Show that $H$ is not a subgroup of the group $G=\mathbb{Z}_{24}$ (with operation +)

Question

Let $G=\{0,1,2,...,23\}$, and I know that a subgroup is closed underneath the operation and has the identity element. So in order to show it isn't a subgroup, do I just have to show that $$H=\{a + 24\mathbb{Z} : 15a ≡ 18 \bmod 24\}$$ doesn't contain identity $(0,0)$?