Finite Group Databasebeta

← C₇₁×D₁₃₃ #34038521

Subgroups — C₇₁×D₁₃₃ #34038521

Order 18886.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₇₁	—	7	1	no	maximal, Hall
3	C₁₉×C₇₁	D₇	1	1	yes	characteristic, complemented, Hall
4	D₇×C₇₁	—	19	1	no	maximal, Hall
5	C₇×C₇₁	D₁₉	1	1	yes	characteristic, complemented, Hall
6	D₁₃₃	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₇₁	—	133	1	no	Hall
8	C₇×C₁₉	C₂×C₇₁	1	1	yes	characteristic, complemented, Hall
9	C₇₁	D₁₃₃	1	1	yes	characteristic, direct product factor, Sylow
10	D₁₉	—	7	1	no	Hall
11	C₁₉	D₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
12	D₇	—	19	1	no	Hall
13	C₇	D₁₉×C₇₁	1	1	yes	characteristic, complemented, Sylow
14	C₂	—	133	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₁	D₁₃₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₇₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₇₁	C₂
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₇₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×C₇₁	C₂	semidirect
3. C₁₉×C₇₁	D₇	semidirect
5. C₇×C₇₁	D₁₉	semidirect
6. D₁₃₃	C₇₁	direct (N × H)
8. C₇×C₁₉	C₂×C₇₁	semidirect
9. C₇₁	D₁₃₃	direct (N × H)
11. C₁₉	D₇×C₇₁	semidirect
13. C₇	D₁₉×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₉×C₇₁	2
D₁₉×C₇₁	7
D₇×C₇₁	19
D₁₃₃	71