Subgroups — Dic₉₀⋊C₃ #11761866

Order 1080.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊Dic₅	C₂	1	2	yes	maximal
3	C₃×Dic₃₀	—	3	1	no	maximal
4	Dic₉₀	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×3₋¹⁺²	C₂²	1	1	yes	characteristic
6	3₋¹⁺²⋊Q₈	—	5	1	no	maximal, Hall
7	C₃²×C₄×C₅	D₃	1	1	yes	characteristic
8	C₃×Dic₁₅	—	3	2	no	—
9	C₄×C₅×C₉	—	2	1	no	—
10	C₄×C₅×C₉	C₂×C₃	1	1	yes	characteristic
11	Dic₄₅	C₂×C₃	1	2	yes	—
12	C₅×3₋¹⁺²	Q₈	1	1	yes	characteristic, complemented, Hall
13	Dic₃₀	—	3	1	no	—
14	C₃×Dic₁₀	—	9	1	no	—
15	C₄×3₋¹⁺²	D₅	1	1	yes	characteristic
16	3₋¹⁺²⋊C₄	—	5	2	no	—
17	C₂×C₃²×C₅	C₂×D₃	1	1	yes	characteristic
18	C₂×C₅×C₉	—	2	1	no	—
19	C₂×C₅×C₉	C₂²×C₃	1	1	yes	characteristic
20	C₃×Dic₆	—	15	1	no	—
21	Dic₁₈	—	5	1	no	—
22	C₃×C₄×C₅	—	3	1	no	—
23	C₃×C₄×C₅	C₃×D₃	1	1	yes	characteristic
24	Dic₁₅	—	3	2	no	—
25	C₃×Dic₅	—	9	2	no	—
26	C₂×3₋¹⁺²	C₂×D₅	1	1	yes	characteristic
27	C₃²×C₅	Dic₆	1	1	yes	characteristic
28	C₅×C₉	—	2	1	no	—
29	C₅×C₉	C₃×Q₈	1	1	yes	characteristic, complemented
30	Dic₁₀	—	9	1	no	Hall
31	C₃²×C₄	D₁₅	1	1	yes	characteristic
32	C₃×Dic₃	—	15	2	no	—
33	C₄×C₉	—	2	1	no	—
34	C₄×C₉	C₃×D₅	1	1	yes	characteristic
35	Dic₉	—	5	2	no	—
36	C₂×C₃×C₅	—	3	1	no	—
37	C₂×C₃×C₅	C₂×C₃×D₃	1	1	yes	characteristic
38	3₋¹⁺²	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
39	C₃×Q₈	—	45	1	no	—
40	Dic₆	—	15	1	no	—
41	C₄×C₅	AGL(1,ℤ/9)	1	1	yes	characteristic
42	Dic₅	—	9	2	no	—
43	C₂×C₃²	C₂×D₁₅	1	1	yes	characteristic
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	C₂×C₃×D₅	1	1	yes	characteristic
46	C₃×C₅	—	3	1	no	—
47	C₃×C₅	C₃×Dic₆	1	1	yes	characteristic
48	C₃×C₄	—	3	1	no	—
49	C₃×C₄	—	45	2	no	—
50	C₃×C₄	C₃×D₁₅	1	1	yes	characteristic
51	Dic₃	—	15	2	no	—
52	C₂×C₅	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
53	C₃²	Dic₃₀	1	1	yes	characteristic
54	C₉	—	2	1	no	—
55	C₉	C₃×Dic₁₀	1	1	yes	characteristic, complemented
56	Q₈	—	45	1	no	Sylow
57	C₂×C₃	—	3	1	no	—
58	C₂×C₃	C₂×C₃×D₁₅	1	1	yes	characteristic
59	C₅	3₋¹⁺²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
60	C₄	—	45	2	no	—
61	C₄	C₅⋊AGL(1,ℤ/9)	1	1	yes	characteristic
62	C₃	—	3	1	no	—
63	C₃	C₃×Dic₃₀	1	1	yes	characteristic
64	C₂	C₂×C₅⋊AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₅⋊AGL(1,ℤ/9)
commutator, cosocle	C₂×C₅×C₉	C₂²×C₃
Frattini	C₂×C₃	C₂×C₃×D₁₅
Fitting	C₄×C₅×3₋¹⁺²	C₂
socle	C₂×C₃×C₅	C₂×C₃×D₃
prime radical	C₂×C₃²×C₅	C₂×D₃
hypercenter	C₄	C₅⋊AGL(1,ℤ/9)
hypocenter	C₅×C₉	C₃×Q₈
LCS	G ▷ C₂×C₅×C₉ ▷ C₅×C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
4. Dic₉₀	C₃	semidirect
12. C₅×3₋¹⁺²	Q₈	semidirect
29. C₅×C₉	C₃×Q₈	semidirect
38. 3₋¹⁺²	Dic₁₀	semidirect
55. C₉	C₃×Dic₁₀	semidirect
59. C₅	3₋¹⁺²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×3₋¹⁺²	2
3₋¹⁺²⋊Dic₅	2
C₃×Dic₃₀	3
Dic₉₀	3
3₋¹⁺²⋊Q₈	5

Subgroups — Dic90⋊C3 #11761866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉₀⋊C₃ #11761866