Subgroups — C₅×D₃×D₁₄₁ #22554913

Order 8460.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₁₄₁	—	3	1	no	maximal
5	C₅×D₃×D₄₇	—	3	1	no	maximal
6	C₃²×C₅×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₁₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×C₄₇	—	3	1	no	—
9	C₅×D₁₄₁	—	3	1	no	—
10	C₅×D₁₄₁	—	3	1	no	—
11	C₅×D₁₄₁	—	6	1	no	—
12	C₅×D₁₄₁	D₃	1	1	yes	characteristic, direct product factor
13	C₅×D₃×C₄₇	D₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₄₇	—	3	1	no	—
15	C₂×C₅×D₄₇	—	9	1	no	Hall
16	C₃⋊D₁₄₁	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×D₁₄₁	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₄₇	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₄₇	—	2	1	no	—
20	C₃×C₅×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₁₄₁	—	3	1	no	—
23	D₃×D₄₇	—	3	1	no	—
24	C₂×C₅×C₄₇	—	3	1	no	—
25	C₅×D₄₇	—	3	1	no	—
26	C₅×D₄₇	—	9	1	no	—
27	C₃²×C₄₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₄₇	—	3	1	no	—
29	D₁₄₁	—	3	1	no	—
30	D₁₄₁	—	3	1	no	—
31	D₁₄₁	—	6	1	no	—
32	D₁₄₁	C₅×D₃	1	1	yes	characteristic, direct product factor
33	C₃×D₄₇	—	3	1	no	—
34	D₃×C₄₇	C₅×D₃	1	1	yes	characteristic, complemented
35	C₅×C₄₇	D₃²	1	1	yes	characteristic, complemented, Hall
36	C₂×D₄₇	—	9	1	no	Hall
37	C₅×D₃²	—	47	1	no	maximal, Hall
38	C₃×C₄₇	—	2	1	no	—
39	C₃×C₄₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented
40	C₃×C₄₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented
41	C₂×C₄₇	—	3	1	no	—
42	D₄₇	—	3	1	no	—
43	D₄₇	—	9	1	no	—
44	C₅×C₃⋊D₃	—	47	1	no	—
45	C₃×C₅×D₃	—	47	1	no	—
46	C₃×C₅×D₃	D₄₇	1	1	yes	characteristic, complemented
47	C₂×C₅×D₃	—	141	1	no	—
48	C₂×C₅×D₃	—	141	1	no	—
49	C₄₇	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
50	C₃²×C₅	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
51	D₃²	—	47	1	no	Hall
52	C₂×C₃×C₅	—	3	1	no	—
53	C₂×C₃×C₅	—	141	1	no	—
54	C₅×D₃	—	282	1	no	—
55	C₅×D₃	—	47	1	no	—
56	C₅×D₃	—	141	1	no	—
57	C₅×D₃	—	141	1	no	—
58	C₅×D₃	D₁₄₁	1	1	yes	characteristic, direct product factor
59	C₂²×C₅	—	423	1	no	Hall
60	C₃⋊D₃	—	47	1	no	—
61	C₃×D₃	—	47	1	no	—
62	C₃×D₃	C₅×D₄₇	1	1	yes	characteristic, complemented
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₄₇	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₁₄₁	1	1	yes	characteristic, complemented
66	C₂×D₃	—	141	1	no	—
67	C₂×D₃	—	141	1	no	—
68	C₂×C₅	—	3	1	no	—
69	C₂×C₅	—	141	1	no	—
70	C₂×C₅	—	423	1	no	—
71	C₃²	C₂×C₅×D₄₇	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	141	1	no	—
74	D₃	—	282	1	no	—
75	D₃	—	47	1	no	—
76	D₃	—	141	1	no	—
77	D₃	—	141	1	no	—
78	D₃	C₅×D₁₄₁	1	1	yes	characteristic, direct product factor
79	C₅	D₃×D₁₄₁	1	1	yes	characteristic, direct product factor, Sylow
80	C₂²	—	423	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₅×D₃×D₄₇	1	1	yes	characteristic, complemented
83	C₃	C₂×C₅×D₁₄₁	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	141	1	no	—
86	C₂	—	423	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃×D₁₄₁
commutator, hypocenter	C₃²×C₄₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₄₇	C₂²
LCS	G ▷ C₃²×C₄₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₁₄₁	C₂	semidirect
2. C₃×C₅×D₁₄₁	C₂	semidirect
3. C₃×C₅×D₃×C₄₇	C₂	semidirect
6. C₃²×C₅×C₄₇	C₂²	semidirect
7. D₃×D₁₄₁	C₅	direct (N × H)
12. C₅×D₁₄₁	D₃	direct (N × H)
13. C₅×D₃×C₄₇	D₃	semidirect
16. C₃⋊D₁₄₁	C₂×C₅	semidirect
17. C₃×D₁₄₁	C₂×C₅	semidirect
18. C₃×D₃×C₄₇	C₂×C₅	semidirect
20. C₃×C₅×C₄₇	C₂×D₃	semidirect
21. C₃×C₅×C₄₇	C₂×D₃	semidirect
27. C₃²×C₄₇	C₂²×C₅	semidirect
32. D₁₄₁	C₅×D₃	direct (N × H)
34. D₃×C₄₇	C₅×D₃	semidirect
35. C₅×C₄₇	D₃²	semidirect
39. C₃×C₄₇	C₂×C₅×D₃	semidirect
40. C₃×C₄₇	C₂×C₅×D₃	semidirect
46. C₃×C₅×D₃	D₄₇	semidirect
49. C₄₇	C₅×D₃²	semidirect
50. C₃²×C₅	C₂×D₄₇	semidirect
58. C₅×D₃	D₁₄₁	direct (N × H)
62. C₃×D₃	C₅×D₄₇	semidirect
64. C₃×C₅	D₃×D₄₇	semidirect
65. C₃×C₅	C₂×D₁₄₁	semidirect
71. C₃²	C₂×C₅×D₄₇	semidirect
78. D₃	C₅×D₁₄₁	direct (N × H)
79. C₅	D₃×D₁₄₁	direct (N × H)
82. C₃	C₅×D₃×D₄₇	semidirect
83. C₃	C₂×C₅×D₁₄₁	semidirect

Subgroups — C5×D3×D141 #22554913

Conjugacy classes of subgroups

Complements

Subgroups — C₅×D₃×D₁₄₁ #22554913