Order-unique subgroup

Definition
A finite subgroup of a group is termed order-unique if it is the only subgroup of that order in the whole group.

Stronger properties

 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup
 * Weaker than::Order-containing subgroup

Weaker properties

 * Stronger than::Order-conjugate subgroup
 * Stronger than::Order-automorphic subgroup
 * Stronger than::Order-isomorphic subgroup
 * Stronger than::Isomorph-free subgroup
 * Stronger than::Isomorph-conjugate subgroup
 * Stronger than::Isomorph-automorphic subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Automorph-conjugate subgroup
 * Stronger than::Normal subgroup