Finite Group Databasebeta

← C9⋊(C19⋊(Dic11⋊C5)) #49178317

Subgroups — C9⋊(C19⋊(Dic11⋊C5)) #49178317

Order 37620.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C19×C11⋊C5C211yesmaximal, characteristic
2C3⋊(C19⋊(Dic11⋊C5))—31nomaximal
3C9×C19×C11⋊C5C411yescharacteristic, complemented, Hall
4Dic1881C511yesmaximal, characteristic, complemented, Hall
5C2×C3×C19×C11⋊C5D311yescharacteristic
6C19⋊(Dic11⋊C5)—91noHall
7C2×C9×C11×C19C2×C511yescharacteristic
8C5×Dic171—111nomaximal, Hall
9C3×C19×C11⋊C5Dic311yescharacteristic
10Dic627—31no—
11C2×C19×C11⋊C5D911yescharacteristic
12C9⋊(Dic11⋊C5)—191nomaximal, Hall
13C9×C11×C19C4×C511yescharacteristic, complemented, Hall
14C2×C5×C9×C19—111no—
15C2×C3×C11×C19C5×D311yescharacteristic
16C5×Dic57—331no—
17C19×C11⋊C5Dic911yescharacteristic, complemented, Hall
18C2×C9×C11⋊C5D1911yescharacteristic
19C5×C9×C19—111noHall
20Dic209—91noHall
21Dic171—111noHall
22C3⋊(Dic11⋊C5)—571no—
23C3×C11×C19C5×Dic311yescharacteristic
24C2×C3×C5×C19—111no—
25C9×C11⋊C5Dic1911yescharacteristic, complemented, Hall
26C2×C11×C19C5×D911yescharacteristic
27Dic99—191noHall
28C5×Dic19—991noHall
29C2×C9×C19AGL(1,𝔽11)11yescharacteristic
30C2×C3×C11⋊C5D5711yescharacteristic
31C3×C5×C19—111no—
32Dic57—331no—
33Dic11⋊C5—1711noHall
34C11×C19C5×Dic911yescharacteristic, complemented, Hall
35C2×C9×C11C5×D1911yescharacteristic
36C2×C5×C19—111no—
37C5×Dic9—2091noHall
38C9×C19Dic11⋊C511yescharacteristic, complemented, Hall
39C3×C11⋊C5Dic5711yescharacteristic
40Dic33—571no—
41C2×C3×C19C3⋊AGL(1,𝔽11)11yescharacteristic
42C2×C11⋊C5D17111yescharacteristic
43C9×C11C5×Dic1911yescharacteristic, complemented, Hall
44C5×C19—111noHall
45C2×C5×C9—111no—
46Dic19—991noHall
47C2×C3×C11C5×D5711yescharacteristic
48C5×Dic3—6271no—
49C3×C19C3⋊(Dic11⋊C5)11yescharacteristic
50C11⋊C5Dic17111yescharacteristic, complemented, Hall
51C5×C9—111noHall
52Dic11—1711noHall
53C2×C19C9⋊AGL(1,𝔽11)11yescharacteristic
54Dic9—2091noHall
55C3×C11C5×Dic5711yescharacteristic
56C2×C3×C5—111no—
57C2×C11C5×D17111yescharacteristic
58C4×C5—18811noHall
59C19C9⋊(Dic11⋊C5)11yescharacteristic, complemented, Sylow
60C2×C9C19⋊AGL(1,𝔽11)11yescharacteristic
61C3×C5—111no—
62Dic3—6271no—
63C11C5×Dic17111yescharacteristic, complemented, Sylow
64C2×C5—111no—
65C9C19⋊(Dic11⋊C5)11yescharacteristic, complemented, Sylow
66C2×C3C3⋊(C19⋊AGL(1,𝔽11))11yescharacteristic
67C5—111noSylow
68C4—18811noSylow
69C3C3⋊(C19⋊(Dic11⋊C5))11yescharacteristic
70C2C9⋊(C19⋊AGL(1,𝔽11))11yescharacteristic
subgroupG/H
center, hypercenterC2C9⋊(C19⋊AGL(1,𝔽11))
commutator, hypocenterC9×C11×C19C4×C5
FrattiniC2×C3C3⋊(C19⋊AGL(1,𝔽11))
Fitting, cosocleC2×C9×C11×C19C2×C5
socleC2×C3×C11×C19C5×D3
prime radicalC2×C3×C19×C11⋊C5D3
LCSG ▷ C9×C11×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C9×C19×C11⋊C5C4semidirect
4. Dic1881C5semidirect
13. C9×C11×C19C4×C5semidirect
17. C19×C11⋊C5Dic9semidirect
25. C9×C11⋊C5Dic19semidirect
34. C11×C19C5×Dic9semidirect
38. C9×C19Dic11⋊C5semidirect
43. C9×C11C5×Dic19semidirect
50. C11⋊C5Dic171semidirect
59. C19C9⋊(Dic11⋊C5)semidirect
63. C11C5×Dic171semidirect
65. C9C19⋊(Dic11⋊C5)semidirect

Maximal subgroups

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

subgroupindex
C2×C9×C19×C11⋊C52
C3⋊(C19⋊(Dic11⋊C5))3
Dic18815
C5×Dic17111
C9⋊(Dic11⋊C5)19