Subgroups — C₅³ #1251

Order 125.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²	C₅	1	31	yes	maximal, direct product factor
2	C₅	C₅²	1	31	yes	direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅²	C₅	direct (N × H)
2. C₅	C₅²	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅²	5