Isomorph-free subgroup of finite group

Definition
An isomorph-free subgroup of finite group is a subgroup of a finite group satisfying the following equivalent conditions:


 * 1) It is an isomorph-free subgroup of the whole group: there is no other subgroup of the whole group isomorphic to it.
 * 2) It is an defining ingredient::isomorph-containing subgroupconjunction involving::isomorph-containing subgroup of the whole group: it contains every subgroup of the whole group isomorphic to it.

The equivalence of definitions follows from the fact that if a finite group contains an isomorphic subgroup, they are in fact equal.