Finite Group Databasebeta

← C₇⋊(D₁₅₁⋊C₅) #24902307

Subgroups — C₇⋊(D₁₅₁⋊C₅) #24902307

Order 10570.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₅₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₅₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₅₁⋊C₅	—	7	1	no	maximal, Hall
4	C₇×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₁₅₁⋊C₅	D₇	1	1	yes	characteristic, complemented, Hall
6	D₁₅₁	—	7	1	no	Hall
7	C₁₅₁	C₅×D₇	1	1	yes	characteristic, complemented, Sylow
8	C₅×D₇	—	151	1	no	maximal, Hall
9	C₅×C₇	—	151	1	no	Hall
10	D₇	—	151	1	no	Hall
11	C₂×C₅	—	1057	1	no	Hall
12	C₇	D₁₅₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
13	C₅	—	151	1	no	Sylow
14	C₂	—	1057	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₅₁	C₂×C₅
LCS	G ▷ C₇×C₁₅₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₅₁⋊C₅	C₂	semidirect
2. D₁₀₅₇	C₅	semidirect
4. C₇×C₁₅₁	C₂×C₅	semidirect
5. C₁₅₁⋊C₅	D₇	semidirect
7. C₁₅₁	C₅×D₇	semidirect
12. C₇	D₁₅₁⋊C₅	semidirect