Subgroups — C₁₁×C₁₉⋊#1035 #35229839

Order 20900.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₉×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₉×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	maximal
4	D₅×C₁₁×C₁₉	—	5	1	no	—
5	C₁₉⋊#1035	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×#1035	—	19	1	no	maximal, Hall
7	C₅×C₁₁×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic
8	C₁₉×D₂₅	C₂×C₁₁	1	1	yes	characteristic
9	C₁₁×Dic₁₉	—	25	1	no	Hall
10	C₁₁×D₂₅	D₁₉	1	1	yes	characteristic
11	C₁₉×C₂₅	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₉	—	25	1	no	—
13	C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	—
14	C₁₁×C₂₅	Dic₁₉	1	1	yes	characteristic, complemented, Hall
15	C₁₁×AGL(1,𝔽₅)	—	95	1	no	—
16	C₁₁×C₁₉	#1035	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₉	—	5	1	no	—
18	D₅×C₁₁	—	5	1	no	—
19	#1035	—	19	1	no	Hall
20	C₅×C₁₉	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
21	Dic₁₉	—	25	1	no	Hall
22	C₅×C₁₁	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
23	D₂₅	C₁₁×D₁₉	1	1	yes	characteristic
24	C₄×C₁₁	—	475	1	no	Hall
25	C₂×C₁₉	—	25	1	no	—
26	C₂₅	C₁₁×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	25	1	no	—
28	AGL(1,𝔽₅)	—	95	1	no	—
29	C₁₉	C₁₁×#1035	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₁₉⋊#1035	1	1	yes	characteristic, direct product factor, Sylow
31	D₅	—	5	1	no	—
32	C₅	C₁₁×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
33	C₄	—	475	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₁₉⋊#1035
commutator, hypocenter	C₁₉×C₂₅	C₄×C₁₁
Frattini	C₅	C₁₁×C₁₉⋊AGL(1,𝔽₅)
Fitting	C₁₁×C₁₉×C₂₅	C₄
socle	C₅×C₁₁×C₁₉	AGL(1,𝔽₅)
prime radical	C₁₁×C₁₉×D₂₅	C₂
cosocle	C₁₉×D₂₅	C₂×C₁₁
LCS	G ▷ C₁₉×C₂₅
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₁₉×C₂₅	C₄	semidirect
5. C₁₉⋊#1035	C₁₁	direct (N × H)
11. C₁₉×C₂₅	C₄×C₁₁	semidirect
14. C₁₁×C₂₅	Dic₁₉	semidirect
16. C₁₁×C₁₉	#1035	semidirect
26. C₂₅	C₁₁×Dic₁₉	semidirect
29. C₁₉	C₁₁×#1035	semidirect
30. C₁₁	C₁₉⋊#1035	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×C₁₉×D₂₅	2
C₁₁×C₁₉⋊AGL(1,𝔽₅)	5
C₁₉⋊#1035	11
C₁₁×#1035	19

Subgroups — C11×C19⋊#1035 #35229839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₉⋊#1035 #35229839