Finite Group Databasebeta

← (C11⋊C5)⋊(D31⋊C9) #44501725

Subgroups — (C11⋊C5)⋊(D31⋊C9) #44501725

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11⋊C5×C31⋊C9C211yesmaximal, characteristic, complemented, Hall
2C3×(C11⋊C5)⋊D31C311yesmaximal, characteristic
3C11⋊(D31⋊C9)C511yesmaximal, characteristic, complemented, Hall
4C3×C31×C11⋊C5C2×C311yescharacteristic
5(C11⋊C5)⋊D31C911yescharacteristic, complemented, Hall
6C11×C31⋊C9C2×C511yescharacteristic, complemented, Hall
7C5×D31⋊C9—111nomaximal, Hall
8C3×D341C3×C511yescharacteristic
9C31×C11⋊C5C2×C911yescharacteristic, complemented, Hall
10C5×C31⋊C9—111noHall
11C3×C11×C31C2×C3×C511yescharacteristic
12C9×AGL(1,𝔽11)—311nomaximal, Hall
13C3×C5×D31—111no—
14D341C5×C911yescharacteristic, complemented, Hall
15D31⋊C9—111noHall
16C9×C11⋊C5—311noHall
17C3×C5×C31—111no—
18C11×C31C2×C5×C911yescharacteristic, complemented, Hall
19C3×AGL(1,𝔽11)—311no—
20C5×D31—111noHall
21C31⋊C9AGL(1,𝔽11)11yescharacteristic, complemented, Hall
22C9×D11—311noHall
23C3×D31—111no—
24C3×C11⋊C5D31⋊C311yescharacteristic
25C5×C31—111noHall
26AGL(1,𝔽11)—311noHall
27C9×C11—311noHall
28C3×C31C3×AGL(1,𝔽11)11yescharacteristic
29C2×C5×C9—3411noHall
30C3×D11—311no—
31D31—111noHall
32C11⋊C5D31⋊C911yescharacteristic, complemented, Hall
33C5×C9—3411noHall
34C3×C11C5×D31⋊C311yescharacteristic
35C31C9×AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
36C2×C3×C5—3411no—
37D11—311noHall
38C2×C9—3411noHall
39C3×C5—111no—
40C11C5×D31⋊C911yescharacteristic, complemented, Sylow
41C2×C5—3411noHall
42C9—311noSylow
43C2×C3—3411no—
44C5—111noSylow
45C3(C11⋊C5)⋊(D31⋊C3)11yescharacteristic
46C2—3411noSylow
subgroupG/H
center, Frattini, hypercenterC3(C11⋊C5)⋊(D31⋊C3)
commutator, hypocenterC11×C31C2×C5×C9
Fitting, socle, cosocleC3×C11×C31C2×C3×C5
prime radicalC3×(C11⋊C5)⋊D31C3
LCSG ▷ C11×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×C31⋊C9C2semidirect
3. C11⋊(D31⋊C9)C5semidirect
5. (C11⋊C5)⋊D31C9semidirect
6. C11×C31⋊C9C2×C5semidirect
9. C31×C11⋊C5C2×C9semidirect
14. D341C5×C9semidirect
18. C11×C31C2×C5×C9semidirect
21. C31⋊C9AGL(1,𝔽11)semidirect
32. C11⋊C5D31⋊C9semidirect
35. C31C9×AGL(1,𝔽11)semidirect
40. C11C5×D31⋊C9semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×C31⋊C92
C3×(C11⋊C5)⋊D313
C11⋊(D31⋊C9)5
C5×D31⋊C911
C9×AGL(1,𝔽11)31