I have worked out the elements in $D_5$ (has order 10) and the conjugacy classes
I want to find all the subgroups of $D_5$ and the normal subgroups
By Lagrange I know the subgroups must be of sizes 1,2,5 or 10 Obviously the trivial ones are e and $D_5$ but I am not sure how to find the others( I know they must all contain the identity)
Secondly which ones of these would be normal? I am guessing it has something to do with the conjugacy classes
Thanks