Isomorph-normal characteristic subgroup of group of prime power order

Definition
A subgroup $$H$$ of a group $$P$$ is termed an isomorph-normal characteristic subgroup of group of prime power order if $$P$$ is a group of prime power order and $$H$$ is an isomorph-normal characteristic subgroup: $$H$$ is an isomorph-normal subgroup of $$P$$ (every subgroup isomorphic to it is normal) and $$H$$ is a characteristic subgroup of $$P$$.

Stronger properties

 * Weaker than::Isomorph-free subgroup of group of prime power order
 * Weaker than::Subisomorph-containing subgroup of group of prime power order
 * Weaker than::Characteristic maximal subgroup of group of prime power order

Weaker properties

 * Stronger than::Characteristic subgroup of group of prime power order, characteristic subgroup
 * Stronger than::Isomorph-normal subgroup of group of prime power order, isomorph-normal subgroup
 * Stronger than::Normal subgroup of group of prime power order, normal subgroup
 * Stronger than::Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order, isomorph-normal coprime automorphism-invariant subgroup
 * Stronger than::Fusion system-relatively weakly closed subgroup
 * Stronger than::Sylow-relatively weakly closed subgroup