Suppose that $ N $ is a normal subgroup of a finite group $ G $. If $ |N| = 5 $ and $ |G| $ is odd, why is $ N $ contained in $ Z(G) $, the center of $ G $?
I know how to do this when $ |N| = 2 $ and $ |G| $ is even, but am not sure what to do with this one. Sylow's theorems maybe?
Thank you guys!