When Sebastian Shaw overthrew Ned Buchman and his Council of the Chosen, he created the Inner Circle of the Hellfire Club in their place. The Inner Circle oversaw the Hellfire Club's public and private dealings, outwardly providing funding for the government's Project: Wideawake and Sentinel programs, while secretly prepping the Hellions of tomorrow for the day of mutant supremacy.
The Inner Circle was eventually destroyed by one of their own, the Black Queen Selene, who constructed the Upstarts competition to eliminate all her rivals in the Hellfire Club. Shinobi Shaw killed his father Sebastian in X-Factor (1st series) #67, Fabian Cortez disposed of Magneto in X-Men (2nd series) #3, and Trevor Fitzroy incapacitated Emma Frost and Donald Pierce in Uncanny X-men #281-283. (Gideon's assassination of Emmanuel Dacosta in New Mutants (1st series) #98 was timely, but apparently unrelated.)