Finite Group Databasebeta

← C₅×C₇×D₂₂₇ #30629596

Subgroups — C₅×C₇×D₂₂₇ #30629596

Order 15890.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₂₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₂₂₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₂₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	D₂₂₇	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂₂₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×C₇	—	227	1	no	maximal, Hall
9	C₅×C₇	D₂₂₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇	—	227	1	no	Hall
11	C₂×C₅	—	227	1	no	Hall
12	C₇	C₅×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₅	C₇×D₂₂₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	227	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	D₂₂₇
commutator, cosocle, hypocenter	C₂₂₇	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₂₇	C₂
LCS	G ▷ C₂₂₇
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₂₂₇	C₂	semidirect
2. C₇×D₂₂₇	C₅	direct (N × H)
3. C₅×D₂₂₇	C₇	direct (N × H)
4. C₇×C₂₂₇	C₂×C₅	semidirect
5. C₅×C₂₂₇	C₂×C₇	semidirect
6. D₂₂₇	C₅×C₇	direct (N × H)
7. C₂₂₇	C₂×C₅×C₇	semidirect
9. C₅×C₇	D₂₂₇	direct (N × H)
12. C₇	C₅×D₂₂₇	direct (N × H)
13. C₅	C₇×D₂₂₇	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×C₇×C₂₂₇	2
C₇×D₂₂₇	5
C₅×D₂₂₇	7
C₂×C₅×C₇	227