Group in which every subgroup is automorph-conjugate

Definition
A group in which every subgroup is automorph-conjugate is a group satisfying the following equivalent conditions:


 * Every subgroup of the group is an automorph-conjugate subgroup.
 * Any two automorphic subgroups of the group are conjugate subgroups.
 * Every automorphism of the group is a subgroup-conjugating automorphism.