Subgroups — C₁₁⋊(#4296⋊Dic₅) #49178447

Order 37620.

72 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
2	C₁₁⋊((C₁₉⋊C₃)⋊Dic₅)	C₃	1	1	yes	maximal, characteristic
3	C₅×C₁₁×#4296	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊(#4296⋊C₄)	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
6	Dic₁₀₄₅	C₉	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₁×#4296	D₅	1	1	yes	characteristic
8	#4296⋊Dic₅	—	11	1	no	maximal, Hall
9	C₅×C₁₁×C₁₉⋊C₃	C₃×C₄	1	1	yes	characteristic
10	C₁₁⋊((C₁₉⋊C₃)⋊C₄)	—	5	1	no	—
11	C₂×C₅×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic
12	C₉×Dic₅₅	—	19	1	no	maximal, Hall
13	C₁₁×#4296	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×#4296	D₁₁	1	1	yes	characteristic
15	C₂×C₁₁×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic
16	(C₁₉⋊C₃)⋊Dic₅	—	11	1	no	—
17	C₅×C₁₁×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₁	—	19	1	no	—
19	C₅×#4296	Dic₁₁	1	1	yes	characteristic, complemented, Hall
20	Dic₂₀₉	—	5	1	no	Hall
21	#4296⋊C₄	—	55	1	no	Hall
22	C₃×Dic₅₅	—	19	1	no	—
23	C₁₁×C₁₉⋊C₃	C₃×Dic₅	1	1	yes	characteristic
24	C₂×C₅×C₁₉⋊C₃	C₃×D₁₁	1	1	yes	characteristic
25	C₅×C₉×C₁₁	—	19	1	no	Hall
26	C₂×C₁₁×C₁₉	C₉×D₅	1	1	yes	characteristic
27	C₉×Dic₁₁	—	95	1	no	Hall
28	Dic₉₅	—	11	1	no	Hall
29	C₂×#4296	D₅₅	1	1	yes	characteristic
30	C₂×C₃×C₅×C₁₁	—	19	1	no	—
31	C₅×C₁₉⋊C₃	C₃×Dic₁₁	1	1	yes	characteristic
32	(C₁₉⋊C₃)⋊C₄	—	55	1	no	—
33	Dic₅₅	—	19	1	no	Hall
34	C₁₁×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
35	C₂×C₉×C₁₁	—	19	1	no	—
36	C₂×C₅×C₁₉	C₉×D₁₁	1	1	yes	characteristic
37	C₉×Dic₅	—	209	1	no	Hall
38	#4296	Dic₅₅	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₁	—	19	1	no	—
40	C₃×Dic₁₁	—	95	1	no	—
41	C₂×C₁₉⋊C₃	C₃×D₅₅	1	1	yes	characteristic
42	C₂×C₅×C₁₁	AGL(1,𝔽₁₉)	1	1	yes	characteristic
43	C₉×C₁₁	—	19	1	no	Hall
44	C₅×C₁₉	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×C₉	—	19	1	no	—
46	Dic₁₉	—	55	1	no	Hall
47	C₂×C₃×C₁₁	—	19	1	no	—
48	C₃×Dic₅	—	209	1	no	—
49	C₁₉⋊C₃	C₃×Dic₅₅	1	1	yes	characteristic
50	C₅×C₁₁	#4296⋊C₄	1	1	yes	characteristic, complemented, Hall
51	C₅×C₉	—	19	1	no	Hall
52	Dic₁₁	—	95	1	no	Hall
53	C₂×C₁₉	C₉×D₅₅	1	1	yes	characteristic
54	C₄×C₉	—	1045	1	no	Hall
55	C₃×C₁₁	—	19	1	no	—
56	C₂×C₃×C₅	—	19	1	no	—
57	C₂×C₁₁	C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic
58	Dic₅	—	209	1	no	Hall
59	C₁₉	C₉×Dic₅₅	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₉	—	19	1	no	—
61	C₃×C₅	—	19	1	no	—
62	C₃×C₄	—	1045	1	no	—
63	C₁₁	#4296⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	C₁₁⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic
65	C₉	—	19	1	no	Sylow
66	C₂×C₃	—	19	1	no	—
67	C₅	C₁₁⋊(#4296⋊C₄)	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	1045	1	no	Sylow
69	C₃	—	19	1	no	—
70	C₂	C₅⋊(C₁₁⋊AGL(1,𝔽₁₉))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₅⋊(C₁₁⋊AGL(1,𝔽₁₉))
commutator, hypocenter	C₅×C₁₁×C₁₉	C₄×C₉
Fitting, socle	C₂×C₅×C₁₁×C₁₉	C₂×C₉
prime radical, cosocle	C₂×C₅×C₁₁×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₁₁×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₁×#4296	C₄	semidirect
6. Dic₁₀₄₅	C₉	semidirect
13. C₁₁×#4296	Dic₅	semidirect
17. C₅×C₁₁×C₁₉	C₄×C₉	semidirect
19. C₅×#4296	Dic₁₁	semidirect
34. C₁₁×C₁₉	C₉×Dic₅	semidirect
38. #4296	Dic₅₅	semidirect
44. C₅×C₁₉	C₉×Dic₁₁	semidirect
50. C₅×C₁₁	#4296⋊C₄	semidirect
59. C₁₉	C₉×Dic₅₅	semidirect
63. C₁₁	#4296⋊Dic₅	semidirect
67. C₅	C₁₁⋊(#4296⋊C₄)	semidirect

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
C₁₁⋊((C₁₉⋊C₃)⋊Dic₅)	3
C₁₁⋊(#4296⋊C₄)	5
#4296⋊Dic₅	11
C₉×Dic₅₅	19

Subgroups — C11⋊(#4296⋊Dic5) #49178447

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊(#4296⋊Dic₅) #49178447