> 
> Determine the isomorphism classes of the automorphism group of the group $\mathbb{Z}\_2\times\mathbb{Z}\_3\times\mathbb{Z}\_5$.
> 
> 
> 

We know that $\gcd(2,3,5)=1$. So $\mathbb{Z}\_2\times\mathbb{Z}\_3\times\mathbb{Z}\_5$ is isomorphic to $\mathbb{Z}\_{30}$.

After that how can I proceed?