Subgroups — C₉×C₂²⋊Dic₅ #10623579

Order 720.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊Dic₅	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₅×C₉	—	2	2	no	—
5	C₂²×C₅×C₉	C₄	1	2	yes	complemented
6	C₂²×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₉×Dic₅	—	2	2	no	—
8	C₉×C₂²⋊C₄	—	5	1	no	maximal, Hall
9	C₂³×C₃×C₅	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×Dic₅	C₂×C₃	1	2	yes	—
11	C₂×C₅×C₉	—	2	2	no	—
12	C₂×C₅×C₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₅×C₉	D₄	1	2	yes	—
14	C₂²⋊Dic₅	C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂³×C₉	D₅	1	1	yes	characteristic
16	C₂×C₄×C₉	—	5	2	no	—
17	C₂²×C₃×C₅	—	2	2	no	—
18	C₂²×C₃×C₅	C₃×C₄	1	2	yes	—
19	C₂²×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
20	C₃×Dic₅	—	2	2	no	—
21	C₃×C₂²⋊C₄	—	5	1	no	—
22	C₅×C₉	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
23	C₂³×C₅	C₂×C₉	1	1	yes	characteristic
24	C₂×Dic₅	C₂×C₉	1	2	yes	complemented
25	C₂²×C₉	—	2	2	no	—
26	C₂²×C₉	Dic₅	1	2	yes	complemented
27	C₂²×C₉	C₂×D₅	1	1	yes	characteristic
28	C₄×C₉	—	10	2	no	—
29	C₂×C₃×C₅	—	2	2	no	—
30	C₂×C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅	C₃×D₄	1	2	yes	—
32	C₂³×C₃	C₃×D₅	1	1	yes	characteristic
33	C₂×C₃×C₄	—	5	2	no	—
34	C₂²×C₅	—	2	2	no	—
35	C₂²×C₅	C₄×C₉	1	2	yes	complemented
36	C₂²×C₅	C₂²×C₉	1	1	yes	characteristic
37	Dic₅	—	2	2	no	—
38	C₂×C₉	—	2	2	no	—
39	C₂×C₉	C₂×Dic₅	1	1	yes	characteristic
40	C₂×C₉	C₂²⋊D₅	1	2	yes	—
41	C₂²⋊C₄	—	5	1	no	Sylow
42	C₃×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₃	—	2	2	no	—
44	C₂²×C₃	C₃×Dic₅	1	2	yes	—
45	C₂²×C₃	C₂×C₃×D₅	1	1	yes	characteristic
46	C₃×C₄	—	10	2	no	—
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₂×C₄×C₉	1	1	yes	characteristic
49	C₂×C₅	D₄×C₉	1	2	yes	—
50	C₉	C₂²⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
51	C₂³	C₉×D₅	1	1	yes	characteristic
52	C₂×C₄	—	5	2	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	C₂×C₃×Dic₅	1	1	yes	characteristic
55	C₂×C₃	C₃×C₂²⋊D₅	1	2	yes	—
56	C₅	C₉×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	2	2	no	—
58	C₂²	C₉×Dic₅	1	2	yes	complemented
59	C₂²	C₂×C₉×D₅	1	1	yes	characteristic
60	C₄	—	10	2	no	—
61	C₃	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
62	C₂	—	2	2	no	—
63	C₂	C₂×C₉×Dic₅	1	1	yes	characteristic
64	C₂	C₉×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂×D₅
commutator	C₂×C₅	C₂×C₄×C₉
Frattini	C₂²×C₃	C₂×C₃×D₅
Fitting	C₂³×C₅×C₉	C₂
socle, cosocle	C₂²×C₃×C₅	C₂²×C₃
prime radical	C₂³×C₃×C₅	C₂×C₃
hypercenter	C₂³×C₉	D₅
hypocenter	C₅	C₉×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₉

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×Dic₅	C₂	semidirect
5. C₂²×C₅×C₉	C₄	semidirect
14. C₂²⋊Dic₅	C₉	direct (N × H)
22. C₅×C₉	C₂²⋊C₄	semidirect
24. C₂×Dic₅	C₂×C₉	semidirect
26. C₂²×C₉	Dic₅	semidirect
35. C₂²×C₅	C₄×C₉	semidirect
50. C₉	C₂²⋊Dic₅	direct (N × H)
56. C₅	C₉×C₂²⋊C₄	semidirect
58. C₂²	C₉×Dic₅	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×C₉	2
C₂×C₉×Dic₅	2
C₃×C₂²⋊Dic₅	3
C₉×C₂²⋊C₄	5

Subgroups — C9×C22⋊Dic5 #10623579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂²⋊Dic₅ #10623579