Subgroups — C₃×D₃×C₁₉×D₁₃ #22580353

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₃×C₁₉

Complements

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

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

Subgroups — C3×D3×C19×D13 #22580353

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×C₁₉×D₁₃ #22580353