Order-isomorphic subgroup

Definition
A (finite) subgroup $$H$$ of a group $$G$$ is termed an order-isomorphic subgroup if it is isomorphic to every subgroup $$K$$ of $$G$$ for which the order of $$H$$ equals the order of $$K$$.

Stronger properties

 * Weaker than::Sylow subgroup
 * Weaker than::Hall subgroup of finite solvable group
 * Weaker than::Order-unique subgroup
 * Weaker than::Order-conjugate subgroup
 * Weaker than::Order-automorphic subgroup