far more to the firm’s market value than the amount it will have to pay in the settlement.

Even so, the settlement is humbling for Goldman, whose elite reputation and lucrative banking business endured through the financial crisis, only to be battered by government investigations that shed light on potential conflicts of interest in its dealings.