Subgroups — C₁₉×C₃⋊#64470 #30685665

Order 17100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₉×Dic₁₅	—	3	1	no	maximal
3	C₁₉×#64470	—	3	3	no	maximal
4	C₃×C₁₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₅²⋊C₃	D₃	1	3	yes	—
6	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic
7	C₅×C₁₉×Dic₅	—	9	1	no	Hall
8	C₃×C₅²×C₁₉	Dic₃	1	1	yes	characteristic, complemented
9	C₁₉×C₅²⋊C₃	Dic₃	1	3	yes	complemented
10	C₁₉×Dic₁₅	—	3	1	no	—
11	C₅×Dic₃×C₁₉	—	15	1	no	—
12	C₂×C₅²×C₁₉	C₃⋊D₃	1	1	yes	characteristic
13	C₃⋊#64470	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₁₉×C₃⋊Dic₃	—	25	1	no	maximal, Hall
15	C₂×C₃×C₅×C₁₉	—	3	1	no	—
16	C₂×C₃×C₅×C₁₉	—	3	1	no	—
17	C₅²×C₁₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅²⋊C₃	C₂×C₁₉	1	1	yes	characteristic
19	C₄×C₅×C₁₉	—	45	1	no	—
20	C₁₉×Dic₅	—	9	1	no	—
21	C₂×C₃²×C₁₉	—	25	1	no	—
22	C₅×Dic₁₅	—	3	1	no	—
23	#64470	—	3	3	no	—
24	C₃×C₅×C₁₉	—	3	1	no	—
25	C₃×C₅×C₁₉	—	3	1	no	—
26	Dic₃×C₁₉	—	15	1	no	—
27	Dic₃×C₁₉	—	75	3	no	—
28	C₃×C₅²⋊C₃	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₁₉	—	3	1	no	—
30	C₂×C₅×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	—	25	1	no	Hall
32	C₂×C₃×C₅²	D₃×C₁₉	1	1	yes	characteristic
33	C₂×C₅²⋊C₃	D₃×C₁₉	1	3	yes	—
34	C₂×C₃×C₁₉	—	25	3	no	—
35	C₂×C₃×C₁₉	#3874	1	1	yes	characteristic
36	C₅×Dic₅	—	9	1	no	Hall
37	C₅×C₁₉	—	3	1	no	—
38	C₅×C₁₉	—	3	1	no	—
39	C₄×C₁₉	—	45	1	no	Hall
40	C₃×C₅²	Dic₃×C₁₉	1	1	yes	characteristic, complemented
41	C₅²⋊C₃	Dic₃×C₁₉	1	3	yes	complemented
42	Dic₁₅	—	3	1	no	—
43	C₅×Dic₃	—	15	1	no	—
44	C₃×C₁₉	—	25	3	no	—
45	C₃×C₁₉	#64470	1	1	yes	characteristic, complemented
46	C₂×C₅²	C₃⋊D₃×C₁₉	1	1	yes	characteristic
47	C₂×C₁₉	C₃⋊#3874	1	1	yes	characteristic
48	C₃⋊Dic₃	—	25	1	no	Hall
49	C₂×C₃×C₅	—	3	1	no	—
50	C₂×C₃×C₅	—	3	1	no	—
51	C₅²	C₁₉×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
52	C₄×C₅	—	45	1	no	—
53	Dic₅	—	9	1	no	—
54	C₁₉	C₃⋊#64470	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₃²	—	25	1	no	—
56	C₃×C₅	—	3	1	no	—
57	C₃×C₅	—	3	1	no	—
58	Dic₃	—	15	1	no	—
59	Dic₃	—	75	3	no	—
60	C₂×C₅	—	3	1	no	—
61	C₂×C₅	—	3	1	no	—
62	C₃²	—	25	1	no	Sylow
63	C₂×C₃	—	25	3	no	—
64	C₂×C₃	C₁₉×#3874	1	1	yes	characteristic
65	C₅	—	3	1	no	—
66	C₅	—	3	1	no	—
67	C₄	—	45	1	no	Sylow
68	C₃	—	25	3	no	—
69	C₃	C₁₉×#64470	1	1	yes	characteristic, complemented
70	C₂	C₁₉×C₃⋊#3874	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊#3874
commutator, hypocenter	C₃×C₅²⋊C₃	C₄×C₁₉
Frattini	C₂	C₁₉×C₃⋊#3874
Fitting, socle	C₂×C₃×C₅²×C₁₉	D₃
prime radical	C₂×C₃×C₁₉×C₅²⋊C₃	C₂
cosocle	C₂×C₃×C₅²⋊C₃	C₂×C₁₉
LCS	G ▷ C₃×C₅²⋊C₃
UCS	C₁ ◁ C₂×C₁₉

Complements

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

N	H ≅ G/N	type
4. C₃×C₁₉×C₅²⋊C₃	C₄	semidirect
8. C₃×C₅²×C₁₉	Dic₃	semidirect
9. C₁₉×C₅²⋊C₃	Dic₃	semidirect
13. C₃⋊#64470	C₁₉	direct (N × H)
17. C₅²×C₁₉	C₃⋊Dic₃	semidirect
28. C₃×C₅²⋊C₃	C₄×C₁₉	semidirect
40. C₃×C₅²	Dic₃×C₁₉	semidirect
41. C₅²⋊C₃	Dic₃×C₁₉	semidirect
45. C₃×C₁₉	#64470	semidirect
51. C₅²	C₁₉×C₃⋊Dic₃	semidirect
54. C₁₉	C₃⋊#64470	direct (N × H)
69. C₃	C₁₉×#64470	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₉×C₅²⋊C₃	2
C₅×C₁₉×Dic₁₅	3
C₁₉×#64470	3
C₃⋊#64470	19
C₁₉×C₃⋊Dic₃	25

Subgroups — C19×C3⋊#64470 #30685665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×C₃⋊#64470 #30685665