Subgroups — C₂×C₁₁×D₁₅×C₄₇ #44526694

Order 31020.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₁₅×C₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₁×C₄₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃×C₁₁×C₄₇	—	5	1	no	maximal, Hall
6	D₅×C₁₁×C₄₇	—	3	2	no	—
7	C₂×C₅×C₁₁×C₄₇	D₃	1	1	yes	characteristic, complemented
8	D₃×C₁₁×C₄₇	—	5	2	no	—
9	C₂×C₃×C₁₁×C₄₇	D₅	1	1	yes	characteristic, complemented
10	C₂×D₁₅×C₄₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₁×C₄₇	—	15	1	no	Hall
13	C₃×C₁₁×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅×C₄₇	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₁₅×C₄₇	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₁₁×C₄₇	—	15	2	no	—
17	C₂×C₁₁×C₄₇	D₁₅	1	1	yes	characteristic, direct product factor
18	C₂×D₅×C₄₇	—	3	1	no	Hall
19	C₃×C₅×C₄₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₁₁×D₁₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×D₃×C₄₇	—	5	1	no	Hall
22	C₁₁×C₄₇	C₂×D₁₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₄₇	D₃×C₁₁	1	1	yes	characteristic, complemented
24	D₅×C₄₇	—	3	2	no	—
25	C₂×C₃×C₅×C₁₁	C₂×C₄₇	1	1	yes	characteristic, complemented
26	C₁₁×D₁₅	C₂×C₄₇	1	2	yes	direct product factor
27	C₂×C₃×C₄₇	D₅×C₁₁	1	1	yes	characteristic, complemented
28	D₃×C₄₇	—	5	2	no	—
29	C₅×C₄₇	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₂×D₅×C₁₁	—	3	1	no	Hall
31	C₂²×C₄₇	—	15	1	no	Hall
32	C₃×C₅×C₁₁	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₄₇	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₁₁	—	5	1	no	Hall
35	C₂×C₅×C₁₁	D₃×C₄₇	1	1	yes	characteristic, complemented
36	D₅×C₁₁	—	3	2	no	—
37	C₂×C₄₇	—	15	2	no	—
38	C₂×C₄₇	C₁₁×D₁₅	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₁₁	D₅×C₄₇	1	1	yes	characteristic, complemented
40	D₃×C₁₁	—	5	2	no	—
41	C₂×D₁₅	C₁₁×C₄₇	1	1	yes	characteristic, direct product factor, Hall
42	C₅×C₁₁	C₂×D₃×C₄₇	1	1	yes	characteristic, complemented, Hall
43	C₄₇	C₂×C₁₁×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²×C₁₁	—	15	1	no	Hall
45	C₃×C₁₁	C₂×D₅×C₄₇	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₅	C₂×C₁₁×C₄₇	1	1	yes	characteristic, complemented
47	D₁₅	C₂×C₁₁×C₄₇	1	2	yes	direct product factor
48	C₂×C₁₁	—	15	2	no	—
49	C₂×C₁₁	D₁₅×C₄₇	1	1	yes	characteristic, direct product factor
50	C₂×D₅	—	3	1	no	Hall
51	C₃×C₅	C₂²×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Hall
52	C₂×D₃	—	5	1	no	Hall
53	C₁₁	C₂×D₁₅×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	D₃×C₁₁×C₄₇	1	1	yes	characteristic, complemented
55	D₅	—	3	2	no	—
56	C₂×C₃	D₅×C₁₁×C₄₇	1	1	yes	characteristic, complemented
57	D₃	—	5	2	no	—
58	C₅	C₂×D₃×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	15	1	no	Sylow
60	C₃	C₂×D₅×C₁₁×C₄₇	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	15	2	no	—
62	C₂	C₁₁×D₁₅×C₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₄₇	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₁₁×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₄₇	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₁₁×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₁₅×C₄₇	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₄₇	C₂	semidirect
4. C₃×C₅×C₁₁×C₄₇	C₂²	semidirect
7. C₂×C₅×C₁₁×C₄₇	D₃	semidirect
9. C₂×C₃×C₁₁×C₄₇	D₅	semidirect
10. C₂×D₁₅×C₄₇	C₁₁	direct (N × H)
11. C₅×C₁₁×C₄₇	C₂×D₃	semidirect
13. C₃×C₁₁×C₄₇	C₂×D₅	semidirect
14. C₂×C₃×C₅×C₄₇	C₂×C₁₁	semidirect
15. D₁₅×C₄₇	C₂×C₁₁	direct (N × H)
17. C₂×C₁₁×C₄₇	D₁₅	direct (N × H)
19. C₃×C₅×C₄₇	C₂²×C₁₁	semidirect
20. C₂×C₁₁×D₁₅	C₄₇	direct (N × H)
22. C₁₁×C₄₇	C₂×D₁₅	direct (N × H)
23. C₂×C₅×C₄₇	D₃×C₁₁	semidirect
25. C₂×C₃×C₅×C₁₁	C₂×C₄₇	semidirect
26. C₁₁×D₁₅	C₂×C₄₇	direct (N × H)
27. C₂×C₃×C₄₇	D₅×C₁₁	semidirect
29. C₅×C₄₇	C₂×D₃×C₁₁	semidirect
32. C₃×C₅×C₁₁	C₂²×C₄₇	semidirect
33. C₃×C₄₇	C₂×D₅×C₁₁	semidirect
35. C₂×C₅×C₁₁	D₃×C₄₇	semidirect
38. C₂×C₄₇	C₁₁×D₁₅	direct (N × H)
39. C₂×C₃×C₁₁	D₅×C₄₇	semidirect
41. C₂×D₁₅	C₁₁×C₄₇	direct (N × H)
42. C₅×C₁₁	C₂×D₃×C₄₇	semidirect
43. C₄₇	C₂×C₁₁×D₁₅	direct (N × H)
45. C₃×C₁₁	C₂×D₅×C₄₇	semidirect
46. C₂×C₃×C₅	C₂×C₁₁×C₄₇	semidirect
47. D₁₅	C₂×C₁₁×C₄₇	direct (N × H)
49. C₂×C₁₁	D₁₅×C₄₇	direct (N × H)
51. C₃×C₅	C₂²×C₁₁×C₄₇	semidirect
53. C₁₁	C₂×D₁₅×C₄₇	direct (N × H)
54. C₂×C₅	D₃×C₁₁×C₄₇	semidirect
56. C₂×C₃	D₅×C₁₁×C₄₇	semidirect
58. C₅	C₂×D₃×C₁₁×C₄₇	semidirect
60. C₃	C₂×D₅×C₁₁×C₄₇	semidirect
62. C₂	C₁₁×D₁₅×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₁₅×C₄₇	2
C₂×C₃×C₅×C₁₁×C₄₇	2
C₂×D₅×C₁₁×C₄₇	3
C₂×D₃×C₁₁×C₄₇	5
C₂×D₁₅×C₄₇	11
C₂×C₁₁×D₁₅	47

Subgroups — C2×C11×D15×C47 #44526694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₁₅×C₄₇ #44526694