Normal Subgroup of Prime Index: Properties

[dori1123]

Show that if H is a normal subgroup of G of prime index p, then for all subgroups K of G, either
(i) K is a subgroup of H, or
(ii) G = HK and |K : K intersect H| = p.

 

[morphism]

Well, what have you tried? And is G a finite group?