Infimum and Supremum of Subgroups

Theorem
Let $\left({G, \circ}\right)$ be a group.

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

Let $\left({\mathbb G, \subseteq}\right)$ be the complete lattice formed by $\mathbb G$ and $\subseteq$.

Let $H, K \in \mathbb G$.