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?