What familiar group is $G/H$?

Question

I'm stuck in a homework problem.

Let $H$ be a subgroup of $G$, where $G = \Bbb Z_4 \oplus U(8)$ and $H =\langle (1, 3)\rangle$. What familiar group is $G/H?$

I know $H=\{(1,3),(2,1),(3,3),(0,1)\}$ and

$$G/H = \{gH : g \in G\}$$

which is $$\{(0,1)H , (0,3)H, (0,5) H, (0,7)H\}= \begin{align}\{ & (1,3),(2,1),(3,3),(0,1), \\ &(1,1),(2,3),(3,1),(0,3), \\ &(1,7),(2,5),(3,7),(0,5), \\ &(1,5),(2,7),(3,5),(0,7)\}.\end{align}$$

I cannot see what familiar group is this could someone give me a hint?

Answer 1

Hint: $G$ has $16$ elements and $H$ has four, which means that $G/H$ has four elements. That means you only have two options to choose from.