 More generally, given any subset "S" of "G" ("S" not necessarily a subgroup), we define a subset "T" of "G" to be conjugate to "S" if there exists some "g" in "G" such that "T" = "gSg"−1.We can define Cl("S") as the set of all subsets "T" of "G" such that "T" is conjugate to "S".A frequently used theorem is that, given any subset "S" of "G", the index of N("S") (the normalizer of "S") in "G" equals the order of Cl("S")