Order-containing subgroup

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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 $H$, $K\leq H$.

Relation with other properties

Stronger properties

• Normal Sylow subgroup
• Normal Hall subgroup

Weaker properties

• Homomorph-containing subgroup
• Intermediately fully characteristic subgroup
• Fully characteristic subgroup
• Order-unique subgroup
• Order-dominating subgroup