Number of subgroups

This article defines an arithmetic function on groups
View other such arithmetic functions

Definition

Let $G$ be a group. The number of subgroups of $G$ is the number of subgroups that $G$ has.

Note that the number of subgroups of $G$ is finite if and only if $G$ is a finite group. For full proof, refer: Finitely many subgroups iff finite

See also

• Number of normal subgroups