Normal subgroup of prime index

Definition
A normal maximal subgroup or normal subgroup of prime index is defined in the following equivalent ways:


 * It is a normal subgroup that is also maximal among proper subgroups: it is not contained in any strictly bigger proper subgroup.
 * It is a normal subgroup and its index is a prime number.

Stronger properties

 * Weaker than::Subgroup of index two:
 * Weaker than::Subgroup of least prime index:

Weaker properties

 * Stronger than::Maximal normal subgroup: Note that the properties are equivalent for a solvable group, and more generally, for an imperfect group.
 * Stronger than::Subgroup of prime index: Note that the properties are equivalent for a nilpotent group.
 * Stronger than::Maximal subgroup: Note that the properties are equivalent for a nilpotent group.