Subgroups — D₃×C₁₉×D₃₉ #22580368

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₃₉	—	3	1	no	maximal
5	D₃×C₁₉×D₁₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₁₉	—	3	1	no	—
8	C₁₉×D₃₉	—	3	1	no	—
9	C₁₉×D₃₉	—	3	1	no	—
10	C₁₉×D₃₉	—	6	1	no	—
11	C₁₉×D₃₉	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₉×D₁₃	—	3	1	no	—
14	C₂×C₁₉×D₁₃	—	9	1	no	Hall
15	C₃×C₁₃×C₁₉	—	2	1	no	—
16	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃²×C₁₉	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₁₉	—	3	1	no	—
20	C₁₉×D₁₃	—	3	1	no	—
21	C₁₉×D₁₃	—	9	1	no	—
22	D₃×D₃₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₃⋊D₃×C₁₉	—	13	1	no	—
24	C₃×D₃×C₁₉	—	13	1	no	—
25	C₃×D₃×C₁₉	D₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, complemented, Hall
27	C₃⋊D₃₉	C₂×C₁₉	1	1	yes	characteristic, complemented
28	C₃×D₃₉	C₂×C₁₉	1	1	yes	characteristic, complemented
29	C₃×D₃×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
30	C₂×D₃×C₁₉	—	39	1	no	—
31	C₂×D₃×C₁₉	—	39	1	no	—
32	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃₉	—	3	1	no	—
34	D₃×D₁₃	—	3	1	no	—
35	C₃²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₉	—	3	1	no	—
37	C₂×C₃×C₁₉	—	39	1	no	—
38	D₃×C₁₉	—	13	1	no	—
39	D₃×C₁₉	—	39	1	no	—
40	D₃×C₁₉	—	39	1	no	—
41	D₃×C₁₉	—	78	1	no	—
42	D₃×C₁₉	D₃₉	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₁₃	—	3	1	no	—
44	D₃₉	—	3	1	no	—
45	D₃₉	—	3	1	no	—
46	D₃₉	—	6	1	no	—
47	D₃₉	D₃×C₁₉	1	1	yes	characteristic, direct product factor
48	C₃×D₁₃	—	3	1	no	—
49	D₃×C₁₃	D₃×C₁₉	1	1	yes	characteristic, complemented
50	C₂²×C₁₉	—	117	1	no	Hall
51	C₃×C₁₉	—	2	1	no	—
52	C₃×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	9	1	no	Hall
55	C₃×C₁₃	—	2	1	no	—
56	C₃×C₁₃	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	3	1	no	—
59	C₂×C₁₉	—	39	1	no	—
60	C₂×C₁₉	—	117	1	no	—
61	D₃²	—	13	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	3	1	no	—
64	D₁₃	—	9	1	no	—
65	C₁₉	D₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₃⋊D₃	—	13	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	C₁₉×D₁₃	1	1	yes	characteristic, complemented
69	C₁₃	D₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	39	1	no	—
71	C₂×D₃	—	39	1	no	—
72	C₃²	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	39	1	no	—
75	D₃	—	13	1	no	—
76	D₃	—	39	1	no	—
77	D₃	—	39	1	no	—
78	D₃	—	78	1	no	—
79	D₃	C₁₉×D₃₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	117	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented
83	C₃	C₂×C₁₉×D₃₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₃×D₃₉
commutator, hypocenter	C₃²×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₃⋊D₃₉	C₂	semidirect
2. C₃×C₁₉×D₃₉	C₂	semidirect
3. C₃×D₃×C₁₃×C₁₉	C₂	semidirect
6. C₃²×C₁₃×C₁₉	C₂²	semidirect
11. C₁₉×D₃₉	D₃	direct (N × H)
12. D₃×C₁₃×C₁₉	D₃	semidirect
16. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
22. D₃×D₃₉	C₁₉	direct (N × H)
25. C₃×D₃×C₁₉	D₁₃	semidirect
26. C₁₃×C₁₉	D₃²	semidirect
27. C₃⋊D₃₉	C₂×C₁₉	semidirect
28. C₃×D₃₉	C₂×C₁₉	semidirect
29. C₃×D₃×C₁₃	C₂×C₁₉	semidirect
32. C₃²×C₁₉	C₂×D₁₃	semidirect
35. C₃²×C₁₃	C₂²×C₁₉	semidirect
42. D₃×C₁₉	D₃₉	direct (N × H)
47. D₃₉	D₃×C₁₉	direct (N × H)
49. D₃×C₁₃	D₃×C₁₉	semidirect
52. C₃×C₁₉	D₃×D₁₃	semidirect
53. C₃×C₁₉	C₂×D₃₉	semidirect
56. C₃×C₁₃	C₂×D₃×C₁₉	semidirect
57. C₃×C₁₃	C₂×D₃×C₁₉	semidirect
65. C₁₉	D₃×D₃₉	direct (N × H)
68. C₃×D₃	C₁₉×D₁₃	semidirect
69. C₁₃	D₃²×C₁₉	semidirect
72. C₃²	C₂×C₁₉×D₁₃	semidirect
79. D₃	C₁₉×D₃₉	direct (N × H)
82. C₃	D₃×C₁₉×D₁₃	semidirect
83. C₃	C₂×C₁₉×D₃₉	semidirect

Subgroups — D3×C19×D39 #22580368

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₉×D₃₉ #22580368