Finite Group Databasebeta

← #564×D79 #23777542

Subgroups — #564×D79 #23777542

Order 10112.

896 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79⋊#564C2115yesmaximal, complemented
2#125×D79C2115yesmaximal
3#564×C79C211yesmaximal, characteristic, complemented
4#14579153C22115yes—
5#14579152C22130yes—
6#14579151C22160yes—
7C4⋊C4×D79C22130yes—
8C42×D79C2215yes—
9#125×C79C22115yes—
10C2×C4×D79C23115yes—
11C4⋊Dic79C23130yes—
12Dic79⋊C4C23160yes—
13C4×Dic79C23115yes—
14C4⋊C4×C79C23130yes—
15C42×C79C2315yes—
16C22×D79C2411yescharacteristic
17C2×C4×C79C24115yes—
18C2×Dic79C24115yes—
19C4×D79—230no—
20C22×C79C2511yescharacteristic
21C2×D792−1+416yes—
22C4×C79—215no—
23Dic79—215no—
24C2×C79C2×2−1+413yes—
25D79#56414yesdirect product factor
26C2×#564—791nomaximal, Sylow
27C79C2×#56411yescharacteristic, complemented, Sylow
28#564—7915no—
29#564D7911yescharacteristic, direct product factor
30C2×#125—7915no—
31#125—7960no—
32#125—7930no—
33#125—7915no—
34#125C2×D79115yes—
35C2×C4⋊C4—7930no—
36C2×C42—795no—
37C22×C4—7915no—
38C4⋊C4—7960no—
39C4⋊C4—7930no—
40C4⋊C4C22×D79130yes—
41C42—7915no—
42C42C22×D7915yes—
43C23—791no—
44C2×C4—7915no—
45C2×C4—15830no—
46C2×C4C23×D79115yes—
47C22—796no—
48C22C24×D7911yescharacteristic
49C4—215no—
50C4—15815no—
51C2—794no—
52C22−1+4×D7913yes—
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#564×C79C2
prime radicalC22×D79C24
hypercenter#564D79
hypocenterC79C2×#564
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #564

Complements

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

NH ≅ G/Ntype
1. C79⋊#564C2semidirect
3. #564×C79C2semidirect
25. D79#564direct (N × H)
27. C79C2×#564semidirect
29. #564D79direct (N × H)