The binary polyhedral groups are finite subgroups of the quaternions corresponding (via McKay's ADE classification) to the $E$ series of affine Dynkin diagrams. They are also the lifts to $\mathrm{Spin}(3) \cong \mathrm{Sp}(1)$ of the groups of rotational symmetries of the platonic solids: the tetrahedron, the cube/octahedron and the dodecahedron/icosahedron.

The normal subgroups of these groups are well-known: they are even listed in their respective Wikipedia entries, but without a reference.

I need this result in a paper that I am writing and need a slightly more authoritative reference than the wikipedia page. Can someone point me in the right direction?