Cayley's Representation Theorem

Theorem
Let $S_n$ denote the symmetric group on $n$ letters.

Every finite group is isomorphic to a subgroup of $S_n$ for some $n \in \Z$.

Also known as
It is also known as the Representation Theorem for Groups.

Also see
What this theorem tells us is that in order to study groups, it is necessary only to study subgroups of the symmetric groups.