A subgroup of a [[Group|group]] $[G,\circ]$ is another [[Group|group]] $[S,\circ]$ where $S$ is a [[Subset]] of $G$, $S\subseteq G$. The [[Axiom|Axioms]] defining a [[Group]] must also be satisfied when pulling elements for a subgroup. >[!info] >A subgroup is an example of a [[Algebraic Subsytem]] in the contexts of [[Group|groups]]. [[Universal Quantifier|For any]] group $[G,\circ]$ with at least $2$ elements, $G$ has two subgroups. - The [[Group]] itself, as $G \subseteq G$ - The [[Group]] constituting of only the [[Identity Property|identity]] of $G$, $[\set{e}, \circ]$, also known as the [[Trivial Group]] of $G$.