Subgroups — C₅×Dic₄₅ #11744613

Order 900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₅	—	3	1	no	maximal
3	C₅²×C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×Dic₉	—	5	1	no	maximal
6	C₂×C₃×C₅²	D₃	1	1	yes	characteristic
7	C₅×Dic₅	—	9	1	no	Hall
8	C₂×C₅×C₉	—	2	2	no	—
9	C₂×C₅×C₉	D₅	1	1	yes	characteristic
10	C₂×C₅×C₉	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²	Dic₃	1	1	yes	characteristic
12	Dic₁₅	—	3	1	no	—
13	C₅×Dic₃	—	15	1	no	—
14	C₂×C₅²	D₉	1	1	yes	characteristic
15	C₅×C₉	—	2	2	no	—
16	C₅×C₉	Dic₅	1	1	yes	characteristic, complemented
17	C₅×C₉	C₄×C₅	1	1	yes	characteristic, complemented
18	Dic₉	—	5	1	no	Hall
19	C₂×C₃×C₅	—	2	2	no	—
20	C₂×C₃×C₅	C₅×D₃	1	1	yes	characteristic
21	C₂×C₃×C₅	D₁₅	1	1	yes	characteristic
22	C₅²	Dic₉	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₅	—	45	1	no	—
24	Dic₅	—	9	1	no	—
25	C₂×C₉	C₅×D₅	1	1	yes	characteristic
26	C₃×C₅	—	2	2	no	—
27	C₃×C₅	C₅×Dic₃	1	1	yes	characteristic
28	C₃×C₅	Dic₁₅	1	1	yes	characteristic
29	Dic₃	—	15	1	no	—
30	C₂×C₅	—	2	2	no	—
31	C₂×C₅	C₅×D₉	1	1	yes	characteristic
32	C₂×C₅	D₄₅	1	1	yes	characteristic
33	C₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	C₅×D₁₅	1	1	yes	characteristic
35	C₅	—	2	2	no	—
36	C₅	C₅×Dic₉	1	1	yes	characteristic, complemented
37	C₅	Dic₄₅	1	1	yes	characteristic, direct product factor
38	C₄	—	45	1	no	Sylow
39	C₃	C₅×Dic₁₅	1	1	yes	characteristic
40	C₂	C₅×D₄₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	D₄₅
commutator, hypocenter	C₅×C₉	C₄×C₅
Frattini	C₂×C₃	C₅×D₁₅
Fitting	C₂×C₅²×C₉	C₂
socle, prime radical	C₂×C₃×C₅²	D₃
cosocle	C₂×C₅×C₉	C₂×C₅
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉	C₄	semidirect
4. Dic₄₅	C₅	direct (N × H)
16. C₅×C₉	Dic₅	semidirect
17. C₅×C₉	C₄×C₅	semidirect
22. C₅²	Dic₉	semidirect
33. C₉	C₅×Dic₅	semidirect
36. C₅	C₅×Dic₉	semidirect
37. C₅	Dic₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²×C₉	2
C₅×Dic₁₅	3
Dic₄₅	5
C₅×Dic₉	5

Subgroups — C5×Dic45 #11744613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₄₅ #11744613