Subgroups — D₉×C₁₉×C₅⋊D₅ #30685600

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₅⋊D₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₉×C₅⋊D₅	—	3	1	no	maximal
5	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₉×C₁₉	—	5	6	no	maximal
7	C₁₉×C₃⋊(C₅⋊D₅)	—	3	1	no	—
8	C₅²×D₃×C₁₉	—	3	1	no	—
9	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic
10	C₂×C₁₉×C₅⋊D₅	—	9	1	no	Hall
11	C₁₉×D₄₅	—	5	6	no	—
12	C₅×D₉×C₁₉	D₅	1	6	yes	complemented
13	C₉×D₅×C₁₉	—	5	6	no	—
14	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
15	D₃×D₅×C₁₉	—	15	6	no	—
16	C₂×C₅²×C₁₉	—	9	1	no	—
17	C₁₉×C₅⋊D₅	—	9	1	no	—
18	C₁₉×C₅⋊D₅	D₉	1	1	yes	characteristic, direct product factor
19	D₉×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₅×C₉×C₁₉	C₂×D₅	1	6	yes	complemented
21	C₂×D₉×C₁₉	—	25	1	no	Hall
22	C₁₉×D₁₅	—	15	6	no	—
23	C₅×D₃×C₁₉	—	3	6	no	—
24	C₃×D₅×C₁₉	—	5	6	no	—
25	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
26	C₅⋊D₄₅	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₅²×D₉	C₂×C₁₉	1	1	yes	characteristic, complemented
28	C₉×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic, complemented
29	C₂×D₅×C₁₉	—	45	6	no	—
30	C₂×C₉×C₁₉	—	25	1	no	—
31	D₉×C₁₉	—	25	1	no	—
32	D₉×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
33	D₃×C₅⋊D₅	—	3	1	no	—
34	C₃×C₅×C₁₉	D₃×D₅	1	6	yes	—
35	C₂×D₃×C₁₉	—	75	1	no	—
36	C₅²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₅×C₁₉	—	9	6	no	—
38	D₅×C₁₉	—	5	6	no	—
39	D₅×C₁₉	—	45	6	no	—
40	D₅×D₉	—	5	6	no	—
41	C₉×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
42	C₃⋊(C₅⋊D₅)	—	3	1	no	—
43	C₅²×D₃	—	3	1	no	—
44	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic
45	C₂×C₃×C₁₉	—	25	1	no	—
46	D₃×C₁₉	—	3	1	no	—
47	D₃×C₁₉	—	75	1	no	—
48	C₂×C₅⋊D₅	—	9	1	no	Hall
49	C₅×C₁₉	D₅×D₉	1	6	yes	complemented
50	D₄₅	—	5	6	no	—
51	C₉×D₅	—	5	6	no	—
52	C₅×D₉	D₅×C₁₉	1	6	yes	complemented
53	C₂²×C₁₉	—	225	1	no	Hall
54	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic
55	D₃×D₅	—	15	6	no	—
56	C₃×C₁₉	D₃×C₅⋊D₅	1	1	yes	characteristic
57	C₂×C₅²	—	9	1	no	—
58	C₅⋊D₅	—	9	1	no	—
59	C₅⋊D₅	D₉×C₁₉	1	1	yes	characteristic, direct product factor
60	C₅×C₉	C₂×D₅×C₁₉	1	6	yes	complemented
61	C₂×C₁₉	—	9	1	no	—
62	C₂×C₁₉	—	25	1	no	—
63	C₂×C₁₉	—	225	1	no	—
64	C₂×D₉	—	25	1	no	Hall
65	D₁₅	—	15	6	no	—
66	C₃×D₅	—	5	6	no	—
67	C₅×D₃	—	3	6	no	—
68	C₅²	C₂×D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	45	6	no	—
70	C₁₉	D₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₉	—	25	1	no	—
72	D₉	—	25	1	no	—
73	D₉	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
74	C₃×C₅	D₃×D₅×C₁₉	1	6	yes	—
75	C₂×D₃	—	75	1	no	—
76	C₂×C₅	—	9	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	45	6	no	—
79	C₉	C₂×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	25	1	no	—
81	D₃	—	3	1	no	—
82	D₃	—	75	1	no	—
83	C₅	D₅×D₉×C₁₉	1	6	yes	complemented
84	C₂²	—	225	1	no	Sylow
85	C₃	D₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic
86	C₂	—	9	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	D₉×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂²×C₁₉
Frattini	C₃	D₃×C₁₉×C₅⋊D₅
Fitting	C₅²×C₉×C₁₉	C₂²
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⋊D₄₅	C₂	semidirect
2. C₅²×D₉×C₁₉	C₂	semidirect
3. C₉×C₁₉×C₅⋊D₅	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
12. C₅×D₉×C₁₉	D₅	semidirect
18. C₁₉×C₅⋊D₅	D₉	direct (N × H)
19. D₉×C₅⋊D₅	C₁₉	direct (N × H)
20. C₅×C₉×C₁₉	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂×D₉	semidirect
26. C₅⋊D₄₅	C₂×C₁₉	semidirect
27. C₅²×D₉	C₂×C₁₉	semidirect
28. C₉×C₅⋊D₅	C₂×C₁₉	semidirect
32. D₉×C₁₉	C₅⋊D₅	direct (N × H)
36. C₅²×C₉	C₂²×C₁₉	semidirect
41. C₉×C₁₉	C₂×C₅⋊D₅	semidirect
49. C₅×C₁₉	D₅×D₉	semidirect
52. C₅×D₉	D₅×C₁₉	semidirect
59. C₅⋊D₅	D₉×C₁₉	direct (N × H)
60. C₅×C₉	C₂×D₅×C₁₉	semidirect
68. C₅²	C₂×D₉×C₁₉	semidirect
70. C₁₉	D₉×C₅⋊D₅	direct (N × H)
73. D₉	C₁₉×C₅⋊D₅	direct (N × H)
79. C₉	C₂×C₁₉×C₅⋊D₅	semidirect
83. C₅	D₅×D₉×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₅⋊D₄₅	2
C₅²×D₉×C₁₉	2
C₉×C₁₉×C₅⋊D₅	2
D₃×C₁₉×C₅⋊D₅	3
D₅×D₉×C₁₉	5
D₉×C₅⋊D₅	19

Subgroups — D9×C19×C5⋊D5 #30685600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×C₁₉×C₅⋊D₅ #30685600