# Is $U_8$ isomorphic to $K_4$ ( Klein Group)

$$U_8=1,3,5,7$$ since this group has one element of order one, three elements of two order and no element of $$4$$ order .. so does the Klein group.

Both $$U(8)$$ and the Klein group are non cyclic groups whose every proper subgroup is cyclic, so the Klein group is isomorphic to U(8)?

As all elements of $$U(8)$$ are of order $$2$$, $$U(8)$$ is indeed isomorphic as a group to the Klein group.