Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order

Definition
A subgroup $$H$$ of a group of prime power order $$P$$ is termed an isomorph-normal coprime automorphism-invariant subgroup of group of prime power order if it satisfies both the following conditions:


 * 1) $$H$$ is an defining ingredient::isomorph-normal subgroup  of $$P$$ (in particular, it is an defining ingredient::isomorph-normal subgroup of group of prime power order ): In other words, for any subgroup $$K$$ of $$P$$ isomorphic to $$H$$, $$K$$ is a normal subgroup of $$P$$.
 * 2) $$H$$ is a defining ingredient::coprime automorphism-invariant subgroup  of $$P$$ (in particular, it is a defining ingredient::coprime automorphism-invariant subgroup of group of prime power order ).

Stronger properties

 * Weaker than::Isomorph-free subgroup of group of prime power order
 * Weaker than::Isomorph-normal characteristic subgroup of group of prime power order
 * Weaker than::Characteristic subgroup of group of prime power order

Weaker properties

 * Stronger than::Fusion system-relatively weakly closed subgroup:
 * Stronger than::Sylow-relatively weakly closed subgroup
 * Stronger than::Coprime automorphism-invariant normal subgroup of group of prime power order, stronger than::coprime automorphism-invariant normal subgroup
 * Stronger than::Coprime automorphism-invariant subgroup of group of prime power order, stronger than::coprime automorphism-invariant subgroup