Subgroups — C₂²×Dic₉₀ #13085344

Order 1440.

468 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₅	C₂	1	2	yes	maximal
3	C₂×Dic₉₀	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₃₀	—	3	1	no	maximal
5	C₂³×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₅×C₉	C₂²	1	6	yes	—
7	C₂×Dic₄₅	C₂²	1	12	yes	—
8	Dic₉₀	C₂²	1	16	yes	direct product factor
9	C₂²×Dic₁₈	—	5	1	no	maximal, Hall
10	C₂²×C₃×C₄×C₅	D₃	1	1	yes	characteristic
11	C₂²×Dic₁₅	—	3	2	no	—
12	C₂×Dic₃₀	—	3	12	no	—
13	C₂²×C₅×C₉	Q₈	1	4	yes	complemented
14	C₂²×C₅×C₉	C₂³	1	3	yes	—
15	C₄×C₅×C₉	C₂³	1	4	yes	—
16	Dic₄₅	C₂³	1	8	yes	—
17	C₂²×Dic₁₀	—	9	1	no	Hall
18	C₂²×C₄×C₉	D₅	1	1	yes	characteristic
19	C₂²×Dic₉	—	5	2	no	—
20	C₂×Dic₁₈	—	5	12	no	—
21	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃×C₄×C₅	C₂×D₃	1	6	yes	—
23	C₂×Dic₁₅	—	3	12	no	—
24	Dic₃₀	—	3	16	no	—
25	C₂²×Dic₆	—	15	1	no	—
26	C₂×C₅×C₉	C₂×Q₈	1	6	yes	complemented
27	C₂×C₅×C₉	C₂⁴	1	1	yes	characteristic
28	C₂²×C₄×C₅	D₉	1	1	yes	characteristic
29	C₂²×Dic₅	—	9	2	no	—
30	C₂×Dic₁₀	—	9	12	no	—
31	C₂³×C₉	C₂×D₅	1	1	yes	characteristic
32	C₂×C₄×C₉	C₂×D₅	1	6	yes	—
33	C₂×Dic₉	—	5	12	no	—
34	Dic₁₈	—	5	16	no	—
35	C₂²×C₃×C₅	Dic₆	1	4	yes	—
36	C₂²×C₃×C₅	C₂²×D₃	1	3	yes	—
37	C₃×C₄×C₅	C₂²×D₃	1	4	yes	—
38	Dic₁₅	—	3	8	no	—
39	C₂²×C₃×C₄	D₁₅	1	1	yes	characteristic
40	C₂²×Dic₃	—	15	2	no	—
41	C₂×Dic₆	—	15	12	no	—
42	C₅×C₉	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
43	C₂³×C₅	C₂×D₉	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×D₉	1	6	yes	—
45	C₂×Dic₅	—	9	12	no	—
46	Dic₁₀	—	9	16	no	—
47	C₂²×C₉	Dic₁₀	1	4	yes	complemented
48	C₂²×C₉	C₂²×D₅	1	3	yes	—
49	C₄×C₉	C₂²×D₅	1	4	yes	—
50	Dic₉	—	5	8	no	—
51	C₂²×Q₈	—	45	1	no	Sylow
52	C₂×C₃×C₅	C₂×Dic₆	1	6	yes	—
53	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
54	C₂³×C₃	C₂×D₁₅	1	1	yes	characteristic
55	C₂×C₃×C₄	C₂×D₁₅	1	6	yes	—
56	C₂×Dic₃	—	15	12	no	—
57	Dic₆	—	15	16	no	—
58	C₂²×C₅	Dic₁₈	1	4	yes	complemented
59	C₂²×C₅	C₂²×D₉	1	3	yes	—
60	C₄×C₅	C₂²×D₉	1	4	yes	—
61	Dic₅	—	9	8	no	—
62	C₂×C₉	C₂×Dic₁₀	1	6	yes	complemented
63	C₂×C₉	C₂³×D₅	1	1	yes	characteristic
64	C₂×Q₈	—	45	12	no	—
65	C₂²×C₄	—	45	2	no	—
66	C₂²×C₄	D₄₅	1	1	yes	characteristic
67	C₃×C₅	C₂²×Dic₆	1	1	yes	characteristic
68	C₂²×C₃	Dic₃₀	1	4	yes	—
69	C₂²×C₃	C₂²×D₁₅	1	3	yes	—
70	C₃×C₄	C₂²×D₁₅	1	4	yes	—
71	Dic₃	—	15	8	no	—
72	C₂×C₅	C₂×Dic₁₈	1	6	yes	complemented
73	C₂×C₅	C₂³×D₉	1	1	yes	characteristic
74	C₉	C₂²×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
75	C₂³	C₂×D₄₅	1	1	yes	characteristic
76	Q₈	—	45	16	no	—
77	C₂×C₄	—	45	12	no	—
78	C₂×C₄	C₂×D₄₅	1	6	yes	—
79	C₂×C₃	C₂×Dic₃₀	1	6	yes	—
80	C₂×C₃	C₂³×D₁₅	1	1	yes	characteristic
81	C₅	C₂²×Dic₁₈	1	1	yes	characteristic, complemented, Sylow
82	C₂²	Dic₉₀	1	4	yes	direct product factor
83	C₂²	C₂²×D₄₅	1	3	yes	—
84	C₄	—	45	8	no	—
85	C₄	C₂²×D₄₅	1	4	yes	—
86	C₃	C₂²×Dic₃₀	1	1	yes	characteristic
87	C₂	C₂×Dic₉₀	1	6	yes	direct product factor
88	C₂	C₂³×D₄₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄₅
commutator, cosocle	C₂×C₅×C₉	C₂⁴
Frattini	C₂×C₃	C₂³×D₁₅
Fitting	C₂²×C₄×C₅×C₉	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₃
hypercenter	C₂²×C₄	D₄₅
hypocenter	C₅×C₉	C₂²×Q₈
LCS	G ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₉₀	C₂	direct (N × H)
8. Dic₉₀	C₂²	direct (N × H)
13. C₂²×C₅×C₉	Q₈	semidirect
26. C₂×C₅×C₉	C₂×Q₈	semidirect
42. C₅×C₉	C₂²×Q₈	semidirect
47. C₂²×C₉	Dic₁₀	semidirect
58. C₂²×C₅	Dic₁₈	semidirect
62. C₂×C₉	C₂×Dic₁₀	semidirect
72. C₂×C₅	C₂×Dic₁₈	semidirect
74. C₉	C₂²×Dic₁₀	semidirect
81. C₅	C₂²×Dic₁₈	semidirect
82. C₂²	Dic₉₀	direct (N × H)
87. C₂	C₂×Dic₉₀	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×C₄×C₅×C₉	2
C₂²×Dic₄₅	2
C₂×Dic₉₀	2
C₂²×Dic₃₀	3
C₂²×Dic₁₈	5

Subgroups — C22×Dic90 #13085344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₉₀ #13085344