Subgroups — C₉×D₆₀ #11761862

Order 1080.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₆₀	C₃	1	1	yes	maximal, characteristic
4	C₉×D₂₀	—	3	1	no	maximal
5	C₂×C₃×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₉×D₁₅	—	2	2	no	—
7	C₉×D₁₂	—	5	1	no	maximal, Hall
8	C₂×C₃×D₁₅	C₂×C₃	1	2	yes	—
9	C₃²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
10	C₂×C₉×D₅	—	3	2	no	—
11	C₄×C₅×C₉	—	2	1	no	—
12	C₄×C₅×C₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₉	D₄	1	1	yes	characteristic, complemented, Hall
14	D₆₀	C₉	1	1	yes	characteristic, direct product factor
15	C₃×D₂₀	—	3	1	no	—
16	C₂×D₃×C₉	—	5	2	no	—
17	C₃×C₄×C₉	D₅	1	1	yes	characteristic, complemented
18	C₂×C₃²×C₅	C₂²×C₃	1	1	yes	characteristic
19	C₃×D₁₅	—	2	2	no	—
20	C₂×C₅×C₉	—	2	1	no	—
21	C₂×C₅×C₉	C₂×D₃	1	1	yes	characteristic
22	C₉×D₅	—	6	2	no	—
23	C₃×D₁₂	—	5	1	no	—
24	D₄×C₉	—	15	1	no	—
25	C₂×D₁₅	C₂×C₉	1	2	yes	complemented
26	C₂×C₃×D₅	—	3	2	no	—
27	C₃×C₄×C₅	—	2	1	no	—
28	C₃×C₄×C₅	C₂×C₉	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅	C₃×D₃	1	1	yes	characteristic
30	C₂×C₃×C₉	C₂×D₅	1	1	yes	characteristic
31	D₃×C₉	—	10	2	no	—
32	C₃²×C₅	C₃×D₄	1	1	yes	characteristic
33	C₅×C₉	—	2	1	no	—
34	C₅×C₉	D₁₂	1	1	yes	characteristic, complemented
35	D₂₀	—	3	1	no	Hall
36	C₂×C₃×D₃	—	5	2	no	—
37	C₃²×C₄	C₃×D₅	1	1	yes	characteristic
38	C₂²×C₉	—	15	2	no	—
39	C₄×C₉	—	2	1	no	—
40	C₄×C₉	D₁₅	1	1	yes	characteristic, complemented
41	C₂×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅	C₂²×C₉	1	1	yes	characteristic
43	C₂×C₃×C₅	C₂×C₃×D₃	1	1	yes	characteristic
44	D₁₅	—	2	2	no	—
45	C₃×D₅	—	6	2	no	—
46	C₃×C₉	D₂₀	1	1	yes	characteristic, complemented, Sylow
47	C₃×D₄	—	15	1	no	—
48	D₁₂	—	5	1	no	—
49	C₂×D₅	—	3	2	no	—
50	C₄×C₅	D₃×C₉	1	1	yes	characteristic, complemented
51	C₂×C₃²	C₂×C₃×D₅	1	1	yes	characteristic
52	C₃×D₃	—	10	2	no	—
53	C₂×C₉	—	2	1	no	—
54	C₂×C₉	—	30	2	no	—
55	C₂×C₉	C₂×D₁₅	1	1	yes	characteristic
56	C₃×C₅	—	2	1	no	—
57	C₃×C₅	D₄×C₉	1	1	yes	characteristic, complemented
58	C₃×C₅	C₃×D₁₂	1	1	yes	characteristic
59	C₂²×C₃	—	15	2	no	—
60	C₂×D₃	—	5	2	no	—
61	C₃×C₄	—	2	1	no	—
62	C₃×C₄	C₉×D₅	1	1	yes	characteristic, complemented
63	C₃×C₄	C₃×D₁₅	1	1	yes	characteristic
64	C₂×C₅	C₂×D₃×C₉	1	1	yes	characteristic
65	D₅	—	6	2	no	—
66	C₃²	C₃×D₂₀	1	1	yes	characteristic
67	C₉	—	2	1	no	—
68	C₉	D₆₀	1	1	yes	characteristic, direct product factor
69	D₄	—	15	1	no	Sylow
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	30	2	no	—
72	C₂×C₃	C₂×C₉×D₅	1	1	yes	characteristic
73	C₂×C₃	C₂×C₃×D₁₅	1	1	yes	characteristic
74	D₃	—	10	2	no	—
75	C₅	C₉×D₁₂	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	15	2	no	—
77	C₄	C₉×D₁₅	1	1	yes	characteristic, complemented
78	C₃	—	2	1	no	—
79	C₃	C₉×D₂₀	1	1	yes	characteristic, complemented
80	C₃	C₃×D₆₀	1	1	yes	characteristic
81	C₂	—	30	2	no	—
82	C₂	C₂×C₉×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×D₁₅
commutator	C₂×C₃×C₅	C₂²×C₉
Frattini	C₂×C₃	C₂×C₃×D₁₅
Fitting	C₃×C₄×C₅×C₉	C₂
socle, cosocle	C₂×C₃²×C₅	C₂²×C₃
prime radical	C₃×D₆₀	C₃
hypercenter	C₄×C₉	D₁₅
hypocenter	C₃×C₅	D₄×C₉
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×D₁₅	C₂	semidirect
2. C₃×C₄×C₅×C₉	C₂	semidirect
12. C₄×C₅×C₉	D₃	semidirect
13. C₃×C₅×C₉	D₄	semidirect
14. D₆₀	C₉	direct (N × H)
17. C₃×C₄×C₉	D₅	semidirect
25. C₂×D₁₅	C₂×C₉	semidirect
28. C₃×C₄×C₅	C₂×C₉	semidirect
34. C₅×C₉	D₁₂	semidirect
40. C₄×C₉	D₁₅	semidirect
46. C₃×C₉	D₂₀	semidirect
50. C₄×C₅	D₃×C₉	semidirect
57. C₃×C₅	D₄×C₉	semidirect
62. C₃×C₄	C₉×D₅	semidirect
68. C₉	D₆₀	direct (N × H)
75. C₅	C₉×D₁₂	semidirect
77. C₄	C₉×D₁₅	semidirect
79. C₃	C₉×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×D₁₅	2
C₃×C₄×C₅×C₉	2
C₃×D₆₀	3
C₉×D₂₀	3
C₉×D₁₂	5

Subgroups — C9×D60 #11761862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₆₀ #11761862