Finite Group Databasebeta

← C13×#10624864 #23745015

Subgroups — C13×#10624864 #23745015

Order 9477.

926 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C13×#737C311yesmaximal, characteristic
2C9×C13×3−1+2C3124yesmaximal, complemented
3C9×C13×H(3,𝔽3)C313yesmaximal
4C13×#6887C318yesmaximal, complemented
5C3×C13×C9⋊C9C314yesmaximal, complemented
6C13×#737C9127yescomplemented
7C3×C13×3−1+2C3218yes—
8C3×C13×H(3,𝔽3)C3211yescharacteristic
9C32×C9×C13C32112yes—
10C32×C9×C13C3214yes—
11C13×C9⋊C9C3211yescharacteristic
12C13×C9⋊C9C3218yes—
13C13×C9⋊C9C32124yes—
14C13×C9⋊C9C32124yes—
15C13×C32⋊C9C32124yes—
16C92×C13C32124yes—
17#10624864C1311yesmaximal, characteristic, direct product factor, Sylow
18C33×C13C3314yes—
19C13×3−1+2C3×C9172yescomplemented
20C13×H(3,𝔽3)C3×C919yes—
21C3×C9×C13—912no—
22C3×C9×C13C3×C9136yescomplemented
23C3×C9×C13C33124yes—
24C3×C9×C13C3313yes—
25C3×C9×C13C3318yes—
26C3×C9×C13C3311yescharacteristic
27C3×#737C3×C1311yescharacteristic
28C9×3−1+2C3×C13124yescomplemented
29C9×H(3,𝔽3)C3×C1313yes—
30#6887C3×C1318yescomplemented
31C3×C9⋊C9C3×C1314yescomplemented
32C32×C13—312no—
33C32×C13C32×C9112yes—
34C32×C13C3411yescharacteristic
35C9×C13—33no—
36C9×C13—324no—
37C9×C13C32×C913yes—
38C9×C13C32×C9124yes—
39#737C9×C13127yescomplemented
40C3×3−1+2C32×C1318yes—
41C3×H(3,𝔽3)C32×C1311yescharacteristic
42C32×C9C32×C13112yes—
43C32×C9C32×C1314yes—
44C9⋊C9C32×C1311yescharacteristic
45C9⋊C9C32×C1318yes—
46C9⋊C9C32×C13124yes—
47C9⋊C9C32×C13124yes—
48C32⋊C9C32×C13124yes—
49C92C32×C13124yes—
50C3×C13—312no—
51C3×C13C33×C911yescharacteristic
52C3×C133−1+413yes—
53C33C33×C1314yes—
543−1+2C3×C9×C13172yescomplemented
55H(3,𝔽3)C3×C9×C1319yes—
56C3×C9—912no—
57C3×C9C3×C9×C13136yescomplemented
58C3×C9C33×C13124yes—
59C3×C9C33×C1313yes—
60C3×C9C33×C1318yes—
61C3×C9C33×C1311yescharacteristic
62C13#1062486411yescharacteristic, direct product factor, Sylow
63C32—312no—
64C32C32×C9×C13112yes—
65C32C34×C1311yescharacteristic
66C9—33no—
67C9—324no—
68C9C32×C9×C1313yes—
69C9C32×C9×C13124yes—
70C3—312no—
71C3C33×C9×C1311yescharacteristic
72C3C13×3−1+413yes—
subgroupG/H
center, socleC32×C13C34
commutatorC3C33×C9×C13
Frattini, cosocleC32C34×C13
prime radicalC3×C13×H(3,𝔽3)C32
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C32×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×C13×3−1+2C3semidirect
4. C13×#6887C3semidirect
5. C3×C13×C9⋊C9C3semidirect
6. C13×#737C9semidirect
17. #10624864C13direct (N × H)
19. C13×3−1+2C3×C9semidirect
22. C3×C9×C13C3×C9semidirect
28. C9×3−1+2C3×C13semidirect
30. #6887C3×C13semidirect
31. C3×C9⋊C9C3×C13semidirect
39. #737C9×C13semidirect
54. 3−1+2C3×C9×C13semidirect
57. C3×C9C3×C9×C13semidirect
62. C13#10624864direct (N × H)