Finite Group Databasebeta

← D13×#564 #13128978

Subgroups — D13×#564 #13128978

Order 1664.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#564C211yesmaximal, characteristic, complemented
2D13×#125C2115yesmaximal
3C13⋊#564C2115yesmaximal, complemented
4C13×#125C22115yes—
5C4⋊C4×D13C22130yes—
6#88144C22130yes—
7#88143C22160yes—
8C42×D13C2215yes—
9#88124C22115yes—
10C2×C4×D13C23115yes—
11C13×C4⋊C4C23130yes—
12C42×C13C2315yes—
13C4⋊Dic13C23130yes—
14#6101C23160yes—
15C4×Dic13C23115yes—
16C2×#564—131nomaximal, Sylow
17C22×D13C2411yescharacteristic
18C2×C4×C13C24115yes—
19C2×Dic13C24115yes—
20C4×D13—230no—
21#564—1315no—
22#564D1311yescharacteristic, direct product factor
23C2×#125—1315no—
24C22×C13C2511yescharacteristic
25C2×D132−1+416yes—
26C4×C13—215no—
27Dic13—215no—
28#125—1360no—
29#125—1330no—
30#125—1315no—
31#125C2×D13115yes—
32C2×C4⋊C4—1330no—
33C2×C42—135no—
34C2×C13C2×2−1+413yes—
35D13#56414yesdirect product factor
36C22×C4—1315no—
37C4⋊C4—1360no—
38C4⋊C4—1330no—
39C4⋊C4C22×D13130yes—
40C42—1315no—
41C42C22×D1315yes—
42C13C2×#56411yescharacteristic, complemented, Sylow
43C23—131no—
44C2×C4—1315no—
45C2×C4—2630no—
46C2×C4C23×D13115yes—
47C22—136no—
48C22C24×D1311yescharacteristic
49C4—215no—
50C4—2615no—
51C2—134no—
52C2D13×2−1+413yes—
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#564C2
prime radicalC22×D13C24
hypercenter#564D13
hypocenterC13C2×#564
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C13×#564C2semidirect
3. C13⋊#564C2semidirect
22. #564D13direct (N × H)
35. D13#564direct (N × H)
42. C13C2×#564semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#5642
D13×#1252
C13⋊#5642
C2×#56413