Subgroups — C₂×C₃²×C₅×C₇×D₁₉ #37561629

Order 23940.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×D₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₇×D₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₇×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×D₁₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²×C₅×D₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇×D₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₇×D₁₉	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	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃²×C₅×C₁₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃²×C₅×D₁₉	C₂×C₇	1	2	yes	direct product factor
15	C₂×C₃×C₇×D₁₉	C₃×C₅	1	4	yes	direct product factor
16	C₂×C₅×C₇×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₅×C₇×D₁₉	C₂×C₃²	1	2	yes	direct product factor
18	C₂²×C₃²×C₅×C₇	—	19	1	no	maximal, Hall
19	C₃²×C₇×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅×D₁₉	C₃×C₇	1	4	yes	direct product factor
21	C₃²×C₅×C₁₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	1	4	yes	complemented
23	C₃×C₇×D₁₉	C₂×C₃×C₅	1	8	yes	direct product factor
24	C₂×C₃²×D₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
25	C₅×C₇×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃²×C₅×C₇	—	19	2	no	—
27	C₂×C₃²×C₅×C₇	D₁₉	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₅×C₁₉	C₂×C₃×C₇	1	4	yes	complemented
29	C₃×C₅×D₁₉	C₂×C₃×C₇	1	8	yes	direct product factor
30	C₂×C₇×D₁₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
31	C₂²×C₃×C₅×C₇	—	19	4	no	—
32	C₃×C₇×C₁₉	C₂²×C₃×C₅	1	4	yes	complemented
33	C₂×C₅×D₁₉	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃²×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
35	C₃²×D₁₉	C₂×C₅×C₇	1	2	yes	direct product factor
36	C₃²×C₅×C₇	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₅×C₁₉	C₂²×C₃×C₇	1	4	yes	complemented
38	C₂×C₇×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
39	C₇×D₁₉	C₂×C₃²×C₅	1	2	yes	direct product factor
40	C₂²×C₃²×C₇	—	19	1	no	Hall
41	C₂×C₃×D₁₉	C₃×C₅×C₇	1	4	yes	direct product factor
42	C₂×C₃×C₅×C₇	—	19	8	no	—
43	C₂×C₃×C₅×C₇	C₃×D₁₉	1	4	yes	direct product factor
44	C₂×C₅×C₁₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
45	C₅×D₁₉	C₂×C₃²×C₇	1	2	yes	direct product factor
46	C₂²×C₃²×C₅	—	19	1	no	Hall
47	C₃²×C₁₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅×C₇	—	19	1	no	Hall
49	C₇×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃²×C₇	—	19	2	no	—
51	C₂×C₃²×C₇	C₅×D₁₉	1	1	yes	characteristic, direct product factor
52	C₂×C₃×C₁₉	C₂×C₃×C₅×C₇	1	4	yes	complemented
53	C₃×D₁₉	C₂×C₃×C₅×C₇	1	8	yes	direct product factor
54	C₃×C₅×C₇	C₂×C₃×D₁₉	1	4	yes	direct product factor
55	C₅×C₁₉	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃²×C₅	—	19	2	no	—
57	C₂×C₃²×C₅	C₇×D₁₉	1	1	yes	characteristic, direct product factor
58	C₂²×C₃×C₇	—	19	4	no	—
59	C₂×D₁₉	C₃²×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
60	C₂×C₅×C₇	—	19	2	no	—
61	C₂×C₅×C₇	C₃²×D₁₉	1	1	yes	characteristic, direct product factor
62	C₃²×C₇	C₂×C₅×D₁₉	1	1	yes	characteristic, direct product factor, Hall
63	C₂²×C₃×C₅	—	19	4	no	—
64	C₃×C₁₉	C₂²×C₃×C₅×C₇	1	4	yes	complemented
65	C₃²×C₅	C₂×C₇×D₁₉	1	1	yes	characteristic, direct product factor, Hall
66	C₂×C₃×C₇	—	19	8	no	—
67	C₂×C₃×C₇	C₃×C₅×D₁₉	1	4	yes	direct product factor
68	C₂×C₁₉	C₂×C₃²×C₅×C₇	1	1	yes	characteristic, complemented
69	D₁₉	C₂×C₃²×C₅×C₇	1	2	yes	direct product factor
70	C₂²×C₃²	—	19	1	no	Hall
71	C₅×C₇	C₂×C₃²×D₁₉	1	1	yes	characteristic, direct product factor, Hall
72	C₂×C₃×C₅	—	19	8	no	—
73	C₂×C₃×C₅	C₃×C₇×D₁₉	1	4	yes	direct product factor
74	C₂²×C₇	—	19	1	no	Hall
75	C₃×C₇	C₂×C₃×C₅×D₁₉	1	4	yes	direct product factor
76	C₂²×C₅	—	19	1	no	Hall
77	C₁₉	C₂²×C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₃²	—	19	2	no	—
79	C₂×C₃²	C₅×C₇×D₁₉	1	1	yes	characteristic, direct product factor
80	C₃×C₅	C₂×C₃×C₇×D₁₉	1	4	yes	direct product factor
81	C₂×C₇	—	19	2	no	—
82	C₂×C₇	C₃²×C₅×D₁₉	1	1	yes	characteristic, direct product factor
83	C₂²×C₃	—	19	4	no	—
84	C₂×C₅	—	19	2	no	—
85	C₂×C₅	C₃²×C₇×D₁₉	1	1	yes	characteristic, direct product factor
86	C₃²	C₂×C₅×C₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₃²×C₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	19	8	no	—
89	C₂×C₃	C₃×C₅×C₇×D₁₉	1	4	yes	direct product factor
90	C₅	C₂×C₃²×C₇×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	19	1	no	Sylow
92	C₃	C₂×C₃×C₅×C₇×D₁₉	1	4	yes	direct product factor
93	C₂	—	19	2	no	—
94	C₂	C₃²×C₅×C₇×D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅×C₇	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃²×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×D₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₉	C₂	semidirect
3. C₂×C₃×C₅×C₇×D₁₉	C₃	direct (N × H)
4. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
5. C₂×C₃²×C₇×D₁₉	C₅	direct (N × H)
6. C₃×C₅×C₇×D₁₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
8. C₂×C₃²×C₅×D₁₉	C₇	direct (N × H)
9. C₂×C₅×C₇×D₁₉	C₃²	direct (N × H)
10. C₃²×C₇×D₁₉	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₁₉	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₁₉	C₂²×C₃	semidirect
13. C₂×C₃²×C₅×C₁₉	C₂×C₇	semidirect
14. C₃²×C₅×D₁₉	C₂×C₇	direct (N × H)
15. C₂×C₃×C₇×D₁₉	C₃×C₅	direct (N × H)
16. C₂×C₅×C₇×C₁₉	C₂×C₃²	semidirect
17. C₅×C₇×D₁₉	C₂×C₃²	direct (N × H)
19. C₃²×C₇×C₁₉	C₂²×C₅	semidirect
20. C₂×C₃×C₅×D₁₉	C₃×C₇	direct (N × H)
21. C₃²×C₅×C₁₉	C₂²×C₇	semidirect
22. C₂×C₃×C₇×C₁₉	C₂×C₃×C₅	semidirect
23. C₃×C₇×D₁₉	C₂×C₃×C₅	direct (N × H)
24. C₂×C₃²×D₁₉	C₅×C₇	direct (N × H)
25. C₅×C₇×C₁₉	C₂²×C₃²	semidirect
27. C₂×C₃²×C₅×C₇	D₁₉	direct (N × H)
28. C₂×C₃×C₅×C₁₉	C₂×C₃×C₇	semidirect
29. C₃×C₅×D₁₉	C₂×C₃×C₇	direct (N × H)
30. C₂×C₇×D₁₉	C₃²×C₅	direct (N × H)
32. C₃×C₇×C₁₉	C₂²×C₃×C₅	semidirect
33. C₂×C₅×D₁₉	C₃²×C₇	direct (N × H)
34. C₂×C₃²×C₁₉	C₂×C₅×C₇	semidirect
35. C₃²×D₁₉	C₂×C₅×C₇	direct (N × H)
36. C₃²×C₅×C₇	C₂×D₁₉	direct (N × H)
37. C₃×C₅×C₁₉	C₂²×C₃×C₇	semidirect
38. C₂×C₇×C₁₉	C₂×C₃²×C₅	semidirect
39. C₇×D₁₉	C₂×C₃²×C₅	direct (N × H)
41. C₂×C₃×D₁₉	C₃×C₅×C₇	direct (N × H)
43. C₂×C₃×C₅×C₇	C₃×D₁₉	direct (N × H)
44. C₂×C₅×C₁₉	C₂×C₃²×C₇	semidirect
45. C₅×D₁₉	C₂×C₃²×C₇	direct (N × H)
47. C₃²×C₁₉	C₂²×C₅×C₇	semidirect
49. C₇×C₁₉	C₂²×C₃²×C₅	semidirect
51. C₂×C₃²×C₇	C₅×D₁₉	direct (N × H)
52. C₂×C₃×C₁₉	C₂×C₃×C₅×C₇	semidirect
53. C₃×D₁₉	C₂×C₃×C₅×C₇	direct (N × H)
54. C₃×C₅×C₇	C₂×C₃×D₁₉	direct (N × H)
55. C₅×C₁₉	C₂²×C₃²×C₇	semidirect
57. C₂×C₃²×C₅	C₇×D₁₉	direct (N × H)
59. C₂×D₁₉	C₃²×C₅×C₇	direct (N × H)
61. C₂×C₅×C₇	C₃²×D₁₉	direct (N × H)
62. C₃²×C₇	C₂×C₅×D₁₉	direct (N × H)
64. C₃×C₁₉	C₂²×C₃×C₅×C₇	semidirect
65. C₃²×C₅	C₂×C₇×D₁₉	direct (N × H)
67. C₂×C₃×C₇	C₃×C₅×D₁₉	direct (N × H)
68. C₂×C₁₉	C₂×C₃²×C₅×C₇	semidirect
69. D₁₉	C₂×C₃²×C₅×C₇	direct (N × H)
71. C₅×C₇	C₂×C₃²×D₁₉	direct (N × H)
73. C₂×C₃×C₅	C₃×C₇×D₁₉	direct (N × H)
75. C₃×C₇	C₂×C₃×C₅×D₁₉	direct (N × H)
77. C₁₉	C₂²×C₃²×C₅×C₇	semidirect
79. C₂×C₃²	C₅×C₇×D₁₉	direct (N × H)
80. C₃×C₅	C₂×C₃×C₇×D₁₉	direct (N × H)
82. C₂×C₇	C₃²×C₅×D₁₉	direct (N × H)
85. C₂×C₅	C₃²×C₇×D₁₉	direct (N × H)
86. C₃²	C₂×C₅×C₇×D₁₉	direct (N × H)
87. C₇	C₂×C₃²×C₅×D₁₉	direct (N × H)
89. C₂×C₃	C₃×C₅×C₇×D₁₉	direct (N × H)
90. C₅	C₂×C₃²×C₇×D₁₉	direct (N × H)
92. C₃	C₂×C₃×C₅×C₇×D₁₉	direct (N × H)
94. C₂	C₃²×C₅×C₇×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×D₁₉	2
C₂×C₃²×C₅×C₇×C₁₉	2
C₂×C₃×C₅×C₇×D₁₉	3
C₂×C₃²×C₇×D₁₉	5
C₂×C₃²×C₅×D₁₉	7
C₂²×C₃²×C₅×C₇	19

Subgroups — C2×C32×C5×C7×D19 #37561629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₇×D₁₉ #37561629