Subgroups — C₂³×C₅×Dic₉ #13085342

Order 1440.

708 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×Dic₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₅×Dic₃	—	3	1	no	maximal
4	C₂³×C₅×C₉	C₄	1	8	yes	complemented
5	C₂³×C₅×C₉	C₂²	1	7	yes	—
6	C₂×C₅×Dic₉	C₂²	1	28	yes	direct product factor
7	C₂³×Dic₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×C₅	D₃	1	1	yes	characteristic
9	C₂²×C₅×Dic₃	—	3	14	no	—
10	C₂²×C₅×C₉	C₂×C₄	1	28	yes	complemented
11	C₂²×C₅×C₉	C₂³	1	7	yes	—
12	C₅×Dic₉	C₂³	1	8	yes	direct product factor
13	C₂³×C₄×C₅	—	9	1	no	Hall
14	C₂⁴×C₉	C₂×C₅	1	1	yes	characteristic
15	C₂²×Dic₉	C₂×C₅	1	14	yes	direct product factor
16	C₂³×C₃×C₅	Dic₃	1	8	yes	—
17	C₂³×C₃×C₅	C₂×D₃	1	7	yes	—
18	C₂×C₅×Dic₃	—	3	28	no	—
19	C₂³×Dic₃	—	3	1	no	—
20	C₂×C₅×C₉	C₂²×C₄	1	14	yes	complemented
21	C₂×C₅×C₉	C₂⁴	1	1	yes	characteristic
22	C₂⁴×C₅	D₉	1	1	yes	characteristic
23	C₂²×C₄×C₅	—	9	14	no	—
24	C₂³×C₉	C₄×C₅	1	8	yes	complemented
25	C₂³×C₉	C₂²×C₅	1	7	yes	—
26	C₂×Dic₉	C₂²×C₅	1	28	yes	direct product factor
27	C₂²×C₃×C₅	C₂×Dic₃	1	28	yes	—
28	C₂²×C₃×C₅	C₂²×D₃	1	7	yes	—
29	C₅×Dic₃	—	3	8	no	—
30	C₂⁴×C₃	C₅×D₃	1	1	yes	characteristic
31	C₂²×Dic₃	—	3	14	no	—
32	C₅×C₉	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
33	C₂³×C₅	Dic₉	1	8	yes	direct product factor
34	C₂³×C₅	C₂×D₉	1	7	yes	—
35	C₂×C₄×C₅	—	9	28	no	—
36	C₂²×C₉	C₂×C₄×C₅	1	28	yes	complemented
37	C₂²×C₉	C₂³×C₅	1	7	yes	—
38	Dic₉	C₂³×C₅	1	8	yes	direct product factor
39	C₂³×C₄	—	9	1	no	Sylow
40	C₂×C₃×C₅	C₂²×Dic₃	1	14	yes	—
41	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
42	C₂³×C₃	C₅×Dic₃	1	8	yes	—
43	C₂³×C₃	C₂×C₅×D₃	1	7	yes	—
44	C₂×Dic₃	—	3	28	no	—
45	C₂²×C₅	C₂×Dic₉	1	28	yes	direct product factor
46	C₂²×C₅	C₂²×D₉	1	7	yes	—
47	C₄×C₅	—	9	8	no	—
48	C₂×C₉	C₂²×C₄×C₅	1	14	yes	complemented
49	C₂×C₉	C₂⁴×C₅	1	1	yes	characteristic
50	C₂⁴	C₅×D₉	1	1	yes	characteristic
51	C₂²×C₄	—	9	14	no	—
52	C₃×C₅	C₂³×Dic₃	1	1	yes	characteristic
53	C₂²×C₃	C₂×C₅×Dic₃	1	28	yes	—
54	C₂²×C₃	C₂²×C₅×D₃	1	7	yes	—
55	Dic₃	—	3	8	no	—
56	C₂×C₅	C₂²×Dic₉	1	14	yes	direct product factor
57	C₂×C₅	C₂³×D₉	1	1	yes	characteristic
58	C₉	C₂³×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
59	C₂³	C₅×Dic₉	1	8	yes	direct product factor
60	C₂³	C₂×C₅×D₉	1	7	yes	—
61	C₂×C₄	—	9	28	no	—
62	C₂×C₃	C₂²×C₅×Dic₃	1	14	yes	—
63	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
64	C₅	C₂³×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²	C₂×C₅×Dic₉	1	28	yes	direct product factor
66	C₂²	C₂²×C₅×D₉	1	7	yes	—
67	C₄	—	9	8	no	—
68	C₃	C₂³×C₅×Dic₃	1	1	yes	characteristic
69	C₂	C₂²×C₅×Dic₉	1	14	yes	direct product factor
70	C₂	C₂³×C₅×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₅	D₉
commutator, hypocenter	C₉	C₂³×C₄×C₅
Frattini	C₂×C₃	C₂³×C₅×D₃
Fitting	C₂⁴×C₅×C₉	C₂
socle, prime radical	C₂⁴×C₃×C₅	D₃
cosocle	C₂×C₉	C₂⁴×C₅
LCS	G ▷ C₉
UCS	C₁ ◁ C₂⁴×C₅

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×Dic₉	C₂	direct (N × H)
4. C₂³×C₅×C₉	C₄	semidirect
6. C₂×C₅×Dic₉	C₂²	direct (N × H)
7. C₂³×Dic₉	C₅	direct (N × H)
10. C₂²×C₅×C₉	C₂×C₄	semidirect
12. C₅×Dic₉	C₂³	direct (N × H)
15. C₂²×Dic₉	C₂×C₅	direct (N × H)
20. C₂×C₅×C₉	C₂²×C₄	semidirect
24. C₂³×C₉	C₄×C₅	semidirect
26. C₂×Dic₉	C₂²×C₅	direct (N × H)
32. C₅×C₉	C₂³×C₄	semidirect
33. C₂³×C₅	Dic₉	direct (N × H)
36. C₂²×C₉	C₂×C₄×C₅	semidirect
38. Dic₉	C₂³×C₅	direct (N × H)
45. C₂²×C₅	C₂×Dic₉	direct (N × H)
48. C₂×C₉	C₂²×C₄×C₅	semidirect
56. C₂×C₅	C₂²×Dic₉	direct (N × H)
58. C₉	C₂³×C₄×C₅	semidirect
59. C₂³	C₅×Dic₉	direct (N × H)
64. C₅	C₂³×Dic₉	direct (N × H)
65. C₂²	C₂×C₅×Dic₉	direct (N × H)
69. C₂	C₂²×C₅×Dic₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₉	2
C₂²×C₅×Dic₉	2
C₂³×C₅×Dic₃	3
C₂³×Dic₉	5

Subgroups — C23×C5×Dic9 #13085342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×Dic₉ #13085342