Subgroups — C₂²×C₅×D₃×C₉ #11762003

Order 1080.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×C₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×C₅×D₃	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₅×C₉	—	3	1	no	maximal
5	C₂×C₃×C₅×C₉	C₂²	1	3	yes	complemented
6	C₅×D₃×C₉	C₂²	1	4	yes	direct product factor
7	C₂²×D₃×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃²×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₅×D₃	C₂×C₃	1	6	yes	—
10	C₂²×C₅×C₉	—	2	1	no	—
11	C₂²×C₅×C₉	—	3	6	no	—
12	C₂²×C₅×C₉	D₃	1	1	yes	characteristic, direct product factor
13	C₃×C₅×C₉	C₂³	1	1	yes	characteristic, complemented, Hall
14	C₂³×C₃×C₅	—	3	1	no	—
15	C₂²×C₅×D₃	C₉	1	1	yes	characteristic, direct product factor
16	C₂²×C₃×C₉	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂×D₃×C₉	C₂×C₅	1	6	yes	direct product factor
18	C₂×C₃²×C₅	C₂²×C₃	1	3	yes	—
19	C₃×C₅×D₃	C₂²×C₃	1	4	yes	—
20	C₂×C₅×C₉	—	2	3	no	—
21	C₂×C₅×C₉	—	3	4	no	—
22	C₂×C₅×C₉	C₂×D₃	1	3	yes	direct product factor
23	C₂²×C₃×D₃	C₃×C₅	1	1	yes	characteristic
24	C₂³×C₉	—	3	1	no	—
25	C₂²×C₃×C₅	—	2	1	no	—
26	C₂²×C₃×C₅	—	3	6	no	—
27	C₂²×C₃×C₅	C₂×C₉	1	1	yes	characteristic, complemented
28	C₂²×C₃×C₅	C₃×D₃	1	1	yes	characteristic
29	C₂×C₅×D₃	C₂×C₉	1	6	yes	direct product factor
30	C₂×C₃×C₉	C₂²×C₅	1	3	yes	complemented
31	D₃×C₉	C₂²×C₅	1	4	yes	direct product factor
32	C₃²×C₅	C₂³×C₃	1	1	yes	characteristic
33	C₅×C₉	—	2	1	no	—
34	C₅×C₉	C₂²×D₃	1	1	yes	characteristic, direct product factor
35	C₂³×C₅	—	3	1	no	Hall
36	C₂²×C₃²	C₂×C₃×C₅	1	1	yes	characteristic
37	C₂×C₃×D₃	C₂×C₃×C₅	1	6	yes	—
38	C₂²×C₉	—	2	1	no	—
39	C₂²×C₉	—	3	6	no	—
40	C₂²×C₉	C₅×D₃	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₅	—	2	3	no	—
42	C₂×C₃×C₅	—	3	4	no	—
43	C₂×C₃×C₅	C₂²×C₉	1	3	yes	complemented
44	C₂×C₃×C₅	C₂×C₃×D₃	1	3	yes	—
45	C₅×D₃	C₂²×C₉	1	4	yes	direct product factor
46	C₃×C₉	C₂³×C₅	1	1	yes	characteristic, complemented, Sylow
47	C₂³×C₃	—	3	1	no	—
48	C₂²×D₃	C₅×C₉	1	1	yes	characteristic, direct product factor
49	C₂²×C₅	—	3	6	no	—
50	C₂²×C₅	D₃×C₉	1	1	yes	characteristic, direct product factor
51	C₂×C₃²	C₂²×C₃×C₅	1	3	yes	—
52	C₃×D₃	C₂²×C₃×C₅	1	4	yes	—
53	C₂×C₉	—	2	3	no	—
54	C₂×C₉	—	3	4	no	—
55	C₂×C₉	C₂×C₅×D₃	1	3	yes	direct product factor
56	C₃×C₅	—	2	1	no	—
57	C₃×C₅	C₂³×C₉	1	1	yes	characteristic, complemented
58	C₃×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
59	C₂²×C₃	—	2	1	no	—
60	C₂²×C₃	—	3	6	no	—
61	C₂²×C₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented
62	C₂²×C₃	C₃×C₅×D₃	1	1	yes	characteristic
63	C₂×D₃	C₂×C₅×C₉	1	6	yes	direct product factor
64	C₂×C₅	—	3	4	no	—
65	C₂×C₅	C₂×D₃×C₉	1	3	yes	direct product factor
66	C₃²	C₂³×C₃×C₅	1	1	yes	characteristic
67	C₉	—	2	1	no	—
68	C₉	C₂²×C₅×D₃	1	1	yes	characteristic, direct product factor
69	C₂³	—	3	1	no	Sylow
70	C₂×C₃	—	2	3	no	—
71	C₂×C₃	—	3	4	no	—
72	C₂×C₃	C₂²×C₅×C₉	1	3	yes	complemented
73	C₂×C₃	C₂×C₃×C₅×D₃	1	3	yes	—
74	D₃	C₂²×C₅×C₉	1	4	yes	direct product factor
75	C₅	C₂²×D₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²	—	3	6	no	—
77	C₂²	C₅×D₃×C₉	1	1	yes	characteristic, direct product factor
78	C₃	—	2	1	no	—
79	C₃	C₂³×C₅×C₉	1	1	yes	characteristic, complemented
80	C₃	C₂²×C₃×C₅×D₃	1	1	yes	characteristic
81	C₂	—	3	4	no	—
82	C₂	C₂×C₅×D₃×C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅×C₉	D₃
commutator, hypocenter	C₃	C₂³×C₅×C₉
Frattini	C₃	C₂²×C₃×C₅×D₃
Fitting	C₂²×C₃×C₅×C₉	C₂
socle	C₂²×C₃²×C₅	C₂×C₃
prime radical	C₂²×C₃×C₅×D₃	C₃
cosocle	C₃²	C₂³×C₃×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₉	C₂	semidirect
2. C₂×C₅×D₃×C₉	C₂	direct (N × H)
5. C₂×C₃×C₅×C₉	C₂²	semidirect
6. C₅×D₃×C₉	C₂²	direct (N × H)
7. C₂²×D₃×C₉	C₅	direct (N × H)
12. C₂²×C₅×C₉	D₃	direct (N × H)
13. C₃×C₅×C₉	C₂³	semidirect
15. C₂²×C₅×D₃	C₉	direct (N × H)
16. C₂²×C₃×C₉	C₂×C₅	semidirect
17. C₂×D₃×C₉	C₂×C₅	direct (N × H)
22. C₂×C₅×C₉	C₂×D₃	direct (N × H)
27. C₂²×C₃×C₅	C₂×C₉	semidirect
29. C₂×C₅×D₃	C₂×C₉	direct (N × H)
30. C₂×C₃×C₉	C₂²×C₅	semidirect
31. D₃×C₉	C₂²×C₅	direct (N × H)
34. C₅×C₉	C₂²×D₃	direct (N × H)
40. C₂²×C₉	C₅×D₃	direct (N × H)
43. C₂×C₃×C₅	C₂²×C₉	semidirect
45. C₅×D₃	C₂²×C₉	direct (N × H)
46. C₃×C₉	C₂³×C₅	semidirect
48. C₂²×D₃	C₅×C₉	direct (N × H)
50. C₂²×C₅	D₃×C₉	direct (N × H)
55. C₂×C₉	C₂×C₅×D₃	direct (N × H)
57. C₃×C₅	C₂³×C₉	semidirect
61. C₂²×C₃	C₂×C₅×C₉	semidirect
63. C₂×D₃	C₂×C₅×C₉	direct (N × H)
65. C₂×C₅	C₂×D₃×C₉	direct (N × H)
68. C₉	C₂²×C₅×D₃	direct (N × H)
72. C₂×C₃	C₂²×C₅×C₉	semidirect
74. D₃	C₂²×C₅×C₉	direct (N × H)
75. C₅	C₂²×D₃×C₉	direct (N × H)
77. C₂²	C₅×D₃×C₉	direct (N × H)
79. C₃	C₂³×C₅×C₉	semidirect
82. C₂	C₂×C₅×D₃×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₉	2
C₂×C₅×D₃×C₉	2
C₂²×C₃×C₅×D₃	3
C₂³×C₅×C₉	3
C₂²×D₃×C₉	5

Subgroups — C22×C5×D3×C9 #11762003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×D₃×C₉ #11762003