Finite Group Databasebeta

← C13×#10624833 #23744984

Subgroups — C13×#10624833 #23744984

Order 9477.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#6903C311yesmaximal, characteristic
2C13×C81⋊C3C318yesmaximal, complemented
3C3×C13×C81C314yesmaximal, complemented
4C13×#737C911yescharacteristic
5C13×C27⋊C3C918yes—
6C3×C13×C27C3214yes—
7C13×C81C3218yes—
8C13×C81C3211yescharacteristic
9#10624833C1311yesmaximal, characteristic, direct product factor, Sylow
10C13×3−1+2C2718yes—
11C13×H(3,𝔽3)C2711yescharacteristic
12C3×C9×C13C3×C914yes—
13C13×C27C3×C918yes—
14C13×C27C3311yescharacteristic
15#6903C3×C1311yescharacteristic
16C81⋊C3C3×C1318yescomplemented
17C3×C81C3×C1314yescomplemented
18C32×C13C3×C2714yes—
19C9×C13C3×C2718yes—
20C9×C13C32×C911yescharacteristic
21#737C9×C1311yescharacteristic
22C27⋊C3C9×C1318yes—
23C3×C27C32×C1314yes—
24C81C32×C1318yes—
25C81C32×C1311yescharacteristic
26C3×C13—34no—
27C3×C13C32×C2711yescharacteristic
283−1+2C13×C2718yes—
29H(3,𝔽3)C13×C2711yescharacteristic
30C3×C9C3×C9×C1314yes—
31C27C3×C9×C1318yes—
32C27C33×C1311yescharacteristic
33C13#1062483311yescharacteristic, direct product factor, Sylow
34C32C3×C13×C2714yes—
35C9C3×C13×C2718yes—
36C9C32×C9×C1311yescharacteristic
37C3—34no—
38C3C32×C13×C2711yescharacteristic
subgroupG/H
centerC13×C81C32
commutatorC3C32×C13×C27
Frattini, cosocleC27C33×C13
socleC3×C13C32×C27
prime radicalC13×H(3,𝔽3)C27
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C13×C81 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×C81⋊C3C3semidirect
3. C3×C13×C81C3semidirect
9. #10624833C13direct (N × H)
16. C81⋊C3C3×C13semidirect
17. C3×C81C3×C13semidirect
33. C13#10624833direct (N × H)