I'm trying to decide which groups are isomorphic to one another . $\begin{align*} U_5 &= \{1,2,3,4\}\\ U_8 &= \{1,3,5,7\}\\ U_{10} &= \{1,3,7,9\} \end{align*}$
I've checked and verified that $U_{10}$ and $U_5$ are cyclic , by finding the creator generator of each group: The creator generator of $U_5$ is $2$ and the creator generator of $U_{10}$ is $3$).
The question is, how can I verify that $U_8$ is not cyclic ? Is there a fast way to determine that, without checking if one of the elements creates generates all other elements in the group ?