Finite Group Databasebeta

← C₂×C₇×C₃₃₁⋊C₅ #37550722

Subgroups — C₂×C₇×C₃₃₁⋊C₅ #37550722

Order 23170.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₃₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₃₃₁⋊C₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₃₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₃₃₁⋊C₅	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃₃₁	C₅×C₇	1	1	yes	characteristic, complemented, Hall
7	C₃₃₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×C₇	—	331	1	no	maximal, Hall
9	C₅×C₇	—	331	1	no	Hall
10	C₂×C₇	C₃₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅	—	331	1	no	Hall
12	C₇	C₂×C₃₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
13	C₅	—	331	1	no	Sylow
14	C₂	C₇×C₃₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃₃₁⋊C₅
commutator, cosocle, hypocenter	C₃₃₁	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₃₃₁	C₅
LCS	G ▷ C₃₃₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₃₁⋊C₅	C₂	direct (N × H)
2. C₂×C₇×C₃₃₁	C₅	semidirect
3. C₂×C₃₃₁⋊C₅	C₇	direct (N × H)
4. C₇×C₃₃₁	C₂×C₅	semidirect
5. C₃₃₁⋊C₅	C₂×C₇	direct (N × H)
6. C₂×C₃₃₁	C₅×C₇	semidirect
7. C₃₃₁	C₂×C₅×C₇	semidirect
10. C₂×C₇	C₃₃₁⋊C₅	direct (N × H)
12. C₇	C₂×C₃₃₁⋊C₅	direct (N × H)
14. C₂	C₇×C₃₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₃₃₁⋊C₅	2
C₂×C₇×C₃₃₁	5
C₂×C₃₃₁⋊C₅	7
C₂×C₅×C₇	331