Subgroups — C₅×#611 #67094

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×C₅×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#67	—	3	1	no	maximal
5	C₂×C₅×C₉	—	2	1	no	—
6	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₅×D₉	—	2	1	no	—
8	#611	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅	D₃	1	1	yes	characteristic
10	C₂×C₅×D₃	—	3	1	no	—
11	C₅×Dic₃	—	3	1	no	—
12	C₅×C₉	D₄	1	1	yes	characteristic, complemented, Hall
13	C₅×D₄	—	9	1	no	Hall
14	C₂²×C₉	C₂×C₅	1	1	yes	characteristic, complemented
15	C₂×D₉	C₂×C₅	1	1	yes	characteristic, complemented
16	Dic₉	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅	—	2	1	no	—
18	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
19	C₅×D₃	—	6	1	no	—
20	#67	—	3	1	no	—
21	C₂²×C₅	—	9	1	no	—
22	C₂²×C₅	D₉	1	1	yes	characteristic, complemented
23	C₄×C₅	—	9	1	no	—
24	C₂×C₉	—	2	1	no	—
25	C₂×C₉	C₂²×C₅	1	1	yes	characteristic
26	D₉	—	2	1	no	—
27	C₃×C₅	#67	1	1	yes	characteristic
28	C₂²×C₃	C₅×D₃	1	1	yes	characteristic
29	C₂×D₃	—	3	1	no	—
30	Dic₃	—	3	1	no	—
31	C₂×C₅	—	2	1	no	—
32	C₂×C₅	—	18	1	no	—
33	C₂×C₅	C₂×D₉	1	1	yes	characteristic
34	C₉	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
35	D₄	—	9	1	no	Sylow
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	C₂×C₅×D₃	1	1	yes	characteristic
38	D₃	—	6	1	no	—
39	C₅	#611	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	9	1	no	—
41	C₂²	C₅×D₉	1	1	yes	characteristic, complemented
42	C₄	—	9	1	no	—
43	C₃	C₅×#67	1	1	yes	characteristic
44	C₂	—	2	1	no	—
45	C₂	—	18	1	no	—
46	C₂	C₂×C₅×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×D₉
commutator, cosocle	C₂×C₉	C₂²×C₅
Frattini	C₂×C₃	C₂×C₅×D₃
Fitting	C₂²×C₅×C₉	C₂
socle	C₂×C₃×C₅	C₂×D₃
hypercenter	C₂²×C₅	D₉
hypocenter	C₉	C₅×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₉	C₂	semidirect
2. C₂×C₅×D₉	C₂	semidirect
3. C₅×Dic₉	C₂	semidirect
8. #611	C₅	direct (N × H)
12. C₅×C₉	D₄	semidirect
14. C₂²×C₉	C₂×C₅	semidirect
15. C₂×D₉	C₂×C₅	semidirect
16. Dic₉	C₂×C₅	semidirect
22. C₂²×C₅	D₉	semidirect
34. C₉	C₅×D₄	semidirect
39. C₅	#611	direct (N × H)
41. C₂²	C₅×D₉	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×C₅×D₉	2
C₅×Dic₉	2
C₅×#67	3
#611	5

Subgroups — C5×#611 #67094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#611 #67094