Finite Group Databasebeta

← (C11⋊C5)⋊Dic145 #44542017

Subgroups — (C11⋊C5)⋊Dic145 #44542017

Order 31900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C29×C11⋊C5C211yesmaximal, characteristic
2C5×C29×C11⋊C5C411yescharacteristic, complemented, Hall
3(C11⋊C5)⋊Dic29—51nomaximal
4Dic1595C511yesmaximal, characteristic, complemented
5C2×C29×C11⋊C5—22no—
6C2×C29×C11⋊C5D511yescharacteristic
7C2×C5×C11×C29C2×C511yescharacteristic
8C5×Dic145—111nomaximal, Hall
9C5×C11×C29C4×C511yescharacteristic, complemented
10C29×C11⋊C5—22no—
11C29×C11⋊C5Dic511yescharacteristic, complemented
12C2×C52×C29—111no—
13Dic319—51noHall
14(C11⋊C5)⋊Dic5—291nomaximal, Hall
15C52×C29—111noHall
16C2×C11×C29C5×D511yescharacteristic
17Dic145—111no—
18C5×Dic29—551no—
19C2×C5×C11⋊C5D2911yescharacteristic
20C11×C29C5×Dic511yescharacteristic, complemented, Hall
21C2×C5×C29—111no—
22C2×C5×C29—222no—
23C2×C5×C29AGL(1,𝔽11)11yescharacteristic
24C5×C11⋊C5Dic2911yescharacteristic, complemented, Hall
25Dic55—291no—
26Dic11⋊C5—1451no—
27C5×C29—111no—
28C5×C29—222no—
29C5×C29Dic11⋊C511yescharacteristic, complemented
30Dic29—551noHall
31C2×C5×C11C5×D2911yescharacteristic
32C2×C11⋊C5—22no—
33C2×C11⋊C5D14511yescharacteristic
34C5×Dic5—3191noHall
35C2×C29C5⋊AGL(1,𝔽11)11yescharacteristic
36C5×C11C5×Dic2911yescharacteristic, complemented
37C11⋊C5—22no—
38C11⋊C5Dic14511yescharacteristic, complemented
39C2×C52—111no—
40Dic11—1451noHall
41C29(C11⋊C5)⋊Dic511yescharacteristic, complemented, Sylow
42C52—111noSylow
43C2×C11C5×D14511yescharacteristic
44C4×C5—15951no—
45Dic5—3191no—
46C11C5×Dic14511yescharacteristic, complemented, Sylow
47C2×C5—111no—
48C2×C5—222no—
49C2×C5C29⋊AGL(1,𝔽11)11yescharacteristic
50C5—111no—
51C5—222no—
52C5(C11⋊C5)⋊Dic2911yescharacteristic, complemented
53C4—15951noSylow
54C2C5⋊(C29⋊AGL(1,𝔽11))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C5⋊(C29⋊AGL(1,𝔽11))
commutator, hypocenterC5×C11×C29C4×C5
Fitting, socle, cosocleC2×C5×C11×C29C2×C5
prime radicalC2×C5×C29×C11⋊C5C2
LCSG ▷ C5×C11×C29
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C5×C29×C11⋊C5C4semidirect
4. Dic1595C5semidirect
9. C5×C11×C29C4×C5semidirect
11. C29×C11⋊C5Dic5semidirect
20. C11×C29C5×Dic5semidirect
24. C5×C11⋊C5Dic29semidirect
29. C5×C29Dic11⋊C5semidirect
36. C5×C11C5×Dic29semidirect
38. C11⋊C5Dic145semidirect
41. C29(C11⋊C5)⋊Dic5semidirect
46. C11C5×Dic145semidirect
52. C5(C11⋊C5)⋊Dic29semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C29×C11⋊C52
(C11⋊C5)⋊Dic295
Dic15955
C5×Dic14511
(C11⋊C5)⋊Dic529