Coprime automorphism-invariant maximal subgroup of group of prime power order

Definition
A subgroup of a group of prime power order (say, a finite $$p$$-group where $$p$$ is a prime number) is termed a coprime automorphism-invariant maximal subgroup if it is both a defining ingredient::coprime automorphism-invariant subgroup (i.e., it is invariant under all the $$p'$$-automorphisms) and a maximal subgroup.

Stronger properties

 * Weaker than::Characteristic maximal subgroup of group of prime power order
 * Weaker than::Isomorph-free maximal subgroup of group of prime power order
 * Weaker than::Maximal subgroup of finite p-group whose automorphism group is a p-group

Weaker properties

 * Stronger than::Isomorph-normal coprime automorphism-invariant subgroup
 * Stronger than::Fusion system-relatively weakly closed subgroup
 * Stronger than::Sylow-relatively weakly closed subgroup