Re: is C2xD5 isomorphe with D10?

You're using some rather unusual notation here -- usually the dihedral
group of order 2n is denoted by D_2n. This seems to have confused a
couple people there. If I use Z_2 for the cyclic group of order 2,
then yes, Z_2 x D_10 is isomorphic to D_20.

By the way, D_10 has five elements of order 2; anything with an s in it
is its own inverse, since sr^n sr^n = s^2 r^-n r^n = 1.

.