Group homomorphism/Image/Subgroup/Fact

Let ${\displaystyle {}G}$ and ${\displaystyle {}H}$ denote groups, and let ${\displaystyle {}\varphi \colon G\rightarrow H}$ be a group homomorphism.

Then the

image of ${\displaystyle {}\varphi }$ is a subgroup

of ${\displaystyle {}H}$.