Finite Group Databasebeta

← C₅×C₄₇×D₆₇ #44538433

Subgroups — C₅×C₄₇×D₆₇ #44538433

Order 31490.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₇×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₇×D₆₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₇×C₆₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×D₆₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₄₇	—	67	1	no	maximal, Hall
6	C₅×C₆₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
7	C₅×C₄₇	D₆₇	1	1	yes	characteristic, direct product factor, Hall
8	D₆₇	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₄₇	—	67	1	no	Hall
10	C₆₇	C₂×C₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
11	C₄₇	C₅×D₆₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₅	—	67	1	no	Hall
13	C₅	C₄₇×D₆₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	67	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₄₇	D₆₇
commutator, cosocle, hypocenter	C₆₇	C₂×C₅×C₄₇
Frattini	C₁	G
Fitting, socle	C₅×C₄₇×C₆₇	C₂
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₅×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₄₇×C₆₇	C₂	semidirect
2. C₄₇×D₆₇	C₅	direct (N × H)
3. C₄₇×C₆₇	C₂×C₅	semidirect
4. C₅×D₆₇	C₄₇	direct (N × H)
6. C₅×C₆₇	C₂×C₄₇	semidirect
7. C₅×C₄₇	D₆₇	direct (N × H)
8. D₆₇	C₅×C₄₇	direct (N × H)
10. C₆₇	C₂×C₅×C₄₇	semidirect
11. C₄₇	C₅×D₆₇	direct (N × H)
13. C₅	C₄₇×D₆₇	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×C₄₇×C₆₇	2
C₄₇×D₆₇	5
C₅×D₆₇	47
C₂×C₅×C₄₇	67