Group theory (algebra)/Lagrange's theorem/Fact

Let ${\displaystyle {}G}$ be a finite group, and let ${\displaystyle {}H\subseteq G}$ denote a subgroup of ${\displaystyle {}G}$.

Then the cardinality ${\displaystyle {}{\#\left(H\right)}}$ divides the cardinality ${\displaystyle {}{\#\left(G\right)}}$.