Subgroups — C₉×D₅²×C₁₉ #30685582

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₉×D₅×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₃×D₅²×C₁₉	C₃	1	1	yes	maximal, characteristic
4	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₅×C₁₉	—	5	2	no	maximal
6	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅×D₅×C₁₉	C₂×C₃	1	2	yes	—
8	D₅²×C₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₉×C₁₉	—	5	2	no	—
10	C₉×D₅×C₁₉	—	5	2	no	—
11	C₉×D₅×C₁₉	—	10	2	no	—
12	C₉×D₅×C₁₉	D₅	1	2	yes	direct product factor
13	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
14	C₂×C₃×D₅×C₁₉	—	5	2	no	—
15	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₅×D₅×C₁₉	C₂×C₉	1	2	yes	complemented
17	C₉×D₅²	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₅×C₉×C₁₉	—	2	2	no	—
19	C₅×C₉×C₁₉	C₂×D₅	1	2	yes	complemented
20	C₂²×C₉×C₁₉	—	25	1	no	Hall
21	C₂×C₃×C₅×C₁₉	—	5	2	no	—
22	C₃×D₅×C₁₉	—	5	2	no	—
23	C₃×D₅×C₁₉	—	10	2	no	—
24	C₃×D₅×C₁₉	C₃×D₅	1	2	yes	—
25	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₉×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic, complemented
27	C₅×C₉×D₅	C₂×C₁₉	1	2	yes	complemented
28	C₂×D₅×C₁₉	—	5	2	no	—
29	C₂×C₉×C₁₉	—	5	2	no	—
30	C₂×C₉×C₁₉	—	25	1	no	—
31	C₃×D₅²	C₃×C₁₉	1	1	yes	characteristic
32	C₃×C₅×C₁₉	—	2	2	no	—
33	C₃×C₅×C₁₉	C₂×C₃×D₅	1	2	yes	—
34	C₂²×C₃×C₁₉	—	25	1	no	—
35	C₅²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₅×C₁₉	—	5	2	no	—
37	D₅×C₁₉	—	5	2	no	—
38	D₅×C₁₉	—	10	2	no	—
39	D₅×C₁₉	C₉×D₅	1	2	yes	direct product factor
40	C₂×C₉×D₅	—	5	2	no	—
41	C₉×C₁₉	D₅²	1	1	yes	characteristic, direct product factor, Hall
42	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	1	yes	characteristic
43	C₃×C₅×D₅	C₂×C₃×C₁₉	1	2	yes	—
44	C₂×C₃×C₁₉	—	5	2	no	—
45	C₂×C₃×C₁₉	—	25	1	no	—
46	D₅²	C₉×C₁₉	1	1	yes	characteristic, direct product factor, Hall
47	C₅×C₁₉	—	2	2	no	—
48	C₅×C₁₉	C₂×C₉×D₅	1	2	yes	complemented
49	C₂×C₅×C₉	—	5	2	no	—
50	C₉×D₅	—	5	2	no	—
51	C₉×D₅	—	10	2	no	—
52	C₉×D₅	D₅×C₁₉	1	2	yes	direct product factor
53	C₂²×C₁₉	—	25	1	no	Hall
54	C₃×C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic
55	C₂×C₃×D₅	—	5	2	no	—
56	C₃×C₁₉	C₃×D₅²	1	1	yes	characteristic
57	C₅⋊D₅	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented
58	C₅×D₅	C₂×C₉×C₁₉	1	2	yes	complemented
59	C₅×C₉	—	2	2	no	—
60	C₅×C₉	C₂×D₅×C₁₉	1	2	yes	complemented
61	C₂×C₁₉	—	5	2	no	—
62	C₂×C₁₉	—	25	1	no	—
63	C₂²×C₉	—	25	1	no	Hall
64	C₂×C₃×C₅	—	5	2	no	—
65	C₃×D₅	—	5	2	no	—
66	C₃×D₅	—	10	2	no	—
67	C₃×D₅	C₃×D₅×C₁₉	1	2	yes	—
68	C₅²	C₂²×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	5	2	no	—
70	C₁₉	C₉×D₅²	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₉	—	5	2	no	—
72	C₂×C₉	—	25	1	no	—
73	C₃×C₅	—	2	2	no	—
74	C₃×C₅	C₂×C₃×D₅×C₁₉	1	2	yes	—
75	C₂²×C₃	—	25	1	no	—
76	C₂×C₅	—	5	2	no	—
77	D₅	—	5	2	no	—
78	D₅	—	10	2	no	—
79	D₅	C₉×D₅×C₁₉	1	2	yes	direct product factor
80	C₉	D₅²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×C₃	—	5	2	no	—
82	C₂×C₃	—	25	1	no	—
83	C₅	—	2	2	no	—
84	C₅	C₂×C₉×D₅×C₁₉	1	2	yes	complemented
85	C₂²	—	25	1	no	Sylow
86	C₃	C₃×D₅²×C₁₉	1	1	yes	characteristic
87	C₂	—	5	2	no	—
88	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₅²
commutator, hypocenter	C₅²	C₂²×C₉×C₁₉
Frattini	C₃	C₃×D₅²×C₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×D₅²×C₁₉	C₃
cosocle	C₃×C₅²	C₂²×C₃×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₉×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₉×C₅⋊D₅	C₂	semidirect
2. C₅×C₉×D₅×C₁₉	C₂	semidirect
4. C₅²×C₉×C₁₉	C₂²	semidirect
8. D₅²×C₁₉	C₉	direct (N × H)
12. C₉×D₅×C₁₉	D₅	direct (N × H)
15. C₁₉×C₅⋊D₅	C₂×C₉	semidirect
16. C₅×D₅×C₁₉	C₂×C₉	semidirect
17. C₉×D₅²	C₁₉	direct (N × H)
19. C₅×C₉×C₁₉	C₂×D₅	semidirect
25. C₅²×C₁₉	C₂²×C₉	semidirect
26. C₉×C₅⋊D₅	C₂×C₁₉	semidirect
27. C₅×C₉×D₅	C₂×C₁₉	semidirect
35. C₅²×C₉	C₂²×C₁₉	semidirect
39. D₅×C₁₉	C₉×D₅	direct (N × H)
41. C₉×C₁₉	D₅²	direct (N × H)
46. D₅²	C₉×C₁₉	direct (N × H)
48. C₅×C₁₉	C₂×C₉×D₅	semidirect
52. C₉×D₅	D₅×C₁₉	direct (N × H)
57. C₅⋊D₅	C₂×C₉×C₁₉	semidirect
58. C₅×D₅	C₂×C₉×C₁₉	semidirect
60. C₅×C₉	C₂×D₅×C₁₉	semidirect
68. C₅²	C₂²×C₉×C₁₉	semidirect
70. C₁₉	C₉×D₅²	direct (N × H)
79. D₅	C₉×D₅×C₁₉	direct (N × H)
80. C₉	D₅²×C₁₉	direct (N × H)
84. C₅	C₂×C₉×D₅×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₁₉×C₅⋊D₅	2
C₅×C₉×D₅×C₁₉	2
C₃×D₅²×C₁₉	3
C₂×C₉×D₅×C₁₉	5
C₉×D₅²	19

Subgroups — C9×D52×C19 #30685582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅²×C₁₉ #30685582