Subgroups — C₂²×C₃×C₁₁⋊C₅×C₁₉⋊C₃ #49178571

Order 37620.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁⋊C₅×C₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₁₁⋊C₅×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₃×C₁₁×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₁₁⋊C₅×C₁₉⋊C₃	C₂×C₃	1	9	yes	direct product factor
7	C₂×C₃×C₁₉×C₁₁⋊C₅	C₂×C₃	1	3	yes	complemented
8	C₂²×C₁₉×C₁₁⋊C₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁×C₁₉⋊C₃	C₂×C₅	1	3	yes	complemented
10	C₂²×C₃×C₅×C₁₉⋊C₃	—	11	1	no	maximal, Hall
11	C₁₁⋊C₅×C₁₉⋊C₃	C₂²×C₃	1	3	yes	direct product factor
12	C₃×C₁₉×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₁₁×C₁₉⋊C₃	C₃×C₅	1	3	yes	complemented
14	C₂²×C₃×C₁₁×C₁₉	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂×C₁₉×C₁₁⋊C₅	C₂×C₃²	1	3	yes	complemented
16	C₂²×C₃²×C₁₁⋊C₅	—	19	1	no	maximal, Hall
17	C₃×C₁₁×C₁₉⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₉⋊C₃	—	11	3	no	—
19	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	3	yes	complemented
20	C₂×C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	1	9	yes	complemented
21	C₂²×C₃×C₅×C₁₉	—	11	1	no	—
22	C₂²×C₅×C₁₉⋊C₃	—	11	3	no	—
23	C₁₉×C₁₁⋊C₅	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₁₁⋊C₅	—	19	3	no	—
25	C₃×C₅×C₁₉⋊C₃	—	11	1	no	Hall
26	C₂²×C₁₁×C₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₁₉⋊C₃	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₃×C₁₁⋊C₅	—	19	3	no	—
29	C₂²×C₃×C₁₁⋊C₅	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
30	C₃×C₁₁×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
31	C₁₁×C₁₉⋊C₃	C₂²×C₃×C₅	1	3	yes	complemented
32	C₂×C₃×C₅×C₁₉	—	11	3	no	—
33	C₂×C₅×C₁₉⋊C₃	—	11	9	no	—
34	C₃²×C₁₁⋊C₅	—	19	1	no	Hall
35	C₂×C₁₁×C₁₉	C₂×C₃²×C₅	1	3	yes	complemented
36	C₂²×C₃²×C₁₁	—	19	1	no	Hall
37	C₂²×C₅×C₁₉	—	11	1	no	Hall
38	C₂×C₃×C₁₉⋊C₃	C₂×C₁₁⋊C₅	1	3	yes	direct product factor
39	C₂×C₃×C₁₁⋊C₅	—	19	9	no	—
40	C₂×C₃×C₁₁⋊C₅	C₂×C₁₉⋊C₃	1	3	yes	direct product factor
41	C₃×C₅×C₁₉	—	11	1	no	—
42	C₅×C₁₉⋊C₃	—	11	3	no	—
43	C₂²×C₃×C₁₉	C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
44	C₂²×C₁₉⋊C₃	C₃×C₁₁⋊C₅	1	3	yes	direct product factor
45	C₂²×C₁₁⋊C₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
46	C₁₁×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃²×C₁₁	—	19	3	no	—
48	C₂×C₅×C₁₉	—	11	3	no	—
49	C₂²×C₃²×C₅	—	209	1	no	Hall
50	C₃×C₁₉⋊C₃	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
51	C₃×C₁₁⋊C₅	—	19	3	no	—
52	C₃×C₁₁⋊C₅	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
53	C₂²×C₃×C₁₁	—	19	3	no	—
54	C₂²×C₃×C₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×C₁₉	C₂×C₃×C₁₁⋊C₅	1	3	yes	complemented
56	C₂×C₁₉⋊C₃	C₂×C₃×C₁₁⋊C₅	1	9	yes	direct product factor
57	C₂×C₁₁⋊C₅	C₂×C₃×C₁₉⋊C₃	1	3	yes	direct product factor
58	C₃²×C₁₁	—	19	1	no	Hall
59	C₅×C₁₉	—	11	1	no	Hall
60	C₂×C₃²×C₅	—	209	3	no	—
61	C₂²×C₁₉	C₃²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃×C₁₁	—	19	9	no	—
63	C₂×C₃×C₁₁	C₂×C₅×C₁₉⋊C₃	1	3	yes	complemented
64	C₂²×C₃×C₅	—	11	1	no	—
65	C₂²×C₃×C₅	—	209	3	no	—
66	C₃×C₁₉	C₂²×C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
67	C₁₉⋊C₃	C₂²×C₃×C₁₁⋊C₅	1	3	yes	direct product factor
68	C₁₁⋊C₅	C₂²×C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
69	C₃²×C₅	—	209	1	no	Hall
70	C₂²×C₁₁	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
71	C₂×C₁₉	C₂×C₃²×C₁₁⋊C₅	1	3	yes	complemented
72	C₂²×C₃²	—	19	1	no	Hall
73	C₃×C₁₁	—	19	3	no	—
74	C₃×C₁₁	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
75	C₂×C₃×C₅	—	11	3	no	—
76	C₂×C₃×C₅	—	209	9	no	—
77	C₂×C₁₁	C₂×C₃×C₅×C₁₉⋊C₃	1	3	yes	complemented
78	C₂²×C₅	—	11	1	no	Hall
79	C₁₉	C₂²×C₃²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃²	—	19	3	no	—
81	C₃×C₅	—	11	1	no	—
82	C₃×C₅	—	209	3	no	—
83	C₂²×C₃	—	19	3	no	—
84	C₂²×C₃	C₁₁⋊C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
85	C₁₁	C₂²×C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
86	C₂×C₅	—	11	3	no	—
87	C₃²	—	19	1	no	Sylow
88	C₂×C₃	—	19	9	no	—
89	C₂×C₃	C₂×C₁₁⋊C₅×C₁₉⋊C₃	1	3	yes	direct product factor
90	C₅	—	11	1	no	Sylow
91	C₂²	C₃×C₁₁⋊C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
92	C₃	—	19	3	no	—
93	C₃	C₂²×C₁₁⋊C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
94	C₂	C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₁⋊C₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂²×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₁×C₁₉	C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	C₂	direct (N × H)
2. C₂²×C₃×C₁₉×C₁₁⋊C₅	C₃	semidirect
3. C₂²×C₁₁⋊C₅×C₁₉⋊C₃	C₃	direct (N × H)
4. C₃×C₁₁⋊C₅×C₁₉⋊C₃	C₂²	direct (N × H)
5. C₂²×C₃×C₁₁×C₁₉⋊C₃	C₅	semidirect
6. C₂×C₁₁⋊C₅×C₁₉⋊C₃	C₂×C₃	direct (N × H)
7. C₂×C₃×C₁₉×C₁₁⋊C₅	C₂×C₃	semidirect
8. C₂²×C₁₉×C₁₁⋊C₅	C₃²	semidirect
9. C₂×C₃×C₁₁×C₁₉⋊C₃	C₂×C₅	semidirect
11. C₁₁⋊C₅×C₁₉⋊C₃	C₂²×C₃	direct (N × H)
12. C₃×C₁₉×C₁₁⋊C₅	C₂²×C₃	semidirect
13. C₂²×C₁₁×C₁₉⋊C₃	C₃×C₅	semidirect
14. C₂²×C₃×C₁₁×C₁₉	C₃×C₅	semidirect
15. C₂×C₁₉×C₁₁⋊C₅	C₂×C₃²	semidirect
17. C₃×C₁₁×C₁₉⋊C₃	C₂²×C₅	semidirect
19. C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	semidirect
20. C₂×C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
23. C₁₉×C₁₁⋊C₅	C₂²×C₃²	semidirect
26. C₂²×C₁₁×C₁₉	C₃²×C₅	semidirect
27. C₂²×C₃×C₁₉⋊C₃	C₁₁⋊C₅	direct (N × H)
29. C₂²×C₃×C₁₁⋊C₅	C₁₉⋊C₃	direct (N × H)
30. C₃×C₁₁×C₁₉	C₂²×C₃×C₅	semidirect
31. C₁₁×C₁₉⋊C₃	C₂²×C₃×C₅	semidirect
35. C₂×C₁₁×C₁₉	C₂×C₃²×C₅	semidirect
38. C₂×C₃×C₁₉⋊C₃	C₂×C₁₁⋊C₅	direct (N × H)
40. C₂×C₃×C₁₁⋊C₅	C₂×C₁₉⋊C₃	direct (N × H)
43. C₂²×C₃×C₁₉	C₃×C₁₁⋊C₅	semidirect
44. C₂²×C₁₉⋊C₃	C₃×C₁₁⋊C₅	direct (N × H)
45. C₂²×C₁₁⋊C₅	C₃×C₁₉⋊C₃	direct (N × H)
46. C₁₁×C₁₉	C₂²×C₃²×C₅	semidirect
50. C₃×C₁₉⋊C₃	C₂²×C₁₁⋊C₅	direct (N × H)
52. C₃×C₁₁⋊C₅	C₂²×C₁₉⋊C₃	direct (N × H)
54. C₂²×C₃×C₁₁	C₅×C₁₉⋊C₃	semidirect
55. C₂×C₃×C₁₉	C₂×C₃×C₁₁⋊C₅	semidirect
56. C₂×C₁₉⋊C₃	C₂×C₃×C₁₁⋊C₅	direct (N × H)
57. C₂×C₁₁⋊C₅	C₂×C₃×C₁₉⋊C₃	direct (N × H)
61. C₂²×C₁₉	C₃²×C₁₁⋊C₅	semidirect
63. C₂×C₃×C₁₁	C₂×C₅×C₁₉⋊C₃	semidirect
66. C₃×C₁₉	C₂²×C₃×C₁₁⋊C₅	semidirect
67. C₁₉⋊C₃	C₂²×C₃×C₁₁⋊C₅	direct (N × H)
68. C₁₁⋊C₅	C₂²×C₃×C₁₉⋊C₃	direct (N × H)
70. C₂²×C₁₁	C₃×C₅×C₁₉⋊C₃	semidirect
71. C₂×C₁₉	C₂×C₃²×C₁₁⋊C₅	semidirect
74. C₃×C₁₁	C₂²×C₅×C₁₉⋊C₃	semidirect
77. C₂×C₁₁	C₂×C₃×C₅×C₁₉⋊C₃	semidirect
79. C₁₉	C₂²×C₃²×C₁₁⋊C₅	semidirect
84. C₂²×C₃	C₁₁⋊C₅×C₁₉⋊C₃	direct (N × H)
85. C₁₁	C₂²×C₃×C₅×C₁₉⋊C₃	semidirect
89. C₂×C₃	C₂×C₁₁⋊C₅×C₁₉⋊C₃	direct (N × H)
91. C₂²	C₃×C₁₁⋊C₅×C₁₉⋊C₃	direct (N × H)
93. C₃	C₂²×C₁₁⋊C₅×C₁₉⋊C₃	direct (N × H)
94. C₂	C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₁⋊C₅×C₁₉⋊C₃	2
C₂²×C₃×C₁₉×C₁₁⋊C₅	3
C₂²×C₁₁⋊C₅×C₁₉⋊C₃	3
C₂²×C₃×C₁₁×C₁₉⋊C₃	5
C₂²×C₃×C₅×C₁₉⋊C₃	11
C₂²×C₃²×C₁₁⋊C₅	19

Subgroups — C22×C3×C11⋊C5×C19⋊C3 #49178571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₁₁⋊C₅×C₁₉⋊C₃ #49178571