Order-containing subgroup

Definition
A finite subgroup $$H$$ of a group $$G$$ is termed order-containing if for any subgroup $$K$$ such that the order of $$K$$ divides the order of $$H$$, $$K \le H$$.

Stronger properties

 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup

Weaker properties

 * Stronger than::Homomorph-containing subgroup
 * Stronger than::Intermediately fully characteristic subgroup
 * Stronger than::Fully characteristic subgroup
 * Stronger than::Order-unique subgroup
 * Stronger than::Order-dominating subgroup