Let n be a positive integer and let m be a factor of 2n. Show that Dn (the dihedral group) contains a subgroup of order m. I'm not really sure where to start with this one. I know that Dn is generated by two types of rotations: flipping the n-gon over about an axis, and rotating it 2π/n around an axis through the center. But how do I show that you can have a subgroup of order m for every factor of 2n? Thanks.