Subgroups — C₇×C₁₉×D₁₁₉ #44539613

Order 31654.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₁₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor
3	C₇×C₁₉×D₁₇	—	7	1	no	maximal
4	C₇×C₁₇×C₁₉	—	2	3	no	—
5	C₇×C₁₇×C₁₉	D₇	1	1	yes	characteristic, complemented
6	C₇×C₁₇×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₇×D₇×C₁₉	—	17	1	no	maximal, Hall
8	C₇×D₁₁₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇²×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₇²×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₁₉×D₁₇	—	7	1	no	Hall
12	C₁₇×C₁₉	C₇×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₁₉	—	119	1	no	—
14	D₇×C₁₉	—	17	1	no	—
15	D₁₁₉	C₇×C₁₉	1	1	yes	characteristic, direct product factor
16	C₇×D₁₇	—	7	1	no	—
17	C₇×C₁₉	—	2	3	no	—
18	C₇×C₁₉	C₇×D₁₇	1	1	yes	characteristic, complemented
19	C₇×C₁₉	D₁₁₉	1	1	yes	characteristic, direct product factor
20	C₇×C₁₇	—	2	3	no	—
21	C₇×C₁₇	D₇×C₁₉	1	1	yes	characteristic, complemented
22	C₇×C₁₇	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
23	C₇×D₇	—	17	1	no	Hall
24	C₇²	C₁₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₉	—	119	1	no	Hall
26	D₁₇	—	7	1	no	Hall
27	C₁₉	C₇×D₁₁₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₁₇	C₇×D₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₇	—	119	1	no	—
30	D₇	—	17	1	no	—
31	C₇	—	2	3	no	—
32	C₇	C₇×C₁₉×D₁₇	1	1	yes	characteristic, complemented
33	C₇	C₁₉×D₁₁₉	1	1	yes	characteristic, direct product factor
34	C₂	—	119	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₁₁₉
commutator, cosocle, hypocenter	C₇×C₁₇	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₇×C₁₉	C₂
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₇²×C₁₇×C₁₉	C₂	semidirect
2. C₁₉×D₁₁₉	C₇	direct (N × H)
5. C₇×C₁₇×C₁₉	D₇	semidirect
6. C₇×C₁₇×C₁₉	C₂×C₇	semidirect
8. C₇×D₁₁₉	C₁₉	direct (N × H)
9. C₇²×C₁₉	D₁₇	semidirect
10. C₇²×C₁₇	C₂×C₁₉	semidirect
12. C₁₇×C₁₉	C₇×D₇	semidirect
15. D₁₁₉	C₇×C₁₉	direct (N × H)
18. C₇×C₁₉	C₇×D₁₇	semidirect
19. C₇×C₁₉	D₁₁₉	direct (N × H)
21. C₇×C₁₇	D₇×C₁₉	semidirect
22. C₇×C₁₇	C₂×C₇×C₁₉	semidirect
24. C₇²	C₁₉×D₁₇	semidirect
27. C₁₉	C₇×D₁₁₉	direct (N × H)
28. C₁₇	C₇×D₇×C₁₉	semidirect
32. C₇	C₇×C₁₉×D₁₇	semidirect
33. C₇	C₁₉×D₁₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇²×C₁₇×C₁₉	2
C₁₉×D₁₁₉	7
C₇×C₁₉×D₁₇	7
C₇×D₇×C₁₉	17
C₇×D₁₁₉	19

Subgroups — C7×C19×D119 #44539613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₉×D₁₁₉ #44539613