Lagrange's theorem
The orbit-stabilizer theorem says that there is a natural bijection for each "x" ∈ "X" between the orbit of "x", "G.x" = {"g.x" | "g" ∈ "G"} ⊆ "X", and the set of left cosets "G/Gx" of its stabilizer subgroup "Gx". With Lagrange's theorem this implies