Subgroups — C₃⋊#19152831 #30685798

Order 17100.

80 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	#19152831	—	3	1	no	maximal
4	C₃×C₁₉⋊(C₅²⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	(C₅⋊D₅)⋊(C₁₉⋊C₃)	—	2	1	no	—
7	(C₅⋊D₅)⋊(C₁₉⋊C₃)	D₃	1	1	yes	characteristic
8	C₁₉⋊#1043	—	3	1	no	Hall
9	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₉⋊(C₅²⋊C₃)	—	2	1	no	—
11	C₁₉⋊(C₅²⋊C₃)	Dic₃	1	1	yes	characteristic, complemented
12	C₃⋊(C₁₉⋊AGL(1,𝔽₅))	—	15	2	no	—
13	C₁₉×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	C₃⋊(#1043⋊C₃)	—	19	1	no	maximal, Hall
15	C₃⋊((C₁₉⋊C₃)⋊C₄)	—	25	1	no	maximal, Hall
16	C₃×D₅×C₁₉	—	15	2	no	—
17	C₅²×C₁₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₃×(C₅⋊D₅)⋊C₃	—	38	1	no	—
19	C₁₉⋊AGL(1,𝔽₅)	—	45	2	no	—
20	C₂×C₃×C₁₉⋊C₃	—	25	1	no	—
21	C₃⋊#1043	—	19	1	no	—
22	#1043⋊C₃	—	57	1	no	—
23	C₃×C₅×C₁₉	—	3	2	no	—
24	Dic₅₇	—	25	1	no	—
25	(C₁₉⋊C₃)⋊C₄	—	75	1	no	—
26	C₃×C₅²⋊C₃	—	38	1	no	Hall
27	D₅×C₁₉	—	15	2	no	—
28	C₃×C₁₉⋊C₃	—	100	1	no	Hall
29	C₃×C₅⋊D₅	D₁₉⋊C₃	1	1	yes	characteristic
30	(C₅⋊D₅)⋊C₃	—	38	1	no	—
31	(C₅⋊D₅)⋊C₃	—	38	1	no	—
32	C₂×C₃×C₁₉	—	25	1	no	—
33	C₂×C₁₉⋊C₃	—	25	1	no	—
34	C₂×C₁₉⋊C₃	—	50	1	no	—
35	#1043	—	57	1	no	Hall
36	C₅×C₁₉	—	3	2	no	—
37	Dic₁₉	—	75	1	no	Hall
38	C₃×C₅²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
39	C₅²⋊C₃	—	38	1	no	—
40	C₅²⋊C₃	—	38	1	no	—
41	ΓL(1,𝔽₁₆)	—	285	2	no	—
42	C₃×C₁₉	#1043⋊C₃	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	100	1	no	—
44	C₁₉⋊C₃	—	100	1	no	—
45	C₅⋊D₅	C₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
46	C₂×C₁₉	—	25	1	no	—
47	C₃×Dic₃	—	475	1	no	Hall
48	C₃×D₅	—	15	2	no	—
49	C₅²	C₃⋊((C₁₉⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
50	AGL(1,𝔽₅)	—	855	2	no	—
51	C₁₉	C₃⋊(#1043⋊C₃)	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃²	—	950	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	1425	1	no	—
55	Dic₃	—	475	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	1900	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	950	1	no	—
60	C₂×C₃	—	950	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	1425	1	no	Sylow
63	C₃	—	1900	1	no	—
64	C₃	—	1900	1	no	—
65	C₃	#19152831	1	1	yes	characteristic, complemented
66	C₂	—	25	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₁₉⋊#1043)	C₃	semidirect
4. C₃×C₁₉⋊(C₅²⋊C₃)	C₄	semidirect
9. C₃×C₅²×C₁₉	C₃×C₄	semidirect
11. C₁₉⋊(C₅²⋊C₃)	Dic₃	semidirect
17. C₅²×C₁₉	C₃×Dic₃	semidirect
38. C₃×C₅²	(C₁₉⋊C₃)⋊C₄	semidirect
42. C₃×C₁₉	#1043⋊C₃	semidirect
49. C₅²	C₃⋊((C₁₉⋊C₃)⋊C₄)	semidirect
51. C₁₉	C₃⋊(#1043⋊C₃)	semidirect
65. C₃	#19152831	semidirect

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
#19152831	3
C₃⋊(#1043⋊C₃)	19
C₃⋊((C₁₉⋊C₃)⋊C₄)	25

Subgroups — C3⋊#19152831 #30685798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#19152831 #30685798