The "Mafia" in Chicago during the Torrio/Capone era was the Unione Siciliana, which was like a civic association with muscle. Torrio and Capone paid them great respect. Capone consulted them when he planned to whack his enemies, the Genna brothers, who were Sicilians. Capone, who was of Neapolitan descent, could not join the Unione, and constantly strove to have one of his Sicilians named as the Unione's president so he could exert more influence.

As others have noted, the Outfit in the Torrio/Capone years had lots of non-Sicilians and non-Italians in high places. When Capone came to Chicago ca. 1919, Torrio assigned him to work for Jack Guzik, Torrio's business manager, #2 man and chief political protector. Capone idolized Guzik, the two were fast friends, and the only person Capone killed with his own hands in Chicago was a wiseguy who had slapped Guzik around. Guzik ran the Outfit, along with Frank Nitti, when Capone went to Federal prison. Others have mentioned Epstein, Korshak, Humphreys, etc.

Keep in mind, too, that Charlie Luciano, though born in Sicily, was a thoroughy American businessman who had the same broadminded approach. He accepted help and advice from non-Sicilians and non-Italians, too. His closest associate was Meyer Lansky. He, Bugsy Siegel and Dutch Shultz, all Jews, sat with the Commission after Luciano formed it, though they could not be members. Luciano invited Capone to be the Commission's chairman. It was a brilliant move: it signaled that Organized Crime was more than just Sicilians, and it helped keep Chicago in the fold. He also named Joe Bonanno as "secretary," another effort to keep a "Sicilians-only" Don in the fold with the non-Sicilians.