Subgroups — C₂×C₅×D₁₁×#4296 #49178564

Order 37620.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₁×#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₁×#4296	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₁₁×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₅×C₁₁×#4296	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁×#4296	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₁₁×C₁₉⋊C₃	C₂×C₃	1	2	yes	—
7	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×C₁₉×D₁₁	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×#4296	C₂×C₅	1	1	yes	characteristic, complemented
10	D₁₁×#4296	C₂×C₅	1	2	yes	direct product factor
11	C₂²×C₅×#4296	—	11	1	no	maximal, Hall
12	C₅×C₁₁×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×D₁₁×C₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic
14	C₅×C₁₉×D₁₁	C₂×C₉	1	2	yes	complemented
15	C₂×C₅×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₅×C₉×D₁₁	—	19	1	no	maximal, Hall
17	C₁₁×#4296	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×#4296	—	11	2	no	—
19	C₂×C₅×#4296	D₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic
21	D₁₁×C₁₉⋊C₃	C₂×C₃×C₅	1	2	yes	—
22	C₂²×C₅×C₁₉⋊C₃	—	11	1	no	—
23	C₅×C₁₁×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₉×C₁₁	—	19	1	no	—
25	C₅×C₉×D₁₁	—	19	2	no	—
26	C₅×#4296	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₁₉×D₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂²×#4296	—	11	1	no	Hall
29	C₂×C₃×C₅×D₁₁	—	19	1	no	—
30	C₁₁×C₁₉⋊C₃	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₅×C₁₉⋊C₃	—	11	2	no	—
32	C₂×C₅×C₁₉⋊C₃	C₃×D₁₁	1	1	yes	characteristic
33	C₅×C₉×C₁₁	—	19	1	no	Hall
34	C₂×C₁₁×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
35	C₁₉×D₁₁	C₂×C₅×C₉	1	2	yes	complemented
36	C₂×C₉×D₁₁	—	19	1	no	Hall
37	C₂²×C₅×C₁₉	—	11	1	no	Hall
38	C₂×#4296	—	11	2	no	—
39	C₂×#4296	C₅×D₁₁	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₅×C₁₁	—	19	1	no	—
41	C₃×C₅×D₁₁	—	19	2	no	—
42	C₅×C₁₉⋊C₃	C₂×C₃×D₁₁	1	1	yes	characteristic
43	C₂²×C₁₉⋊C₃	—	11	1	no	—
44	C₂×C₅×D₁₁	#4296	1	1	yes	characteristic, direct product factor, Hall
45	C₁₁×C₁₉	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
46	C₂×C₉×C₁₁	—	19	1	no	—
47	C₉×D₁₁	—	19	2	no	—
48	C₂×C₅×C₁₉	—	11	2	no	—
49	C₂×C₅×C₁₉	C₉×D₁₁	1	1	yes	characteristic, complemented
50	C₂²×C₅×C₉	—	209	1	no	Hall
51	#4296	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
52	C₃×C₅×C₁₁	—	19	1	no	—
53	C₂×C₃×D₁₁	—	19	1	no	—
54	C₂×C₁₉⋊C₃	—	11	2	no	—
55	C₂×C₁₉⋊C₃	C₃×C₅×D₁₁	1	1	yes	characteristic
56	C₂×C₅×C₁₁	C₂×#4296	1	1	yes	characteristic, complemented
57	C₅×D₁₁	C₂×#4296	1	2	yes	direct product factor
58	C₉×C₁₁	—	19	1	no	Hall
59	C₅×C₁₉	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
60	C₂×C₅×C₉	—	19	1	no	—
61	C₂×C₅×C₉	—	209	2	no	—
62	C₂²×C₁₉	—	11	1	no	Hall
63	C₂×C₃×C₁₁	—	19	1	no	—
64	C₃×D₁₁	—	19	2	no	—
65	C₂²×C₃×C₅	—	209	1	no	—
66	C₁₉⋊C₃	C₂×C₃×C₅×D₁₁	1	1	yes	characteristic
67	C₅×C₁₁	C₂²×#4296	1	1	yes	characteristic, complemented, Hall
68	C₅×C₉	—	19	1	no	Hall
69	C₂×D₁₁	C₅×#4296	1	1	yes	characteristic, direct product factor, Hall
70	C₂×C₁₉	—	11	2	no	—
71	C₂×C₁₉	C₅×C₉×D₁₁	1	1	yes	characteristic, complemented
72	C₂²×C₉	—	209	1	no	Hall
73	C₃×C₁₁	—	19	1	no	—
74	C₂×C₃×C₅	—	19	1	no	—
75	C₂×C₃×C₅	—	209	2	no	—
76	C₂×C₁₁	C₂×C₅×#4296	1	1	yes	characteristic, complemented
77	D₁₁	C₂×C₅×#4296	1	2	yes	direct product factor
78	C₂²×C₅	—	11	1	no	Hall
79	C₁₉	C₂×C₅×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₉	—	19	1	no	—
81	C₂×C₉	—	209	2	no	—
82	C₃×C₅	—	19	1	no	—
83	C₂²×C₃	—	209	1	no	—
84	C₁₁	C₂²×C₅×#4296	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	2	no	—
86	C₂×C₅	D₁₁×#4296	1	1	yes	characteristic, direct product factor
87	C₉	—	19	1	no	Sylow
88	C₂×C₃	—	19	1	no	—
89	C₂×C₃	—	209	2	no	—
90	C₅	C₂×D₁₁×#4296	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	11	1	no	Sylow
92	C₃	—	19	1	no	—
93	C₂	—	11	2	no	—
94	C₂	C₅×D₁₁×#4296	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₁×#4296
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₅×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₉	C₂×C₉
prime radical	C₂×C₅×D₁₁×C₁₉⋊C₃	C₃
cosocle	C₁₁×C₁₉⋊C₃	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₁×#4296	C₂	semidirect
2. C₅×D₁₁×#4296	C₂	direct (N × H)
4. C₅×C₁₁×#4296	C₂²	semidirect
5. C₂×D₁₁×#4296	C₅	direct (N × H)
8. C₂×C₅×C₁₉×D₁₁	C₉	semidirect
9. C₂×C₁₁×#4296	C₂×C₅	semidirect
10. D₁₁×#4296	C₂×C₅	direct (N × H)
14. C₅×C₁₉×D₁₁	C₂×C₉	semidirect
15. C₂×C₅×C₁₁×C₁₉	C₂×C₉	semidirect
17. C₁₁×#4296	C₂²×C₅	semidirect
19. C₂×C₅×#4296	D₁₁	direct (N × H)
23. C₅×C₁₁×C₁₉	C₂²×C₉	semidirect
26. C₅×#4296	C₂×D₁₁	direct (N × H)
27. C₂×C₁₉×D₁₁	C₅×C₉	semidirect
34. C₂×C₁₁×C₁₉	C₂×C₅×C₉	semidirect
35. C₁₉×D₁₁	C₂×C₅×C₉	semidirect
39. C₂×#4296	C₅×D₁₁	direct (N × H)
44. C₂×C₅×D₁₁	#4296	direct (N × H)
45. C₁₁×C₁₉	C₂²×C₅×C₉	semidirect
49. C₂×C₅×C₁₉	C₉×D₁₁	semidirect
51. #4296	C₂×C₅×D₁₁	direct (N × H)
56. C₂×C₅×C₁₁	C₂×#4296	semidirect
57. C₅×D₁₁	C₂×#4296	direct (N × H)
59. C₅×C₁₉	C₂×C₉×D₁₁	semidirect
67. C₅×C₁₁	C₂²×#4296	semidirect
69. C₂×D₁₁	C₅×#4296	direct (N × H)
71. C₂×C₁₉	C₅×C₉×D₁₁	semidirect
76. C₂×C₁₁	C₂×C₅×#4296	semidirect
77. D₁₁	C₂×C₅×#4296	direct (N × H)
79. C₁₉	C₂×C₅×C₉×D₁₁	semidirect
84. C₁₁	C₂²×C₅×#4296	semidirect
86. C₂×C₅	D₁₁×#4296	direct (N × H)
90. C₅	C₂×D₁₁×#4296	direct (N × H)
94. C₂	C₅×D₁₁×#4296	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×C₅×C₁₁×#4296	2
C₅×D₁₁×#4296	2
C₂×C₅×D₁₁×C₁₉⋊C₃	3
C₂×D₁₁×#4296	5
C₂²×C₅×#4296	11
C₂×C₅×C₉×D₁₁	19

Subgroups — C2×C5×D11×#4296 #49178564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₁₁×#4296 #49178564