Jewish gangs were very big during Prohibition--generally much bigger than Italian gangs--and dominated the booze trade in most big cities. But, many Prohibition-era Jewish gangsters went legit after Repeal, and focused on gambling. They often worked with Mafia families but were never part of them,

Individual Jewish gangsters sometimes advised Mafia families. Lansky was very close to Luciano, Costello and Adonis, often partnering with them. Jack Guzik was Capone's close friend, advisor and mentor when he was new in Chicago. Rothstein gathered a cadre of up-and-coming Italian gangsters around him in the early '20's--including Luciano and Costello (also Lansky and Siegel), advised them and gave them political protection. But, he was killed in '28. Longy Zwillman was the OC leader of northern NJ and often was a senior partner to Boiardo and Catena. Moe Dalitz was "Mr. Las Vegas" and probably helped Mafia guys.

Overall: They often cooperated with Mafia families, and some Jewish individuals advised powerful Mafiosi, but they weren't always, or even often, the financial guiding lights of the Mafia.