**First Sylow Theorem**: The group $G$ contains at least one subgroup of order $p^m$

**Second Sylow Theorem**: Any two subgroups of $G$ of order $p^m$ are conjugate

**Third Sylow Theorem**: The number of subgroups of $G$ of order $p^m$ is congruent to $1$ modulo $p$ and is a factor of $k$