Subgroups — C₃×C₁₉⋊C₃×#1044 #30685740

Order 17100.

192 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×#1044	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₉⋊C₃×#1044	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	2	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×#1044	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₁₉⋊C₃	—	5	2	no	—
10	C₃×D₅×C₁₉⋊C₃	—	10	2	no	—
11	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅²×C₁₉⋊C₃	C₃×C₄	1	3	yes	complemented
13	C₃×C₁₉×AGL(1,𝔽₅)	—	5	2	no	—
14	AGL(1,𝔽₅)×C₁₉⋊C₃	—	5	6	no	—
15	C₁₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
16	C₃²×#1044	—	19	1	no	maximal, Hall
17	C₃×C₅×C₁₉⋊C₃	—	2	2	no	—
18	C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	1	2	yes	complemented
19	C₃×C₄×C₁₉⋊C₃	—	25	1	no	Hall
20	C₃×D₅×C₁₉	—	5	2	no	—
21	C₃×D₅×C₁₉	—	10	2	no	—
22	D₅×C₁₉⋊C₃	—	5	6	no	—
23	D₅×C₁₉⋊C₃	—	10	6	no	—
24	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
25	C₃²×C₅⋊D₅	—	19	1	no	—
26	C₁₉×AGL(1,𝔽₅)	—	5	2	no	—
27	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
28	C₃×#1044	—	19	3	no	—
29	C₃×#1044	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
30	C₃×C₅×C₁₉	—	2	2	no	—
31	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
32	C₅×C₁₉⋊C₃	—	2	6	no	—
33	C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
34	C₃×C₄×C₁₉	—	25	1	no	—
35	C₄×C₁₉⋊C₃	—	25	3	no	—
36	C₃²×C₅²	—	19	1	no	Hall
37	D₅×C₁₉	—	5	2	no	—
38	D₅×C₁₉	—	10	2	no	—
39	C₃²×AGL(1,𝔽₅)	—	95	2	no	—
40	C₃×C₁₉⋊C₃	#1044	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₅⋊D₅	—	19	3	no	—
42	C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
43	C₂×C₃×C₁₉	—	25	1	no	—
44	C₂×C₁₉⋊C₃	—	25	3	no	—
45	#1044	C₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
46	C₅×C₁₉	—	2	2	no	—
47	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	2	yes	complemented
48	C₃²×D₅	—	95	2	no	—
49	C₃²×D₅	—	190	2	no	—
50	C₄×C₁₉	—	25	1	no	Hall
51	C₃×C₅²	—	19	3	no	—
52	C₃×C₅²	C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented
53	C₃×AGL(1,𝔽₅)	—	5	2	no	—
54	C₃×AGL(1,𝔽₅)	—	95	6	no	—
55	C₃×C₁₉	C₃×#1044	1	1	yes	characteristic, complemented
56	C₁₉⋊C₃	C₃×#1044	1	3	yes	direct product factor
57	C₅⋊D₅	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic
58	C₃²×C₅	—	19	2	no	—
59	C₃²×C₅	—	38	2	no	—
60	C₂×C₁₉	—	25	1	no	—
61	C₃²×C₄	—	475	1	no	Hall
62	C₃×D₅	—	5	2	no	—
63	C₃×D₅	—	10	2	no	—
64	C₃×D₅	—	95	6	no	—
65	C₃×D₅	—	190	6	no	—
66	C₅²	C₃×C₄×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
67	AGL(1,𝔽₅)	—	5	2	no	—
68	C₁₉	C₃²×#1044	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₃²	—	475	1	no	—
70	C₃×C₅	—	2	2	no	—
71	C₃×C₅	—	19	6	no	—
72	C₃×C₅	—	38	6	no	—
73	C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	1	2	yes	complemented
74	C₃×C₄	—	25	1	no	—
75	C₃×C₄	—	475	3	no	—
76	D₅	—	5	2	no	—
77	D₅	—	10	2	no	—
78	C₃²	—	19	1	no	Sylow
79	C₂×C₃	—	25	1	no	—
80	C₂×C₃	—	475	3	no	—
81	C₅	—	2	2	no	—
82	C₅	C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	1	2	yes	complemented
83	C₄	—	25	1	no	Sylow
84	C₃	—	19	3	no	—
85	C₃	C₁₉⋊C₃×#1044	1	1	yes	characteristic, direct product factor
86	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₉⋊C₃×#1044
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×#1044	C₃	semidirect
3. C₁₉⋊C₃×#1044	C₃	direct (N × H)
4. C₃×C₅²×C₁₉⋊C₃	C₄	semidirect
8. C₁₉×#1044	C₃²	semidirect
11. C₃×C₅²×C₁₉	C₃×C₄	semidirect
12. C₅²×C₁₉⋊C₃	C₃×C₄	semidirect
18. C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	semidirect
24. C₅²×C₁₉	C₃²×C₄	semidirect
29. C₃×#1044	C₁₉⋊C₃	direct (N × H)
31. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
33. C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
40. C₃×C₁₉⋊C₃	#1044	direct (N × H)
45. #1044	C₃×C₁₉⋊C₃	direct (N × H)
47. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
52. C₃×C₅²	C₄×C₁₉⋊C₃	semidirect
55. C₃×C₁₉	C₃×#1044	semidirect
56. C₁₉⋊C₃	C₃×#1044	direct (N × H)
66. C₅²	C₃×C₄×C₁₉⋊C₃	semidirect
68. C₁₉	C₃²×#1044	semidirect
73. C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	semidirect
82. C₅	C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	semidirect
85. C₃	C₁₉⋊C₃×#1044	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×#1044	3
C₁₉⋊C₃×#1044	3
C₃×AGL(1,𝔽₅)×C₁₉⋊C₃	5
C₃²×#1044	19

Subgroups — C3×C19⋊C3×#1044 #30685740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉⋊C₃×#1044 #30685740