Subgroups — C₂₅×C₁₂₈₃ #44545503

Order 32075.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₂₈₃	C₅	1	1	yes	maximal, characteristic
2	C₁₂₈₃	C₂₅	1	1	yes	characteristic, direct product factor, Sylow
3	C₂₅	C₁₂₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₅	C₅×C₁₂₈₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₁₂₈₃	C₂₅	direct (N × H)
3. C₂₅	C₁₂₈₃	direct (N × H)

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

subgroup	index
C₅×C₁₂₈₃	5
C₂₅	1283