Subgroups — C₂×C₅×C₇×C₃⋊D₃×C₁₉ #37561644

Order 23940.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₃⋊D₃×C₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₇×C₁₉	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₃⋊D₃×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₇×C₁₉	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₁₉	D₃	1	4	yes	complemented
8	C₂×C₅×C₃⋊D₃×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₇×C₁₉	—	9	1	no	Hall
10	C₇×C₃⋊D₃×C₁₉	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₃²×C₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₁₉	C₂×D₃	1	4	yes	complemented
13	C₂×C₃²×C₅×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₅×C₃⋊D₃×C₁₉	C₂×C₇	1	2	yes	direct product factor
15	C₂×D₃×C₇×C₁₉	—	3	4	no	—
16	C₂×C₅×C₇×C₁₉	—	9	2	no	—
17	C₂×C₅×C₇×C₁₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₅×C₇×C₃⋊D₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃²×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₃×C₁₉	—	3	4	no	—
21	C₃²×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₉	C₅×D₃	1	4	yes	complemented
23	D₃×C₇×C₁₉	—	3	8	no	—
24	C₂×C₃⋊D₃×C₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
25	C₅×C₇×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃²×C₅×C₇	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₅×C₇×C₃⋊D₃	C₂×C₁₉	1	2	yes	direct product factor
28	C₂×C₃×C₅×C₁₉	D₃×C₇	1	4	yes	complemented
29	C₅×D₃×C₁₉	—	3	8	no	—
30	C₂²×C₇×C₁₉	—	9	1	no	Hall
31	C₂×C₅×D₃×C₇	—	3	4	no	—
32	C₃×C₇×C₁₉	C₂×C₅×D₃	1	4	yes	complemented
33	C₂²×C₅×C₁₉	—	9	1	no	Hall
34	C₂×C₃²×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
35	C₃⋊D₃×C₁₉	C₂×C₅×C₇	1	2	yes	direct product factor
36	C₃²×C₅×C₇	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₉	C₂×D₃×C₇	1	4	yes	complemented
38	C₂×C₇×C₁₉	—	9	2	no	—
39	C₂×C₇×C₁₉	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
40	C₂×C₇×C₃⋊D₃	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
41	C₂×D₃×C₁₉	—	3	4	no	—
42	C₂×C₃×C₅×C₇	D₃×C₁₉	1	4	yes	complemented
43	C₅×D₃×C₇	—	3	8	no	—
44	C₂×C₅×C₁₉	—	9	2	no	—
45	C₂×C₅×C₁₉	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
46	C₂×C₅×C₃⋊D₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
47	C₃²×C₁₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅×C₇	—	9	1	no	Hall
49	C₇×C₁₉	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₃²×C₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
51	C₇×C₃⋊D₃	C₂×C₅×C₁₉	1	2	yes	direct product factor
52	C₂×C₃×C₁₉	C₅×D₃×C₇	1	4	yes	complemented
53	D₃×C₁₉	—	3	8	no	—
54	C₃×C₅×C₇	C₂×D₃×C₁₉	1	4	yes	complemented
55	C₅×C₁₉	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
56	C₂×C₃²×C₅	C₂×C₇×C₁₉	1	1	yes	characteristic, complemented
57	C₅×C₃⋊D₃	C₂×C₇×C₁₉	1	2	yes	direct product factor
58	C₂×D₃×C₇	—	3	4	no	—
59	C₂²×C₁₉	—	9	1	no	Hall
60	C₂×C₅×C₇	—	9	2	no	—
61	C₂×C₅×C₇	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
62	C₃²×C₇	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
63	C₂×C₅×D₃	—	3	4	no	—
64	C₃×C₁₉	C₂×C₅×D₃×C₇	1	4	yes	complemented
65	C₃²×C₅	C₂²×C₇×C₁₉	1	1	yes	characteristic, complemented, Hall
66	C₂×C₃×C₇	C₅×D₃×C₁₉	1	4	yes	complemented
67	D₃×C₇	—	3	8	no	—
68	C₂×C₁₉	—	9	2	no	—
69	C₂×C₁₉	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
70	C₂×C₃⋊D₃	C₅×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
71	C₅×C₇	C₂×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
72	C₂×C₃×C₅	D₃×C₇×C₁₉	1	4	yes	complemented
73	C₅×D₃	—	3	8	no	—
74	C₂²×C₇	—	9	1	no	Hall
75	C₃×C₇	C₂×C₅×D₃×C₁₉	1	4	yes	complemented
76	C₂²×C₅	—	9	1	no	Hall
77	C₁₉	C₂×C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₃²	C₂×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented
79	C₃⋊D₃	C₂×C₅×C₇×C₁₉	1	2	yes	direct product factor
80	C₃×C₅	C₂×D₃×C₇×C₁₉	1	4	yes	complemented
81	C₂×C₇	—	9	2	no	—
82	C₂×C₇	C₅×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
83	C₂×D₃	—	3	4	no	—
84	C₂×C₅	—	9	2	no	—
85	C₂×C₅	C₇×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
86	C₃²	C₂²×C₅×C₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₅×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	C₅×D₃×C₇×C₁₉	1	4	yes	complemented
89	D₃	—	3	8	no	—
90	C₅	C₂×C₇×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	9	1	no	Sylow
92	C₃	C₂×C₅×D₃×C₇×C₁₉	1	4	yes	complemented
93	C₂	—	9	2	no	—
94	C₂	C₅×C₇×C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₃⋊D₃×C₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₉	C₂	semidirect
4. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
5. C₂×C₇×C₃⋊D₃×C₁₉	C₅	direct (N × H)
7. C₂×C₃×C₅×C₇×C₁₉	D₃	semidirect
8. C₂×C₅×C₃⋊D₃×C₁₉	C₇	direct (N × H)
10. C₇×C₃⋊D₃×C₁₉	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₁₉	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₁₉	C₂×D₃	semidirect
13. C₂×C₃²×C₅×C₁₉	C₂×C₇	semidirect
14. C₅×C₃⋊D₃×C₁₉	C₂×C₇	direct (N × H)
17. C₂×C₅×C₇×C₁₉	C₃⋊D₃	direct (N × H)
18. C₂×C₅×C₇×C₃⋊D₃	C₁₉	direct (N × H)
19. C₃²×C₇×C₁₉	C₂²×C₅	semidirect
21. C₃²×C₅×C₁₉	C₂²×C₇	semidirect
22. C₂×C₃×C₇×C₁₉	C₅×D₃	semidirect
24. C₂×C₃⋊D₃×C₁₉	C₅×C₇	direct (N × H)
25. C₅×C₇×C₁₉	C₂×C₃⋊D₃	direct (N × H)
26. C₂×C₃²×C₅×C₇	C₂×C₁₉	semidirect
27. C₅×C₇×C₃⋊D₃	C₂×C₁₉	direct (N × H)
28. C₂×C₃×C₅×C₁₉	D₃×C₇	semidirect
32. C₃×C₇×C₁₉	C₂×C₅×D₃	semidirect
34. C₂×C₃²×C₁₉	C₂×C₅×C₇	semidirect
35. C₃⋊D₃×C₁₉	C₂×C₅×C₇	direct (N × H)
36. C₃²×C₅×C₇	C₂²×C₁₉	semidirect
37. C₃×C₅×C₁₉	C₂×D₃×C₇	semidirect
39. C₂×C₇×C₁₉	C₅×C₃⋊D₃	direct (N × H)
40. C₂×C₇×C₃⋊D₃	C₅×C₁₉	direct (N × H)
42. C₂×C₃×C₅×C₇	D₃×C₁₉	semidirect
45. C₂×C₅×C₁₉	C₇×C₃⋊D₃	direct (N × H)
46. C₂×C₅×C₃⋊D₃	C₇×C₁₉	direct (N × H)
47. C₃²×C₁₉	C₂²×C₅×C₇	semidirect
49. C₇×C₁₉	C₂×C₅×C₃⋊D₃	direct (N × H)
50. C₂×C₃²×C₇	C₂×C₅×C₁₉	semidirect
51. C₇×C₃⋊D₃	C₂×C₅×C₁₉	direct (N × H)
52. C₂×C₃×C₁₉	C₅×D₃×C₇	semidirect
54. C₃×C₅×C₇	C₂×D₃×C₁₉	semidirect
55. C₅×C₁₉	C₂×C₇×C₃⋊D₃	direct (N × H)
56. C₂×C₃²×C₅	C₂×C₇×C₁₉	semidirect
57. C₅×C₃⋊D₃	C₂×C₇×C₁₉	direct (N × H)
61. C₂×C₅×C₇	C₃⋊D₃×C₁₉	direct (N × H)
62. C₃²×C₇	C₂²×C₅×C₁₉	semidirect
64. C₃×C₁₉	C₂×C₅×D₃×C₇	semidirect
65. C₃²×C₅	C₂²×C₇×C₁₉	semidirect
66. C₂×C₃×C₇	C₅×D₃×C₁₉	semidirect
69. C₂×C₁₉	C₅×C₇×C₃⋊D₃	direct (N × H)
70. C₂×C₃⋊D₃	C₅×C₇×C₁₉	direct (N × H)
71. C₅×C₇	C₂×C₃⋊D₃×C₁₉	direct (N × H)
72. C₂×C₃×C₅	D₃×C₇×C₁₉	semidirect
75. C₃×C₇	C₂×C₅×D₃×C₁₉	semidirect
77. C₁₉	C₂×C₅×C₇×C₃⋊D₃	direct (N × H)
78. C₂×C₃²	C₂×C₅×C₇×C₁₉	semidirect
79. C₃⋊D₃	C₂×C₅×C₇×C₁₉	direct (N × H)
80. C₃×C₅	C₂×D₃×C₇×C₁₉	semidirect
82. C₂×C₇	C₅×C₃⋊D₃×C₁₉	direct (N × H)
85. C₂×C₅	C₇×C₃⋊D₃×C₁₉	direct (N × H)
86. C₃²	C₂²×C₅×C₇×C₁₉	semidirect
87. C₇	C₂×C₅×C₃⋊D₃×C₁₉	direct (N × H)
88. C₂×C₃	C₅×D₃×C₇×C₁₉	semidirect
90. C₅	C₂×C₇×C₃⋊D₃×C₁₉	direct (N × H)
92. C₃	C₂×C₅×D₃×C₇×C₁₉	semidirect
94. C₂	C₅×C₇×C₃⋊D₃×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₃⋊D₃×C₁₉	2
C₂×C₃²×C₅×C₇×C₁₉	2
C₂×C₅×D₃×C₇×C₁₉	3
C₂×C₇×C₃⋊D₃×C₁₉	5
C₂×C₅×C₃⋊D₃×C₁₉	7
C₂×C₅×C₇×C₃⋊D₃	19

Subgroups — C2×C5×C7×C3⋊D3×C19 #37561644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₃⋊D₃×C₁₉ #37561644