Not one family in particular, but at one time Tony mentions them having more than 200 soldiers so in that regard it must be either the Gambinos or the Genoveses. But I think Chase said in one of his interviews that the Lupertazzis represented New York in general..

The Sopranos also never interacted or talked about other made men belonging to the five families active in New Jersey, I think that would've made it a little too convoluted for the average viewer, who's not as knowledgeable about the mob like ourselves over here..