Order-isomorphic subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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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 $K$.

Relation with other properties

Stronger properties

• Sylow subgroup
• Hall subgroup of finite solvable group
• Order-unique subgroup
• Order-conjugate subgroup
• Order-automorphic subgroup