Subgroups — C₂×C₅×C₁₁⋊(#4294⋊C₂) #49178362

Order 37620.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁⋊(#4294⋊C₂)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₁×#4294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₂₀₉	C₃	1	1	yes	maximal, characteristic
4	C₅×C₁₁×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁⋊(#4294⋊C₂)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₂₀₉	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×D₂₀₉	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×#4294	C₂×C₅	1	1	yes	characteristic, complemented
10	C₁₁⋊(#4294⋊C₂)	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₅×#4294⋊C₂	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₉	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×D₂₀₉	C₃×C₅	1	1	yes	characteristic
14	C₅×D₂₀₉	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×#4294	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×#4294	D₁₁	1	1	yes	characteristic, complemented
19	C₅×#4294⋊C₂	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×D₂₀₉	C₂×C₃×C₅	1	2	yes	—
22	C₂×C₃×C₅×D₁₉	—	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×#4294	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×D₂₀₉	C₅×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×#4294⋊C₂	—	11	1	no	Hall
29	C₂×C₃×C₅×D₁₁	—	19	1	no	—
30	C₃×C₁₁×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₉	C₃×D₁₁	1	1	yes	characteristic
32	C₃×C₅×D₁₉	—	11	2	no	—
33	C₅×C₉×C₁₁	—	19	1	no	Hall
34	C₂×C₁₁×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
35	D₂₀₉	C₂×C₅×C₉	1	2	yes	complemented
36	C₂×C₉×D₁₁	—	19	1	no	Hall
37	C₂×C₅×D₁₉	—	11	1	no	Hall
38	C₂×#4294	C₅×D₁₁	1	1	yes	characteristic, complemented
39	#4294⋊C₂	—	11	2	no	—
40	C₂×C₃×C₅×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic
41	C₃×C₅×D₁₁	—	19	2	no	—
42	C₃×C₅×C₁₉	C₂×C₃×D₁₁	1	1	yes	characteristic
43	C₂×C₃×D₁₉	—	11	1	no	—
44	C₂×C₅×D₁₁	—	19	1	no	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	C₉×D₁₁	1	1	yes	characteristic, complemented
49	C₅×D₁₉	—	11	2	no	—
50	C₂²×C₅×C₉	—	209	1	no	Hall
51	#4294	C₂×C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
52	C₃×C₅×C₁₁	C₂×D₁₉⋊C₃	1	1	yes	characteristic
53	C₂×C₃×D₁₁	—	19	1	no	—
54	C₂×C₃×C₁₉	C₃×C₅×D₁₁	1	1	yes	characteristic
55	C₃×D₁₉	—	11	2	no	—
56	C₂×C₅×C₁₁	#4294⋊C₂	1	1	yes	characteristic, complemented
57	C₅×D₁₁	—	19	2	no	—
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	C₂×D₁₉	—	11	1	no	Hall
63	C₂×C₃×C₁₁	C₅×D₁₉⋊C₃	1	1	yes	characteristic
64	C₃×D₁₁	—	19	2	no	—
65	C₂²×C₃×C₅	—	209	1	no	—
66	C₃×C₁₉	C₂×C₃×C₅×D₁₁	1	1	yes	characteristic
67	C₅×C₁₁	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Hall
68	C₅×C₉	—	19	1	no	Hall
69	C₂×D₁₁	—	19	1	no	Hall
70	C₂×C₁₉	C₅×C₉×D₁₁	1	1	yes	characteristic, complemented
71	D₁₉	—	11	2	no	—
72	C₂²×C₉	—	209	1	no	Hall
73	C₃×C₁₁	C₂×C₅×D₁₉⋊C₃	1	1	yes	characteristic
74	C₂×C₃×C₅	—	209	2	no	—
75	C₂×C₃×C₅	C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
76	C₂×C₁₁	C₅×#4294⋊C₂	1	1	yes	characteristic, complemented
77	D₁₁	—	19	2	no	—
78	C₂²×C₅	—	209	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	C₂×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
83	C₂²×C₃	—	209	1	no	—
84	C₁₁	C₂×C₅×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	209	2	no	—
86	C₂×C₅	C₁₁⋊(#4294⋊C₂)	1	1	yes	characteristic, direct product factor
87	C₉	—	19	1	no	Sylow
88	C₂×C₃	—	209	2	no	—
89	C₂×C₃	C₅×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
90	C₅	C₂×C₁₁⋊(#4294⋊C₂)	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	209	1	no	Sylow
92	C₃	C₂×C₅×C₁₁⋊(D₁₉⋊C₃)	1	1	yes	characteristic
93	C₂	—	209	2	no	—
94	C₂	C₅×C₁₁⋊(#4294⋊C₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	C₁₁⋊(D₁₉⋊C₃)
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₂×C₅×C₁₁⋊(D₁₉⋊C₃)
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅×D₂₀₉	C₃
cosocle	C₃×C₁₁×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁⋊(#4294⋊C₂)	C₂	direct (N × H)
2. C₂×C₅×C₁₁×#4294	C₂	semidirect
4. C₅×C₁₁×#4294	C₂²	semidirect
5. C₂×C₁₁⋊(#4294⋊C₂)	C₅	direct (N × H)
8. C₂×C₅×D₂₀₉	C₉	semidirect
9. C₂×C₁₁×#4294	C₂×C₅	semidirect
10. C₁₁⋊(#4294⋊C₂)	C₂×C₅	direct (N × H)
14. C₅×D₂₀₉	C₂×C₉	semidirect
15. C₂×C₅×C₁₁×C₁₉	C₂×C₉	semidirect
17. C₁₁×#4294	C₂²×C₅	semidirect
18. C₂×C₅×#4294	D₁₁	semidirect
23. C₅×C₁₁×C₁₉	C₂²×C₉	semidirect
26. C₅×#4294	C₂×D₁₁	semidirect
27. C₂×D₂₀₉	C₅×C₉	semidirect
34. C₂×C₁₁×C₁₉	C₂×C₅×C₉	semidirect
35. D₂₀₉	C₂×C₅×C₉	semidirect
38. C₂×#4294	C₅×D₁₁	semidirect
45. C₁₁×C₁₉	C₂²×C₅×C₉	semidirect
48. C₂×C₅×C₁₉	C₉×D₁₁	semidirect
51. #4294	C₂×C₅×D₁₁	semidirect
56. C₂×C₅×C₁₁	#4294⋊C₂	semidirect
59. C₅×C₁₉	C₂×C₉×D₁₁	semidirect
67. C₅×C₁₁	C₂×#4294⋊C₂	semidirect
70. C₂×C₁₉	C₅×C₉×D₁₁	semidirect
76. C₂×C₁₁	C₅×#4294⋊C₂	semidirect
79. C₁₉	C₂×C₅×C₉×D₁₁	semidirect
84. C₁₁	C₂×C₅×#4294⋊C₂	semidirect
86. C₂×C₅	C₁₁⋊(#4294⋊C₂)	direct (N × H)
90. C₅	C₂×C₁₁⋊(#4294⋊C₂)	direct (N × H)
94. C₂	C₅×C₁₁⋊(#4294⋊C₂)	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×C₁₁⋊(#4294⋊C₂)	2
C₂×C₅×C₁₁×#4294	2
C₂×C₃×C₅×D₂₀₉	3
C₂×C₁₁⋊(#4294⋊C₂)	5
C₂×C₅×#4294⋊C₂	11
C₂×C₅×C₉×D₁₁	19

Subgroups — C2×C5×C11⋊(#4294⋊C2) #49178362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₁⋊(#4294⋊C₂) #49178362