Isomorph-normal subgroup

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

Stronger properties

 * Weaker than::Isomorph-free subgroup
 * Weaker than::Isomorph-characteristic subgroup
 * Weaker than::Isomorph-normal characteristic subgroup
 * Weaker than::Maximal subgroup of finite nilpotent group
 * Weaker than::Maximal subgroup of group of prime power order
 * Weaker than::Order-normal subgroup

Weaker properties

 * Stronger than::Normal subgroup

Metaproperties
An arbitrary join of isomorph-normal subgroups is isomorph-normal.

An intersection of isomorph-normal subgroups need not be isomorph-normal.