Subgroups — C₃×C₁₉×C₃⋊#1043 #30685876

Order 17100.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₃⋊#1043	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₉×#1043	—	3	1	no	maximal
4	C₃²×C₅²×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×ΓL(1,𝔽₁₆)	—	5	6	no	maximal
6	C₃×C₁₉×C₅⋊D₅	—	2	1	no	—
7	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
8	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
9	C₁₉×#1043	—	3	1	no	Hall
10	C₃²×D₅×C₁₉	—	5	6	no	—
11	C₃×C₅²×C₁₉	—	2	1	no	—
12	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
14	C₁₉×ΓL(1,𝔽₁₆)	—	5	6	no	—
15	C₃×C₁₉×AGL(1,𝔽₅)	—	15	6	no	—
16	C₁₉×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
17	C₃×C₃⋊#1043	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	6	yes	complemented
19	C₃×Dic₃×C₁₉	—	25	1	no	Hall
20	C₃×D₅×C₁₉	—	5	6	no	—
21	C₃×D₅×C₁₉	—	5	6	no	—
22	C₃×D₅×C₁₉	—	10	6	no	—
23	C₅²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
24	C₃²×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic
25	C₁₉×AGL(1,𝔽₅)	—	15	6	no	—
26	C₂×C₃²×C₁₉	—	25	1	no	—
27	C₃⋊#1043	C₃×C₁₉	1	1	yes	characteristic, direct product factor
28	C₃×#1043	—	3	1	no	—
29	C₃×C₅×C₁₉	—	2	6	no	—
30	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
31	C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	1	6	yes	complemented
32	C₃×C₄×C₁₉	—	75	1	no	—
33	Dic₃×C₁₉	—	25	1	no	—
34	C₃²×C₅²	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
35	D₅×C₁₉	—	5	6	no	—
36	C₃×ΓL(1,𝔽₁₆)	—	5	6	no	—
37	C₃²×C₁₉	#1043	1	1	yes	characteristic, complemented, Hall
38	C₃×C₅⋊D₅	—	2	1	no	—
39	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic
40	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	1	yes	characteristic
41	C₂×C₃×C₁₉	—	25	1	no	—
42	C₂×C₃×C₁₉	—	25	1	no	—
43	C₂×C₃×C₁₉	—	50	1	no	—
44	#1043	—	3	1	no	Hall
45	C₅×C₁₉	C₃×ΓL(1,𝔽₁₆)	1	6	yes	complemented
46	C₃²×D₅	—	5	6	no	—
47	C₄×C₁₉	—	75	1	no	Hall
48	C₃×C₅²	—	2	1	no	—
49	C₃×C₅²	Dic₃×C₁₉	1	1	yes	characteristic, complemented
50	C₃×C₅²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented
51	ΓL(1,𝔽₁₆)	—	5	6	no	—
52	C₃×AGL(1,𝔽₅)	—	15	6	no	—
53	C₃×C₁₉	—	2	1	no	—
54	C₃×C₁₉	C₃×#1043	1	1	yes	characteristic, complemented
55	C₃×C₁₉	C₃⋊#1043	1	1	yes	characteristic, direct product factor
56	C₅⋊D₅	C₃×D₃×C₁₉	1	1	yes	characteristic
57	C₃²×C₅	C₁₉×AGL(1,𝔽₅)	1	6	yes	complemented
58	C₂×C₁₉	—	25	1	no	—
59	C₃×Dic₃	—	25	1	no	Hall
60	C₃×D₅	—	5	6	no	—
61	C₃×D₅	—	5	6	no	—
62	C₃×D₅	—	10	6	no	—
63	C₅²	C₃×Dic₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
64	AGL(1,𝔽₅)	—	15	6	no	—
65	C₁₉	C₃×C₃⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃²	—	25	1	no	—
67	C₃×C₅	—	2	6	no	—
68	C₃×C₅	C₃×C₁₉×AGL(1,𝔽₅)	1	6	yes	complemented
69	C₃×C₅	C₁₉×ΓL(1,𝔽₁₆)	1	6	yes	complemented
70	C₃×C₄	—	75	1	no	—
71	Dic₃	—	25	1	no	—
72	D₅	—	5	6	no	—
73	C₃²	C₁₉×#1043	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₃	—	25	1	no	—
75	C₂×C₃	—	25	1	no	—
76	C₂×C₃	—	50	1	no	—
77	C₅	C₃×C₁₉×ΓL(1,𝔽₁₆)	1	6	yes	complemented
78	C₄	—	75	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×C₁₉×#1043	1	1	yes	characteristic, complemented
81	C₃	C₁₉×C₃⋊#1043	1	1	yes	characteristic, direct product factor
82	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₉×C₃⋊#1043	C₃	direct (N × H)
4. C₃²×C₅²×C₁₉	C₄	semidirect
12. C₃×C₅²×C₁₉	Dic₃	semidirect
13. C₃×C₅²×C₁₉	C₃×C₄	semidirect
17. C₃×C₃⋊#1043	C₁₉	direct (N × H)
18. C₃²×C₅×C₁₉	AGL(1,𝔽₅)	semidirect
23. C₅²×C₁₉	C₃×Dic₃	semidirect
27. C₃⋊#1043	C₃×C₁₉	direct (N × H)
30. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
31. C₃×C₅×C₁₉	ΓL(1,𝔽₁₆)	semidirect
34. C₃²×C₅²	C₄×C₁₉	semidirect
37. C₃²×C₁₉	#1043	semidirect
45. C₅×C₁₉	C₃×ΓL(1,𝔽₁₆)	semidirect
49. C₃×C₅²	Dic₃×C₁₉	semidirect
50. C₃×C₅²	C₃×C₄×C₁₉	semidirect
54. C₃×C₁₉	C₃×#1043	semidirect
55. C₃×C₁₉	C₃⋊#1043	direct (N × H)
57. C₃²×C₅	C₁₉×AGL(1,𝔽₅)	semidirect
63. C₅²	C₃×Dic₃×C₁₉	semidirect
65. C₁₉	C₃×C₃⋊#1043	direct (N × H)
68. C₃×C₅	C₃×C₁₉×AGL(1,𝔽₅)	semidirect
69. C₃×C₅	C₁₉×ΓL(1,𝔽₁₆)	semidirect
73. C₃²	C₁₉×#1043	semidirect
77. C₅	C₃×C₁₉×ΓL(1,𝔽₁₆)	semidirect
80. C₃	C₃×C₁₉×#1043	semidirect
81. 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
C₃²×C₁₉×C₅⋊D₅	2
C₁₉×C₃⋊#1043	3
C₃×C₁₉×#1043	3
C₃×C₁₉×ΓL(1,𝔽₁₆)	5
C₃×C₃⋊#1043	19

Subgroups — C3×C19×C3⋊#1043 #30685876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₉×C₃⋊#1043 #30685876