# Order-isomorphic subgroup

From Groupprops

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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 (finite) subgroup of a group is termed an **order-isomorphic subgroup** if it is isomorphic to every subgroup of for which the order of equals the order of .