Finite Group Databasebeta

← C3×C43×Dic15 #21440887

Subgroups — C3×C43×Dic15 #21440887

Order 7740.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C5×C43C211yesmaximal, characteristic
2C43×Dic15C311yesmaximal, characteristic, direct product factor
3C3×Dic5×C43—31nomaximal
4C32×C5×C43C411yescharacteristic, complemented, Hall
5C3×Dic3×C43—51nomaximal, Hall
6C2×C3×C5×C43—21no—
7C2×C3×C5×C43D311yescharacteristic
8C2×C3×C5×C43C2×C311yescharacteristic
9Dic5×C43—31noHall
10C2×C32×C43D511yescharacteristic
11C3×C5×C43—21no—
12C3×C5×C43Dic311yescharacteristic, complemented
13C3×C5×C43C3×C411yescharacteristic, complemented
14C3×C4×C43—151no—
15Dic3×C43—51no—
16C2×C5×C43C3×D311yescharacteristic
17C32×C43Dic511yescharacteristic, complemented, Hall
18C2×C3×C43—21no—
19C2×C3×C43C3×D511yescharacteristic
20C2×C3×C43D1511yescharacteristic
21C5×C43C3×Dic311yescharacteristic, complemented, Hall
22C3×Dic15C4311yesmaximal, characteristic, direct product factor, Hall
23C4×C43—151noHall
24C3×C43—21no—
25C3×C43C3×Dic511yescharacteristic, complemented
26C3×C43Dic1511yescharacteristic, direct product factor
27C2×C32×C5C2×C4311yescharacteristic
28C2×C43C3×D1511yescharacteristic
29Dic15C3×C4311yescharacteristic, direct product factor
30C3×Dic5—31no—
31C32×C5C4×C4311yescharacteristic, complemented, Hall
32C43C3×Dic1511yescharacteristic, direct product factor, Sylow
33C3×Dic3—51noHall
34C2×C3×C5—21no—
35C2×C3×C5D3×C4311yescharacteristic
36C2×C3×C5C2×C3×C4311yescharacteristic
37Dic5—31noHall
38C2×C32D5×C4311yescharacteristic
39C3×C5—21no—
40C3×C5Dic3×C4311yescharacteristic, complemented
41C3×C5C3×C4×C4311yescharacteristic, complemented
42C3×C4—151no—
43Dic3—51no—
44C2×C5C3×D3×C4311yescharacteristic
45C32Dic5×C4311yescharacteristic, complemented, Sylow
46C2×C3—21no—
47C2×C3C3×D5×C4311yescharacteristic
48C2×C3D15×C4311yescharacteristic
49C5C3×Dic3×C4311yescharacteristic, complemented, Sylow
50C4—151noSylow
51C3—21no—
52C3C3×Dic5×C4311yescharacteristic, complemented
53C3C43×Dic1511yescharacteristic, direct product factor
54C2C3×D15×C4311yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C43D15
commutator, hypocenterC3×C5C3×C4×C43
FrattiniC2C3×D15×C43
Fitting, socleC2×C32×C5×C43C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C43

Complements

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

NH ≅ G/Ntype
2. C43×Dic15C3direct (N × H)
4. C32×C5×C43C4semidirect
12. C3×C5×C43Dic3semidirect
13. C3×C5×C43C3×C4semidirect
17. C32×C43Dic5semidirect
21. C5×C43C3×Dic3semidirect
22. C3×Dic15C43direct (N × H)
25. C3×C43C3×Dic5semidirect
26. C3×C43Dic15direct (N × H)
29. Dic15C3×C43direct (N × H)
31. C32×C5C4×C43semidirect
32. C43C3×Dic15direct (N × H)
40. C3×C5Dic3×C43semidirect
41. C3×C5C3×C4×C43semidirect
45. C32Dic5×C43semidirect
49. C5C3×Dic3×C43semidirect
52. C3C3×Dic5×C43semidirect
53. C3C43×Dic15direct (N × H)