Subgroups — C₁₉×C₉⋊#1043 #30685593

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#1043	—	3	1	no	maximal
3	C₅²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×C₉⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₁₉×#1043	—	9	1	no	Hall
7	C₉×D₅×C₁₉	—	5	6	no	—
8	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic
9	C₁₉×ΓL(1,𝔽₁₆)	—	15	6	no	—
10	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic
11	C₉⋊#1043	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₉×C₁₉	AGL(1,𝔽₅)	1	6	yes	complemented
13	C₁₉×Dic₉	—	25	1	no	Hall
14	C₃×D₅×C₁₉	—	5	6	no	—
15	C₅²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
16	C₉×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic
17	C₁₉×AGL(1,𝔽₅)	—	45	6	no	—
18	C₂×C₉×C₁₉	—	25	1	no	—
19	C₃⋊#1043	—	3	1	no	—
20	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	6	yes	—
21	Dic₃×C₁₉	—	75	1	no	—
22	C₅²×C₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
23	D₅×C₁₉	—	5	6	no	—
24	C₉⋊AGL(1,𝔽₅)	—	5	6	no	—
25	C₉×C₁₉	#1043	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic
27	C₂×C₃×C₁₉	—	25	1	no	—
28	#1043	—	9	1	no	Hall
29	C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
30	C₉×D₅	—	5	6	no	—
31	C₄×C₁₉	—	225	1	no	Hall
32	C₃×C₅²	Dic₃×C₁₉	1	1	yes	characteristic
33	ΓL(1,𝔽₁₆)	—	15	6	no	—
34	C₃×C₁₉	C₃⋊#1043	1	1	yes	characteristic
35	C₅⋊D₅	D₉×C₁₉	1	1	yes	characteristic
36	C₅×C₉	C₁₉×AGL(1,𝔽₅)	1	6	yes	complemented
37	C₂×C₁₉	—	25	1	no	—
38	Dic₉	—	25	1	no	Hall
39	C₃×D₅	—	5	6	no	—
40	C₅²	C₁₉×Dic₉	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	45	6	no	—
42	C₁₉	C₉⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₉	—	25	1	no	—
44	C₃×C₅	C₁₉×ΓL(1,𝔽₁₆)	1	6	yes	—
45	Dic₃	—	75	1	no	—
46	D₅	—	5	6	no	—
47	C₉	C₁₉×#1043	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	C₁₉×C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
50	C₄	—	225	1	no	Sylow
51	C₃	C₁₉×C₃⋊#1043	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#1043
commutator, hypocenter	C₅²×C₉	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#1043
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₁₉×C₅⋊D₅	D₃
cosocle	C₉×C₅⋊D₅	C₂×C₁₉
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₉	C₄	semidirect
11. C₉⋊#1043	C₁₉	direct (N × H)
12. C₅×C₉×C₁₉	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₉	Dic₉	semidirect
22. C₅²×C₉	C₄×C₁₉	semidirect
25. C₉×C₁₉	#1043	semidirect
29. C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	semidirect
36. C₅×C₉	C₁₉×AGL(1,𝔽₅)	semidirect
40. C₅²	C₁₉×Dic₉	semidirect
42. C₁₉	C₉⋊#1043	direct (N × H)
47. C₉	C₁₉×#1043	semidirect
49. C₅	C₁₉×C₉⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₅⋊D₅	2
C₁₉×C₃⋊#1043	3
C₁₉×C₉⋊AGL(1,𝔽₅)	5
C₉⋊#1043	19

Subgroups — C19×C9⋊#1043 #30685593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₉⋊#1043 #30685593