List the elements of G So we are asked to write out the elements of G and H where G= $ \mathbb{Z}/ &lt;20&gt; $ and

H = $&lt;4, 20&gt;$ . I understand how to do H and I got: 
{$0 + &lt;20&gt;, 4 + &lt;20&gt; , 8 + &lt;20&gt;, 12 + &lt;20&gt;, 16 + &lt;20&gt;$ } from here through, would G=
{$1+ &lt;20&gt;, 2+ &lt;20&gt;, 3+ &lt;20&gt;$, etc....} or how do I find this???
Your $G$ is correct... But you are mentioning $H=&lt;4,20&gt;$, now see $&lt;20&gt;$ $\subset &lt;4&gt;$, so $&lt;4,20&gt;=&lt;4&gt;$ = {$0, \pm4, \pm 8 \ldots \ldots$}.
You are correct about both of them.