Lagrange’s Theorem

Recall that a group is called finite if it has a finite number of elements. The number of elements in a group $G$ is called the order of $G$ and denoted by $|G|$.

Lagrange’s Theorem

The order of a finite group is divisible by the order of any subgroup.

In other words, if $G$ is a finite group and $H$ is a subgroup of $G$, then $|H|$ divides $|G|$.