OPENAI, INC., a corporation,
OPENAI, L.P., a limited partnership,
OPENAI, L.L.C., a limited liability company,
OPENAI GP, L.L.C., a limited liability company,
OPENAI OPCO, LLC, a limited liability company,
OPENAI GLOBAL, LLC, a limited liability company,
OAI CORPORATION, LLC, a limited liability company,
OPENAI HOLDINGS, LLC, a limited liability company,You can imagine a non-profit buying enough shares of a for-profit company that it can appoint the for-profit company's board of directors, at which point it's a subsidiary.
Heck a non-profit is even allowed and encouraged to make a profit. There are certainly rules about what non-profits can and can't do, but the big rule is that a non-profit can't distribute its profits, ie. pay out a dividend. It must demonstrate that their expenditures support their tax exempt status, but the for-profit subsidiary is more than welcome to pay out dividends or engage in activities that serve private interests.