Subgroups — D₅×C₄²⋊C₉ #13083945

Order 1440.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄²×D₅	C₃	1	1	yes	maximal, characteristic
3	D₅×C₂²⋊C₉	—	4	1	no	maximal
4	C₂×C₄²⋊C₉	—	5	1	no	maximal, Hall
5	C₂×C₃×C₄×D₅	—	3	1	no	—
6	C₃×C₄²×C₅	C₂×C₃	1	1	yes	characteristic
7	C₃×C₄×Dic₅	—	3	1	no	—
8	C₅×C₂²⋊C₉	—	4	1	no	—
9	C₄²×D₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₄²⋊C₉	D₅	1	1	yes	characteristic, direct product factor
11	C₂²×C₃×D₅	A₄	1	1	yes	characteristic
12	C₂×C₃×C₄×C₅	—	3	1	no	—
13	C₂×C₃×Dic₅	—	3	1	no	—
14	C₃×C₄×D₅	—	3	2	no	—
15	C₃×C₄×D₅	—	3	2	no	—
16	C₂×C₃×C₄²	—	5	1	no	—
17	C₉×D₅	—	16	1	no	—
18	C₂×C₄×D₅	—	3	1	no	—
19	C₄²×C₅	C₂×C₉	1	1	yes	characteristic, complemented
20	C₄×Dic₅	—	3	1	no	—
21	C₂×C₂²⋊C₉	—	20	1	no	—
22	C₂²×C₃×C₅	C₂×A₄	1	1	yes	characteristic
23	C₂×C₃×D₅	—	3	1	no	—
24	C₂×C₃×D₅	—	3	1	no	—
25	C₃×C₄×C₅	—	3	2	no	—
26	C₃×Dic₅	—	3	2	no	—
27	C₂²×C₃×C₄	—	15	1	no	—
28	C₃×C₄²	—	15	1	no	—
29	C₃×C₄²	C₃×D₅	1	1	yes	characteristic
30	C₅×C₉	—	16	1	no	Hall
31	C₂²×D₅	C₂²⋊C₉	1	1	yes	characteristic
32	C₂×C₄×C₅	—	3	1	no	—
33	C₂×Dic₅	—	3	1	no	—
34	C₄×D₅	—	3	2	no	—
35	C₄×D₅	—	3	2	no	—
36	C₂²⋊C₉	—	4	1	no	—
37	C₂×C₄²	—	5	1	no	Sylow
38	C₂×C₃×C₅	—	3	1	no	—
39	C₃×D₅	—	3	1	no	—
40	C₃×D₅	C₄²⋊C₃	1	1	yes	characteristic
41	C₂³×C₃	—	5	1	no	—
42	C₂×C₃×C₄	—	3	1	no	—
43	C₂×C₃×C₄	—	15	2	no	—
44	C₂×C₃×C₄	—	15	2	no	—
45	C₂×C₃×C₄	—	15	1	no	—
46	C₂²×C₅	C₂×C₂²⋊C₉	1	1	yes	characteristic
47	C₂×D₅	—	3	1	no	—
48	C₂×D₅	—	3	1	no	—
49	C₄×C₅	—	3	2	no	—
50	Dic₅	—	3	2	no	—
51	C₂×C₉	—	80	1	no	—
52	C₂²×C₄	—	15	1	no	—
53	C₄²	—	15	1	no	—
54	C₄²	C₉×D₅	1	1	yes	characteristic, complemented
55	C₃×C₅	C₂×C₄²⋊C₃	1	1	yes	characteristic
56	C₂²×C₃	—	15	1	no	—
57	C₂²×C₃	—	15	1	no	—
58	C₂²×C₃	D₅×A₄	1	1	yes	characteristic
59	C₃×C₄	—	3	2	no	—
60	C₃×C₄	—	15	2	no	—
61	C₂×C₅	—	3	1	no	—
62	D₅	—	3	1	no	—
63	D₅	C₄²⋊C₉	1	1	yes	characteristic, direct product factor
64	C₉	—	16	1	no	Sylow
65	C₂³	—	5	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	15	2	no	—
68	C₂×C₄	—	15	2	no	—
69	C₂×C₄	—	15	1	no	—
70	C₂×C₃	—	3	1	no	—
71	C₂×C₃	—	5	1	no	—
72	C₂×C₃	—	15	1	no	—
73	C₅	C₂×C₄²⋊C₉	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	15	1	no	—
75	C₂²	—	15	1	no	—
76	C₂²	D₅×C₂²⋊C₉	1	1	yes	characteristic
77	C₄	—	3	2	no	—
78	C₄	—	15	2	no	—
79	C₃	D₅×C₄²⋊C₃	1	1	yes	characteristic
80	C₂	—	3	1	no	—
81	C₂	—	5	1	no	—
82	C₂	—	15	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×C₄²⋊C₃
commutator, hypocenter	C₄²×C₅	C₂×C₉
Frattini	C₂²×C₃	D₅×A₄
Fitting, cosocle	C₃×C₄²×C₅	C₂×C₃
socle	C₂²×C₃×C₅	C₂×A₄
prime radical	C₂²×C₃×D₅	A₄
LCS	G ▷ C₄²×C₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₄²⋊C₉	C₂	semidirect
9. C₄²×D₅	C₉	semidirect
10. C₄²⋊C₉	D₅	direct (N × H)
19. C₄²×C₅	C₂×C₉	semidirect
54. C₄²	C₉×D₅	semidirect
63. D₅	C₄²⋊C₉	direct (N × H)
73. C₅	C₂×C₄²⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₄²⋊C₉	2
C₃×C₄²×D₅	3
D₅×C₂²⋊C₉	4
C₂×C₄²⋊C₉	5

Subgroups — D5×C42⋊C9 #13083945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₄²⋊C₉ #13083945