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List all proper, non-trivial subgroups of $U_6$ where $U_6$ is the group of $6$th roots of unity. Also, list the generators.

A) List all proper, non-trivial subgroups of $U_6$ where $U_6$ is the group of $6$th roots of unity:

So 6th roots of unity are $\pm1, \pm \frac{1}{2} \pm \frac{\sqrt{3}}2i$ How do these relate to the subgroups?

B) List the generators:

If I am not mistaken the generators of the 6th roots of unity are $\frac{1}{2} \pm \frac{\sqrt{3}}{2}i$. Is that correct?

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