Subgroups — C₅×C₁₉×C₉⋊AGL(1,𝔽₅) #30685586

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

	subgroup	G/H
center, hypercenter	C₅×C₁₉	C₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₉	C₄×C₅×C₁₉
Frattini	C₃	C₅×C₁₉×ΓL(1,𝔽₁₆)
Fitting	C₅²×C₉×C₁₉	C₄
socle	C₃×C₅²×C₁₉	Dic₃
prime radical	C₃×C₅×D₅×C₁₉	D₃
cosocle	C₉×D₅	C₂×C₅×C₁₉
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₉	C₄	semidirect
4. C₁₉×C₉⋊AGL(1,𝔽₅)	C₅	direct (N × H)
14. C₅×C₉⋊AGL(1,𝔽₅)	C₁₉	direct (N × H)
16. C₅×C₉×C₁₉	C₄×C₅	semidirect
17. C₅×C₉×C₁₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	Dic₉	semidirect
31. C₅²×C₉	C₄×C₁₉	semidirect
34. C₉⋊AGL(1,𝔽₅)	C₅×C₁₉	direct (N × H)
36. C₉×C₁₉	C₅×AGL(1,𝔽₅)	semidirect
41. C₅×C₁₉	C₅×Dic₉	semidirect
42. C₅×C₁₉	C₉⋊AGL(1,𝔽₅)	direct (N × H)
52. C₅×C₉	C₄×C₅×C₁₉	semidirect
53. C₅×C₉	C₁₉×AGL(1,𝔽₅)	semidirect
58. C₅²	C₁₉×Dic₉	semidirect
61. C₁₉	C₅×C₉⋊AGL(1,𝔽₅)	direct (N × H)
69. C₉	C₅×C₁₉×AGL(1,𝔽₅)	semidirect
72. C₅	C₅×C₁₉×Dic₉	semidirect
73. C₅	C₁₉×C₉⋊AGL(1,𝔽₅)	direct (N × H)

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
C₅×C₁₉×ΓL(1,𝔽₁₆)	3
C₁₉×C₉⋊AGL(1,𝔽₅)	5
C₅×C₁₉×Dic₉	5
C₅×C₉⋊AGL(1,𝔽₅)	19

Subgroups — C5×C19×C9⋊AGL(1,𝔽5) #30685586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×C₉⋊AGL(1,𝔽₅) #30685586