Subgroups — Dic₅×C₉⋊C₈ #13083708

Order 1440.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊#168	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₉×Dic₅	C₂	1	1	yes	maximal, characteristic
4	Dic₅×C₃⋊C₈	—	3	1	no	maximal
5	C₂×C₄×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₉×Dic₅	C₄	1	2	yes	—
7	C₉⋊#168	C₄	1	2	yes	complemented
8	C₅×C₉⋊C₈	C₄	1	2	yes	complemented
9	C₄×C₉⋊C₈	—	5	1	no	maximal, Hall
10	C₂×C₃⋊#168	—	3	1	no	—
11	C₂×C₅×C₃⋊C₈	—	3	1	no	—
12	C₃×C₄×Dic₅	D₃	1	1	yes	characteristic
13	C₂²×C₅×C₉	C₂×C₄	1	1	yes	characteristic
14	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×Dic₅	C₈	1	4	yes	complemented
17	C₈×Dic₅	—	9	1	no	Hall
18	C₄²×C₉	—	5	1	no	—
19	C₂×C₉⋊C₈	—	5	1	no	—
20	C₂×C₉⋊C₈	D₅	1	1	yes	characteristic
21	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃×Dic₅	Dic₃	1	2	yes	—
23	C₃⋊#168	—	3	2	no	—
24	C₅×C₃⋊C₈	—	3	2	no	—
25	C₄×C₃⋊C₈	—	15	1	no	—
26	C₂×C₅×C₉	C₄²	1	1	yes	characteristic
27	C₂×C₅×C₉	C₂×C₈	1	2	yes	—
28	C₂×C₅×C₈	—	9	1	no	—
29	C₄×Dic₅	D₉	1	1	yes	characteristic
30	C₂×#168	—	9	1	no	—
31	C₂×C₄×C₉	—	5	2	no	—
32	C₂×C₄×C₉	C₂×D₅	1	1	yes	characteristic
33	C₉⋊C₈	—	5	2	no	—
34	C₉⋊C₈	Dic₅	1	2	yes	direct product factor
35	C₂²×C₃×C₅	C₂×Dic₃	1	1	yes	characteristic
36	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
37	C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
38	C₃×Dic₅	C₃⋊C₈	1	4	yes	—
39	C₃×C₄²	—	5	1	no	—
40	C₂×C₃⋊C₈	—	3	1	no	—
41	C₂×C₃⋊C₈	—	15	1	no	—
42	C₅×C₉	C₄×C₈	1	1	yes	characteristic, complemented, Hall
43	C₂×C₄×C₅	C₂×D₉	1	1	yes	characteristic
44	C₂×Dic₅	Dic₉	1	2	yes	—
45	C₅×C₈	—	9	2	no	—
46	#168	—	9	2	no	—
47	C₂²×C₉	C₄×D₅	1	1	yes	characteristic
48	C₄×C₉	—	5	4	no	—
49	C₄×C₉	C₄×D₅	1	1	yes	characteristic
50	C₄×C₉	C₂×Dic₅	1	1	yes	characteristic
51	C₄×C₈	—	45	1	no	Sylow
52	C₂×C₃×C₅	C₂×C₃⋊C₈	1	2	yes	—
53	C₂×C₃×C₅	C₄×Dic₃	1	1	yes	characteristic
54	C₂×C₃×C₄	—	5	2	no	—
55	C₂×C₃×C₄	D₃×D₅	1	1	yes	characteristic
56	C₃⋊C₈	—	3	2	no	—
57	C₃⋊C₈	—	15	2	no	—
58	C₂²×C₅	C₂×Dic₉	1	1	yes	characteristic
59	C₄×C₅	C₄×D₉	1	1	yes	characteristic
60	C₄×C₅	C₄×D₉	1	1	yes	characteristic
61	Dic₅	C₉⋊C₈	1	4	yes	direct product factor
62	C₂×C₉	C₈×D₅	1	2	yes	—
63	C₂×C₉	C₄×Dic₅	1	1	yes	characteristic
64	C₂×C₈	—	9	1	no	—
65	C₂×C₈	—	45	1	no	—
66	C₄²	—	5	1	no	—
67	C₃×C₅	C₄×C₃⋊C₈	1	1	yes	characteristic
68	C₂²×C₃	D₅×Dic₃	1	1	yes	characteristic
69	C₃×C₄	—	5	4	no	—
70	C₃×C₄	D₃×Dic₅	1	1	yes	characteristic
71	C₃×C₄	#1200	1	1	yes	characteristic
72	C₂×C₅	C₂×C₉⋊C₈	1	2	yes	—
73	C₂×C₅	C₄×Dic₉	1	1	yes	characteristic
74	C₉	C₈×Dic₅	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₄	—	5	2	no	—
76	C₂×C₄	D₅×D₉	1	1	yes	characteristic
77	C₈	—	9	2	no	—
78	C₈	—	45	2	no	—
79	C₂×C₃	D₅×C₃⋊C₈	1	2	yes	—
80	C₂×C₃	Dic₃×Dic₅	1	1	yes	characteristic
81	C₅	C₄×C₉⋊C₈	1	1	yes	characteristic, complemented, Sylow
82	C₂²	D₅×Dic₉	1	1	yes	characteristic
83	C₄	—	5	4	no	—
84	C₄	D₉×Dic₅	1	1	yes	characteristic
85	C₄	#67079	1	1	yes	characteristic
86	C₃	Dic₅×C₃⋊C₈	1	1	yes	characteristic
87	C₂	D₅×C₉⋊C₈	1	2	yes	—
88	C₂	Dic₅×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×D₉
commutator, hypocenter	C₅×C₉	C₄×C₈
Frattini	C₂×C₃×C₄	D₃×D₅
Fitting, cosocle	C₂×C₄×C₅×C₉	C₂²
socle, prime radical	C₂²×C₃×C₅	C₂×Dic₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
7. C₉⋊#168	C₄	semidirect
8. C₅×C₉⋊C₈	C₄	semidirect
16. C₉×Dic₅	C₈	semidirect
34. C₉⋊C₈	Dic₅	direct (N × H)
42. C₅×C₉	C₄×C₈	semidirect
61. Dic₅	C₉⋊C₈	direct (N × H)
74. C₉	C₈×Dic₅	semidirect
81. C₅	C₄×C₉⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉⋊#168	2
C₂×C₅×C₉⋊C₈	2
C₄×C₉×Dic₅	2
Dic₅×C₃⋊C₈	3
C₄×C₉⋊C₈	5

Subgroups — Dic5×C9⋊C8 #13083708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×C₉⋊C₈ #13083708