The lodge was implicated in numerous Italian crimes and mysteries, including the Vatican Bank scandal, the death of Pope John Paul I and the murder of Vatican banker Frederick Keinszig. P2 was sometimes referred to as a "state within a state" or a "shadow government". The lodge had among its members prominent journalists, members of parliament, industrialists, military leaders and members of the mafia.
In the early 1960s, Sicilian Don Cesare Indelicato proposed Michael Corleone for membership, discussing the benefits it would bring. Michael would be the first American admitted. However, Michael presumably turned down the offer to become a member, as he otherwise wouldn't have had the problems he endured with Licio Lucchesi and others when he was trying to buy Immobiliare in 1979.