Finite Group Databasebeta

← C₅×D₂₄₁₃ #37563243

Subgroups — C₅×D₂₄₁₃ #37563243

Order 24130.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₉×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₄₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₉×C₁₂₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₁₂₇	—	19	1	no	maximal, Hall
5	C₅×C₁₂₇	D₁₉	1	1	yes	characteristic, complemented, Hall
6	D₁₂₇	—	19	1	no	Hall
7	C₅×D₁₉	—	127	1	no	maximal, Hall
8	C₁₂₇	C₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
9	C₅×C₁₉	D₁₂₇	1	1	yes	characteristic, complemented, Hall
10	D₁₉	—	127	1	no	Hall
11	C₁₉	C₅×D₁₂₇	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅	—	2413	1	no	Hall
13	C₅	D₂₄₁₃	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	2413	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₄₁₃
commutator, cosocle, hypocenter	C₁₉×C₁₂₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₂₇	C₂
LCS	G ▷ C₁₉×C₁₂₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₂₇	C₂	semidirect
2. D₂₄₁₃	C₅	direct (N × H)
3. C₁₉×C₁₂₇	C₂×C₅	semidirect
5. C₅×C₁₂₇	D₁₉	semidirect
8. C₁₂₇	C₅×D₁₉	semidirect
9. C₅×C₁₉	D₁₂₇	semidirect
11. C₁₉	C₅×D₁₂₇	semidirect
13. C₅	D₂₄₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₉×C₁₂₇	2
D₂₄₁₃	5
C₅×D₁₂₇	19
C₅×D₁₉	127