Maschke's Theorem
Theorem. (Maschke) Assume that a group $G$ is finite, $\mathbb{F}$ is a field, and $V$ is a vector space over $\mathbb{F}$. Suppose $\text{char}\mathbb{F}\nmid |G|$. Then any representation $T:G\to GL(V)$ is completely reducible.
Theorem. (Maschke) Assume that a group $G$ is finite, $\mathbb{F}$ is a field, and $V$ is a vector space over $\mathbb{F}$. Suppose $\text{char}\mathbb{F}\nmid |G|$. Then any representation $T:G\to GL(V)$ is completely reducible.