take a look at the mighty tetrahedron and its mirror image. explore the subgroup lattice of s4 and get a geometric perspective on why some of its subgroups are normal while others have conjugates.

see the sylow-3 and sylow-5 subgroups of a5, and learn how counting to 20 in greek can help you remember how many of them there are. it's quite simple, actually - but we'll finish off with the following not-entirely-trivial question: can you see s5 by holding a dodecahedron up to a mirror?