Coprime automorphism group

Definition
Let $$G$$ be a finite group. A subgroup $$H$$ of the automorphism group $$\operatorname{Aut}(G)$$ is termed a coprime automorphism group of $$G$$ if the orders of $$G$$ and $$H$$ are relatively prime.

Note that the whole group $$\operatorname{Aut}(G)$$ is very rarely coprime to $$G$$ in order.