Finite Group Databasebeta

← C₅×D₇×C₃₄₇ #37566374

Subgroups — C₅×D₇×C₃₄₇ #37566374

Order 24290.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₃₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₃₄₇	—	7	1	no	maximal, Hall
4	C₇×C₃₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₃₄₇	D₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₄₇	—	7	1	no	Hall
7	C₃₄₇	C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×D₇	C₃₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇	C₂×C₃₄₇	1	1	yes	characteristic, complemented, Hall
10	D₇	C₅×C₃₄₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	—	7	1	no	Hall
12	C₇	C₂×C₅×C₃₄₇	1	1	yes	characteristic, complemented, Sylow
13	C₅	D₇×C₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₄₇	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₅×C₃₄₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₄₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₃₄₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₃₄₇	C₂	semidirect
2. D₇×C₃₄₇	C₅	direct (N × H)
4. C₇×C₃₄₇	C₂×C₅	semidirect
5. C₅×C₃₄₇	D₇	direct (N × H)
7. C₃₄₇	C₅×D₇	direct (N × H)
8. C₅×D₇	C₃₄₇	direct (N × H)
9. C₅×C₇	C₂×C₃₄₇	semidirect
10. D₇	C₅×C₃₄₇	direct (N × H)
12. C₇	C₂×C₅×C₃₄₇	semidirect
13. C₅	D₇×C₃₄₇	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×C₃₄₇	2
D₇×C₃₄₇	5
C₂×C₅×C₃₄₇	7
C₅×D₇	347