Subgroups — C₃²×C₅×C₁₉⋊AGL(1,𝔽₅) #30685856

Order 17100.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₁₉⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅×Dic₁₉	—	5	1	no	maximal
6	C₃×C₅×D₅×C₁₉	C₂×C₃	1	4	yes	—
7	C₅×C₁₉⋊AGL(1,𝔽₅)	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃²×C₅×C₁₉	—	5	1	no	—
9	C₃²×D₅×C₁₉	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₁₉	C₃×C₄	1	4	yes	complemented
11	C₃×C₁₉⋊AGL(1,𝔽₅)	C₃×C₅	1	4	yes	direct product factor
12	C₃×C₅×Dic₁₉	—	5	4	no	—
13	C₅×D₅×C₁₉	C₂×C₃²	1	1	yes	characteristic
14	C₃²×C₅×AGL(1,𝔽₅)	—	19	1	no	maximal, Hall
15	C₃²×C₅×C₁₉	—	4	1	no	—
16	C₃²×C₅×C₁₉	C₄×C₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
18	C₃²×Dic₁₉	—	5	1	no	Hall
19	C₂×C₃×C₅×C₁₉	—	5	4	no	—
20	C₃×D₅×C₁₉	C₂×C₃×C₅	1	4	yes	—
21	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₅×D₅	D₁₉	1	1	yes	characteristic
23	C₁₉⋊AGL(1,𝔽₅)	C₃²×C₅	1	1	yes	characteristic, direct product factor
24	C₅×Dic₁₉	—	5	1	no	—
25	C₂×C₃²×C₁₉	—	5	1	no	—
26	C₃×C₅×AGL(1,𝔽₅)	—	19	4	no	—
27	C₃×C₅×C₁₉	—	4	4	no	—
28	C₃×C₅×C₁₉	C₃×C₄×C₅	1	4	yes	complemented
29	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
30	C₃×Dic₁₉	—	5	4	no	—
31	C₃²×C₅²	Dic₁₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅×C₁₉	—	5	1	no	—
33	D₅×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic
34	C₃²×AGL(1,𝔽₅)	—	19	1	no	—
35	C₃²×C₄×C₅	—	95	1	no	—
36	C₃²×C₁₉	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×D₅	C₃×D₁₉	1	4	yes	—
38	C₂×C₃×C₁₉	—	5	4	no	—
39	C₅×AGL(1,𝔽₅)	—	19	1	no	Hall
40	C₅×C₁₉	—	4	1	no	—
41	C₅×C₁₉	C₃²×C₄×C₅	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
43	C₂×C₃²×C₅	—	5	1	no	—
44	C₃²×D₅	C₅×D₁₉	1	1	yes	characteristic
45	Dic₁₉	—	5	1	no	Hall
46	C₃×C₅²	C₃×Dic₁₉	1	4	yes	complemented
47	C₃×AGL(1,𝔽₅)	—	19	4	no	—
48	C₃×C₄×C₅	—	95	4	no	—
49	C₃×C₁₉	C₃×C₅×AGL(1,𝔽₅)	1	4	yes	complemented
50	C₅×D₅	C₃²×D₁₉	1	1	yes	characteristic
51	C₃²×C₅	—	4	1	no	—
52	C₃²×C₅	C₅×Dic₁₉	1	1	yes	characteristic, complemented
53	C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
54	C₂×C₁₉	—	5	1	no	—
55	C₃²×C₄	—	95	1	no	Hall
56	C₂×C₃×C₅	—	5	4	no	—
57	C₃×D₅	C₃×C₅×D₁₉	1	4	yes	—
58	C₅²	C₃²×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
59	AGL(1,𝔽₅)	—	19	1	no	—
60	C₄×C₅	—	95	1	no	—
61	C₁₉	C₃²×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₃²	—	5	1	no	—
63	C₃×C₅	—	4	4	no	—
64	C₃×C₅	C₃×C₅×Dic₁₉	1	4	yes	complemented
65	C₃×C₅	C₃×C₁₉⋊AGL(1,𝔽₅)	1	4	yes	direct product factor
66	C₃×C₄	—	95	4	no	—
67	C₂×C₅	—	5	1	no	—
68	D₅	C₃²×C₅×D₁₉	1	1	yes	characteristic
69	C₃²	C₅×C₁₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₃	—	5	4	no	—
71	C₅	—	4	1	no	—
72	C₅	C₃²×C₅×Dic₁₉	1	1	yes	characteristic, complemented
73	C₅	C₃²×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	4	yes	direct product factor
76	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₉	C₃²×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₄
prime radical	C₃²×C₅×D₅×C₁₉	C₂
cosocle	D₅×C₁₉	C₂×C₃²×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃²×C₅

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃²×C₅²×C₁₉	C₄	semidirect
4. C₃²×C₁₉⋊AGL(1,𝔽₅)	C₅	direct (N × H)
7. C₅×C₁₉⋊AGL(1,𝔽₅)	C₃²	direct (N × H)
10. C₃×C₅²×C₁₉	C₃×C₄	semidirect
11. C₃×C₁₉⋊AGL(1,𝔽₅)	C₃×C₅	direct (N × H)
16. C₃²×C₅×C₁₉	C₄×C₅	semidirect
17. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
21. C₅²×C₁₉	C₃²×C₄	semidirect
23. C₁₉⋊AGL(1,𝔽₅)	C₃²×C₅	direct (N × H)
28. C₃×C₅×C₁₉	C₃×C₄×C₅	semidirect
29. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
31. C₃²×C₅²	Dic₁₉	semidirect
36. C₃²×C₁₉	C₅×AGL(1,𝔽₅)	semidirect
41. C₅×C₁₉	C₃²×C₄×C₅	semidirect
42. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
46. C₃×C₅²	C₃×Dic₁₉	semidirect
49. C₃×C₁₉	C₃×C₅×AGL(1,𝔽₅)	semidirect
52. C₃²×C₅	C₅×Dic₁₉	semidirect
53. C₃²×C₅	C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
58. C₅²	C₃²×Dic₁₉	semidirect
61. C₁₉	C₃²×C₅×AGL(1,𝔽₅)	semidirect
64. C₃×C₅	C₃×C₅×Dic₁₉	semidirect
65. C₃×C₅	C₃×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
69. C₃²	C₅×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
72. C₅	C₃²×C₅×Dic₁₉	semidirect
73. C₅	C₃²×C₁₉⋊AGL(1,𝔽₅)	direct (N × H)
75. C₃	C₃×C₅×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
C₃²×C₅×D₅×C₁₉	2
C₃×C₅×C₁₉⋊AGL(1,𝔽₅)	3
C₃²×C₁₉⋊AGL(1,𝔽₅)	5
C₃²×C₅×Dic₁₉	5
C₃²×C₅×AGL(1,𝔽₅)	19

Subgroups — C32×C5×C19⋊AGL(1,𝔽5) #30685856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₁₉⋊AGL(1,𝔽₅) #30685856