Set of Subgroups forms Complete Lattice

Theorem
Let $\struct {G, \circ}$ be a group.

Let $\mathbb G$ be the set of all subgroups of $G$.

Then:
 * $\struct {\mathbb G, \subseteq}$ is a complete lattice.

where for every set $\mathbb H$ of subgroups of $G$:
 * the infimum of $\mathbb H$ necessarily admitted by $\mathbb H$ is $\ds \bigcap \mathbb H$.