What NY mob family does Johnny Sac run?

So watching the Sopranos again got me thinking. The Johnny Sac character... what family in New York is he supposed to be running? The Gambinos? Lucchese? Which one?

I know in the show his family has a different name but what is that family based off of in real life?

OC Shorts did a video on this like a week ago funnily enough. His rough conclusion was Lucchese's assuming their leadership is Brooklyn. In general it's probably not specific to any one family.

There are mentions to all of the Five Families throughout the show also so on that basis the Lupertazzi's would be a "6th" family

OK so I'm confused a little bit. In the show there are multiple families but the only family that is ever mentioned to have the same name as the families in real life is Colombo. They do mention certain mafia figures such as Gravano in the series. Therefore what families in the show represent which families in real life? Can someone list them here? Thank you.

For example we all know Dimeo = DeCalvacante

In season 1 when Meadow is messing with Tony asking "Who invented the Mafia?" She mentions the Five Families and Luciano as the inventor of La Cosa Nostra, but identifies the Families as "Lucchese, Gambino, Bannanno, Profaci" never mentioning the 5th. Paulie brings up the Columbos later on when they're talking about taking out Phil Leotardo. "I lived thru the 70's by the skin of my nuts when the Columbos were goin' at it." Which I don't really get because why would Paulie have anything to do with an internal war in the Columbos? I know he was an associate of them in real life. They mention John Gotti and Sammy Gravano a couple times on the show. When they have the sit down where Butch gives Tony the OK to take out Phil, it's brokered by a "semi-retired" George Paglieri, Boss of the Paglieri Family.

I don't think the creators had an particular family in mind.
The Sopranos is often praised for its authenticity, and that's because Chase employed an expert with a deep and complex understanding of the mob. As reported in the same Today article, that man was Dan Castleman, who worked as a technical advisor throughout the show's six seasons.

He was paid a total of $15,000 for his work throughout the first season ($3,000 for the pilot and $1,000 for each of the remaining 12 episodes), and he even made cameos throughout the show as the federal prosecutor prosecuting Junior Soprano.

The Sopranos are actually based on the Genovese crew of Ruggiero "Richie the Boot" Boiardo. The first 2 seasons shows this strongly, with Boston and Decavalcante having inspirations for characters, places and storylines. After season 2, the Sopranos had other elements added to them from other families.

The Lupertazzis were generic from the 5 families and slightly Philadelphia. Johny Sacs move to New Jersey without telling the Sopranos is a reference to Vito Genovese move to New Jersey. Carmine Lupertazzis Srn, on pressing the splits on construction jobs is a reference to Big Paul Castellano on his greed when it came to construction. The Santoro hit was taken from Big Paul and Tommy Bilotti murder, so two Gambino references right there, plus the Joey Peeps hit had similarities to one of John Gottis own drivers and bodyguard being hit, while another aspect Joey Peeps hit was that he was a protege of an administration member, same as in the 3rd Colombo war. On Colombo connections, Jimmy Petrille had been an informant for nearly 20 years, like how Greg Scarpa was for years, but I dont think Petrille was a vicious killer. During the war between Johnny Sac and Carmine Jr, Johnny and Phil Leotardo were similar to how Luccheses Vic Amuso and Anthony Casso were with the exemption of Leotardo did not turn rat. Carmine Jr actions and how he went about business is almost the same way Bill Bonanno acted when his father took off, and he was relying on others to support and lead the family. The list can go on, but the New York war has many similarities among the 5 families.