Subgroups — C₁₁⋊(C₁₉⋊#4380) #49178652

Order 37620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₁×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊(C₁₉⋊#157)	—	5	1	no	maximal, Hall
4	C₁₁×C₁₉×D₁₅	—	6	2	no	—
5	C₁₁⋊(C₁₉⋊AGL(1,𝔽₅))	—	9	1	no	maximal, Hall
6	C₁₁×C₃⋊D₃×C₁₉	—	5	1	no	—
7	C₁₉⋊#4380	—	11	1	no	maximal, Hall
8	C₃×C₅×C₁₁×C₁₉	—	2	2	no	—
9	D₅×C₁₁×C₁₉	—	9	1	no	—
10	C₁₁⋊#4380	—	19	1	no	maximal, Hall
11	C₃²×C₁₁×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₉×C₃⋊D₁₅	D₁₁	1	1	yes	characteristic
13	D₃×C₁₁×C₁₉	—	30	2	no	—
14	C₅×C₁₁×C₁₉	#157	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₃⋊D₁₅	D₁₉	1	1	yes	characteristic
16	C₃²×C₅×C₁₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
17	Dic₂₀₉	—	45	1	no	Hall
18	C₁₉⋊#157	—	55	1	no	Hall
19	C₃×C₁₁×C₁₉	—	2	2	no	—
20	C₁₉×D₁₅	—	6	2	no	—
21	C₃²×C₅×C₁₁	Dic₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₁×C₁₉	—	45	1	no	—
23	C₁₁⋊#157	—	95	1	no	Hall
24	C₁₉⋊AGL(1,𝔽₅)	—	99	1	no	Hall
25	C₃⋊D₃×C₁₉	—	5	1	no	—
26	C₁₁×D₁₅	—	6	2	no	—
27	C₃×C₅×C₁₉	—	2	2	no	—
28	C₁₁⋊AGL(1,𝔽₅)	—	171	1	no	Hall
29	C₁₁×C₁₉	#4380	1	1	yes	characteristic, complemented, Hall
30	C₁₁×C₃⋊D₃	—	5	1	no	—
31	D₅×C₁₉	—	9	1	no	—
32	#4380	—	209	1	no	Hall
33	C₃²×C₁₉	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×C₁₁	—	2	2	no	—
35	D₃×C₁₉	—	30	2	no	—
36	D₅×C₁₁	—	9	1	no	—
37	C₃²×C₁₁	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
38	C₅×C₁₉	C₁₁⋊#157	1	1	yes	characteristic, complemented, Hall
39	C₃⋊D₁₅	D₂₀₉	1	1	yes	characteristic
40	Dic₁₉	—	495	1	no	Hall
41	D₃×C₁₁	—	30	2	no	—
42	C₃×C₁₉	—	2	2	no	—
43	C₅×C₁₁	C₁₉⋊#157	1	1	yes	characteristic, complemented, Hall
44	C₃²×C₅	Dic₂₀₉	1	1	yes	characteristic, complemented, Hall
45	Dic₁₁	—	855	1	no	Hall
46	C₂×C₁₉	—	45	1	no	—
47	#157	—	1045	1	no	Hall
48	C₃×C₁₁	—	2	2	no	—
49	D₁₅	—	6	2	no	—
50	C₂×C₁₁	—	45	1	no	—
51	AGL(1,𝔽₅)	—	1881	1	no	Hall
52	C₁₉	C₁₁⋊#4380	1	1	yes	characteristic, complemented, Sylow
53	C₃⋊D₃	—	5	1	no	—
54	C₃×C₅	—	2	2	no	—
55	C₁₁	C₁₉⋊#4380	1	1	yes	characteristic, complemented, Sylow
56	D₅	—	9	1	no	—
57	C₃²	C₁₁⋊(C₁₉⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
58	D₃	—	30	2	no	—
59	C₅	C₁₁⋊(C₁₉⋊#157)	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	9405	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₁₁×C₁₉	C₄
prime radical, cosocle	C₁₁×C₁₉×C₃⋊D₁₅	C₂
LCS	G ▷ C₃²×C₅×C₁₁×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₁₁×C₁₉	C₄	semidirect
11. C₃²×C₁₁×C₁₉	AGL(1,𝔽₅)	semidirect
14. C₅×C₁₁×C₁₉	#157	semidirect
16. C₃²×C₅×C₁₉	Dic₁₁	semidirect
21. C₃²×C₅×C₁₁	Dic₁₉	semidirect
29. C₁₁×C₁₉	#4380	semidirect
33. C₃²×C₁₉	C₁₁⋊AGL(1,𝔽₅)	semidirect
37. C₃²×C₁₁	C₁₉⋊AGL(1,𝔽₅)	semidirect
38. C₅×C₁₉	C₁₁⋊#157	semidirect
43. C₅×C₁₁	C₁₉⋊#157	semidirect
44. C₃²×C₅	Dic₂₀₉	semidirect
52. C₁₉	C₁₁⋊#4380	semidirect
55. C₁₁	C₁₉⋊#4380	semidirect
57. C₃²	C₁₁⋊(C₁₉⋊AGL(1,𝔽₅))	semidirect
59. C₅	C₁₁⋊(C₁₉⋊#157)	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×C₃⋊D₁₅	2
C₁₁⋊(C₁₉⋊#157)	5
C₁₁⋊(C₁₉⋊AGL(1,𝔽₅))	9
C₁₉⋊#4380	11
C₁₁⋊#4380	19

Subgroups — C11⋊(C19⋊#4380) #49178652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊(C₁₉⋊#4380) #49178652