Finite Group Databasebeta

← C₇×D₂₅₀₉ #47975673

Subgroups — C₇×D₂₅₀₉ #47975673

Order 35126.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₉₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₅₀₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×D₁₉₃	—	13	1	no	maximal, Hall
4	C₁₃×C₁₉₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₉₃	D₁₃	1	1	yes	characteristic, complemented, Hall
6	D₁₉₃	—	13	1	no	Hall
7	C₁₉₃	C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₇×D₁₃	—	193	1	no	maximal, Hall
9	C₇×C₁₃	D₁₉₃	1	1	yes	characteristic, complemented, Hall
10	D₁₃	—	193	1	no	Hall
11	C₂×C₇	—	2509	1	no	Hall
12	C₁₃	C₇×D₁₉₃	1	1	yes	characteristic, complemented, Sylow
13	C₇	D₂₅₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	2509	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₅₀₉
commutator, cosocle, hypocenter	C₁₃×C₁₉₃	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉₃	C₂
LCS	G ▷ C₁₃×C₁₉₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₉₃	C₂	semidirect
2. D₂₅₀₉	C₇	direct (N × H)
4. C₁₃×C₁₉₃	C₂×C₇	semidirect
5. C₇×C₁₉₃	D₁₃	semidirect
7. C₁₉₃	C₇×D₁₃	semidirect
9. C₇×C₁₃	D₁₉₃	semidirect
12. C₁₃	C₇×D₁₉₃	semidirect
13. C₇	D₂₅₀₉	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×C₁₃×C₁₉₃	2
D₂₅₀₉	7
C₇×D₁₉₃	13
C₇×D₁₃	193