Subgroups — C₂²×C₅×C₁₁×C₁₉⋊C₃ #27160093

Order 12540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₅×C₁₁×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₁×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₁₁×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₁×C₁₉	C₂×C₃	1	3	yes	complemented
6	C₂×C₁₁×C₁₉⋊C₃	C₂×C₅	1	3	yes	direct product factor
7	C₂²×C₅×C₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₁×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃×C₅×C₁₁	—	19	1	no	maximal, Hall
11	C₁₁×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₁₉⋊C₃	C₂×C₁₁	1	3	yes	direct product factor
13	C₂×C₁₁×C₁₉	C₂×C₃×C₅	1	3	yes	complemented
14	C₂²×C₅×C₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₁	—	19	3	no	—
16	C₅×C₁₉⋊C₃	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₁₉⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂²×C₅×C₁₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₁₁×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₁₉	C₂×C₃×C₁₁	1	3	yes	complemented
21	C₃×C₅×C₁₁	—	19	1	no	Hall
22	C₂²×C₃×C₁₁	—	19	1	no	Hall
23	C₂×C₁₉⋊C₃	C₂×C₅×C₁₁	1	3	yes	direct product factor
24	C₂×C₅×C₁₁	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
25	C₅×C₁₉	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
26	C₂²×C₁₉	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₁	—	19	3	no	—
28	C₂²×C₃×C₅	—	19	1	no	Hall
29	C₁₉⋊C₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₅×C₁₁	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₁₉	C₂×C₃×C₅×C₁₁	1	3	yes	complemented
33	C₃×C₁₁	—	19	1	no	Hall
34	C₂×C₃×C₅	—	19	3	no	—
35	C₂×C₁₁	C₂×C₅×C₁₉⋊C₃	1	3	yes	direct product factor
36	C₂²×C₅	C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
37	C₁₉	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₅	—	19	1	no	Hall
39	C₂²×C₃	—	19	1	no	Hall
40	C₁₁	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₅	C₂×C₁₁×C₁₉⋊C₃	1	3	yes	direct product factor
42	C₂×C₃	—	19	3	no	—
43	C₅	C₂²×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₅×C₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	19	1	no	Sylow
46	C₂	C₂×C₅×C₁₁×C₁₉⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₁₁	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₁×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂²×C₅×C₁₁×C₁₉	C₃	semidirect
3. C₅×C₁₁×C₁₉⋊C₃	C₂²	direct (N × H)
4. C₂²×C₁₁×C₁₉⋊C₃	C₅	direct (N × H)
5. C₂×C₅×C₁₁×C₁₉	C₂×C₃	semidirect
6. C₂×C₁₁×C₁₉⋊C₃	C₂×C₅	direct (N × H)
7. C₂²×C₅×C₁₉⋊C₃	C₁₁	direct (N × H)
8. C₅×C₁₁×C₁₉	C₂²×C₃	semidirect
9. C₂²×C₁₁×C₁₉	C₃×C₅	semidirect
11. C₁₁×C₁₉⋊C₃	C₂²×C₅	direct (N × H)
12. C₂×C₅×C₁₉⋊C₃	C₂×C₁₁	direct (N × H)
13. C₂×C₁₁×C₁₉	C₂×C₃×C₅	semidirect
14. C₂²×C₅×C₁₉	C₃×C₁₁	semidirect
16. C₅×C₁₉⋊C₃	C₂²×C₁₁	direct (N × H)
17. C₂²×C₁₉⋊C₃	C₅×C₁₁	direct (N × H)
18. C₂²×C₅×C₁₁	C₁₉⋊C₃	direct (N × H)
19. C₁₁×C₁₉	C₂²×C₃×C₅	semidirect
20. C₂×C₅×C₁₉	C₂×C₃×C₁₁	semidirect
23. C₂×C₁₉⋊C₃	C₂×C₅×C₁₁	direct (N × H)
24. C₂×C₅×C₁₁	C₂×C₁₉⋊C₃	direct (N × H)
25. C₅×C₁₉	C₂²×C₃×C₁₁	semidirect
26. C₂²×C₁₉	C₃×C₅×C₁₁	semidirect
29. C₁₉⋊C₃	C₂²×C₅×C₁₁	direct (N × H)
30. C₅×C₁₁	C₂²×C₁₉⋊C₃	direct (N × H)
31. C₂²×C₁₁	C₅×C₁₉⋊C₃	direct (N × H)
32. C₂×C₁₉	C₂×C₃×C₅×C₁₁	semidirect
35. C₂×C₁₁	C₂×C₅×C₁₉⋊C₃	direct (N × H)
36. C₂²×C₅	C₁₁×C₁₉⋊C₃	direct (N × H)
37. C₁₉	C₂²×C₃×C₅×C₁₁	semidirect
40. C₁₁	C₂²×C₅×C₁₉⋊C₃	direct (N × H)
41. C₂×C₅	C₂×C₁₁×C₁₉⋊C₃	direct (N × H)
43. C₅	C₂²×C₁₁×C₁₉⋊C₃	direct (N × H)
44. C₂²	C₅×C₁₁×C₁₉⋊C₃	direct (N × H)
46. C₂	C₂×C₅×C₁₁×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₁₁×C₁₉⋊C₃	2
C₂²×C₅×C₁₁×C₁₉	3
C₂²×C₁₁×C₁₉⋊C₃	5
C₂²×C₅×C₁₉⋊C₃	11
C₂²×C₃×C₅×C₁₁	19

Subgroups — C22×C5×C11×C19⋊C3 #27160093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₁₁×C₁₉⋊C₃ #27160093