Subgroups — D₃×C₁₉×D₁₄₃ #45656807

Order 32604.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₄₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₁×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₁₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₁₄₃	—	3	1	no	maximal, Hall
5	C₃×C₁₁×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₁₄₃	—	3	1	no	—
7	C₁₉×D₁₄₃	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₁₁×C₁₃×C₁₉	—	3	1	no	—
9	D₃×C₁₉×D₁₃	—	11	1	no	maximal, Hall
10	C₁₁×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₉×D₁₁	—	13	1	no	maximal, Hall
12	D₃×D₁₄₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₉×D₃₉	—	11	1	no	—
14	D₃×C₁₃×C₁₉	D₁₁	1	1	yes	characteristic, complemented
15	C₃×C₁₉×D₁₃	—	11	1	no	—
16	C₁₉×D₃₃	—	13	1	no	—
17	D₃×C₁₁×C₁₉	D₁₃	1	1	yes	characteristic, complemented
18	C₃×C₁₉×D₁₁	—	13	1	no	—
19	C₂×C₁₉×D₁₃	—	33	1	no	Hall
20	D₄₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented
21	D₃×C₁₁×C₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₃×D₁₄₃	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₂×C₁₉×D₁₁	—	39	1	no	Hall
24	C₃×C₁₃×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₁₄₃	—	3	1	no	Hall
27	C₂×C₁₃×C₁₉	—	3	1	no	—
28	C₁₉×D₁₃	—	11	1	no	—
29	C₁₉×D₁₃	—	33	1	no	—
30	C₃×C₁₁×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₁₁×C₁₉	—	3	1	no	—
32	C₁₉×D₁₁	—	13	1	no	—
33	C₁₉×D₁₁	—	39	1	no	—
34	C₂×C₁₁×C₁₃	—	3	1	no	—
35	D₁₄₃	—	3	1	no	—
36	D₁₄₃	D₃×C₁₉	1	1	yes	characteristic, direct product factor
37	C₁₃×C₁₉	D₃×D₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃×C₁₉	—	143	1	no	Hall
39	C₁₁×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
40	D₃×D₁₃	—	11	1	no	Hall
41	C₁₁×C₁₃	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
42	D₃×D₁₁	—	13	1	no	Hall
43	C₂×C₃×C₁₉	—	143	1	no	—
44	D₃×C₁₉	—	143	1	no	—
45	D₃×C₁₉	D₁₄₃	1	1	yes	characteristic, direct product factor
46	D₃₉	—	11	1	no	—
47	C₃×D₁₃	—	11	1	no	—
48	D₃×C₁₃	C₁₉×D₁₁	1	1	yes	characteristic, complemented
49	C₂²×C₁₉	—	429	1	no	Hall
50	D₃₃	—	13	1	no	—
51	C₃×D₁₁	—	13	1	no	—
52	D₃×C₁₁	C₁₉×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×D₁₄₃	1	1	yes	characteristic, complemented, Hall
54	C₂×D₁₃	—	33	1	no	Hall
55	C₂×D₁₁	—	39	1	no	Hall
56	C₃×C₁₃	C₂×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
57	C₂×C₁₉	—	3	1	no	—
58	C₂×C₁₉	—	143	1	no	—
59	C₂×C₁₉	—	429	1	no	—
60	C₃×C₁₁	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Hall
61	C₂×C₁₃	—	3	1	no	—
62	D₁₃	—	11	1	no	—
63	D₁₃	—	33	1	no	—
64	C₂×C₁₁	—	3	1	no	—
65	D₁₁	—	13	1	no	—
66	D₁₁	—	39	1	no	—
67	C₁₉	D₃×D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
68	C₁₃	D₃×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	143	1	no	Hall
70	C₁₁	D₃×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	143	1	no	—
72	D₃	—	143	1	no	—
73	D₃	C₁₉×D₁₄₃	1	1	yes	characteristic, direct product factor
74	C₂²	—	429	1	no	Sylow
75	C₃	C₂×C₁₉×D₁₄₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	143	1	no	—
78	C₂	—	429	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₃×D₁₄₃
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₁×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₄₂₉	C₂	semidirect
2. D₃×C₁₁×C₁₃×C₁₉	C₂	semidirect
3. C₃×C₁₉×D₁₄₃	C₂	semidirect
5. C₃×C₁₁×C₁₃×C₁₉	C₂²	semidirect
7. C₁₉×D₁₄₃	D₃	direct (N × H)
10. C₁₁×C₁₃×C₁₉	C₂×D₃	semidirect
12. D₃×D₁₄₃	C₁₉	direct (N × H)
14. D₃×C₁₃×C₁₉	D₁₁	semidirect
17. D₃×C₁₁×C₁₉	D₁₃	semidirect
20. D₄₂₉	C₂×C₁₉	semidirect
21. D₃×C₁₁×C₁₃	C₂×C₁₉	semidirect
22. C₃×D₁₄₃	C₂×C₁₉	semidirect
24. C₃×C₁₃×C₁₉	C₂×D₁₁	semidirect
25. C₃×C₁₁×C₁₉	C₂×D₁₃	semidirect
30. C₃×C₁₁×C₁₃	C₂²×C₁₉	semidirect
36. D₁₄₃	D₃×C₁₉	direct (N × H)
37. C₁₃×C₁₉	D₃×D₁₁	semidirect
39. C₁₁×C₁₉	D₃×D₁₃	semidirect
41. C₁₁×C₁₃	C₂×D₃×C₁₉	semidirect
45. D₃×C₁₉	D₁₄₃	direct (N × H)
48. D₃×C₁₃	C₁₉×D₁₁	semidirect
52. D₃×C₁₁	C₁₉×D₁₃	semidirect
53. C₃×C₁₉	C₂×D₁₄₃	semidirect
56. C₃×C₁₃	C₂×C₁₉×D₁₁	semidirect
60. C₃×C₁₁	C₂×C₁₉×D₁₃	semidirect
67. C₁₉	D₃×D₁₄₃	direct (N × H)
68. C₁₃	D₃×C₁₉×D₁₁	semidirect
70. C₁₁	D₃×C₁₉×D₁₃	semidirect
73. D₃	C₁₉×D₁₄₃	direct (N × H)
75. C₃	C₂×C₁₉×D₁₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×D₄₂₉	2
D₃×C₁₁×C₁₃×C₁₉	2
C₃×C₁₉×D₁₄₃	2
C₂×C₁₉×D₁₄₃	3
D₃×C₁₉×D₁₃	11
D₃×C₁₉×D₁₁	13
D₃×D₁₄₃	19

Subgroups — D3×C19×D143 #45656807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×D₁₄₃ #45656807