#1 Bullet Club (formed in 2013)

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It's not unreasonable to compare Bullet Club to the original nWo in WCW. It's the reason why the group uses the "Too Sweet" hand gesture. However, if the nWo help send the popularity of pro wrestling skyrocketing in the United States, Bullet Club took it international. In fact, there's probably a dude in Alpha Centauri wearing a Bullet Club t-shirt.
Did you know a top WWE Superstar just wrestled outside the company? More details HERE
That's what makes Fergal Devitt's little wrestling group such a big deal. It's a group based in a Japanese company (New Japan Pro Wrestling - you, uh, probably knew that) that became, arguably, the hottest act in the business. Not only did it move a bunch of t-shirts and hoodies, but it spurred genuine interest in wrestling outside of WWE.
Not just outside of WWE, but outside of the United States, as well. It's part of the reason why there's an NXT UK - no joke. I mean, I can't prove that but look at the situation. Bullet Club's international popularity spurs interest here in the US in wrestling outside of the country. A bunch of new UK groups pop up (or, in the case of World of Sport, gets revived). Suddenly, we've got WWE creating their own brand in the Kingdom.
Wrestlers join Bullet Club, move on, and become household names. Devitt (aka Finn Balor), AJ Styles, Anderson & Gallows and Adam Cole. Others became the anchors of AEW and, arguably, also became household name: Cody Rhodes, Kenny Omega, The Young Bucks, and Hangman Page.
Bullet Club (and, remember - it's just "Bullet Club", not "THE Bullet Club") is probably the most influental force in wrestling, if not since the nWo, then at least after the closing of WCW. It may not be the pop culture force it was before... and, honestly, it doesn't need to be. The real only club that matters has made its mark, and that's why it's the #1 faction of the 2010s.