Subgroups — C₉×C₂²⋊D₅ #67089

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₉	C₂×D₅
commutator	C₂×C₅	C₂²×C₉
Frattini	C₂×C₃	C₂×C₃×D₅
Fitting	C₂²×C₅×C₉	C₂
socle, cosocle	C₂×C₃×C₅	C₂²×C₃
prime radical	C₃×C₂²⋊D₅	C₃
hypercenter	C₂²×C₉	D₅
hypocenter	C₅	D₄×C₉
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₉	C₂	semidirect
2. C₂×C₉×D₅	C₂	semidirect
3. C₉×Dic₅	C₂	semidirect
12. C₅×C₉	D₄	semidirect
13. C₂²⋊D₅	C₉	direct (N × H)
15. C₂²×C₉	D₅	semidirect
21. C₂²×C₅	C₂×C₉	semidirect
22. C₂×D₅	C₂×C₉	semidirect
23. Dic₅	C₂×C₉	semidirect
34. C₉	C₂²⋊D₅	direct (N × H)
39. C₅	D₄×C₉	semidirect
41. C₂²	C₉×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₉	2
C₂×C₉×D₅	2
C₉×Dic₅	2
C₃×C₂²⋊D₅	3
D₄×C₉	5

Subgroups — C9×C22⋊D5 #67089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂²⋊D₅ #67089