Isomorph-characteristic subgroup

Definition
A subgroup of a group is termed an isomorph-characteristic subgroup if every subgroup of the group isomorphic to it is a characteristic subgroup of the whole group.

Stronger properties

 * Weaker than::Isomorph-free subgroup

Weaker properties

 * Stronger than::Isomorph-normal subgroup
 * Stronger than::Sylow-relatively weakly closed subgroup