Finite Group Databasebeta

← C3×C5×#10621721 #23778366

Subgroups — C3×C5×#10621721 #23778366

Order 10140.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D169C211yesmaximal, characteristic
2C5×#10621721C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C169C411yescharacteristic, complemented, Hall
4C3×#10621721C511yesmaximal, characteristic, direct product factor, Hall
5C5×D169C2×C311yescharacteristic
6C3×D169C2×C511yescharacteristic
7C5×C169C3×C411yescharacteristic, complemented, Hall
8C3×C5×#261—131nomaximal
9#10621721C3×C511yescharacteristic, direct product factor, Hall
10C3×C169C4×C511yescharacteristic, complemented, Hall
11C3×C5×D13—131no—
12D169C2×C3×C511yescharacteristic
13C5×#261—131no—
14C3×C5×C13#26111yescharacteristic
15C169C3×C4×C511yescharacteristic, complemented, Sylow
16C3×#261—131no—
17C5×D13—131no—
18C3×D13—131no—
19C5×C13C3×#26111yescharacteristic
20C3×C4×C5—1691noHall
21#261—131no—
22C3×C13C5×#26111yescharacteristic
23C2×C3×C5—1691no—
24D13—131no—
25C4×C5—1691noHall
26C3×C5#1062172111yescharacteristic, direct product factor, Hall
27C13C3×C5×#26111yescharacteristic
28C3×C4—1691noHall
29C2×C5—1691no—
30C2×C3—1691no—
31C5C3×#1062172111yescharacteristic, direct product factor, Sylow
32C4—1691noSylow
33C3C5×#1062172111yescharacteristic, direct product factor, Sylow
34C2—1691no—
subgroupG/H
center, hypercenterC3×C5#10621721
commutator, hypocenterC169C3×C4×C5
FrattiniC13C3×C5×#261
FittingC3×C5×C169C4
socleC3×C5×C13#261
prime radicalC3×C5×D169C2
cosocleD169C2×C3×C5
LCSG ▷ C169
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
2. C5×#10621721C3direct (N × H)
3. C3×C5×C169C4semidirect
4. C3×#10621721C5direct (N × H)
7. C5×C169C3×C4semidirect
9. #10621721C3×C5direct (N × H)
10. C3×C169C4×C5semidirect
15. C169C3×C4×C5semidirect
26. C3×C5#10621721direct (N × H)
31. C5C3×#10621721direct (N × H)
33. C3C5×#10621721direct (N × H)