Isomorph-normal coprime automorphism-invariant subgroup

Definition
A subgroup $$H$$ of a finite group $$G$$ is termed isomorph-normal coprime automorphism-invariant if it satisfies the following two conditions:


 * $$H$$ is isomorph-normal in $$G$$: Every subgroup of $$G$$ isomorphic to $$H$$ is a normal subgroup of $$G$$.
 * $$H$$ is a coprime automorphism-invariant subgroup of $$G$$: Any automorphism $$\sigma$$ of $$G$$ whose order is relatively prime to the order of $$G$$ satisfies $$\sigma(H) = H$$.

Stronger properties

 * Weaker than::Isomorph-normal characteristic subgroup

Weaker properties

 * Stronger than::Coprime automorphism-invariant normal subgroup
 * Stronger than::Coprime automorphism-invariant subgroup
 * Stronger than::Isomorph-normal subgroup
 * Stronger than::Normal subgroup