Finite Group Databasebeta

← C₁₃⋊(D₁₂₇⋊C₇) #37528813

Subgroups — C₁₃⋊(D₁₂₇⋊C₇) #37528813

Order 23114.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₂₇⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₅₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₂₇⋊C₇	—	13	1	no	maximal, Hall
4	C₁₃×C₁₂₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
5	C₁₂₇⋊C₇	D₁₃	1	1	yes	characteristic, complemented, Hall
6	D₁₂₇	—	13	1	no	Hall
7	C₇×D₁₃	—	127	1	no	maximal, Hall
8	C₁₂₇	C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
9	C₇×C₁₃	—	127	1	no	Hall
10	D₁₃	—	889	1	no	Hall
11	C₂×C₇	—	1651	1	no	Hall
12	C₁₃	D₁₂₇⋊C₇	1	1	yes	characteristic, complemented, Sylow
13	C₇	—	127	1	no	Sylow
14	C₂	—	11557	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₂₇	C₂×C₇
LCS	G ▷ C₁₃×C₁₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₂₇⋊C₇	C₂	semidirect
2. D₁₆₅₁	C₇	semidirect
4. C₁₃×C₁₂₇	C₂×C₇	semidirect
5. C₁₂₇⋊C₇	D₁₃	semidirect
8. C₁₂₇	C₇×D₁₃	semidirect
12. C₁₃	D₁₂₇⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₂₇⋊C₇	2
D₁₆₅₁	7
D₁₂₇⋊C₇	13
C₇×D₁₃	127