Lattice automorphism-invariant 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 subgroup of a group is termed a lattice automorphism-invariant subgroup if it is invariant under all the lattice automorphisms of the lattice of subgroups of the group.

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Projectivity-invariant subgroup	invariant under every projectivity			|FULL LIST, MORE INFO
Characteristic subgroup	invariant under all automorphisms			|FULL LIST, MORE INFO
Normal subgroup	invariant under all inner automorphisms			|FULL LIST, MORE INFO