Subgroup comparable with all normal subgroups

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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]

Definition

A subgroup H of a group G is termed comparable with all normal subgroups if, for any normal subgroup N of G, either N \le H or H \le N.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
subgroup comparable with all characteristic subgroups