Subgroups — C₃×C₅×C₇×D₁₄₁ #44444113

Order 29610.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₁₄₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×C₇×D₄₇	—	3	1	no	maximal
4	C₃×C₇×D₁₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₄₇	—	2	1	no	—
6	C₃×C₅×C₇×C₄₇	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₅×D₁₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇×D₄₇	—	3	1	no	Hall
10	C₃²×C₇×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₅×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₁₄₁	C₃×C₅	1	1	yes	characteristic, direct product factor
13	C₃×C₇×D₄₇	—	3	1	no	—
14	C₅×C₇×C₄₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₄₁	C₃×C₇	1	1	yes	characteristic, direct product factor
16	C₃×C₅×D₄₇	—	3	1	no	—
17	C₃×C₇×C₄₇	—	2	1	no	—
18	C₃×C₇×C₄₇	C₅×D₃	1	1	yes	characteristic, complemented
19	C₃×C₇×C₄₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₃×D₁₄₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅×C₄₇	—	2	1	no	—
22	C₃×C₅×C₄₇	D₃×C₇	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	C₇×D₄₇	—	3	1	no	Hall
25	C₃×C₅×D₃×C₇	—	47	1	no	maximal, Hall
26	C₅×D₄₇	—	3	1	no	Hall
27	C₃²×C₄₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₄₇	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₅×C₇	D₄₇	1	1	yes	characteristic, complemented, Hall
30	D₁₄₁	C₃×C₅×C₇	1	1	yes	characteristic, direct product factor
31	C₃×D₄₇	—	3	1	no	—
32	C₅×C₄₇	C₃×D₃×C₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅×C₇	—	141	1	no	—
34	C₅×D₃×C₇	—	47	1	no	—
35	C₃×C₄₇	—	2	1	no	—
36	C₃×C₄₇	C₅×D₃×C₇	1	1	yes	characteristic, complemented
37	C₃×C₄₇	C₂×C₃×C₅×C₇	1	1	yes	characteristic, complemented
38	C₃×D₃×C₇	—	47	1	no	Hall
39	C₃×C₅×C₇	—	2	1	no	—
40	C₃×C₅×C₇	C₃×D₄₇	1	1	yes	characteristic, complemented
41	C₃×C₅×C₇	D₁₄₁	1	1	yes	characteristic, direct product factor
42	D₄₇	—	3	1	no	Hall
43	C₃×C₅×D₃	—	47	1	no	Hall
44	C₂×C₅×C₇	—	141	1	no	Hall
45	C₃²×C₇	C₅×D₄₇	1	1	yes	characteristic, complemented, Hall
46	C₄₇	C₃×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
47	C₃²×C₅	C₇×D₄₇	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₇	—	141	1	no	—
49	D₃×C₇	—	47	1	no	—
50	C₅×C₇	C₃×D₁₄₁	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₅	—	141	1	no	—
52	C₅×D₃	—	47	1	no	—
53	C₃×C₇	—	2	1	no	—
54	C₃×C₇	C₃×C₅×D₄₇	1	1	yes	characteristic, complemented
55	C₃×C₇	C₅×D₁₄₁	1	1	yes	characteristic, direct product factor
56	C₃×D₃	—	47	1	no	Hall
57	C₃×C₅	—	2	1	no	—
58	C₃×C₅	C₃×C₇×D₄₇	1	1	yes	characteristic, complemented
59	C₃×C₅	C₇×D₁₄₁	1	1	yes	characteristic, direct product factor
60	C₂×C₇	—	141	1	no	Hall
61	C₂×C₅	—	141	1	no	Hall
62	C₃²	C₅×C₇×D₄₇	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₃×C₅×D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	141	1	no	—
65	D₃	—	47	1	no	—
66	C₅	C₃×C₇×D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₅×C₇×D₄₇	1	1	yes	characteristic, complemented
69	C₃	C₅×C₇×D₁₄₁	1	1	yes	characteristic, direct product factor
70	C₂	—	141	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇	D₁₄₁
commutator, cosocle, hypocenter	C₃×C₄₇	C₂×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₄₇	C₂
LCS	G ▷ C₃×C₄₇
UCS	C₁ ◁ C₃×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₄₇	C₂	semidirect
2. C₅×C₇×D₁₄₁	C₃	direct (N × H)
4. C₃×C₇×D₁₄₁	C₅	direct (N × H)
6. C₃×C₅×C₇×C₄₇	D₃	semidirect
7. C₃×C₅×C₇×C₄₇	C₂×C₃	semidirect
8. C₃×C₅×D₁₄₁	C₇	direct (N × H)
10. C₃²×C₇×C₄₇	C₂×C₅	semidirect
11. C₃²×C₅×C₄₇	C₂×C₇	semidirect
12. C₇×D₁₄₁	C₃×C₅	direct (N × H)
14. C₅×C₇×C₄₇	C₃×D₃	semidirect
15. C₅×D₁₄₁	C₃×C₇	direct (N × H)
18. C₃×C₇×C₄₇	C₅×D₃	semidirect
19. C₃×C₇×C₄₇	C₂×C₃×C₅	semidirect
20. C₃×D₁₄₁	C₅×C₇	direct (N × H)
22. C₃×C₅×C₄₇	D₃×C₇	semidirect
23. C₃×C₅×C₄₇	C₂×C₃×C₇	semidirect
27. C₃²×C₄₇	C₂×C₅×C₇	semidirect
28. C₇×C₄₇	C₃×C₅×D₃	semidirect
29. C₃²×C₅×C₇	D₄₇	semidirect
30. D₁₄₁	C₃×C₅×C₇	direct (N × H)
32. C₅×C₄₇	C₃×D₃×C₇	semidirect
36. C₃×C₄₇	C₅×D₃×C₇	semidirect
37. C₃×C₄₇	C₂×C₃×C₅×C₇	semidirect
40. C₃×C₅×C₇	C₃×D₄₇	semidirect
41. C₃×C₅×C₇	D₁₄₁	direct (N × H)
45. C₃²×C₇	C₅×D₄₇	semidirect
46. C₄₇	C₃×C₅×D₃×C₇	semidirect
47. C₃²×C₅	C₇×D₄₇	semidirect
50. C₅×C₇	C₃×D₁₄₁	direct (N × H)
54. C₃×C₇	C₃×C₅×D₄₇	semidirect
55. C₃×C₇	C₅×D₁₄₁	direct (N × H)
58. C₃×C₅	C₃×C₇×D₄₇	semidirect
59. C₃×C₅	C₇×D₁₄₁	direct (N × H)
62. C₃²	C₅×C₇×D₄₇	semidirect
63. C₇	C₃×C₅×D₁₄₁	direct (N × H)
66. C₅	C₃×C₇×D₁₄₁	direct (N × H)
68. C₃	C₃×C₅×C₇×D₄₇	semidirect
69. C₃	C₅×C₇×D₁₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₄₇	2
C₅×C₇×D₁₄₁	3
C₃×C₅×C₇×D₄₇	3
C₃×C₇×D₁₄₁	5
C₃×C₅×D₁₄₁	7
C₃×C₅×D₃×C₇	47

Subgroups — C3×C5×C7×D141 #44444113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₇×D₁₄₁ #44444113