Finite Group Databasebeta

← C13×#10624862 #23745013

Subgroups — C13×#10624862 #23745013

Order 9477.

1178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C13×H(3,𝔽3)C311yesmaximal, characteristic
2C9×C13×H(3,𝔽3)C3127yesmaximal, complemented
3C3×C13×C32⋊C9C3112yesmaximal, complemented
4C34×C13C3214yes—
5C3×C13×H(3,𝔽3)C9127yescomplemented
6C3×C13×H(3,𝔽3)C3219yes—
7C32×C9×C13C32136yescomplemented
8C13×C32⋊C9C3219yes—
9C13×C32⋊C9C32172yescomplemented
10#10624862C1311yesmaximal, characteristic, direct product factor, Sylow
11C33×C13—94no—
12C33×C13—98no—
13C33×C13C3×C9136yescomplemented
14C33×C13C3311yescharacteristic
15C33×C13C33112yes—
16C13×H(3,𝔽3)C3×C9181yescomplemented
17C3×C9×C13—936no—
18C3×C9×C13C33127yes—
19C32×H(3,𝔽3)C3×C1311yescharacteristic
20C9×H(3,𝔽3)C3×C13127yescomplemented
21C3×C32⋊C9C3×C13112yescomplemented
22C32×C13—312no—
23C32×C13—31no—
24C32×C13—32no—
25C32×C13—324no—
26C32×C13—936no—
27C32×C13C32×C9136yes—
28C32×C13C32×C913yes—
29C32×C13C3411yescharacteristic
30C9×C13—327no—
31C34C32×C1314yes—
32C3×H(3,𝔽3)C9×C13127yescomplemented
33C3×H(3,𝔽3)C32×C1319yes—
34C32×C9C32×C13136yescomplemented
35C32⋊C9C32×C1319yes—
36C32⋊C9C32×C13172yescomplemented
37C3×C13—33no—
38C3×C13—336no—
39C3×C13C33×C911yescharacteristic
40C3×C13H(5,𝔽3)11yescharacteristic
41C3×C133−1+412yes—
42C33—94no—
43C33—98no—
44C33C3×C9×C13136yescomplemented
45C33C33×C1311yescharacteristic
46C33C33×C13112yes—
47H(3,𝔽3)C3×C9×C13181yescomplemented
48C3×C9—936no—
49C3×C9C33×C13127yes—
50C13#1062486211yescharacteristic, direct product factor, Sylow
51C32—312no—
52C32—31no—
53C32—32no—
54C32—324no—
55C32—936no—
56C32C32×C9×C13136yes—
57C32C32×C9×C1313yes—
58C32C34×C1311yescharacteristic
59C9—327no—
60C3—33no—
61C3—336no—
62C3C33×C9×C1311yescharacteristic
63C3C13×H(5,𝔽3)11yescharacteristic
64C3C13×3−1+412yes—
subgroupG/H
center, socleC32×C13C34
commutatorC3C33×C9×C13
Frattini, cosocleC32C34×C13
prime radicalC32×C13×H(3,𝔽3)C3
LCSG ▷ C3 ▷ C1
UCSC1 ◁ C32×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C9×C13×H(3,𝔽3)C3semidirect
3. C3×C13×C32⋊C9C3semidirect
5. C3×C13×H(3,𝔽3)C9semidirect
7. C32×C9×C13C32semidirect
9. C13×C32⋊C9C32semidirect
10. #10624862C13direct (N × H)
13. C33×C13C3×C9semidirect
16. C13×H(3,𝔽3)C3×C9semidirect
20. C9×H(3,𝔽3)C3×C13semidirect
21. C3×C32⋊C9C3×C13semidirect
32. C3×H(3,𝔽3)C9×C13semidirect
34. C32×C9C32×C13semidirect
36. C32⋊C9C32×C13semidirect
44. C33C3×C9×C13semidirect
47. H(3,𝔽3)C3×C9×C13semidirect
50. C13#10624862direct (N × H)