Subgroups — C₃×D₅×D₇×C₂₉ #27131768

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₇×C₂₉	—	5	1	no	maximal, Hall
7	C₂₉×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×D₅×C₂₉	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇×C₂₉	—	5	1	no	—
12	C₃×D₇×C₂₉	—	5	1	no	—
13	C₃×D₇×C₂₉	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₂₉	—	7	1	no	—
16	C₃×D₅×C₂₉	—	7	1	no	—
17	C₃×D₅×C₂₉	D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇×C₂₉	—	5	1	no	Hall
19	C₃×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₂₉	—	7	1	no	Hall
21	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₇×C₂₉	—	5	1	no	—
24	D₇×C₂₉	—	5	1	no	—
25	D₇×C₂₉	C₃×D₅	1	1	yes	characteristic, direct product factor
26	C₂²×C₃×C₂₉	—	35	1	no	Hall
27	C₂×C₅×C₂₉	—	7	1	no	—
28	D₅×C₂₉	—	7	1	no	—
29	D₅×C₂₉	C₃×D₇	1	1	yes	characteristic, direct product factor
30	C₃×D₃₅	C₂×C₂₉	1	1	yes	characteristic, complemented
31	C₃×C₇×D₅	C₂×C₂₉	1	1	yes	characteristic, complemented
32	C₃×C₅×D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
33	C₇×C₂₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₉	—	5	1	no	—
35	C₂×C₃×C₂₉	—	7	1	no	—
36	C₂×C₃×C₂₉	—	35	1	no	—
37	C₅×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
38	D₅×D₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
39	C₂²×C₂₉	—	35	1	no	Hall
40	C₃×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	D₅×D₇	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃×D₇	—	5	1	no	Hall
43	D₃₅	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
44	C₅×D₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
45	C₇×D₅	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
46	C₂×C₃×D₅	—	7	1	no	Hall
47	C₂×C₂₉	—	5	1	no	—
48	C₂×C₂₉	—	7	1	no	—
49	C₂×C₂₉	—	35	1	no	—
50	C₂×C₃×C₇	—	5	1	no	—
51	C₃×D₇	—	5	1	no	—
52	C₃×D₇	D₅×C₂₉	1	1	yes	characteristic, direct product factor
53	C₅×C₇	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	7	1	no	—
55	C₃×D₅	—	7	1	no	—
56	C₃×D₅	D₇×C₂₉	1	1	yes	characteristic, direct product factor
57	C₂₉	C₃×D₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×D₇	—	5	1	no	Hall
59	C₃×C₇	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	7	1	no	Hall
61	C₃×C₅	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	5	1	no	—
63	D₇	—	5	1	no	—
64	D₇	C₃×D₅×C₂₉	1	1	yes	characteristic, direct product factor
65	C₂²×C₃	—	35	1	no	Hall
66	C₂×C₅	—	7	1	no	—
67	D₅	—	7	1	no	—
68	D₅	C₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor
69	C₇	C₂×C₃×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	7	1	no	—
72	C₂×C₃	—	35	1	no	—
73	C₅	C₂×C₃×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	35	1	no	Sylow
75	C₃	D₅×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	7	1	no	—
78	C₂	—	35	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₅×D₇
commutator, hypocenter	C₅×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×D₃₅	C₂	semidirect
2. C₃×C₇×D₅×C₂₉	C₂	semidirect
3. C₃×C₅×D₇×C₂₉	C₂	semidirect
4. D₅×D₇×C₂₉	C₃	direct (N × H)
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
7. C₂₉×D₃₅	C₂×C₃	semidirect
8. C₇×D₅×C₂₉	C₂×C₃	semidirect
9. C₅×D₇×C₂₉	C₂×C₃	semidirect
13. C₃×D₇×C₂₉	D₅	direct (N × H)
14. C₅×C₇×C₂₉	C₂²×C₃	semidirect
17. C₃×D₅×C₂₉	D₇	direct (N × H)
19. C₃×C₇×C₂₉	C₂×D₅	semidirect
21. C₃×C₅×C₂₉	C₂×D₇	semidirect
22. C₃×D₅×D₇	C₂₉	direct (N × H)
25. D₇×C₂₉	C₃×D₅	direct (N × H)
29. D₅×C₂₉	C₃×D₇	direct (N × H)
30. C₃×D₃₅	C₂×C₂₉	semidirect
31. C₃×C₇×D₅	C₂×C₂₉	semidirect
32. C₃×C₅×D₇	C₂×C₂₉	semidirect
33. C₇×C₂₉	C₂×C₃×D₅	semidirect
37. C₅×C₂₉	C₂×C₃×D₇	semidirect
38. D₅×D₇	C₃×C₂₉	direct (N × H)
40. C₃×C₅×C₇	C₂²×C₂₉	semidirect
41. C₃×C₂₉	D₅×D₇	direct (N × H)
43. D₃₅	C₂×C₃×C₂₉	semidirect
44. C₅×D₇	C₂×C₃×C₂₉	semidirect
45. C₇×D₅	C₂×C₃×C₂₉	semidirect
52. C₃×D₇	D₅×C₂₉	direct (N × H)
53. C₅×C₇	C₂²×C₃×C₂₉	semidirect
56. C₃×D₅	D₇×C₂₉	direct (N × H)
57. C₂₉	C₃×D₅×D₇	direct (N × H)
59. C₃×C₇	C₂×D₅×C₂₉	semidirect
61. C₃×C₅	C₂×D₇×C₂₉	semidirect
64. D₇	C₃×D₅×C₂₉	direct (N × H)
68. D₅	C₃×D₇×C₂₉	direct (N × H)
69. C₇	C₂×C₃×D₅×C₂₉	semidirect
73. C₅	C₂×C₃×D₇×C₂₉	semidirect
75. C₃	D₅×D₇×C₂₉	direct (N × H)

Subgroups — C3×D5×D7×C29 #27131768

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₅×D₇×C₂₉ #27131768