= Maximal subgroups of A5
{title2=$A_4,\ C_5\rtimes C_2,\ S_3$}
Every maximal proper subgroup normalizes one of its <minimal normal subgroups>. As $A_5$ has no proper nonabelian simple subgroup, that subgroup is elementary abelian. Its possible types are $C_2,C_2^2,C_3,C_5$. Their normalizers have orders $4,12,6,10$ respectively. The order-four normalizer lies in an order-twelve point stabilizer; the other three types are maximal and each forms a single conjugacy class. There are five, six and ten maximal subgroups of orders twelve, ten and six, respectively.
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