Subgroups — C₃×D₃×D₇×C₂₉ #20300649

Order 7308.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₇×C₂₉	—	3	1	no	maximal
5	D₃×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₇×C₂₉	—	3	1	no	—
8	C₂₉×D₂₁	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₇×C₂₉	—	2	1	no	—
11	C₃×D₇×C₂₉	—	3	1	no	—
12	C₃×D₇×C₂₉	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×D₃×C₂₉	—	7	1	no	maximal, Hall
15	C₂×D₇×C₂₉	—	3	1	no	Hall
16	C₃×C₇×C₂₉	—	2	1	no	—
17	C₃×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented
18	C₃×C₇×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃²×C₂₉	—	7	1	no	—
20	C₃×D₃×C₂₉	—	7	1	no	—
21	C₃×D₃×C₂₉	D₇	1	1	yes	characteristic, direct product factor
22	C₂×C₇×C₂₉	—	3	1	no	—
23	D₇×C₂₉	—	3	1	no	—
24	D₇×C₂₉	C₃×D₃	1	1	yes	characteristic, direct product factor
25	C₂²×C₃×C₂₉	—	21	1	no	—
26	C₂×D₃×C₂₉	—	7	1	no	—
27	C₃²×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₃×D₃×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₉	—	3	1	no	—
31	C₂×C₃×C₂₉	—	7	1	no	—
32	C₂×C₃×C₂₉	—	7	1	no	—
33	C₂×C₃×C₂₉	—	14	1	no	—
34	C₂×C₃×C₂₉	—	21	1	no	—
35	D₃×C₂₉	—	7	1	no	—
36	D₃×C₂₉	C₃×D₇	1	1	yes	characteristic, direct product factor
37	C₃×D₂₁	C₂×C₂₉	1	1	yes	characteristic, complemented
38	C₃×D₃×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented
39	C₃²×D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
40	C₂²×C₂₉	—	21	1	no	Hall
41	C₃×C₂₉	—	2	1	no	—
42	C₃×C₂₉	D₃×D₇	1	1	yes	characteristic, direct product factor
43	C₃×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented
44	C₂×C₃×D₇	—	3	1	no	—
45	D₃×D₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor
46	C₃²×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₂₉	—	3	1	no	—
48	C₂×C₂₉	—	7	1	no	—
49	C₂×C₂₉	—	21	1	no	—
50	C₂×C₃×C₇	—	3	1	no	—
51	D₂₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
52	C₃×D₇	—	2	1	no	—
53	C₃×D₇	—	3	1	no	—
54	C₃×D₇	D₃×C₂₉	1	1	yes	characteristic, direct product factor
55	C₃×D₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
56	D₃×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
57	C₂×C₃×D₃	—	7	1	no	Hall
58	C₂₉	C₃×D₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
59	C₂×D₇	—	3	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented
62	C₃×C₇	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	7	1	no	—
64	C₃×D₃	—	7	1	no	—
65	C₃×D₃	D₇×C₂₉	1	1	yes	characteristic, direct product factor
66	C₂×C₇	—	3	1	no	—
67	D₇	—	3	1	no	—
68	D₇	C₃×D₃×C₂₉	1	1	yes	characteristic, direct product factor
69	C₂²×C₃	—	21	1	no	—
70	C₂×D₃	—	7	1	no	—
71	C₃²	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
72	C₇	C₂×C₃×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	7	1	no	—
75	C₂×C₃	—	7	1	no	—
76	C₂×C₃	—	14	1	no	—
77	C₂×C₃	—	21	1	no	—
78	D₃	—	7	1	no	—
79	D₃	C₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	21	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×D₇×C₂₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	7	1	no	—
86	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×D₂₁	C₂	semidirect
2. C₃×D₃×C₇×C₂₉	C₂	semidirect
3. C₃²×D₇×C₂₉	C₂	semidirect
5. D₃×D₇×C₂₉	C₃	direct (N × H)
6. C₃²×C₇×C₂₉	C₂²	semidirect
8. C₂₉×D₂₁	C₂×C₃	semidirect
9. D₃×C₇×C₂₉	C₂×C₃	semidirect
12. C₃×D₇×C₂₉	D₃	direct (N × H)
13. C₃×D₇×C₂₉	C₂×C₃	semidirect
17. C₃×C₇×C₂₉	C₂×D₃	semidirect
18. C₃×C₇×C₂₉	C₂²×C₃	semidirect
21. C₃×D₃×C₂₉	D₇	direct (N × H)
24. D₇×C₂₉	C₃×D₃	direct (N × H)
27. C₃²×C₂₉	C₂×D₇	semidirect
28. C₃×D₃×D₇	C₂₉	direct (N × H)
29. C₇×C₂₉	C₂×C₃×D₃	semidirect
36. D₃×C₂₉	C₃×D₇	direct (N × H)
37. C₃×D₂₁	C₂×C₂₉	semidirect
38. C₃×D₃×C₇	C₂×C₂₉	semidirect
39. C₃²×D₇	C₂×C₂₉	semidirect
42. C₃×C₂₉	D₃×D₇	direct (N × H)
43. C₃×C₂₉	C₂×C₃×D₇	semidirect
45. D₃×D₇	C₃×C₂₉	direct (N × H)
46. C₃²×C₇	C₂²×C₂₉	semidirect
51. D₂₁	C₂×C₃×C₂₉	semidirect
54. C₃×D₇	D₃×C₂₉	direct (N × H)
55. C₃×D₇	C₂×C₃×C₂₉	semidirect
56. D₃×C₇	C₂×C₃×C₂₉	semidirect
58. C₂₉	C₃×D₃×D₇	direct (N × H)
61. C₃×C₇	C₂×D₃×C₂₉	semidirect
62. C₃×C₇	C₂²×C₃×C₂₉	semidirect
65. C₃×D₃	D₇×C₂₉	direct (N × H)
68. D₇	C₃×D₃×C₂₉	direct (N × H)
71. C₃²	C₂×D₇×C₂₉	semidirect
72. C₇	C₂×C₃×D₃×C₂₉	semidirect
79. D₃	C₃×D₇×C₂₉	direct (N × H)
82. C₃	D₃×D₇×C₂₉	direct (N × H)
83. C₃	C₂×C₃×D₇×C₂₉	semidirect

Subgroups — C3×D3×D7×C29 #20300649

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×D₇×C₂₉ #20300649