Subgroups — D₃×C₁₉×D₁₄₅ #45683333

Order 33060.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×D₄₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃×C₁₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×D₁₄₅	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₉×D₂₉	—	5	1	no	maximal, Hall
7	C₁₉×D₁₄₅	—	3	1	no	—
8	C₁₉×D₁₄₅	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅×C₁₉×C₂₉	—	3	1	no	—
10	C₁₉×D₈₇	—	5	1	no	—
11	D₃×C₁₉×C₂₉	D₅	1	1	yes	characteristic, complemented
12	C₃×C₁₉×D₂₉	—	5	1	no	—
13	C₅×C₁₉×C₂₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₉×D₂₉	—	15	1	no	Hall
15	D₃×D₁₄₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₁₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₃×D₅×C₁₉	—	29	1	no	maximal, Hall
18	C₂×C₁₉×C₂₉	—	3	1	no	—
19	C₁₉×D₂₉	—	5	1	no	—
20	C₁₉×D₂₉	—	15	1	no	—
21	D₄₃₅	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₅×D₃×C₂₉	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₃×D₁₄₅	C₂×C₁₉	1	1	yes	characteristic, complemented
24	C₂×D₁₄₅	—	3	1	no	Hall
25	C₁₉×D₁₅	—	29	1	no	—
26	C₅×D₃×C₁₉	D₂₉	1	1	yes	characteristic, complemented
27	C₃×D₅×C₁₉	—	29	1	no	—
28	C₁₉×C₂₉	D₃×D₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×C₂₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
30	C₂×D₅×C₁₉	—	87	1	no	Hall
31	D₃×D₂₉	—	5	1	no	Hall
32	C₂×C₅×C₂₉	—	3	1	no	—
33	D₁₄₅	—	3	1	no	—
34	D₁₄₅	D₃×C₁₉	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
36	C₂×D₃×C₁₉	—	145	1	no	Hall
37	C₂×C₅×C₁₉	—	3	1	no	—
38	D₅×C₁₉	—	29	1	no	—
39	D₅×C₁₉	—	87	1	no	—
40	D₈₇	—	5	1	no	—
41	C₃×D₂₉	—	5	1	no	—
42	D₃×C₂₉	D₅×C₁₉	1	1	yes	characteristic, complemented
43	C₅×C₂₉	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×D₂₉	—	15	1	no	Hall
45	C₂×C₃×C₁₉	—	145	1	no	—
46	D₃×C₁₉	—	145	1	no	—
47	D₃×C₁₉	D₁₄₅	1	1	yes	characteristic, direct product factor
48	C₅×C₁₉	D₃×D₂₉	1	1	yes	characteristic, complemented, Hall
49	C₃×C₂₉	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₁₉	—	435	1	no	Hall
51	D₃×D₅	—	29	1	no	Hall
52	C₂×C₂₉	—	3	1	no	—
53	D₂₉	—	5	1	no	—
54	D₂₉	—	15	1	no	—
55	C₃×C₁₉	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₉	—	3	1	no	—
57	C₂×C₁₉	—	145	1	no	—
58	C₂×C₁₉	—	435	1	no	—
59	D₁₅	—	29	1	no	—
60	C₃×D₅	—	29	1	no	—
61	C₅×D₃	C₁₉×D₂₉	1	1	yes	characteristic, complemented
62	C₂₉	D₃×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	87	1	no	Hall
64	C₁₉	D₃×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₃×C₅	C₂×C₁₉×D₂₉	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	145	1	no	Hall
67	C₂×C₅	—	3	1	no	—
68	D₅	—	29	1	no	—
69	D₅	—	87	1	no	—
70	C₂×C₃	—	145	1	no	—
71	D₃	—	145	1	no	—
72	D₃	C₁₉×D₁₄₅	1	1	yes	characteristic, direct product factor
73	C₅	D₃×C₁₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	435	1	no	Sylow
75	C₃	C₂×C₁₉×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	145	1	no	—
78	C₂	—	435	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₃×D₁₄₅
commutator, cosocle, hypocenter	C₃×C₅×C₂₉	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₂₉	C₂²
LCS	G ▷ C₃×C₅×C₂₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×D₄₃₅	C₂	semidirect
2. C₅×D₃×C₁₉×C₂₉	C₂	semidirect
3. C₃×C₁₉×D₁₄₅	C₂	semidirect
5. C₃×C₅×C₁₉×C₂₉	C₂²	semidirect
8. C₁₉×D₁₄₅	D₃	direct (N × H)
11. D₃×C₁₉×C₂₉	D₅	semidirect
13. C₅×C₁₉×C₂₉	C₂×D₃	semidirect
15. D₃×D₁₄₅	C₁₉	direct (N × H)
16. C₃×C₁₉×C₂₉	C₂×D₅	semidirect
21. D₄₃₅	C₂×C₁₉	semidirect
22. C₅×D₃×C₂₉	C₂×C₁₉	semidirect
23. C₃×D₁₄₅	C₂×C₁₉	semidirect
26. C₅×D₃×C₁₉	D₂₉	semidirect
28. C₁₉×C₂₉	D₃×D₅	semidirect
29. C₃×C₅×C₂₉	C₂²×C₁₉	semidirect
34. D₁₄₅	D₃×C₁₉	direct (N × H)
35. C₃×C₅×C₁₉	C₂×D₂₉	semidirect
42. D₃×C₂₉	D₅×C₁₉	semidirect
43. C₅×C₂₉	C₂×D₃×C₁₉	semidirect
47. D₃×C₁₉	D₁₄₅	direct (N × H)
48. C₅×C₁₉	D₃×D₂₉	semidirect
49. C₃×C₂₉	C₂×D₅×C₁₉	semidirect
55. C₃×C₁₉	C₂×D₁₄₅	semidirect
61. C₅×D₃	C₁₉×D₂₉	semidirect
62. C₂₉	D₃×D₅×C₁₉	semidirect
64. C₁₉	D₃×D₁₄₅	direct (N × H)
65. C₃×C₅	C₂×C₁₉×D₂₉	semidirect
72. D₃	C₁₉×D₁₄₅	direct (N × H)
73. C₅	D₃×C₁₉×D₂₉	semidirect
75. C₃	C₂×C₁₉×D₁₄₅	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×D₄₃₅	2
C₅×D₃×C₁₉×C₂₉	2
C₃×C₁₉×D₁₄₅	2
C₂×C₁₉×D₁₄₅	3
D₃×C₁₉×D₂₉	5
D₃×D₁₄₅	19
D₃×D₅×C₁₉	29

Subgroups — D3×C19×D145 #45683333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉×D₁₄₅ #45683333