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 coprime automorphism-invariant subgroup (i.e., it is invariant under all the $p'$-automorphisms) and a maximal subgroup.

Relation with other properties

Stronger properties

• Characteristic maximal subgroup of group of prime power order
• Isomorph-free maximal subgroup of group of prime power order
• Maximal subgroup of finite p-group whose automorphism group is a p-group

Weaker properties

• Isomorph-normal coprime automorphism-invariant subgroup
• Fusion system-relatively weakly closed subgroup
• Sylow-relatively weakly closed subgroup