Subgroups — C₅×C₃⋊(C₁₉⋊AGL(1,𝔽₁₁)) #44535481

Order 31350.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₉⋊AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
3	C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))	C₅	1	5	yes	maximal, direct product factor
4	C₅×D₆₂₇	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×C₁₉×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₉×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
7	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×D₅₇	—	11	1	no	maximal, Hall
9	C₁₉⋊AGL(1,𝔽₁₁)	—	3	5	no	—
10	C₅×D₂₀₉	—	3	1	no	—
11	C₅×C₃⋊AGL(1,𝔽₁₁)	—	19	1	no	maximal, Hall
12	C₃×C₅²×C₁₉	—	11	1	no	Hall
13	D₆₂₇	C₅²	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₁×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
15	C₁₉×C₁₁⋊C₅	C₅×D₃	1	5	yes	complemented
16	C₅²×D₁₉	—	33	1	no	Hall
17	C₃×C₅×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, complemented, Hall
18	C₃×C₁₁×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₅×D₅₇	—	11	5	no	—
20	C₅×D₅₇	—	11	1	no	—
21	C₅×AGL(1,𝔽₁₁)	—	57	1	no	Hall
22	C₅²×C₁₉	—	11	1	no	Hall
23	D₂₀₉	—	3	1	no	Hall
24	C₅×D₃₃	—	19	1	no	—
25	C₃⋊AGL(1,𝔽₁₁)	—	19	5	no	—
26	C₃×C₅×C₁₉	—	11	5	no	—
27	C₃×C₅×C₁₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
28	C₅×C₁₁⋊C₅	D₅₇	1	1	yes	characteristic, complemented, Hall
29	C₁₁×C₁₉	C₅²×D₃	1	1	yes	characteristic, complemented, Hall
30	C₅×D₁₉	—	33	5	no	—
31	C₅×D₁₉	—	33	1	no	—
32	C₃×C₅×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented
33	C₃×C₁₁⋊C₅	C₅×D₁₉	1	5	yes	complemented
34	C₅²×D₃	—	209	1	no	Hall
35	D₅₇	—	11	1	no	Hall
36	C₅×D₁₁	—	57	1	no	—
37	AGL(1,𝔽₁₁)	—	57	5	no	—
38	C₅×C₁₉	—	11	5	no	—
39	C₅×C₁₉	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
40	C₃×C₅²	—	11	1	no	Hall
41	D₃₃	—	19	1	no	Hall
42	C₃×C₁₉	C₅×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
43	C₅×C₁₁	C₅×D₅₇	1	1	yes	characteristic, complemented
44	C₁₁⋊C₅	C₅×D₅₇	1	5	yes	complemented
45	C₂×C₅²	—	627	1	no	Hall
46	D₁₉	—	33	1	no	Hall
47	C₃×C₁₁	C₅²×D₁₉	1	1	yes	characteristic, complemented, Hall
48	C₅×D₃	—	209	5	no	—
49	C₅×D₃	—	209	1	no	—
50	C₅²	—	11	1	no	Sylow
51	D₁₁	—	57	1	no	Hall
52	C₁₉	C₅×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₅	—	11	5	no	—
54	C₃×C₅	C₁₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
55	C₁₁	C₅²×D₅₇	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	627	5	no	—
57	C₂×C₅	—	627	1	no	—
58	D₃	—	209	1	no	Hall
59	C₅	—	11	5	no	—
60	C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, direct product factor
61	C₃	C₅×C₁₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
62	C₂	—	627	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))
commutator, cosocle, hypocenter	C₃×C₁₁×C₁₉	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₉	C₂×C₅
LCS	G ▷ C₃×C₁₁×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	semidirect
3. C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))	C₅	direct (N × H)
4. C₅×D₆₂₇	C₅	semidirect
5. C₅×C₁₉×C₁₁⋊C₅	D₃	semidirect
6. C₃×C₁₉×C₁₁⋊C₅	C₂×C₅	semidirect
7. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
13. D₆₂₇	C₅²	semidirect
14. C₅×C₁₁×C₁₉	C₅×D₃	semidirect
15. C₁₉×C₁₁⋊C₅	C₅×D₃	semidirect
17. C₃×C₅×C₁₁⋊C₅	D₁₉	semidirect
18. C₃×C₁₁×C₁₉	C₂×C₅²	semidirect
27. C₃×C₅×C₁₉	AGL(1,𝔽₁₁)	semidirect
28. C₅×C₁₁⋊C₅	D₅₇	semidirect
29. C₁₁×C₁₉	C₅²×D₃	semidirect
32. C₃×C₅×C₁₁	C₅×D₁₉	semidirect
33. C₃×C₁₁⋊C₅	C₅×D₁₉	semidirect
39. C₅×C₁₉	C₃⋊AGL(1,𝔽₁₁)	semidirect
42. C₃×C₁₉	C₅×AGL(1,𝔽₁₁)	semidirect
43. C₅×C₁₁	C₅×D₅₇	semidirect
44. C₁₁⋊C₅	C₅×D₅₇	semidirect
47. C₃×C₁₁	C₅²×D₁₉	semidirect
52. C₁₉	C₅×C₃⋊AGL(1,𝔽₁₁)	semidirect
54. C₃×C₅	C₁₉⋊AGL(1,𝔽₁₁)	semidirect
55. C₁₁	C₅²×D₅₇	semidirect
60. C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))	direct (N × H)
61. C₃	C₅×C₁₉⋊AGL(1,𝔽₁₁)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₁₁⋊C₅	2
C₅×C₁₉⋊AGL(1,𝔽₁₁)	3
C₃⋊(C₁₉⋊AGL(1,𝔽₁₁))	5
C₅×D₆₂₇	5
C₅²×D₅₇	11
C₅×C₃⋊AGL(1,𝔽₁₁)	19

Subgroups — C5×C3⋊(C19⋊AGL(1,𝔽11)) #44535481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(C₁₉⋊AGL(1,𝔽₁₁)) #44535481