Subgroups — C₃×C₁₃×D₁₀₅ #22551301

Order 8190.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₁₀₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₃×D₃₅	—	3	1	no	maximal
4	C₃×C₁₃×D₂₁	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₃	—	2	1	no	—
6	C₃×C₅×C₇×C₁₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×C₁₃×D₁₅	—	7	1	no	maximal, Hall
9	C₁₃×D₃₅	—	3	1	no	Hall
10	C₃²×C₇×C₁₃	D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₀₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₅×C₁₃	D₇	1	1	yes	characteristic, complemented, Hall
13	C₁₃×D₂₁	—	5	1	no	—
14	C₃×C₁₃×D₇	—	15	1	no	—
15	C₅×C₇×C₁₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
16	C₁₃×D₁₅	—	7	1	no	—
17	C₃×D₅×C₁₃	—	21	1	no	—
18	C₃²×C₅×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₁₃	—	2	1	no	—
20	C₃×C₇×C₁₃	C₃×D₅	1	1	yes	characteristic, complemented
21	C₃×C₇×C₁₃	D₁₅	1	1	yes	characteristic, complemented
22	C₃×D₃×C₁₃	—	35	1	no	Hall
23	D₁₀₅	C₃×C₁₃	1	1	yes	characteristic, direct product factor
24	C₃×D₃₅	—	3	1	no	—
25	C₃×C₅×C₁₃	—	2	1	no	—
26	C₃×C₅×C₁₃	C₃×D₇	1	1	yes	characteristic, complemented
27	C₃×C₅×C₁₃	D₂₁	1	1	yes	characteristic, complemented
28	C₁₃×D₇	—	15	1	no	Hall
29	D₅×C₁₃	—	21	1	no	Hall
30	C₃×D₂₁	—	5	1	no	Hall
31	C₃²×C₁₃	D₃₅	1	1	yes	characteristic, complemented, Hall
32	C₃×C₅×C₇	—	2	1	no	—
33	C₃×C₅×C₇	D₃×C₁₃	1	1	yes	characteristic, complemented
34	C₃×C₅×C₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
35	C₇×C₁₃	C₃×D₁₅	1	1	yes	characteristic, complemented, Hall
36	C₃×D₁₅	—	7	1	no	Hall
37	C₂×C₃×C₁₃	—	105	1	no	—
38	D₃×C₁₃	—	35	1	no	—
39	D₃₅	—	3	1	no	Hall
40	C₅×C₁₃	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
41	C₃²×C₇	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
42	C₃²×C₅	C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
43	D₂₁	—	5	1	no	—
44	C₃×D₇	—	15	1	no	—
45	C₃×C₁₃	—	2	1	no	—
46	C₃×C₁₃	C₃×D₃₅	1	1	yes	characteristic, complemented
47	C₃×C₁₃	D₁₀₅	1	1	yes	characteristic, direct product factor
48	C₅×C₇	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
49	D₁₅	—	7	1	no	—
50	C₃×D₅	—	21	1	no	—
51	C₂×C₁₃	—	105	1	no	Hall
52	C₃×C₇	—	2	1	no	—
53	C₃×C₇	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented
54	C₃×C₇	C₁₃×D₁₅	1	1	yes	characteristic, complemented
55	C₃×D₃	—	35	1	no	Hall
56	C₃×C₅	—	2	1	no	—
57	C₃×C₅	C₃×C₁₃×D₇	1	1	yes	characteristic, complemented
58	C₃×C₅	C₁₃×D₂₁	1	1	yes	characteristic, complemented
59	D₇	—	15	1	no	Hall
60	C₁₃	C₃×D₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
61	D₅	—	21	1	no	Hall
62	C₃²	C₁₃×D₃₅	1	1	yes	characteristic, complemented, Sylow
63	C₇	C₃×C₁₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	105	1	no	—
65	D₃	—	35	1	no	—
66	C₅	C₃×C₁₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₁₃×D₃₅	1	1	yes	characteristic, complemented
69	C₃	C₁₃×D₁₀₅	1	1	yes	characteristic, direct product factor
70	C₂	—	105	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₁₀₅
commutator, hypocenter	C₃×C₅×C₇	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₁₃	C₂	semidirect
2. C₁₃×D₁₀₅	C₃	direct (N × H)
6. C₃×C₅×C₇×C₁₃	D₃	semidirect
7. C₃×C₅×C₇×C₁₃	C₂×C₃	semidirect
10. C₃²×C₇×C₁₃	D₅	semidirect
11. C₃×D₁₀₅	C₁₃	direct (N × H)
12. C₃²×C₅×C₁₃	D₇	semidirect
15. C₅×C₇×C₁₃	C₃×D₃	semidirect
18. C₃²×C₅×C₇	C₂×C₁₃	semidirect
20. C₃×C₇×C₁₃	C₃×D₅	semidirect
21. C₃×C₇×C₁₃	D₁₅	semidirect
23. D₁₀₅	C₃×C₁₃	direct (N × H)
26. C₃×C₅×C₁₃	C₃×D₇	semidirect
27. C₃×C₅×C₁₃	D₂₁	semidirect
31. C₃²×C₁₃	D₃₅	semidirect
33. C₃×C₅×C₇	D₃×C₁₃	semidirect
34. C₃×C₅×C₇	C₂×C₃×C₁₃	semidirect
35. C₇×C₁₃	C₃×D₁₅	semidirect
40. C₅×C₁₃	C₃×D₂₁	semidirect
41. C₃²×C₇	D₅×C₁₃	semidirect
42. C₃²×C₅	C₁₃×D₇	semidirect
46. C₃×C₁₃	C₃×D₃₅	semidirect
47. C₃×C₁₃	D₁₀₅	direct (N × H)
48. C₅×C₇	C₃×D₃×C₁₃	semidirect
53. C₃×C₇	C₃×D₅×C₁₃	semidirect
54. C₃×C₇	C₁₃×D₁₅	semidirect
57. C₃×C₅	C₃×C₁₃×D₇	semidirect
58. C₃×C₅	C₁₃×D₂₁	semidirect
60. C₁₃	C₃×D₁₀₅	direct (N × H)
62. C₃²	C₁₃×D₃₅	semidirect
63. C₇	C₃×C₁₃×D₁₅	semidirect
66. C₅	C₃×C₁₃×D₂₁	semidirect
68. C₃	C₃×C₁₃×D₃₅	semidirect
69. C₃	C₁₃×D₁₀₅	direct (N × H)

Subgroups — C3×C13×D105 #22551301

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×D₁₀₅ #22551301