Subgroups — C₃×C₁₁×D₇×C₁₉ #22578607

Order 8778.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₁₉	—	7	1	no	maximal, Hall
5	C₃×D₇×C₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₁×C₁₉	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₁₁×D₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₁×C₁₉	—	7	1	no	Hall
9	C₃×C₇×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	D₇×C₁₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₁₉	C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁×D₇	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₉	—	7	1	no	Hall
16	C₇×C₁₁	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₁	—	7	1	no	Hall
18	C₃×C₁₉	C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₇	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₁₉	—	7	1	no	Hall
21	C₃×C₁₁	D₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₁	—	7	1	no	Hall
23	C₃×C₇	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Hall
24	C₁₉	C₃×C₁₁×D₇	1	1	yes	characteristic, direct product factor, Sylow
25	D₇	C₃×C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁	C₃×D₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	7	1	no	Hall
29	C₃	C₁₁×D₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₉	D₇
commutator, hypocenter	C₇	C₂×C₃×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₁₉	C₂	semidirect
2. C₁₁×D₇×C₁₉	C₃	direct (N × H)
3. C₇×C₁₁×C₁₉	C₂×C₃	semidirect
5. C₃×D₇×C₁₉	C₁₁	direct (N × H)
6. C₃×C₁₁×C₁₉	D₇	direct (N × H)
7. C₃×C₁₁×D₇	C₁₉	direct (N × H)
9. C₃×C₇×C₁₉	C₂×C₁₁	semidirect
10. D₇×C₁₉	C₃×C₁₁	direct (N × H)
11. C₃×C₇×C₁₁	C₂×C₁₉	semidirect
12. C₁₁×C₁₉	C₃×D₇	direct (N × H)
13. C₁₁×D₇	C₃×C₁₉	direct (N × H)
14. C₇×C₁₉	C₂×C₃×C₁₁	semidirect
16. C₇×C₁₁	C₂×C₃×C₁₉	semidirect
18. C₃×C₁₉	C₁₁×D₇	direct (N × H)
19. C₃×D₇	C₁₁×C₁₉	direct (N × H)
21. C₃×C₁₁	D₇×C₁₉	direct (N × H)
23. C₃×C₇	C₂×C₁₁×C₁₉	semidirect
24. C₁₉	C₃×C₁₁×D₇	direct (N × H)
25. D₇	C₃×C₁₁×C₁₉	direct (N × H)
26. C₁₁	C₃×D₇×C₁₉	direct (N × H)
27. C₇	C₂×C₃×C₁₁×C₁₉	semidirect
29. C₃	C₁₁×D₇×C₁₉	direct (N × H)

Subgroups — C3×C11×D7×C19 #22578607

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₁×D₇×C₁₉ #22578607