Subgroups — C₃×C₁₉⋊C₃×#1043 #30685738

Order 17100.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#1043	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉⋊C₃×#1043	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅²×C₁₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	—	5	6	no	maximal
6	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
7	C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
8	C₁₉×#1043	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₁₉⋊C₃	—	5	6	no	—
10	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
11	C₅²×C₁₉⋊C₃	C₃×C₄	1	3	yes	complemented
12	C₃×C₁₉×AGL(1,𝔽₅)	—	5	6	no	—
13	AGL(1,𝔽₅)×C₁₉⋊C₃	—	5	18	no	—
14	C₁₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
15	C₃²×#1043	—	19	1	no	maximal, Hall
16	C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
17	C₃×C₄×C₁₉⋊C₃	—	25	1	no	Hall
18	C₃×D₅×C₁₉	—	5	6	no	—
19	D₅×C₁₉⋊C₃	—	5	18	no	—
20	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₅⋊D₅	—	19	1	no	—
22	C₁₉×AGL(1,𝔽₅)	—	5	6	no	—
23	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
24	C₃×#1043	—	19	3	no	—
25	C₃×#1043	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
27	C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	1	18	yes	complemented
28	C₃×C₄×C₁₉	—	25	1	no	—
29	C₄×C₁₉⋊C₃	—	25	3	no	—
30	C₃²×C₅²	—	19	1	no	Hall
31	D₅×C₁₉	—	5	6	no	—
32	C₃²×AGL(1,𝔽₅)	—	95	6	no	—
33	C₃×C₁₉⋊C₃	#1043	1	1	yes	characteristic, direct product factor, Hall
34	C₃×C₅⋊D₅	—	19	3	no	—
35	C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
36	C₂×C₃×C₁₉	—	25	1	no	—
37	C₂×C₁₉⋊C₃	—	25	3	no	—
38	#1043	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
39	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	6	yes	complemented
40	C₃²×D₅	—	95	6	no	—
41	C₄×C₁₉	—	25	1	no	Hall
42	C₃×C₅²	—	19	3	no	—
43	C₃×C₅²	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
44	C₃×AGL(1,𝔽₅)	—	5	6	no	—
45	C₃×AGL(1,𝔽₅)	—	95	18	no	—
46	C₃×C₁₉	C₃×#1043	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	C₃×#1043	1	3	yes	direct product factor
48	C₅⋊D₅	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic
49	C₃²×C₅	—	19	6	no	—
50	C₂×C₁₉	—	25	1	no	—
51	C₃²×C₄	—	475	1	no	Hall
52	C₃×D₅	—	5	6	no	—
53	C₃×D₅	—	95	18	no	—
54	C₅²	C₃×C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
55	AGL(1,𝔽₅)	—	5	6	no	—
56	C₁₉	C₃²×#1043	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃²	—	475	1	no	—
58	C₃×C₅	—	19	18	no	—
59	C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	1	6	yes	complemented
60	C₃×C₄	—	25	1	no	—
61	C₃×C₄	—	475	3	no	—
62	D₅	—	5	6	no	—
63	C₃²	—	19	1	no	Sylow
64	C₂×C₃	—	25	1	no	—
65	C₂×C₃	—	475	3	no	—
66	C₅	C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	1	6	yes	complemented
67	C₄	—	25	1	no	Sylow
68	C₃	—	19	3	no	—
69	C₃	C₁₉⋊C₃×#1043	1	1	yes	characteristic, direct product factor
70	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊C₃×#1043
commutator, hypocenter	C₅²×C₁₉	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical	C₃×C₅⋊D₅×C₁₉⋊C₃	C₂
cosocle	C₁₉×C₅⋊D₅	C₂×C₃²
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₉×#1043	C₃	semidirect
3. C₁₉⋊C₃×#1043	C₃	direct (N × H)
4. C₃×C₅²×C₁₉⋊C₃	C₄	semidirect
8. C₁₉×#1043	C₃²	semidirect
10. C₃×C₅²×C₁₉	C₃×C₄	semidirect
11. C₅²×C₁₉⋊C₃	C₃×C₄	semidirect
16. C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	semidirect
20. C₅²×C₁₉	C₃²×C₄	semidirect
25. C₃×#1043	C₁₉⋊C₃	direct (N × H)
26. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
27. C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
33. C₃×C₁₉⋊C₃	#1043	direct (N × H)
38. #1043	C₃×C₁₉⋊C₃	direct (N × H)
39. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
43. C₃×C₅²	C₄×C₁₉⋊C₃	semidirect
46. C₃×C₁₉	C₃×#1043	semidirect
47. C₁₉⋊C₃	C₃×#1043	direct (N × H)
54. C₅²	C₃×C₄×C₁₉⋊C₃	semidirect
56. C₁₉	C₃²×#1043	semidirect
59. C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	semidirect
66. C₅	C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	semidirect
69. C₃	C₁₉⋊C₃×#1043	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅⋊D₅×C₁₉⋊C₃	2
C₃×C₁₉×#1043	3
C₁₉⋊C₃×#1043	3
C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	5
C₃²×#1043	19

Subgroups — C3×C19⋊C3×#1043 #30685738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊C₃×#1043 #30685738