Subgroups — C₁₉×#90646⋊C₂ #30685547

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#90646	C₂	1	2	yes	maximal, complemented
3	C₁₉×D₁₅⋊D₅	—	3	1	no	maximal
4	C₁₉×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₉×D₁₅	—	3	2	no	—
6	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
7	D₅²×C₁₉	—	9	1	no	Hall
8	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
9	D₃×D₅×C₁₉	—	15	2	no	—
10	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic, complemented
11	C₅×D₅×C₁₉	—	9	2	no	—
12	#90646⋊C₂	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×D₉×C₁₉	—	25	1	no	maximal, Hall
14	C₁₉×D₁₅	—	3	2	no	—
15	C₅×D₃×C₁₉	—	15	2	no	—
16	C₃×D₅×C₁₉	—	15	2	no	—
17	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
18	(C₅⋊D₅)⋊C₉	C₂×C₁₉	1	1	yes	characteristic, complemented
19	#90646	C₂×C₁₉	1	2	yes	complemented
20	C₂×D₅×C₁₉	—	45	2	no	—
21	C₂×C₉×C₁₉	—	25	1	no	—
22	D₉×C₁₉	—	25	2	no	—
23	D₁₅⋊D₅	—	3	1	no	—
24	C₃×C₅×C₁₉	—	3	2	no	—
25	C₂×D₃×C₁₉	—	75	1	no	—
26	C₅²⋊C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅×C₁₉	—	45	2	no	—
28	D₅×C₁₉	—	9	2	no	—
29	D₅×C₁₉	—	15	2	no	—
30	C₉×C₁₉	—	25	1	no	Hall
31	C₅×D₁₅	—	3	2	no	—
32	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic
33	C₂×C₃×C₁₉	—	25	1	no	—
34	D₃×C₁₉	—	15	2	no	—
35	D₅²	—	9	1	no	Hall
36	C₅×C₁₉	—	3	2	no	—
37	C₂²×C₁₉	—	225	1	no	Hall
38	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic
39	D₃×D₅	—	15	2	no	—
40	C₃×C₁₉	#3874⋊C₂	1	1	yes	characteristic
41	C₅⋊D₅	D₉×C₁₉	1	1	yes	characteristic, complemented
42	C₅×D₅	—	9	2	no	—
43	C₂×C₁₉	—	25	1	no	—
44	C₂×C₁₉	—	45	2	no	—
45	C₂×D₉	—	25	1	no	Hall
46	D₁₅	—	3	2	no	—
47	C₃×D₅	—	15	2	no	—
48	C₅×D₃	—	15	2	no	—
49	C₅²	C₂×D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₅	—	45	2	no	—
51	C₁₉	#90646⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₉	—	25	1	no	—
53	D₉	—	25	2	no	—
54	C₃×C₅	—	3	2	no	—
55	C₂×D₃	—	75	1	no	—
56	C₂×C₅	—	45	2	no	—
57	D₅	—	9	2	no	—
58	D₅	—	15	2	no	—
59	C₉	—	25	1	no	Sylow
60	C₂×C₃	—	25	1	no	—
61	D₃	—	15	2	no	—
62	C₅	—	3	2	no	—
63	C₂²	—	225	1	no	Sylow
64	C₃	C₁₉×#3874⋊C₂	1	1	yes	characteristic
65	C₂	—	25	1	no	—
66	C₂	—	45	2	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#90646⋊C₂
commutator, cosocle, hypocenter	C₅²⋊C₉	C₂²×C₁₉
Frattini	C₃	C₁₉×#3874⋊C₂
Fitting, socle	C₃×C₅²×C₁₉	C₂×D₃
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×(C₅⋊D₅)⋊C₉	C₂	semidirect
2. C₁₉×#90646	C₂	semidirect
4. C₁₉×C₅²⋊C₉	C₂²	semidirect
10. C₁₉×C₅⋊D₅	D₉	semidirect
12. #90646⋊C₂	C₁₉	direct (N × H)
17. C₅²×C₁₉	C₂×D₉	semidirect
18. (C₅⋊D₅)⋊C₉	C₂×C₁₉	semidirect
19. #90646	C₂×C₁₉	semidirect
26. C₅²⋊C₉	C₂²×C₁₉	semidirect
41. C₅⋊D₅	D₉×C₁₉	semidirect
49. C₅²	C₂×D₉×C₁₉	semidirect
51. C₁₉	#90646⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×(C₅⋊D₅)⋊C₉	2
C₁₉×#90646	2
C₁₉×D₁₅⋊D₅	3
#90646⋊C₂	19
C₂×D₉×C₁₉	25

Subgroups — C19×#90646⋊C2 #30685547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#90646⋊C₂ #30685547