Subgroups — C₅×D₃×C₇×D₂₉ #27131773

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇×D₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₇×D₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇×D₂₉	—	3	1	no	—
8	C₅×C₇×D₂₉	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₇×C₂₉	—	3	1	no	—
10	C₅×D₃×D₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×D₈₇	C₂×C₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃×C₇×D₂₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₈₇	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅×D₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₇×D₂₉	—	3	1	no	Hall
19	C₃×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₂₉	—	3	1	no	Hall
21	C₃×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×D₃×C₇	—	29	1	no	maximal, Hall
23	C₂×C₇×C₂₉	—	3	1	no	—
24	C₇×D₂₉	—	3	1	no	—
25	C₇×D₂₉	C₅×D₃	1	1	yes	characteristic, direct product factor
26	D₃×D₂₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₂₉	—	3	1	no	—
28	C₅×D₂₉	—	3	1	no	—
29	C₅×D₂₉	D₃×C₇	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₅×C₇	—	29	1	no	—
31	C₅×D₃×C₇	—	29	1	no	—
32	C₅×D₃×C₇	D₂₉	1	1	yes	characteristic, direct product factor
33	C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
34	D₈₇	C₂×C₅×C₇	1	1	yes	characteristic, complemented
35	C₃×D₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
36	D₃×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
37	C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₅×C₇	—	87	1	no	Hall
39	C₂×D₂₉	—	3	1	no	Hall
40	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
42	C₂×D₃×C₇	—	29	1	no	Hall
43	C₂×C₅×C₇	—	3	1	no	—
44	C₂×C₅×C₇	—	29	1	no	—
45	C₂×C₅×C₇	—	87	1	no	—
46	C₂×C₅×D₃	—	29	1	no	Hall
47	C₂×C₂₉	—	3	1	no	—
48	D₂₉	—	3	1	no	—
49	D₂₉	C₅×D₃×C₇	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₇	—	29	1	no	—
51	D₃×C₇	—	29	1	no	—
52	D₃×C₇	C₅×D₂₉	1	1	yes	characteristic, direct product factor
53	C₅×C₇	D₃×D₂₉	1	1	yes	characteristic, direct product factor, Hall
54	C₂×C₃×C₅	—	29	1	no	—
55	C₅×D₃	—	29	1	no	—
56	C₅×D₃	C₇×D₂₉	1	1	yes	characteristic, direct product factor
57	C₂₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₇	—	87	1	no	Hall
59	C₃×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	87	1	no	Hall
61	C₃×C₅	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	3	1	no	—
63	C₂×C₇	—	29	1	no	—
64	C₂×C₇	—	87	1	no	—
65	C₂×D₃	—	29	1	no	Hall
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	29	1	no	—
68	C₂×C₅	—	87	1	no	—
69	C₇	C₅×D₃×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	29	1	no	—
71	D₃	—	29	1	no	—
72	D₃	C₅×C₇×D₂₉	1	1	yes	characteristic, direct product factor
73	C₅	D₃×C₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	87	1	no	Sylow
75	C₃	C₂×C₅×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	29	1	no	—
78	C₂	—	87	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃×D₂₉
commutator, hypocenter	C₃×C₂₉	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₈₇	C₂	semidirect
2. C₅×D₃×C₇×C₂₉	C₂	semidirect
3. C₃×C₅×C₇×D₂₉	C₂	semidirect
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
6. D₃×C₇×D₂₉	C₅	direct (N × H)
8. C₅×C₇×D₂₉	D₃	direct (N × H)
10. C₅×D₃×D₂₉	C₇	direct (N × H)
11. C₇×D₈₇	C₂×C₅	semidirect
12. D₃×C₇×C₂₉	C₂×C₅	semidirect
13. C₃×C₇×D₂₉	C₂×C₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₃	semidirect
15. C₅×D₈₇	C₂×C₇	semidirect
16. C₅×D₃×C₂₉	C₂×C₇	semidirect
17. C₃×C₅×D₂₉	C₂×C₇	semidirect
19. C₃×C₇×C₂₉	C₂²×C₅	semidirect
21. C₃×C₅×C₂₉	C₂²×C₇	semidirect
25. C₇×D₂₉	C₅×D₃	direct (N × H)
26. D₃×D₂₉	C₅×C₇	direct (N × H)
29. C₅×D₂₉	D₃×C₇	direct (N × H)
32. C₅×D₃×C₇	D₂₉	direct (N × H)
33. C₇×C₂₉	C₂×C₅×D₃	semidirect
34. D₈₇	C₂×C₅×C₇	semidirect
35. C₃×D₂₉	C₂×C₅×C₇	semidirect
36. D₃×C₂₉	C₂×C₅×C₇	semidirect
37. C₅×C₂₉	C₂×D₃×C₇	semidirect
40. C₃×C₅×C₇	C₂×D₂₉	semidirect
41. C₃×C₂₉	C₂²×C₅×C₇	semidirect
49. D₂₉	C₅×D₃×C₇	direct (N × H)
52. D₃×C₇	C₅×D₂₉	direct (N × H)
53. C₅×C₇	D₃×D₂₉	direct (N × H)
56. C₅×D₃	C₇×D₂₉	direct (N × H)
57. C₂₉	C₂×C₅×D₃×C₇	semidirect
59. C₃×C₇	C₂×C₅×D₂₉	semidirect
61. C₃×C₅	C₂×C₇×D₂₉	semidirect
69. C₇	C₅×D₃×D₂₉	direct (N × H)
72. D₃	C₅×C₇×D₂₉	direct (N × H)
73. C₅	D₃×C₇×D₂₉	direct (N × H)
75. C₃	C₂×C₅×C₇×D₂₉	semidirect

Subgroups — C5×D3×C7×D29 #27131773

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×C₇×D₂₉ #27131773