The Corleonesi was an alliance were the Corleone clan was head of the the whole alliance, The Corleone clan was not the most powerful clan at the start in the 70's they managed to build up the alliance for a number of years slow.

Corleone clan did not have as much financial power when the big mafia war start in the 80's but their alliance had more personnel then the other side.

The big mistake of the side who was fighting the Corleone clan was in the years before the war they was flooding the United States with heroin and had money coming out of their ears they was good businessmen but did not put some of the money to the more blue collar criminals who they could of had as their muscle and the Corleone clan done just that got all the blue collar grass roots guys and took over the more financial powerful Bontade and Inzerillo side. The Corleonesi and their allies won the war easy.