Subgroups — C₂×C₉×D₁₉×C₁₁⋊C₅ #49178356

Order 37620.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₁₉×C₁₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₉×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic
4	C₉×C₁₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×C₁₁×D₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×D₁₉×C₁₁⋊C₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₁₉×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
8	C₂×D₁₉×C₁₁⋊C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₁₁×D₁₉	C₂×C₅	1	2	yes	complemented
10	C₂×C₉×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₉×D₁₉	—	11	1	no	maximal, Hall
12	C₃×C₁₉×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₁₁×D₁₉	C₃×C₅	1	1	yes	characteristic
14	D₁₉×C₁₁⋊C₅	C₂×C₉	1	2	yes	direct product factor
15	C₂×C₁₉×C₁₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂²×C₉×C₁₁⋊C₅	—	19	1	no	maximal, Hall
17	C₉×C₁₁×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₉	—	11	1	no	—
19	C₅×C₉×D₁₉	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₁₁×D₁₉	C₂×C₃×C₅	1	2	yes	—
22	C₂×C₃×C₅×D₁₉	—	11	1	no	—
23	C₁₉×C₁₁⋊C₅	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₉×C₁₁⋊C₅	—	19	2	no	—
25	C₂×C₉×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, direct product factor
26	C₅×C₉×C₁₉	—	11	1	no	Hall
27	C₂×C₁₁×D₁₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₉×D₁₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃×C₁₁⋊C₅	—	19	1	no	—
30	C₃×C₁₁×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₉	—	11	1	no	—
32	C₃×C₅×D₁₉	—	11	2	no	—
33	C₉×C₁₁⋊C₅	C₂×D₁₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₁×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
35	C₁₁×D₁₉	C₂×C₅×C₉	1	2	yes	complemented
36	C₂²×C₉×C₁₁	—	19	1	no	Hall
37	C₂×C₅×D₁₉	—	11	1	no	Hall
38	C₂×C₉×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
39	C₉×D₁₉	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
40	C₂×C₃×C₁₁⋊C₅	—	19	2	no	—
41	C₂×C₃×C₁₁⋊C₅	C₃×D₁₉	1	1	yes	characteristic
42	C₃×C₅×C₁₉	—	11	1	no	—
43	C₂×C₃×D₁₉	C₃×C₁₁⋊C₅	1	1	yes	characteristic
44	C₂²×C₁₁⋊C₅	—	19	1	no	Hall
45	C₁₁×C₁₉	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
46	C₂×C₉×C₁₁	—	19	2	no	—
47	C₂×C₉×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented
48	C₂×C₅×C₁₉	—	11	1	no	—
49	C₅×D₁₉	—	11	2	no	—
50	C₂²×C₅×C₉	—	209	1	no	Hall
51	C₉×C₁₉	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
52	C₃×C₁₁⋊C₅	C₂×C₃×D₁₉	1	1	yes	characteristic
53	C₂²×C₃×C₁₁	—	19	1	no	—
54	C₂×C₃×C₁₉	C₂×C₃×C₁₁⋊C₅	1	1	yes	characteristic
55	C₃×D₁₉	C₂×C₃×C₁₁⋊C₅	1	2	yes	—
56	C₂×C₁₁⋊C₅	—	19	2	no	—
57	C₂×C₁₁⋊C₅	C₉×D₁₉	1	1	yes	characteristic, direct product factor
58	C₉×C₁₁	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
59	C₅×C₁₉	—	11	1	no	Hall
60	C₂×C₅×C₉	—	11	1	no	—
61	C₂×C₅×C₉	—	209	2	no	—
62	C₂×D₁₉	C₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
63	C₂×C₃×C₁₁	—	19	2	no	—
64	C₂×C₃×C₁₁	C₃×C₅×D₁₉	1	1	yes	characteristic
65	C₂²×C₃×C₅	—	209	1	no	—
66	C₃×C₁₉	C₂²×C₃×C₁₁⋊C₅	1	1	yes	characteristic
67	C₁₁⋊C₅	C₂×C₉×D₁₉	1	1	yes	characteristic, direct product factor, Hall
68	C₅×C₉	—	11	1	no	Hall
69	C₂²×C₁₁	—	19	1	no	Hall
70	C₂×C₁₉	C₂×C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented
71	D₁₉	C₂×C₉×C₁₁⋊C₅	1	2	yes	direct product factor
72	C₂²×C₉	—	19	1	no	Hall
73	C₃×C₁₁	C₂×C₃×C₅×D₁₉	1	1	yes	characteristic
74	C₂×C₃×C₅	—	11	1	no	—
75	C₂×C₃×C₅	—	209	2	no	—
76	C₂×C₁₁	—	19	2	no	—
77	C₂×C₁₁	C₅×C₉×D₁₉	1	1	yes	characteristic, complemented
78	C₂²×C₅	—	209	1	no	Hall
79	C₁₉	C₂²×C₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₉	—	19	2	no	—
81	C₂×C₉	D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
82	C₃×C₅	—	11	1	no	—
83	C₂²×C₃	—	19	1	no	—
84	C₁₁	C₂×C₅×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	1	no	—
86	C₂×C₅	—	209	2	no	—
87	C₉	C₂×D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	19	2	no	—
89	C₂×C₃	C₃×D₁₉×C₁₁⋊C₅	1	1	yes	characteristic
90	C₅	—	11	1	no	Sylow
91	C₂²	—	19	1	no	Sylow
92	C₃	C₂×C₃×D₁₉×C₁₁⋊C₅	1	1	yes	characteristic
93	C₂	—	19	2	no	—
94	C₂	C₉×D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₉×C₁₁⋊C₅
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₂×C₃×D₁₉×C₁₁⋊C₅
Fitting	C₂×C₉×C₁₁×C₁₉	C₂×C₅
socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅
prime radical	C₂×C₃×D₁₉×C₁₁⋊C₅	C₃
cosocle	C₃×C₁₁×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₁₉×C₁₁⋊C₅	C₂	direct (N × H)
2. C₂×C₉×C₁₉×C₁₁⋊C₅	C₂	semidirect
4. C₉×C₁₉×C₁₁⋊C₅	C₂²	semidirect
5. C₂×C₉×C₁₁×D₁₉	C₅	semidirect
8. C₂×D₁₉×C₁₁⋊C₅	C₉	direct (N × H)
9. C₉×C₁₁×D₁₉	C₂×C₅	semidirect
10. C₂×C₉×C₁₁×C₁₉	C₂×C₅	semidirect
14. D₁₉×C₁₁⋊C₅	C₂×C₉	direct (N × H)
15. C₂×C₁₉×C₁₁⋊C₅	C₂×C₉	semidirect
17. C₉×C₁₁×C₁₉	C₂²×C₅	semidirect
23. C₁₉×C₁₁⋊C₅	C₂²×C₉	semidirect
25. C₂×C₉×C₁₁⋊C₅	D₁₉	direct (N × H)
27. C₂×C₁₁×D₁₉	C₅×C₉	semidirect
28. C₂×C₉×D₁₉	C₁₁⋊C₅	direct (N × H)
33. C₉×C₁₁⋊C₅	C₂×D₁₉	direct (N × H)
34. C₂×C₁₁×C₁₉	C₂×C₅×C₉	semidirect
35. C₁₁×D₁₉	C₂×C₅×C₉	semidirect
38. C₂×C₉×C₁₉	C₂×C₁₁⋊C₅	semidirect
39. C₉×D₁₉	C₂×C₁₁⋊C₅	direct (N × H)
45. C₁₁×C₁₉	C₂²×C₅×C₉	semidirect
47. C₂×C₉×C₁₁	C₅×D₁₉	semidirect
51. C₉×C₁₉	C₂²×C₁₁⋊C₅	semidirect
57. C₂×C₁₁⋊C₅	C₉×D₁₉	direct (N × H)
58. C₉×C₁₁	C₂×C₅×D₁₉	semidirect
62. C₂×D₁₉	C₉×C₁₁⋊C₅	direct (N × H)
67. C₁₁⋊C₅	C₂×C₉×D₁₉	direct (N × H)
70. C₂×C₁₉	C₂×C₉×C₁₁⋊C₅	semidirect
71. D₁₉	C₂×C₉×C₁₁⋊C₅	direct (N × H)
77. C₂×C₁₁	C₅×C₉×D₁₉	semidirect
79. C₁₉	C₂²×C₉×C₁₁⋊C₅	semidirect
81. C₂×C₉	D₁₉×C₁₁⋊C₅	direct (N × H)
84. C₁₁	C₂×C₅×C₉×D₁₉	semidirect
87. C₉	C₂×D₁₉×C₁₁⋊C₅	direct (N × H)
94. C₂	C₉×D₁₉×C₁₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₁₉×C₁₁⋊C₅	2
C₂×C₉×C₁₉×C₁₁⋊C₅	2
C₂×C₃×D₁₉×C₁₁⋊C₅	3
C₂×C₉×C₁₁×D₁₉	5
C₂×C₅×C₉×D₁₉	11
C₂²×C₉×C₁₁⋊C₅	19

Subgroups — C2×C9×D19×C11⋊C5 #49178356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₁₉×C₁₁⋊C₅ #49178356