Order-unique subgroup

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

Relation with other properties

Stronger properties

• Normal Sylow subgroup
• Normal Hall subgroup
• Order-containing subgroup

Weaker properties

• Order-conjugate subgroup
• Order-automorphic subgroup
• Order-isomorphic subgroup
• Isomorph-free subgroup
• Isomorph-conjugate subgroup
• Isomorph-automorphic subgroup
• Characteristic subgroup
• Automorph-conjugate subgroup
• Normal subgroup