Lagrange's Theorem
 Theorem 1 (Lagrange's Theorem): Let $(G, \cdot)$ be a finite group and let $(H, \cdot)$ be a subgroup. Then the number of elements in $H$ must divide the number of elements in $G$.
• Therefore $\mid H \mid$ divides $\mid G \mid$, i.e., the number of elements in any subgroup $(H, \cdot)$ of a finite group $(G, \cdot)$ must divide the number of elements in $(G, \cdot)$. $\blacksquare$