# Order-automorphic subgroup

From Groupprops

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BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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

Suppose is a group and is a finite subgroup of . We say that is an **order-automorphic subgroup** of if every subgroup of having the same order as is related to via some automorphism, i.e., and are automorphic subgroups.