Subgroups — C₅×D₃×D₇×C₂₉ #27131776

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₇×C₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₇×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₇×C₂₉	—	3	1	no	—
8	C₅×D₇×C₂₉	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇×C₂₉	—	3	1	no	—
10	C₂×C₅×D₃×C₂₉	—	7	1	no	maximal, Hall
11	C₂₉×D₂₁	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×D₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₂₉	—	7	1	no	—
16	C₅×D₃×C₂₉	—	7	1	no	—
17	C₅×D₃×C₂₉	D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇×C₂₉	—	3	1	no	Hall
19	C₃×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₅×C₂₉	—	21	1	no	Hall
21	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₇×C₂₉	—	3	1	no	—
24	D₇×C₂₉	—	3	1	no	—
25	D₇×C₂₉	C₅×D₃	1	1	yes	characteristic, direct product factor
26	C₂×D₃×C₂₉	—	7	1	no	Hall
27	C₂×C₅×C₂₉	—	3	1	no	—
28	C₂×C₅×C₂₉	—	7	1	no	—
29	C₂×C₅×C₂₉	—	21	1	no	—
30	C₅×D₂₁	C₂×C₂₉	1	1	yes	characteristic, complemented
31	C₅×D₃×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented
32	C₃×C₅×D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
33	C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₉	—	7	1	no	—
35	D₃×C₂₉	—	7	1	no	—
36	D₃×C₂₉	C₅×D₇	1	1	yes	characteristic, direct product factor
37	C₅×C₂₉	D₃×D₇	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₅×D₇	—	3	1	no	Hall
39	C₂²×C₂₉	—	21	1	no	Hall
40	C₃×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
42	D₃×D₇	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₅×C₇	—	3	1	no	—
44	C₅×D₇	—	3	1	no	—
45	C₅×D₇	D₃×C₂₉	1	1	yes	characteristic, direct product factor
46	C₂×C₅×D₃	—	7	1	no	Hall
47	C₂×C₂₉	—	3	1	no	—
48	C₂×C₂₉	—	7	1	no	—
49	C₂×C₂₉	—	21	1	no	—
50	D₂₁	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
51	C₃×D₇	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
52	D₃×C₇	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
53	C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	7	1	no	—
55	C₅×D₃	—	7	1	no	—
56	C₅×D₃	D₇×C₂₉	1	1	yes	characteristic, direct product factor
57	C₂₉	C₅×D₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×D₇	—	3	1	no	Hall
59	C₃×C₇	C₂²×C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	21	1	no	Hall
61	C₃×C₅	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	D₇	—	3	1	no	—
64	D₇	C₅×D₃×C₂₉	1	1	yes	characteristic, direct product factor
65	C₂×D₃	—	7	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	7	1	no	—
68	C₂×C₅	—	21	1	no	—
69	C₇	C₂×C₅×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	7	1	no	—
71	D₃	—	7	1	no	—
72	D₃	C₅×D₇×C₂₉	1	1	yes	characteristic, direct product factor
73	C₅	D₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	21	1	no	Sylow
75	C₃	C₂×C₅×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₉×D₂₁	C₂	semidirect
2. C₅×D₃×C₇×C₂₉	C₂	semidirect
3. C₃×C₅×D₇×C₂₉	C₂	semidirect
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
6. D₃×D₇×C₂₉	C₅	direct (N × H)
8. C₅×D₇×C₂₉	D₃	direct (N × H)
11. C₂₉×D₂₁	C₂×C₅	semidirect
12. D₃×C₇×C₂₉	C₂×C₅	semidirect
13. C₃×D₇×C₂₉	C₂×C₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₃	semidirect
17. C₅×D₃×C₂₉	D₇	direct (N × H)
19. C₃×C₇×C₂₉	C₂²×C₅	semidirect
21. C₃×C₅×C₂₉	C₂×D₇	semidirect
22. C₅×D₃×D₇	C₂₉	direct (N × H)
25. D₇×C₂₉	C₅×D₃	direct (N × H)
30. C₅×D₂₁	C₂×C₂₉	semidirect
31. C₅×D₃×C₇	C₂×C₂₉	semidirect
32. C₃×C₅×D₇	C₂×C₂₉	semidirect
33. C₇×C₂₉	C₂×C₅×D₃	semidirect
36. D₃×C₂₉	C₅×D₇	direct (N × H)
37. C₅×C₂₉	D₃×D₇	direct (N × H)
40. C₃×C₅×C₇	C₂²×C₂₉	semidirect
41. C₃×C₂₉	C₂×C₅×D₇	semidirect
42. D₃×D₇	C₅×C₂₉	direct (N × H)
45. C₅×D₇	D₃×C₂₉	direct (N × H)
50. D₂₁	C₂×C₅×C₂₉	semidirect
51. C₃×D₇	C₂×C₅×C₂₉	semidirect
52. D₃×C₇	C₂×C₅×C₂₉	semidirect
53. C₅×C₇	C₂×D₃×C₂₉	semidirect
56. C₅×D₃	D₇×C₂₉	direct (N × H)
57. C₂₉	C₅×D₃×D₇	direct (N × H)
59. C₃×C₇	C₂²×C₅×C₂₉	semidirect
61. C₃×C₅	C₂×D₇×C₂₉	semidirect
64. D₇	C₅×D₃×C₂₉	direct (N × H)
69. C₇	C₂×C₅×D₃×C₂₉	semidirect
72. D₃	C₅×D₇×C₂₉	direct (N × H)
73. C₅	D₃×D₇×C₂₉	direct (N × H)
75. C₃	C₂×C₅×D₇×C₂₉	semidirect

Subgroups — C5×D3×D7×C29 #27131776

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×D₇×C₂₉ #27131776