Finite Group Databasebeta

← C₁₃×D₁₁₆₉ #44477253

Subgroups — C₁₃×D₁₁₆₉ #44477253

Order 30394.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₃×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₆₇	—	7	1	no	maximal, Hall
3	D₁₁₆₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₃×C₁₆₇	D₇	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₆₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₁₆₇	—	7	1	no	Hall
7	C₁₃×D₇	—	167	1	no	maximal, Hall
8	C₁₆₇	C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
9	C₇×C₁₃	D₁₆₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₃	—	1169	1	no	Hall
11	D₇	—	167	1	no	Hall
12	C₁₃	D₁₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₇	C₁₃×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	1169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	D₁₁₆₉
commutator, cosocle, hypocenter	C₇×C₁₆₇	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₆₇	C₂
LCS	G ▷ C₇×C₁₆₇
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₃×C₁₆₇	C₂	semidirect
3. D₁₁₆₉	C₁₃	direct (N × H)
4. C₁₃×C₁₆₇	D₇	semidirect
5. C₇×C₁₆₇	C₂×C₁₃	semidirect
8. C₁₆₇	C₁₃×D₇	semidirect
9. C₇×C₁₃	D₁₆₇	semidirect
12. C₁₃	D₁₁₆₉	direct (N × H)
13. C₇	C₁₃×D₁₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₃×C₁₆₇	2
C₁₃×D₁₆₇	7
D₁₁₆₉	13
C₁₃×D₇	167