Subgroups — C₅×C₉×C₁₉⋊AGL(1,𝔽₅) #30685573

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	C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic
3	C₅²×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×C₁₉⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₉×Dic₁₉	—	5	1	no	maximal
6	C₃×C₅×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₅×C₁₉⋊AGL(1,𝔽₅)	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₅×C₉×C₁₉	—	5	1	no	—
9	C₉×D₅×C₁₉	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic
11	C₃×C₁₉⋊AGL(1,𝔽₅)	C₃×C₅	1	1	yes	characteristic
12	C₃×C₅×Dic₁₉	—	5	1	no	—
13	C₅×D₅×C₁₉	C₂×C₉	1	1	yes	characteristic
14	C₅×C₉×AGL(1,𝔽₅)	—	19	1	no	maximal, 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	C₉×Dic₁₉	—	5	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	5	1	no	—
20	C₃×D₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
21	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
22	C₅×C₉×D₅	D₁₉	1	1	yes	characteristic
23	C₁₉⋊AGL(1,𝔽₅)	C₅×C₉	1	1	yes	characteristic, direct product factor
24	C₅×Dic₁₉	—	5	1	no	—
25	C₂×C₉×C₁₉	—	5	1	no	—
26	C₃×C₅×AGL(1,𝔽₅)	—	19	1	no	—
27	C₃×C₅×C₁₉	—	4	1	no	—
28	C₃×C₅×C₁₉	C₃×C₄×C₅	1	1	yes	characteristic
29	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
30	C₃×Dic₁₉	—	5	1	no	—
31	C₅²×C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×C₁₉	—	5	1	no	—
33	D₅×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic
34	C₉×AGL(1,𝔽₅)	—	19	1	no	—
35	C₄×C₅×C₉	—	95	1	no	—
36	C₉×C₁₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×D₅	C₃×D₁₉	1	1	yes	characteristic
38	C₂×C₃×C₁₉	—	5	1	no	—
39	C₅×AGL(1,𝔽₅)	—	19	1	no	Hall
40	C₅×C₁₉	—	4	1	no	—
41	C₅×C₁₉	C₄×C₅×C₉	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	C₅×D₁₉	1	1	yes	characteristic
45	Dic₁₉	—	5	1	no	Hall
46	C₃×C₅²	C₃×Dic₁₉	1	1	yes	characteristic
47	C₃×AGL(1,𝔽₅)	—	19	1	no	—
48	C₃×C₄×C₅	—	95	1	no	—
49	C₃×C₁₉	C₃×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
50	C₅×D₅	C₉×D₁₉	1	1	yes	characteristic
51	C₅×C₉	—	4	1	no	—
52	C₅×C₉	C₅×Dic₁₉	1	1	yes	characteristic, complemented
53	C₅×C₉	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
54	C₂×C₁₉	—	5	1	no	—
55	C₄×C₉	—	95	1	no	Hall
56	C₂×C₃×C₅	—	5	1	no	—
57	C₃×D₅	C₃×C₅×D₁₉	1	1	yes	characteristic
58	C₅²	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
59	AGL(1,𝔽₅)	—	19	1	no	—
60	C₄×C₅	—	95	1	no	—
61	C₁₉	C₅×C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₉	—	5	1	no	—
63	C₃×C₅	—	4	1	no	—
64	C₃×C₅	C₃×C₅×Dic₁₉	1	1	yes	characteristic
65	C₃×C₅	C₃×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
66	C₃×C₄	—	95	1	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₅×C₉×D₁₉	1	1	yes	characteristic
69	C₉	C₅×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	1	no	—
71	C₅	—	4	1	no	—
72	C₅	C₅×C₉×Dic₁₉	1	1	yes	characteristic, complemented
73	C₅	C₉×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
74	C₄	—	95	1	no	Sylow
75	C₃	C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic
76	C₂	—	5	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₁₉	C₄	semidirect
4. C₉×C₁₉⋊AGL(1,𝔽₅)	C₅	direct (N × H)
7. C₅×C₁₉⋊AGL(1,𝔽₅)	C₉	direct (N × H)
16. C₅×C₉×C₁₉	C₄×C₅	semidirect
17. C₅×C₉×C₁₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	C₄×C₉	semidirect
23. C₁₉⋊AGL(1,𝔽₅)	C₅×C₉	direct (N × H)
31. C₅²×C₉	Dic₁₉	semidirect
36. C₉×C₁₉	C₅×AGL(1,𝔽₅)	semidirect
41. C₅×C₁₉	C₄×C₅×C₉	semidirect
42. C₅×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
52. C₅×C₉	C₅×Dic₁₉	semidirect
53. C₅×C₉	C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
58. C₅²	C₉×Dic₁₉	semidirect
61. C₁₉	C₅×C₉×AGL(1,𝔽₅)	semidirect
69. C₉	C₅×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
72. C₅	C₅×C₉×Dic₁₉	semidirect
73. C₅	C₉×C₁₉⋊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
C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	3
C₉×C₁₉⋊AGL(1,𝔽₅)	5
C₅×C₉×Dic₁₉	5
C₅×C₉×AGL(1,𝔽₅)	19

Subgroups — C5×C9×C19⋊AGL(1,𝔽5) #30685573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×C₁₉⋊AGL(1,𝔽₅) #30685573