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]
A subgroup of finite index in a group is termed index-unique if it is the only subgroup of that particular index in the whole group.
Relation with other properties
For a finite group, an index-unique subgroup is the same thing as an order-unique subgroup. This follows from Lagrange's theorem.
If the index of the commutator subgroup is a prime number, or the square of a prime number, or, more generally, any Abelianness-forcing number, then the commutator subgroup is index-unique.