Subgroups — C₅×Dic₉×C₁₈₁ #45656337

Order 32580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₈₁	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₃×C₁₈₁	—	3	1	no	maximal
3	C₅×C₉×C₁₈₁	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₉×C₁₈₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₈₁	D₃	1	1	yes	characteristic
6	C₄×C₅×C₁₈₁	—	9	1	no	Hall
7	C₂×C₉×C₁₈₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₅×C₁₈₁	Dic₃	1	1	yes	characteristic
9	Dic₃×C₁₈₁	—	3	1	no	—
10	C₂×C₅×C₁₈₁	D₉	1	1	yes	characteristic
11	C₉×C₁₈₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₁₈₁	C₅×D₃	1	1	yes	characteristic
13	C₅×C₁₈₁	Dic₉	1	1	yes	characteristic, direct product factor, Hall
14	C₄×C₁₈₁	—	9	1	no	Hall
15	C₃×C₁₈₁	C₅×Dic₃	1	1	yes	characteristic
16	C₂×C₁₈₁	C₅×D₉	1	1	yes	characteristic
17	C₁₈₁	C₅×Dic₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₅×Dic₉	C₁₈₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₉	C₂×C₁₈₁	1	1	yes	characteristic
20	C₅×Dic₃	—	3	1	no	—
21	C₅×C₉	C₄×C₁₈₁	1	1	yes	characteristic, complemented, Hall
22	Dic₉	C₅×C₁₈₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	D₃×C₁₈₁	1	1	yes	characteristic
24	C₄×C₅	—	9	1	no	Hall
25	C₂×C₉	C₂×C₅×C₁₈₁	1	1	yes	characteristic
26	C₃×C₅	Dic₃×C₁₈₁	1	1	yes	characteristic
27	Dic₃	—	3	1	no	—
28	C₂×C₅	D₉×C₁₈₁	1	1	yes	characteristic
29	C₉	C₄×C₅×C₁₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	C₅×D₃×C₁₈₁	1	1	yes	characteristic
31	C₅	Dic₉×C₁₈₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₄	—	9	1	no	Sylow
33	C₃	C₅×Dic₃×C₁₈₁	1	1	yes	characteristic
34	C₂	C₅×D₉×C₁₈₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₈₁	D₉
commutator, hypocenter	C₉	C₄×C₅×C₁₈₁
Frattini	C₂×C₃	C₅×D₃×C₁₈₁
Fitting	C₂×C₅×C₉×C₁₈₁	C₂
socle, prime radical	C₂×C₃×C₅×C₁₈₁	D₃
cosocle	C₂×C₉	C₂×C₅×C₁₈₁
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₅×C₁₈₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₈₁	C₄	semidirect
4. Dic₉×C₁₈₁	C₅	direct (N × H)
11. C₉×C₁₈₁	C₄×C₅	semidirect
13. C₅×C₁₈₁	Dic₉	direct (N × H)
17. C₁₈₁	C₅×Dic₉	direct (N × H)
18. C₅×Dic₉	C₁₈₁	direct (N × H)
21. C₅×C₉	C₄×C₁₈₁	semidirect
22. Dic₉	C₅×C₁₈₁	direct (N × H)
29. C₉	C₄×C₅×C₁₈₁	semidirect
31. C₅	Dic₉×C₁₈₁	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×C₅×C₉×C₁₈₁	2
C₅×Dic₃×C₁₈₁	3
Dic₉×C₁₈₁	5
C₅×Dic₉	181

Subgroups — C5×Dic9×C181 #45656337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₉×C₁₈₁ #45656337