Finite Group Databasebeta

← C101⋊#564 #20265932

Subgroups — C101⋊#564 #20265932

Order 6464.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15692247C212yesmaximal
2#15692246C214yesmaximal
3#15692245C214yesmaximal
4#15692245C214yesmaximal
5#125×C101C211yesmaximal, characteristic
6C4⋊Dic101C2212yes—
7C4⋊Dic101C2214yes—
8C4⋊Dic101C2212yes—
9#13108053C2214yes—
10#13108053C2214yes—
11#13108053C2214yes—
12#13108053C2214yes—
13C4×Dic101C2214yes—
14C4⋊C4×C101C2212yes—
15C4⋊C4×C101C2214yes—
16C42×C101C2211yescharacteristic
17C2×C4×C101C2311yescharacteristic
18C2×C4×C101C2312yes—
19C2×C4×C101C2314yes—
20C2×Dic101C2314yes—
21C2×Dic101C2314yes—
22C22×C101C2411yescharacteristic
23C4×C101—22no—
24C4×C101—24no—
25C4×C101—21no—
26Dic101—24no—
27Dic101—24no—
28C2×C1012−1+412yes—
29C2×C1012−1+411yescharacteristic
30C101#56411yescharacteristic, complemented, Sylow
31#564—1011nomaximal, Sylow
32#125—1014no—
33#125—1014no—
34#125—1014no—
35#125—1012no—
36#125D10111yescharacteristic
37C4⋊C4—1014no—
38C4⋊C4—1014no—
39C4⋊C4—1014no—
40C4⋊C4—1014no—
41C4⋊C4—1014no—
42C4⋊C4—1012no—
43C4⋊C4—1012no—
44C4⋊C4C2×D10112yes—
45C4⋊C4C2×D10114yes—
46C42—1014no—
47C42C2×D10111yescharacteristic
48C2×C4—1014no—
49C2×C4—1014no—
50C2×C4C22×D10114yes—
51C2×C4C22×D10112yes—
52C2×C4C22×D10111yescharacteristic
53C22C23×D10111yescharacteristic
54C4—24no—
55C4—22no—
56C4—21no—
57C4—2024no—
58C4—2024no—
59C2#1569230212yes—
60C2#1569230311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D101
commutator, socleC22×C101C24
Fitting#125×C101C2
hypercenter#125D101
hypocenterC101#564
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
30. C101#564semidirect