Subgroups — C₅×C₄₉₁₃ #72201802

Order 24565.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₅×C₂₈₉	C₁₇	1	1	yes	maximal, characteristic
3	C₂₈₉	C₅×C₁₇	1	1	yes	characteristic
4	C₅×C₁₇	C₂₈₉	1	1	yes	characteristic
5	C₁₇	C₅×C₂₈₉	1	1	yes	characteristic
6	C₅	C₄₉₁₃	1	1	yes	characteristic, direct product factor, Sylow

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

N	H ≅ G/N	type
1. C₄₉₁₃	C₅	direct (N × H)
6. C₅	C₄₉₁₃	direct (N × H)

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

subgroup	index
C₄₉₁₃	5
C₅×C₂₈₉	17