Lagrange's theorem

Let $G$ be a finite group and $H \subseteq G$ a subgroup. Then, the order of $H$ divides the order of $G$:
$$|H| \;\mid\; |G|.$$More precisely, we have : $|G| = [G:H]\cdot |H|$ where $[G,H]$ is the index of $H$ in $G$.