Normal subgroups of Sn

I'm trying to work out the normal subgroups of the symmetric group Sn. All I can think of are the obvious ones: <e> , Sn itself and An (the alternating group or group of even permutations)

Anyone?

Reply 1

coffeym

In order to cut down the process, apply Lagrange's theorem (i.e the order of subgroups is a factor of the order of a group). That may close some doors.

Reply 2

Faaip De Oiad

Erm, but the order of Sn is n-factorial.
So a subgroup can be of any size from 1 to n

Reply 3

dvs

Well, for n>=5, A_n is simple. So in that case the only normal subgroups of S_n are {e}, A_n, and S_n itself. I'll let you figure out what happens for the remaining cases.