  We classify finite-dimensional complex pointed Hopf algebra with group of
group-like elements isomorphic to A_5. We show that any pointed Hopf algebra
with infinitesimal braiding associated with the conjugacy class of $\pi$ \in
$A_n$ is infinite-dimensional if the order of $\pi$ is odd except for $\pi=(1 2
3)$ in $A_4$. We also study pointed Hopf algebras over the dihedral groups.
