Conjugate-comparable 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 subgroup of a group is termed a conjugate-comparable subgroup if it is comparable with each of its conjugate subgroups, in other words, every conjugate subgroup to it either contains it or is contained in it.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Automorph-comparable subgroup	comparable to all its automorphic subgroups			|FULL LIST, MORE INFO	Normal subgroup	equal to each conjuate subgroup	equal things can be compared	conjugate-comparable not implies normal	|FULL LIST, MORE INFO

Facts

• Automorph-comparable of normal implies conjugate-comparable
• Left residual of conjugate-comparable by normal is automorph-comparable