Finite Group Databasebeta

← #564×D53 #20288857

Subgroups — #564×D53 #20288857

Order 6784.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53⋊#564C2115yesmaximal, complemented
2#125×D53C2115yesmaximal
3C53×#564C211yesmaximal, characteristic, complemented
4#13133209C22115yes—
5#13133208C22130yes—
6#13133207C22160yes—
7C4⋊C4×D53C22130yes—
8C42×D53C2215yes—
9#125×C53C22115yes—
10C2×C4×D53C23115yes—
11C4⋊C4×C53C23130yes—
12C42×C53C2315yes—
13C4⋊Dic53C23130yes—
14#11719919C23160yes—
15C4×Dic53C23115yes—
16C22×D53C2411yescharacteristic
17C2×C4×C53C24115yes—
18C2×Dic53C24115yes—
19C4×D53—230no—
20C22×C53C2511yescharacteristic
21C2×D532−1+416yes—
22C4×C53—215no—
23Dic53—215no—
24C2×#564—531nomaximal, Sylow
25C2×C53C2×2−1+413yes—
26D53#56414yesdirect product factor
27#564—5315no—
28#564D5311yescharacteristic, direct product factor
29C2×#125—5315no—
30C53C2×#56411yescharacteristic, complemented, Sylow
31#125—5360no—
32#125—5330no—
33#125—5315no—
34#125C2×D53115yes—
35C2×C4⋊C4—5330no—
36C2×C42—535no—
37C22×C4—5315no—
38C4⋊C4—5360no—
39C4⋊C4—5330no—
40C4⋊C4C22×D53130yes—
41C42—5315no—
42C42C22×D5315yes—
43C23—531no—
44C2×C4—5315no—
45C2×C4—10630no—
46C2×C4C23×D53115yes—
47C22—536no—
48C22C24×D5311yescharacteristic
49C4—215no—
50C4—10615no—
51C2—534no—
52C22−1+4×D5313yes—
subgroupG/H
center, FrattiniC22C24×D53
commutator, socleC22×C53C25
FittingC53×#564C2
hypercenter#564D53
hypocenterC53C2×#564
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C53⋊#564C2semidirect
3. C53×#564C2semidirect
26. D53#564direct (N × H)
28. #564D53direct (N × H)
30. C53C2×#564semidirect