Subgroups — C₅×D₂₁×D₂₉ #27131775

Order 12180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₆₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂₉×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₇×D₂₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₁×D₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₂₀₃	—	3	1	no	—
8	C₅×D₇×C₂₉	—	3	1	no	—
9	C₅×C₇×D₂₉	D₃	1	1	yes	characteristic, complemented
10	C₅×D₃×D₂₉	—	7	1	no	maximal, Hall
11	D₆₀₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₂₉×D₂₁	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	—	7	1	no	—
16	C₅×D₃×C₂₉	—	7	1	no	—
17	C₃×C₅×D₂₉	D₇	1	1	yes	characteristic, complemented
18	D₇×D₂₉	—	3	1	no	Hall
19	C₃×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₂₉	—	21	1	no	Hall
21	C₃×C₅×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×D₂₁	—	29	1	no	maximal, Hall
23	D₂₀₃	—	3	1	no	—
24	C₇×D₂₉	C₅×D₃	1	1	yes	characteristic, complemented
25	D₇×C₂₉	—	3	1	no	—
26	D₃×D₂₉	—	7	1	no	Hall
27	C₂×C₅×C₂₉	—	21	1	no	—
28	C₅×D₂₉	—	21	1	no	—
29	C₅×D₂₉	D₂₁	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₅×C₇	—	29	1	no	—
31	C₅×D₂₁	—	29	1	no	—
32	C₅×D₂₁	D₂₉	1	1	yes	characteristic, direct product factor
33	C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
34	D₈₇	—	7	1	no	—
35	C₃×D₂₉	C₅×D₇	1	1	yes	characteristic, complemented
36	D₃×C₂₉	—	7	1	no	—
37	C₅×C₂₉	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅×D₇	—	87	1	no	Hall
39	C₂×D₂₉	—	21	1	no	Hall
40	C₃×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₂₉	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
42	C₂×D₂₁	—	29	1	no	Hall
43	C₂×C₅×C₇	—	29	1	no	—
44	C₅×D₇	—	3	1	no	—
45	C₅×D₇	—	87	1	no	—
46	C₂×C₅×D₃	—	203	1	no	Hall
47	C₂×C₂₉	—	21	1	no	—
48	D₂₉	—	21	1	no	—
49	D₂₉	C₅×D₂₁	1	1	yes	characteristic, direct product factor
50	C₂×C₃×C₇	—	29	1	no	—
51	D₂₁	—	29	1	no	—
52	D₂₁	C₅×D₂₉	1	1	yes	characteristic, direct product factor
53	C₅×C₇	D₃×D₂₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	29	1	no	—
55	C₅×D₃	—	7	1	no	—
56	C₅×D₃	—	203	1	no	—
57	C₂₉	C₂×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₇	—	87	1	no	Hall
59	C₃×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₅	—	609	1	no	Hall
61	C₃×C₅	D₇×D₂₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	29	1	no	—
63	D₇	—	3	1	no	—
64	D₇	—	87	1	no	—
65	C₂×D₃	—	203	1	no	Hall
66	C₂×C₅	—	21	1	no	—
67	C₂×C₅	—	29	1	no	—
68	C₂×C₅	—	609	1	no	—
69	C₇	C₅×D₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	29	1	no	—
71	D₃	—	7	1	no	—
72	D₃	—	203	1	no	—
73	C₅	D₂₁×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	609	1	no	Sylow
75	C₃	C₅×D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	29	1	no	—
78	C₂	—	609	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₂₁×D₂₉
commutator, hypocenter	C₃×C₇×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂²
LCS	G ▷ C₃×C₇×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₆₀₉	C₂	semidirect
2. C₅×C₂₉×D₂₁	C₂	semidirect
3. C₃×C₅×C₇×D₂₉	C₂	semidirect
5. C₃×C₅×C₇×C₂₉	C₂²	semidirect
6. D₂₁×D₂₉	C₅	direct (N × H)
9. C₅×C₇×D₂₉	D₃	semidirect
11. D₆₀₉	C₂×C₅	semidirect
12. C₂₉×D₂₁	C₂×C₅	semidirect
13. C₃×C₇×D₂₉	C₂×C₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₃	semidirect
17. C₃×C₅×D₂₉	D₇	semidirect
19. C₃×C₇×C₂₉	C₂²×C₅	semidirect
21. C₃×C₅×C₂₉	C₂×D₇	semidirect
24. C₇×D₂₉	C₅×D₃	semidirect
29. C₅×D₂₉	D₂₁	direct (N × H)
32. C₅×D₂₁	D₂₉	direct (N × H)
33. C₇×C₂₉	C₂×C₅×D₃	semidirect
35. C₃×D₂₉	C₅×D₇	semidirect
37. C₅×C₂₉	C₂×D₂₁	semidirect
40. C₃×C₅×C₇	C₂×D₂₉	semidirect
41. C₃×C₂₉	C₂×C₅×D₇	semidirect
49. D₂₉	C₅×D₂₁	direct (N × H)
52. D₂₁	C₅×D₂₉	direct (N × H)
53. C₅×C₇	D₃×D₂₉	semidirect
57. C₂₉	C₂×C₅×D₂₁	semidirect
59. C₃×C₇	C₂×C₅×D₂₉	semidirect
61. C₃×C₅	D₇×D₂₉	semidirect
69. C₇	C₅×D₃×D₂₉	semidirect
73. C₅	D₂₁×D₂₉	direct (N × H)
75. C₃	C₅×D₇×D₂₉	semidirect

Subgroups — C5×D21×D29 #27131775

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₂₁×D₂₉ #27131775