Subgroups — C₂×D₉×C₁₈₁⋊C₅ #45656366

Order 32580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉×C₁₈₁⋊C₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₈₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₈₁⋊C₅	—	3	1	no	maximal
4	C₉×C₁₈₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉×C₁₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	D₃×C₁₈₁⋊C₅	—	3	2	no	—
7	C₂×C₃×C₁₈₁⋊C₅	D₃	1	1	yes	characteristic
8	C₂²×C₁₈₁⋊C₅	—	9	1	no	Hall
9	D₉×C₁₈₁	C₂×C₅	1	2	yes	complemented
10	C₂×C₉×C₁₈₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₁₈₁⋊C₅	C₂×D₃	1	1	yes	characteristic
12	C₂×D₃×C₁₈₁	—	3	1	no	—
13	C₂×C₁₈₁⋊C₅	—	9	2	no	—
14	C₂×C₁₈₁⋊C₅	D₉	1	1	yes	characteristic, direct product factor
15	C₉×C₁₈₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₈₁	C₅×D₃	1	1	yes	characteristic
17	D₃×C₁₈₁	—	3	2	no	—
18	C₁₈₁⋊C₅	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₁₈₁	—	9	1	no	Hall
20	C₃×C₁₈₁	C₂×C₅×D₃	1	1	yes	characteristic
21	C₂×C₁₈₁	—	9	2	no	—
22	C₂×C₁₈₁	C₅×D₉	1	1	yes	characteristic, complemented
23	C₁₈₁	C₂×C₅×D₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₅×D₉	—	181	1	no	maximal, Hall
25	C₂×C₅×C₉	—	181	1	no	—
26	C₅×D₉	—	181	2	no	—
27	C₂×C₅×D₃	—	543	1	no	—
28	C₅×C₉	—	181	1	no	Hall
29	C₂×D₉	C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₅	—	181	1	no	—
31	C₅×D₃	—	543	2	no	—
32	C₂²×C₅	—	1629	1	no	Hall
33	C₂×C₉	C₂×C₁₈₁⋊C₅	1	1	yes	characteristic, complemented
34	D₉	C₂×C₁₈₁⋊C₅	1	2	yes	direct product factor
35	C₃×C₅	—	181	1	no	—
36	C₂×D₃	—	3	1	no	—
37	C₂×C₅	—	1629	2	no	—
38	C₂×C₅	—	181	1	no	—
39	C₉	C₂²×C₁₈₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	D₃×C₁₈₁⋊C₅	1	1	yes	characteristic
41	D₃	—	3	2	no	—
42	C₅	—	181	1	no	Sylow
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₈₁⋊C₅	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	D₉×C₁₈₁⋊C₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₉×C₁₈₁⋊C₅
commutator, cosocle, hypocenter	C₉×C₁₈₁	C₂²×C₅
Frattini	C₃	C₂×D₃×C₁₈₁⋊C₅
Fitting	C₂×C₉×C₁₈₁	C₂×C₅
socle	C₂×C₃×C₁₈₁	C₅×D₃
LCS	G ▷ C₉×C₁₈₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₉×C₁₈₁⋊C₅	C₂	direct (N × H)
2. C₂×C₉×C₁₈₁⋊C₅	C₂	semidirect
4. C₉×C₁₈₁⋊C₅	C₂²	semidirect
5. C₂×D₉×C₁₈₁	C₅	semidirect
9. D₉×C₁₈₁	C₂×C₅	semidirect
10. C₂×C₉×C₁₈₁	C₂×C₅	semidirect
14. C₂×C₁₈₁⋊C₅	D₉	direct (N × H)
15. C₉×C₁₈₁	C₂²×C₅	semidirect
18. C₁₈₁⋊C₅	C₂×D₉	direct (N × H)
22. C₂×C₁₈₁	C₅×D₉	semidirect
23. C₁₈₁	C₂×C₅×D₉	semidirect
29. C₂×D₉	C₁₈₁⋊C₅	direct (N × H)
33. C₂×C₉	C₂×C₁₈₁⋊C₅	semidirect
34. D₉	C₂×C₁₈₁⋊C₅	direct (N × H)
39. C₉	C₂²×C₁₈₁⋊C₅	semidirect
46. C₂	D₉×C₁₈₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
D₉×C₁₈₁⋊C₅	2
C₂×C₉×C₁₈₁⋊C₅	2
C₂×D₃×C₁₈₁⋊C₅	3
C₂×D₉×C₁₈₁	5
C₂×C₅×D₉	181

Subgroups — C2×D9×C181⋊C5 #45656366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₉×C₁₈₁⋊C₅ #45656366