Subgroups — C₉×D₁₉×C₅⋊D₅ #30685581

Order 17100.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅⋊D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₉×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
5	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₉×D₅×D₁₉	—	5	6	no	maximal
7	C₃×C₅⋊D₉₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅²×D₁₉	C₂×C₃	1	1	yes	characteristic
10	D₁₉×C₅⋊D₅	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₉×D₉₅	—	5	6	no	—
12	C₉×D₅×C₁₉	—	5	6	no	—
13	C₅×C₉×D₁₉	D₅	1	6	yes	complemented
14	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
15	C₃×D₅×D₁₉	—	5	6	no	—
16	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₅²×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
19	C₂×C₉×C₅⋊D₅	—	19	1	no	maximal, Hall
20	C₅×C₉×C₁₉	C₂×D₅	1	6	yes	complemented
21	C₂×C₉×D₁₉	—	25	1	no	Hall
22	C₃×D₉₅	—	5	6	no	—
23	C₃×D₅×C₁₉	—	5	6	no	—
24	C₃×C₅×D₁₉	C₃×D₅	1	6	yes	—
25	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅²×C₉	—	19	1	no	—
27	C₉×C₅⋊D₅	—	19	1	no	—
28	C₉×C₅⋊D₅	D₁₉	1	1	yes	characteristic, direct product factor
29	D₅×D₁₉	—	5	6	no	—
30	C₂×C₉×C₁₉	—	25	1	no	—
31	C₉×D₁₉	—	25	1	no	—
32	C₉×D₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₅⋊D₅	—	19	1	no	—
34	C₃×C₅×C₁₉	C₂×C₃×D₅	1	6	yes	—
35	C₂×C₃×D₁₉	—	25	1	no	—
36	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
37	D₉₅	—	5	6	no	—
38	C₅×D₁₉	C₉×D₅	1	6	yes	complemented
39	D₅×C₁₉	—	5	6	no	—
40	C₂×C₉×D₅	—	95	6	no	—
41	C₉×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅²	—	19	1	no	—
43	C₃×C₅⋊D₅	—	19	1	no	—
44	C₃×C₅⋊D₅	C₃×D₁₉	1	1	yes	characteristic
45	C₂×C₃×C₁₉	—	25	1	no	—
46	C₃×D₁₉	—	25	1	no	—
47	C₃×D₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic
48	C₂×C₅⋊D₅	—	19	1	no	Hall
49	C₅×C₁₉	C₂×C₉×D₅	1	6	yes	complemented
50	C₂×C₅×C₉	—	19	6	no	—
51	C₉×D₅	—	5	6	no	—
52	C₉×D₅	—	95	6	no	—
53	C₂×D₁₉	—	25	1	no	Hall
54	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic
55	C₂×C₃×D₅	—	95	6	no	—
56	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic
57	C₂×C₅²	—	19	1	no	—
58	C₅⋊D₅	—	19	1	no	—
59	C₅⋊D₅	C₉×D₁₉	1	1	yes	characteristic, direct product factor
60	C₅×C₉	D₅×D₁₉	1	6	yes	complemented
61	C₂×C₁₉	—	25	1	no	—
62	D₁₉	—	25	1	no	—
63	D₁₉	C₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
64	C₂²×C₉	—	475	1	no	Hall
65	C₂×C₃×C₅	—	19	6	no	—
66	C₃×D₅	—	5	6	no	—
67	C₃×D₅	—	95	6	no	—
68	C₅²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	95	6	no	—
70	C₁₉	C₂×C₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₉	—	19	1	no	—
72	C₂×C₉	—	25	1	no	—
73	C₂×C₉	—	475	1	no	—
74	C₃×C₅	C₃×D₅×D₁₉	1	6	yes	—
75	C₂²×C₃	—	475	1	no	—
76	C₂×C₅	—	19	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	95	6	no	—
79	C₉	D₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂×C₃	—	19	1	no	—
81	C₂×C₃	—	25	1	no	—
82	C₂×C₃	—	475	1	no	—
83	C₅	C₉×D₅×D₁₉	1	6	yes	complemented
84	C₂²	—	475	1	no	Sylow
85	C₃	C₃×D₁₉×C₅⋊D₅	1	1	yes	characteristic
86	C₂	—	19	1	no	—
87	C₂	—	25	1	no	—
88	C₂	—	475	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₁₉×C₅⋊D₅
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₃×D₁₉×C₅⋊D₅
Fitting	C₅²×C₉×C₁₉	C₂²
socle, cosocle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×D₁₉×C₅⋊D₅	C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₅⋊D₉₅	C₂	semidirect
2. C₉×C₁₉×C₅⋊D₅	C₂	semidirect
3. C₅²×C₉×D₁₉	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
10. D₁₉×C₅⋊D₅	C₉	direct (N × H)
13. C₅×C₉×D₁₉	D₅	semidirect
16. C₅⋊D₉₅	C₂×C₉	semidirect
17. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
18. C₅²×D₁₉	C₂×C₉	semidirect
20. C₅×C₉×C₁₉	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂²×C₉	semidirect
28. C₉×C₅⋊D₅	D₁₉	direct (N × H)
32. C₉×D₁₉	C₅⋊D₅	direct (N × H)
36. C₅²×C₉	C₂×D₁₉	semidirect
38. C₅×D₁₉	C₉×D₅	semidirect
41. C₉×C₁₉	C₂×C₅⋊D₅	semidirect
49. C₅×C₁₉	C₂×C₉×D₅	semidirect
59. C₅⋊D₅	C₉×D₁₉	direct (N × H)
60. C₅×C₉	D₅×D₁₉	semidirect
63. D₁₉	C₉×C₅⋊D₅	direct (N × H)
68. C₅²	C₂×C₉×D₁₉	semidirect
70. C₁₉	C₂×C₉×C₅⋊D₅	semidirect
79. C₉	D₁₉×C₅⋊D₅	direct (N × H)
83. C₅	C₉×D₅×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₅⋊D₉₅	2
C₉×C₁₉×C₅⋊D₅	2
C₅²×C₉×D₁₉	2
C₃×D₁₉×C₅⋊D₅	3
C₉×D₅×D₁₉	5
C₂×C₉×C₅⋊D₅	19

Subgroups — C9×D19×C5⋊D5 #30685581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₁₉×C₅⋊D₅ #30685581