Subgroups — C₉⋊(C₁₉⋊#1043) #30685594

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	C₃⋊(C₁₉⋊#1043)	—	3	1	no	maximal
3	C₅²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊(C₁₉⋊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	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	6	no	—
10	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic
11	C₉⋊#1043	—	19	1	no	maximal, Hall
12	C₅×C₉×C₁₉	AGL(1,𝔽₅)	1	6	yes	complemented
13	Dic₁₇₁	—	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	D₁₉	1	1	yes	characteristic
17	C₁₉⋊AGL(1,𝔽₅)	—	45	6	no	—
18	C₂×C₉×C₁₉	—	25	1	no	—
19	C₃⋊#1043	—	57	1	no	—
20	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	6	yes	—
21	Dic₅₇	—	75	1	no	—
22	C₅²×C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
23	D₅×C₁₉	—	5	6	no	—
24	C₉⋊AGL(1,𝔽₅)	—	95	6	no	—
25	C₉×C₁₉	#1043	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅⋊D₅	D₅₇	1	1	yes	characteristic
27	C₂×C₃×C₁₉	—	25	1	no	—
28	#1043	—	171	1	no	Hall
29	C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
30	C₉×D₅	—	5	6	no	—
31	Dic₁₉	—	225	1	no	Hall
32	C₃×C₅²	Dic₅₇	1	1	yes	characteristic
33	ΓL(1,𝔽₁₆)	—	285	6	no	—
34	C₃×C₁₉	C₃⋊#1043	1	1	yes	characteristic
35	C₅⋊D₅	D₁₇₁	1	1	yes	characteristic
36	C₅×C₉	C₁₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
37	C₂×C₁₉	—	25	1	no	—
38	Dic₉	—	475	1	no	Hall
39	C₃×D₅	—	5	6	no	—
40	C₅²	Dic₁₇₁	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	855	6	no	—
42	C₁₉	C₉⋊#1043	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₉	—	25	1	no	—
44	C₃×C₅	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	1	6	yes	—
45	Dic₃	—	1425	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	C₉⋊(C₁₉⋊AGL(1,𝔽₅))	1	6	yes	complemented
50	C₄	—	4275	1	no	Sylow
51	C₃	C₃⋊(C₁₉⋊#1043)	1	1	yes	characteristic
52	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₉	C₄	semidirect
12. C₅×C₉×C₁₉	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₉	Dic₉	semidirect
22. C₅²×C₉	Dic₁₉	semidirect
25. C₉×C₁₉	#1043	semidirect
29. C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	semidirect
36. C₅×C₉	C₁₉⋊AGL(1,𝔽₅)	semidirect
40. C₅²	Dic₁₇₁	semidirect
42. C₁₉	C₉⋊#1043	semidirect
47. C₉	C₁₉⋊#1043	semidirect
49. C₅	C₉⋊(C₁₉⋊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
C₃⋊(C₁₉⋊#1043)	3
C₉⋊(C₁₉⋊AGL(1,𝔽₅))	5
C₉⋊#1043	19

Subgroups — C9⋊(C19⋊#1043) #30685594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(C₁₉⋊#1043) #30685594