Finite Group Databasebeta

← D13×D207 #24924492

Subgroups — D13×D207 #24924492

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D2691C211yesmaximal, characteristic, complemented
2C13×D207C211yesmaximal, characteristic, complemented
3C9×C23×D13C211yesmaximal, characteristic, complemented
4D13×D69—31nomaximal
5C9×C13×C23C2211yescharacteristic, complemented, Hall
6D897—31no—
7C13×D69—31no—
8C3×C23×D13D311yescharacteristic
9D13×D23—91noHall
10C3×C13×C23C2×D311yescharacteristic
11C2×D207—131nomaximal, Hall
12D299—91no—
13C13×D23—91no—
14C23×D13D911yescharacteristic, complemented
15D9×D13—231nomaximal, Hall
16C2×C9×C23—131no—
17D207—131no—
18D207D1311yescharacteristic, direct product factor
19C13×C23C2×D911yescharacteristic, complemented, Hall
20C2×D69—391no—
21D117—231no—
22C9×D13D2311yescharacteristic, complemented
23C13×D9—231no—
24C9×C23C2×D1311yescharacteristic, complemented, Hall
25D3×D13—691no—
26C2×C3×C23—131no—
27D69—31no—
28D69—391no—
29C9×C13C2×D2311yescharacteristic, complemented, Hall
30C2×D23—1171noHall
31D39—691no—
32C3×D13D6911yescharacteristic
33D3×C13—691no—
34C3×C23D3×D1311yescharacteristic
35C2×D13—2071noHall
36C2×C23—131no—
37D23—91no—
38D23—1171no—
39C3×C13C2×D6911yescharacteristic
40C2×D9—2991noHall
41C2×C13—2071no—
42D13—2071no—
43D13D20711yescharacteristic, direct product factor
44C23D9×D1311yescharacteristic, complemented, Sylow
45C2×C9—131no—
46D9—231no—
47D9—2991no—
48C13C2×D20711yescharacteristic, complemented, Sylow
49C2×D3—8971no—
50C9D13×D2311yescharacteristic, complemented, Sylow
51C2×C3—131no—
52D3—691no—
53D3—8971no—
54C22—26911noSylow
55C3D13×D6911yescharacteristic
56C2—131no—
57C2—26911no—
58C2—2071no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC9×C13×C23C22
FrattiniC3D13×D69
socleC3×C13×C23C2×D3
LCSG ▷ C9×C13×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. D2691C2semidirect
2. C13×D207C2semidirect
3. C9×C23×D13C2semidirect
5. C9×C13×C23C22semidirect
14. C23×D13D9semidirect
18. D207D13direct (N × H)
19. C13×C23C2×D9semidirect
22. C9×D13D23semidirect
24. C9×C23C2×D13semidirect
29. C9×C13C2×D23semidirect
43. D13D207direct (N × H)
44. C23D9×D13semidirect
48. C13C2×D207semidirect
50. C9D13×D23semidirect