Subgroups — C₃×D₃×C₇×D₂₉ #20300646

Order 7308.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₇×D₂₉	—	3	1	no	maximal
5	D₃×C₇×D₂₉	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	C₇×D₈₇	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₇×D₂₉	—	2	1	no	—
11	C₃×C₇×D₂₉	—	3	1	no	—
12	C₃×C₇×D₂₉	D₃	1	1	yes	characteristic, direct product factor
13	C₃×C₇×D₂₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×D₃×D₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₇×D₂₉	—	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	C₃×D₈₇	C₂×C₇	1	1	yes	characteristic, complemented
20	C₃×D₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
21	C₃²×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
22	C₂×C₇×C₂₉	—	3	1	no	—
23	C₇×D₂₉	—	3	1	no	—
24	C₇×D₂₉	C₃×D₃	1	1	yes	characteristic, direct product factor
25	C₂×C₃×D₂₉	—	3	1	no	—
26	D₃×D₂₉	C₃×C₇	1	1	yes	characteristic, direct product factor
27	C₃²×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×D₃×C₇	—	29	1	no	maximal, Hall
29	C₇×C₂₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₂₉	—	3	1	no	—
31	D₈₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
32	C₃×D₂₉	—	2	1	no	—
33	C₃×D₂₉	—	3	1	no	—
34	C₃×D₂₉	D₃×C₇	1	1	yes	characteristic, direct product factor
35	C₃×D₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
36	D₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
37	C₂×C₃²×C₇	—	29	1	no	—
38	C₃×D₃×C₇	—	29	1	no	—
39	C₃×D₃×C₇	D₂₉	1	1	yes	characteristic, direct product factor
40	C₂×D₂₉	—	3	1	no	Hall
41	C₃×C₂₉	—	2	1	no	—
42	C₃×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented
43	C₃×C₂₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented
44	C₂²×C₃×C₇	—	87	1	no	—
45	C₂×D₃×C₇	—	29	1	no	—
46	C₃²×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
47	C₂×C₂₉	—	3	1	no	—
48	D₂₉	—	3	1	no	—
49	D₂₉	C₃×D₃×C₇	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₇	—	3	1	no	—
51	C₂×C₃×C₇	—	29	1	no	—
52	C₂×C₃×C₇	—	29	1	no	—
53	C₂×C₃×C₇	—	58	1	no	—
54	C₂×C₃×C₇	—	87	1	no	—
55	D₃×C₇	—	29	1	no	—
56	D₃×C₇	C₃×D₂₉	1	1	yes	characteristic, direct product factor
57	C₂×C₃×D₃	—	29	1	no	Hall
58	C₂₉	C₂×C₃×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₇	—	87	1	no	Hall
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	D₃×D₂₉	1	1	yes	characteristic, direct product factor
62	C₃×C₇	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	29	1	no	—
64	C₃×D₃	—	29	1	no	—
65	C₃×D₃	C₇×D₂₉	1	1	yes	characteristic, direct product factor
66	C₂×C₇	—	3	1	no	—
67	C₂×C₇	—	29	1	no	—
68	C₂×C₇	—	87	1	no	—
69	C₂²×C₃	—	87	1	no	—
70	C₂×D₃	—	29	1	no	—
71	C₃²	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
72	C₇	C₃×D₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	29	1	no	—
75	C₂×C₃	—	29	1	no	—
76	C₂×C₃	—	58	1	no	—
77	C₂×C₃	—	87	1	no	—
78	D₃	—	29	1	no	—
79	D₃	C₃×C₇×D₂₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	87	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₇×D₂₉	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×C₇×D₂₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	29	1	no	—
86	C₂	—	87	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₇	D₃×D₂₉
commutator, hypocenter	C₃×C₂₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×D₈₇	C₂	semidirect
2. C₃×D₃×C₇×C₂₉	C₂	semidirect
3. C₃²×C₇×D₂₉	C₂	semidirect
5. D₃×C₇×D₂₉	C₃	direct (N × H)
6. C₃²×C₇×C₂₉	C₂²	semidirect
8. C₇×D₈₇	C₂×C₃	semidirect
9. D₃×C₇×C₂₉	C₂×C₃	semidirect
12. C₃×C₇×D₂₉	D₃	direct (N × H)
13. C₃×C₇×D₂₉	C₂×C₃	semidirect
14. C₃×D₃×D₂₉	C₇	direct (N × H)
17. C₃×C₇×C₂₉	C₂×D₃	semidirect
18. C₃×C₇×C₂₉	C₂²×C₃	semidirect
19. C₃×D₈₇	C₂×C₇	semidirect
20. C₃×D₃×C₂₉	C₂×C₇	semidirect
21. C₃²×D₂₉	C₂×C₇	semidirect
24. C₇×D₂₉	C₃×D₃	direct (N × H)
26. D₃×D₂₉	C₃×C₇	direct (N × H)
27. C₃²×C₂₉	C₂²×C₇	semidirect
29. C₇×C₂₉	C₂×C₃×D₃	semidirect
31. D₈₇	C₂×C₃×C₇	semidirect
34. C₃×D₂₉	D₃×C₇	direct (N × H)
35. C₃×D₂₉	C₂×C₃×C₇	semidirect
36. D₃×C₂₉	C₂×C₃×C₇	semidirect
39. C₃×D₃×C₇	D₂₉	direct (N × H)
42. C₃×C₂₉	C₂×D₃×C₇	semidirect
43. C₃×C₂₉	C₂²×C₃×C₇	semidirect
46. C₃²×C₇	C₂×D₂₉	semidirect
49. D₂₉	C₃×D₃×C₇	direct (N × H)
56. D₃×C₇	C₃×D₂₉	direct (N × H)
58. C₂₉	C₂×C₃×D₃×C₇	semidirect
61. C₃×C₇	D₃×D₂₉	direct (N × H)
62. C₃×C₇	C₂×C₃×D₂₉	semidirect
65. C₃×D₃	C₇×D₂₉	direct (N × H)
71. C₃²	C₂×C₇×D₂₉	semidirect
72. C₇	C₃×D₃×D₂₉	direct (N × H)
79. D₃	C₃×C₇×D₂₉	direct (N × H)
82. C₃	D₃×C₇×D₂₉	direct (N × H)
83. C₃	C₂×C₃×C₇×D₂₉	semidirect

Subgroups — C3×D3×C7×D29 #20300646

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×C₇×D₂₉ #20300646