Finite Group Databasebeta

← C5×Dic539 #24924695

Subgroups — C5×Dic539 #24924695

Order 10780.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×C49C211yesmaximal, characteristic
2C5×C11×C49C411yescharacteristic, complemented, Hall
3Dic539C511yesmaximal, characteristic, direct product factor, Hall
4C5×Dic77—71nomaximal
5C2×C11×C49C2×C511yescharacteristic
6C5×Dic49—111nomaximal, Hall
7C2×C5×C7×C11D711yescharacteristic
8C11×C49C4×C511yescharacteristic, complemented, Hall
9C2×C5×C49D1111yescharacteristic
10C5×C7×C11Dic711yescharacteristic
11Dic77—71no—
12C5×C49Dic1111yescharacteristic, complemented, Hall
13C5×Dic11—491noHall
14Dic49—111noHall
15C2×C7×C11C5×D711yescharacteristic
16C5×Dic7—771no—
17C2×C5×C11D4911yescharacteristic
18C2×C49C5×D1111yescharacteristic
19C7×C11C5×Dic711yescharacteristic
20C2×C5×C7D7711yescharacteristic
21C5×C11Dic4911yescharacteristic, complemented, Hall
22C49C5×Dic1111yescharacteristic, complemented, Sylow
23Dic11—491noHall
24C5×C7Dic7711yescharacteristic
25Dic7—771no—
26C2×C11C5×D4911yescharacteristic
27C4×C5—5391noHall
28C2×C7C5×D7711yescharacteristic
29C11C5×Dic4911yescharacteristic, complemented, Sylow
30C2×C5D53911yescharacteristic
31C7C5×Dic7711yescharacteristic
32C5Dic53911yescharacteristic, direct product factor, Sylow
33C4—5391noSylow
34C2C5×D53911yescharacteristic
subgroupG/H
center, hypercenterC2×C5D539
commutator, hypocenterC11×C49C4×C5
FrattiniC2×C7C5×D77
FittingC2×C5×C11×C49C2
socle, prime radicalC2×C5×C7×C11D7
cosocleC2×C11×C49C2×C5
LCSG ▷ C11×C49
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C11×C49C4semidirect
3. Dic539C5direct (N × H)
8. C11×C49C4×C5semidirect
12. C5×C49Dic11semidirect
21. C5×C11Dic49semidirect
22. C49C5×Dic11semidirect
29. C11C5×Dic49semidirect
32. C5Dic539direct (N × H)