Subgroups — D₇×C₂₉×D₁₅ #27131792

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×D₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇×C₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₇×C₂₉	—	5	1	no	maximal, Hall
7	C₂₉×D₃₅	—	3	1	no	—
8	C₇×D₅×C₂₉	—	3	1	no	—
9	C₅×D₇×C₂₉	D₃	1	1	yes	characteristic, complemented
10	C₂×C₂₉×D₁₅	—	7	1	no	maximal, Hall
11	C₂₉×D₂₁	—	5	1	no	—
12	D₃×C₇×C₂₉	—	5	1	no	—
13	C₃×D₇×C₂₉	D₅	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	C₂₉×D₁₅	—	7	1	no	—
17	C₂₉×D₁₅	D₇	1	1	yes	characteristic, direct product factor
18	C₂×D₇×C₂₉	—	15	1	no	Hall
19	C₃×C₇×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅×C₂₉	—	21	1	no	Hall
21	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₇×D₁₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₇×C₂₉	—	15	1	no	—
24	D₇×C₂₉	—	15	1	no	—
25	D₇×C₂₉	D₁₅	1	1	yes	characteristic, direct product factor
26	C₂×D₃×C₂₉	—	35	1	no	Hall
27	C₂×C₅×C₂₉	—	7	1	no	—
28	D₅×C₂₉	—	3	1	no	—
29	D₅×C₂₉	—	21	1	no	—
30	D₁₀₅	C₂×C₂₉	1	1	yes	characteristic, complemented
31	C₇×D₁₅	C₂×C₂₉	1	1	yes	characteristic, complemented
32	C₃×C₅×D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
33	C₇×C₂₉	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₂₉	—	7	1	no	—
35	D₃×C₂₉	—	5	1	no	—
36	D₃×C₂₉	—	35	1	no	—
37	C₅×C₂₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
38	D₅×D₇	—	3	1	no	Hall
39	C₂²×C₂₉	—	105	1	no	Hall
40	C₃×C₅×C₇	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
42	D₃×D₇	—	5	1	no	Hall
43	D₃₅	—	3	1	no	—
44	C₅×D₇	D₃×C₂₉	1	1	yes	characteristic, complemented
45	C₇×D₅	—	3	1	no	—
46	C₂×D₁₅	—	7	1	no	Hall
47	C₂×C₂₉	—	7	1	no	—
48	C₂×C₂₉	—	15	1	no	—
49	C₂×C₂₉	—	105	1	no	—
50	D₂₁	—	5	1	no	—
51	C₃×D₇	D₅×C₂₉	1	1	yes	characteristic, complemented
52	D₃×C₇	—	5	1	no	—
53	C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	7	1	no	—
55	D₁₅	—	7	1	no	—
56	D₁₅	D₇×C₂₉	1	1	yes	characteristic, direct product factor
57	C₂₉	D₇×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×D₇	—	15	1	no	Hall
59	C₃×C₇	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	21	1	no	Hall
61	C₃×C₅	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	15	1	no	—
63	D₇	—	15	1	no	—
64	D₇	C₂₉×D₁₅	1	1	yes	characteristic, direct product factor
65	C₂×D₃	—	35	1	no	Hall
66	C₂×C₅	—	7	1	no	—
67	D₅	—	3	1	no	—
68	D₅	—	21	1	no	—
69	C₇	C₂×C₂₉×D₁₅	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	7	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	35	1	no	—
73	C₅	D₃×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	105	1	no	Sylow
75	C₃	D₅×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	7	1	no	—
77	C₂	—	15	1	no	—
78	C₂	—	105	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₇×D₁₅
commutator, hypocenter	C₃×C₅×C₇	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×D₁₀₅	C₂	semidirect
2. C₇×C₂₉×D₁₅	C₂	semidirect
3. C₃×C₅×D₇×C₂₉	C₂	semidirect
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
9. C₅×D₇×C₂₉	D₃	semidirect
13. C₃×D₇×C₂₉	D₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₃	semidirect
17. C₂₉×D₁₅	D₇	direct (N × H)
19. C₃×C₇×C₂₉	C₂×D₅	semidirect
21. C₃×C₅×C₂₉	C₂×D₇	semidirect
22. D₇×D₁₅	C₂₉	direct (N × H)
25. D₇×C₂₉	D₁₅	direct (N × H)
30. D₁₀₅	C₂×C₂₉	semidirect
31. C₇×D₁₅	C₂×C₂₉	semidirect
32. C₃×C₅×D₇	C₂×C₂₉	semidirect
33. C₇×C₂₉	C₂×D₁₅	semidirect
37. C₅×C₂₉	D₃×D₇	semidirect
40. C₃×C₅×C₇	C₂²×C₂₉	semidirect
41. C₃×C₂₉	D₅×D₇	semidirect
44. C₅×D₇	D₃×C₂₉	semidirect
51. C₃×D₇	D₅×C₂₉	semidirect
53. C₅×C₇	C₂×D₃×C₂₉	semidirect
56. D₁₅	D₇×C₂₉	direct (N × H)
57. C₂₉	D₇×D₁₅	direct (N × H)
59. C₃×C₇	C₂×D₅×C₂₉	semidirect
61. C₃×C₅	C₂×D₇×C₂₉	semidirect
64. D₇	C₂₉×D₁₅	direct (N × H)
69. C₇	C₂×C₂₉×D₁₅	semidirect
73. C₅	D₃×D₇×C₂₉	semidirect
75. C₃	D₅×D₇×C₂₉	semidirect

Subgroups — D7×C29×D15 #27131792

Conjugacy classes of subgroups

Complements

Subgroups — D₇×C₂₉×D₁₅ #27131792