Finite Group Databasebeta

← C11⋊C5×#63120 #28384706

Subgroups — C11⋊C5×#63120 #28384706

Order 14300.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C13×C11⋊C5C211yesmaximal, characteristic
2C5×C13×C11⋊C5C411yescharacteristic, complemented, Hall
3C11×#63120C511yesmaximal, characteristic, complemented
4Dic13×C11⋊C5—51nomaximal
5D5×C11×C13C2×C511yescharacteristic
6C2×C13×C11⋊C5—51no—
7C5×#63120—111nomaximal, Hall
8AGL(1,𝔽5)×C11⋊C5—131nomaximal, Hall
9C5×C11×C13C4×C511yescharacteristic, complemented
10C13×C11⋊C5—41no—
11C13×C11⋊C5AGL(1,𝔽5)11yescharacteristic, complemented
12C5×D5×C13—111no—
13C11×Dic13—51noHall
14D5×C11⋊C5D1311yescharacteristic
15C52×C13—111noHall
16C2×C11×C13—51no—
17C5×C11⋊C5Dic1311yescharacteristic, complemented, Hall
18#63120C11⋊C511yescharacteristic, direct product factor
19C5×Dic13—551no—
20C11×AGL(1,𝔽5)—131no—
21C4×C11⋊C5—651no—
22C11×C13C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
23C2×C5×C13—551no—
24D5×C13C2×C11⋊C511yescharacteristic
25D5×C11C5×D1311yescharacteristic
26C2×C11⋊C5—51no—
27C5×AGL(1,𝔽5)—1431noHall
28C5×C13—111no—
29C5×C13—441no—
30C5×C13C4×C11⋊C511yescharacteristic, complemented
31C5×C11C5×Dic1311yescharacteristic, complemented
32C11⋊C5—41no—
33C11⋊C5#6312011yescharacteristic, direct product factor
34Dic13—51noHall
35C5×D5—111no—
36C4×C11—651noHall
37C2×C13—51no—
38C52—111noSylow
39C2×C11—51no—
40AGL(1,𝔽5)—131no—
41C4×C5—7151no—
42C13AGL(1,𝔽5)×C11⋊C511yescharacteristic, complemented, Sylow
43C11C5×#6312011yescharacteristic, complemented, Sylow
44C2×C5—551no—
45D5D13×C11⋊C511yescharacteristic
46C5—111no—
47C5—441no—
48C5Dic13×C11⋊C511yescharacteristic, complemented
49C4—651noSylow
50C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C13C4×C5
prime radicalD5×C13×C11⋊C5C2
cosocleD5×C11×C13C2×C5
LCSG ▷ C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. C5×C13×C11⋊C5C4semidirect
3. C11×#63120C5semidirect
9. C5×C11×C13C4×C5semidirect
11. C13×C11⋊C5AGL(1,𝔽5)semidirect
17. C5×C11⋊C5Dic13semidirect
18. #63120C11⋊C5direct (N × H)
22. C11×C13C5×AGL(1,𝔽5)semidirect
30. C5×C13C4×C11⋊C5semidirect
31. C5×C11C5×Dic13semidirect
33. C11⋊C5#63120direct (N × H)
42. C13AGL(1,𝔽5)×C11⋊C5semidirect
43. C11C5×#63120semidirect
48. C5Dic13×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
D5×C13×C11⋊C52
C11×#631205
Dic13×C11⋊C55
C5×#6312011
AGL(1,𝔽5)×C11⋊C513