Finite Group Databasebeta

← D₅×C₁₉×C₁₂₇ #37563244

Subgroups — D₅×C₁₉×C₁₂₇ #37563244

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	C₂×C₁₉×C₁₂₇	—	5	1	no	maximal, Hall
3	C₁₉×C₁₂₇	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₂₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₂₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₂₇	—	5	1	no	Hall
7	D₅×C₁₉	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₂₇	D₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₅×C₁₉	C₂×C₁₂₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₉	—	5	1	no	Hall
11	C₁₉	D₅×C₁₂₇	1	1	yes	characteristic, direct product factor, Sylow
12	D₅	C₁₉×C₁₂₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅	C₂×C₁₉×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₁₂₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₉×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₁₂₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₉×C₁₂₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₉×C₁₂₇	C₂	semidirect
3. C₁₉×C₁₂₇	D₅	direct (N × H)
4. D₅×C₁₂₇	C₁₉	direct (N × H)
5. C₅×C₁₂₇	C₂×C₁₉	semidirect
7. D₅×C₁₉	C₁₂₇	direct (N × H)
8. C₁₂₇	D₅×C₁₉	direct (N × H)
9. C₅×C₁₉	C₂×C₁₂₇	semidirect
11. C₁₉	D₅×C₁₂₇	direct (N × H)
12. D₅	C₁₉×C₁₂₇	direct (N × H)
13. C₅	C₂×C₁₉×C₁₂₇	semidirect

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
C₂×C₁₉×C₁₂₇	5
D₅×C₁₂₇	19
D₅×C₁₉	127