Subgroups — C₅×D₉×C₃₆₁ #44570425

Order 32490.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₃₆₁	—	3	1	no	maximal
3	D₉×C₃₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₆₁	D₃	1	1	yes	characteristic
5	C₂×C₅×C₃₆₁	—	9	1	no	Hall
6	C₉×C₃₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₃×C₃₆₁	—	3	1	no	—
8	C₅×C₃₆₁	D₉	1	1	yes	characteristic, direct product factor, Hall
9	C₅×D₉×C₁₉	C₁₉	1	1	yes	maximal, characteristic
10	C₃×C₃₆₁	C₅×D₃	1	1	yes	characteristic
11	C₅×C₉×C₁₉	C₂×C₁₉	1	1	yes	characteristic
12	C₂×C₃₆₁	—	9	1	no	Hall
13	C₅×D₃×C₁₉	—	3	1	no	—
14	C₃₆₁	C₅×D₉	1	1	yes	characteristic, direct product factor, Sylow
15	D₉×C₁₉	C₅×C₁₉	1	1	yes	characteristic
16	C₃×C₅×C₁₉	D₃×C₁₉	1	1	yes	characteristic
17	C₂×C₅×C₁₉	—	9	1	no	—
18	C₉×C₁₉	C₂×C₅×C₁₉	1	1	yes	characteristic
19	D₃×C₁₉	—	3	1	no	—
20	C₅×C₁₉	D₉×C₁₉	1	1	yes	characteristic
21	C₅×D₉	C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₉	C₅×D₃×C₁₉	1	1	yes	characteristic
23	C₅×C₉	C₂×C₃₆₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₉	—	9	1	no	—
25	C₅×D₃	—	3	1	no	—
26	C₁₉	C₅×D₉×C₁₉	1	1	yes	characteristic
27	D₉	C₅×C₃₆₁	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₅	D₃×C₃₆₁	1	1	yes	characteristic
29	C₂×C₅	—	9	1	no	Hall
30	C₉	C₂×C₅×C₃₆₁	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	3	1	no	—
32	C₅	D₉×C₃₆₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₅×D₃×C₃₆₁	1	1	yes	characteristic
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₆₁	D₉
commutator, hypocenter	C₉	C₂×C₅×C₃₆₁
Frattini	C₃×C₁₉	C₅×D₃×C₁₉
Fitting	C₅×C₉×C₃₆₁	C₂
socle	C₃×C₅×C₁₉	D₃×C₁₉
prime radical	C₅×D₉×C₁₉	C₁₉
cosocle	C₉×C₁₉	C₂×C₅×C₁₉
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₃₆₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₃₆₁	C₂	semidirect
3. D₉×C₃₆₁	C₅	direct (N × H)
6. C₉×C₃₆₁	C₂×C₅	semidirect
8. C₅×C₃₆₁	D₉	direct (N × H)
14. C₃₆₁	C₅×D₉	direct (N × H)
21. C₅×D₉	C₃₆₁	direct (N × H)
23. C₅×C₉	C₂×C₃₆₁	semidirect
27. D₉	C₅×C₃₆₁	direct (N × H)
30. C₉	C₂×C₅×C₃₆₁	semidirect
32. C₅	D₉×C₃₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₉×C₃₆₁	2
C₅×D₃×C₃₆₁	3
D₉×C₃₆₁	5
C₅×D₉×C₁₉	19

Subgroups — C5×D9×C361 #44570425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₉×C₃₆₁ #44570425