Subgroups — C₁₉×C₉⋊#1042 #30685597

Order 17100.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#1042	—	3	1	no	maximal
3	C₅²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₉×C₉⋊AGL(1,𝔽₅)	—	5	1	no	maximal
5	C₁₉×Dic₄₅	—	5	1	no	maximal
6	C₃×C₅×D₅×C₁₉	D₃	1	1	yes	characteristic
7	C₁₉×#1042	—	9	1	no	Hall
8	C₂×C₅×C₉×C₁₉	—	5	1	no	—
9	C₉×D₅×C₁₉	D₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic
11	C₁₉×ΓL(1,𝔽₁₆)	—	15	1	no	—
12	C₁₉×Dic₁₅	—	15	1	no	—
13	C₅×D₅×C₁₉	D₉	1	1	yes	characteristic
14	C₉⋊#1042	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₅×C₉×C₁₉	—	4	1	no	—
16	C₅×C₉×C₁₉	Dic₅	1	1	yes	characteristic, complemented
17	C₅×C₉×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₁₉×Dic₉	—	25	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	5	1	no	—
20	C₃×D₅×C₁₉	D₁₅	1	1	yes	characteristic
21	C₅²×C₁₉	Dic₉	1	1	yes	characteristic, complemented, Hall
22	C₅×C₉×D₅	C₂×C₁₉	1	1	yes	characteristic
23	C₁₉×AGL(1,𝔽₅)	—	45	1	no	—
24	C₁₉×Dic₅	—	45	1	no	—
25	C₂×C₉×C₁₉	—	5	1	no	—
26	C₃⋊#1042	—	3	1	no	—
27	C₃×C₅×C₁₉	—	4	1	no	—
28	C₃×C₅×C₁₉	Dic₁₅	1	1	yes	characteristic
29	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
30	Dic₃×C₁₉	—	75	1	no	—
31	C₅²×C₉	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×C₁₉	—	5	1	no	—
33	D₅×C₁₉	D₄₅	1	1	yes	characteristic
34	C₉⋊AGL(1,𝔽₅)	—	5	1	no	—
35	Dic₄₅	—	5	1	no	—
36	C₉×C₁₉	#1042	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×D₅	D₃×C₁₉	1	1	yes	characteristic
38	C₂×C₃×C₁₉	—	5	1	no	—
39	#1042	—	9	1	no	Hall
40	C₅×C₁₉	—	4	1	no	—
41	C₅×C₁₉	Dic₄₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
43	C₂×C₅×C₉	—	5	1	no	—
44	C₉×D₅	D₅×C₁₉	1	1	yes	characteristic
45	C₄×C₁₉	—	225	1	no	Hall
46	C₃×C₅²	Dic₃×C₁₉	1	1	yes	characteristic
47	ΓL(1,𝔽₁₆)	—	15	1	no	—
48	Dic₁₅	—	15	1	no	—
49	C₃×C₁₉	C₃⋊#1042	1	1	yes	characteristic
50	C₅×D₅	D₉×C₁₉	1	1	yes	characteristic
51	C₅×C₉	—	4	1	no	—
52	C₅×C₉	C₁₉×Dic₅	1	1	yes	characteristic, complemented
53	C₅×C₉	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
54	C₂×C₁₉	—	5	1	no	—
55	Dic₉	—	25	1	no	Hall
56	C₂×C₃×C₅	—	5	1	no	—
57	C₃×D₅	C₁₉×D₁₅	1	1	yes	characteristic
58	C₅²	C₁₉×Dic₉	1	1	yes	characteristic, complemented, Sylow
59	AGL(1,𝔽₅)	—	45	1	no	—
60	Dic₅	—	45	1	no	—
61	C₁₉	C₉⋊#1042	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₉	—	5	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	C₁₉×Dic₁₅	1	1	yes	characteristic
65	C₃×C₅	C₁₉×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
66	Dic₃	—	75	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₁₉×D₄₅	1	1	yes	characteristic
69	C₉	C₁₉×#1042	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	C₁₉×Dic₄₅	1	1	yes	characteristic, complemented
73	C₅	C₁₉×C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
74	C₄	—	225	1	no	Sylow
75	C₃	C₁₉×C₃⋊#1042	1	1	yes	characteristic
76	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#1042
commutator, hypocenter	C₅²×C₉	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#1042
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₅×D₅×C₁₉	D₃
cosocle	C₅×C₉×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
14. C₉⋊#1042	C₁₉	direct (N × H)
16. C₅×C₉×C₁₉	Dic₅	semidirect
17. C₅×C₉×C₁₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	Dic₉	semidirect
31. C₅²×C₉	C₄×C₁₉	semidirect
36. C₉×C₁₉	#1042	semidirect
41. C₅×C₁₉	Dic₄₅	semidirect
42. C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	semidirect
52. C₅×C₉	C₁₉×Dic₅	semidirect
53. C₅×C₉	C₁₉×AGL(1,𝔽₅)	semidirect
58. C₅²	C₁₉×Dic₉	semidirect
61. C₁₉	C₉⋊#1042	direct (N × H)
69. C₉	C₁₉×#1042	semidirect
72. C₅	C₁₉×Dic₄₅	semidirect
73. 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
C₅×C₉×D₅×C₁₉	2
C₁₉×C₃⋊#1042	3
C₁₉×C₉⋊AGL(1,𝔽₅)	5
C₁₉×Dic₄₅	5
C₉⋊#1042	19

Subgroups — C19×C9⋊#1042 #30685597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₉⋊#1042 #30685597