Subgroups — C₃×(C₁₉⋊C₃)⋊#1043 #30685737

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×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	—	5	5	no	maximal
6	C₃×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	—	5	1	no	maximal
7	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
8	C₅⋊D₅×C₁₉⋊C₃	C₂×C₃	1	3	yes	—
9	C₁₉⋊#1043	C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₅×C₁₉⋊C₃	—	5	5	no	—
11	C₃×D₅×C₁₉⋊C₃	—	5	1	no	—
12	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
13	C₅²×C₁₉⋊C₃	C₃×C₄	1	3	yes	complemented
14	C₃×C₁₉⋊AGL(1,𝔽₅)	—	5	5	no	—
15	C₃×C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	—
16	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	—	5	15	no	—
17	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	—	5	3	no	—
18	C₁₉×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
19	C₃²×#1043	—	19	1	no	maximal, Hall
20	C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	1	5	yes	complemented
21	C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
22	C₃×(C₁₉⋊C₃)⋊C₄	—	25	1	no	Hall
23	C₃×D₅×C₁₉	—	5	5	no	—
24	C₃×D₅×C₁₉	—	5	1	no	—
25	D₅×C₁₉⋊C₃	—	5	15	no	—
26	D₅×C₁₉⋊C₃	—	5	3	no	—
27	C₅²×C₁₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₅⋊D₅	—	19	1	no	—
29	C₁₉⋊AGL(1,𝔽₅)	—	5	5	no	—
30	C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	—
31	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
32	C₃×#1043	—	19	3	no	—
33	C₃×#1043	—	57	1	no	—
34	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	5	yes	complemented
35	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
36	C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	1	15	yes	complemented
37	C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	1	3	yes	complemented
38	C₃×Dic₁₉	—	25	1	no	—
39	(C₁₉⋊C₃)⋊C₄	—	25	3	no	—
40	C₃²×C₅²	—	19	1	no	Hall
41	D₅×C₁₉	—	5	5	no	—
42	D₅×C₁₉	—	5	1	no	—
43	C₃²×AGL(1,𝔽₅)	—	95	5	no	—
44	C₃²×AGL(1,𝔽₅)	—	95	1	no	—
45	C₃×C₁₉⋊C₃	#1043	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅⋊D₅	—	19	3	no	—
47	C₃×C₅⋊D₅	D₁₉⋊C₃	1	1	yes	characteristic
48	C₂×C₃×C₁₉	—	25	1	no	—
49	C₂×C₁₉⋊C₃	—	25	3	no	—
50	#1043	—	57	1	no	Hall
51	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	5	yes	complemented
52	C₅×C₁₉	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
53	C₃²×D₅	—	95	5	no	—
54	C₃²×D₅	—	95	1	no	—
55	Dic₁₉	—	25	1	no	Hall
56	C₃×C₅²	—	19	3	no	—
57	C₃×C₅²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
58	C₃×AGL(1,𝔽₅)	—	285	5	no	—
59	C₃×AGL(1,𝔽₅)	—	95	1	no	—
60	C₃×AGL(1,𝔽₅)	—	95	15	no	—
61	C₃×AGL(1,𝔽₅)	—	95	3	no	—
62	C₃×C₁₉	C₃×#1043	1	1	yes	characteristic, complemented
63	C₁₉⋊C₃	C₃×#1043	1	3	yes	complemented
64	C₅⋊D₅	C₃×D₁₉⋊C₃	1	1	yes	characteristic
65	C₃²×C₅	—	19	5	no	—
66	C₃²×C₅	—	19	1	no	—
67	C₂×C₁₉	—	25	1	no	—
68	C₃²×C₄	—	475	1	no	Hall
69	C₃×D₅	—	5	5	no	—
70	C₃×D₅	—	5	1	no	—
71	C₃×D₅	—	95	15	no	—
72	C₃×D₅	—	95	3	no	—
73	C₅²	C₃×(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
74	AGL(1,𝔽₅)	—	285	5	no	—
75	AGL(1,𝔽₅)	—	95	1	no	—
76	C₁₉	C₃²×#1043	1	1	yes	characteristic, complemented, Sylow
77	C₂×C₃²	—	475	1	no	—
78	C₃×C₅	—	19	15	no	—
79	C₃×C₅	—	19	3	no	—
80	C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	5	yes	complemented
81	C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
82	C₃×C₄	—	1425	1	no	—
83	C₃×C₄	—	475	3	no	—
84	D₅	—	5	5	no	—
85	D₅	—	5	1	no	—
86	C₃²	—	19	1	no	Sylow
87	C₂×C₃	—	25	1	no	—
88	C₂×C₃	—	475	3	no	—
89	C₅	C₃×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	5	yes	complemented
90	C₅	C₃×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
91	C₄	—	1425	1	no	Sylow
92	C₃	—	19	3	no	—
93	C₃	(C₁₉⋊C₃)⋊#1043	1	1	yes	characteristic, direct product factor
94	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
9. C₁₉⋊#1043	C₃²	semidirect
12. C₃×C₅²×C₁₉	C₃×C₄	semidirect
13. C₅²×C₁₉⋊C₃	C₃×C₄	semidirect
20. C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	semidirect
21. C₃×C₅×C₁₉⋊C₃	AGL(1,𝔽₅)	semidirect
27. C₅²×C₁₉	C₃²×C₄	semidirect
34. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
35. C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	semidirect
36. C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
37. C₅×C₁₉⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
45. C₃×C₁₉⋊C₃	#1043	semidirect
51. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
52. C₅×C₁₉	C₃²×AGL(1,𝔽₅)	semidirect
57. C₃×C₅²	(C₁₉⋊C₃)⋊C₄	semidirect
62. C₃×C₁₉	C₃×#1043	semidirect
63. C₁₉⋊C₃	C₃×#1043	semidirect
73. C₅²	C₃×(C₁₉⋊C₃)⋊C₄	semidirect
76. C₁₉	C₃²×#1043	semidirect
80. C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	semidirect
81. C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	semidirect
89. C₅	C₃×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	semidirect
90. C₅	C₃×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	semidirect
93. 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×(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	5
C₃²×#1043	19

Subgroups — C3×(C19⋊C3)⋊#1043 #30685737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₁₉⋊C₃)⋊#1043 #30685737