How to determine whether an isomorphism $\varphi: {U_{12}} \to U_5$ exists? I have 2 groups $U_5$ and $U_{12}$ , .. 
$U_5 = \{1,2,3,4\}, U_{12} = \{1,5,7,11\}$. 
I have to determine whether an isomorphism $\varphi: {U_{12}} \to U_5$ exists.
I started with the "$yes$" case: there is an isomorphism.
So I searched an isomorphism $\varphi$ , but I didn't found. So I guess there is no an isomorphism $\varphi$  . 
How can I prove it? or at least explain? please help.

Note that $x^2\equiv 1\pmod {12}$ for all elements of $U_{12}$ whereas the corresponding property does not hold in $U_5$.
