[Math] Find a non-cyclic subgroup of order $4$ in $U(40).$

Question

Find a non-cyclic subgroup of order $4$ in $U(40).$

I've got no idea how to approach this problem.

I've listed the whole group of $U(40)$ and picked $4$ elements to see if they made a subgroup but the trial and error method isn't working out.

The part that seems too be causing the most problems is the closure part; I can't find $4$ elements that when I multiply them they give me back only elements I started with.

Answer 1

Hint: $U(40)\cong U(8)\times U(5)\cong (C_2\times C_2)\times C_4$.

Reference:

Is the group $U(8)$ cyclic?