Finite Group Databasebeta

← C22×C5×C11×C49 #24924700

Subgroups — C22×C5×C11×C49 #24924700

Order 10780.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×C49C213yesmaximal, direct product factor
2C5×C11×C49C2211yescharacteristic, direct product factor, Hall
3C22×C11×C49C511yesmaximal, characteristic, direct product factor, Hall
4C22×C5×C7×C11C711yesmaximal, characteristic
5C2×C11×C49C2×C513yesdirect product factor
6C22×C5×C49C1111yesmaximal, characteristic, direct product factor, Hall
7C2×C5×C7×C11C2×C713yes—
8C11×C49C22×C511yescharacteristic, direct product factor, Hall
9C2×C5×C49C2×C1113yesdirect product factor
10C5×C7×C11C22×C711yescharacteristic
11C22×C7×C11C5×C711yescharacteristic
12C5×C49C22×C1111yescharacteristic, direct product factor, Hall
13C22×C5×C11C4911yescharacteristic, direct product factor, Hall
14C22×C49C5×C1111yescharacteristic, direct product factor, Hall
15C2×C7×C11C2×C5×C713yes—
16C22×C5×C7C7×C1111yescharacteristic
17C2×C5×C11C2×C4913yesdirect product factor
18C2×C49C2×C5×C1113yesdirect product factor
19C7×C11C22×C5×C711yescharacteristic
20C2×C5×C7C2×C7×C1113yes—
21C5×C11C22×C4911yescharacteristic, direct product factor, Hall
22C49C22×C5×C1111yescharacteristic, direct product factor, Sylow
23C22×C11C5×C4911yescharacteristic, direct product factor, Hall
24C5×C7C22×C7×C1111yescharacteristic
25C22×C7C5×C7×C1111yescharacteristic
26C2×C11C2×C5×C4913yesdirect product factor
27C22×C5C11×C4911yescharacteristic, direct product factor, Hall
28C2×C7C2×C5×C7×C1113yes—
29C11C22×C5×C4911yescharacteristic, direct product factor, Sylow
30C2×C5C2×C11×C4913yesdirect product factor
31C7C22×C5×C7×C1111yescharacteristic
32C5C22×C11×C4911yescharacteristic, direct product factor, Sylow
33C22C5×C11×C4911yescharacteristic, direct product factor, Sylow
34C2C2×C5×C11×C4913yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C22×C5×C7×C11
socle, prime radicalC22×C5×C7×C11C7
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×C11×C49C2direct (N × H)
2. C5×C11×C49C22direct (N × H)
3. C22×C11×C49C5direct (N × H)
5. C2×C11×C49C2×C5direct (N × H)
6. C22×C5×C49C11direct (N × H)
8. C11×C49C22×C5direct (N × H)
9. C2×C5×C49C2×C11direct (N × H)
12. C5×C49C22×C11direct (N × H)
13. C22×C5×C11C49direct (N × H)
14. C22×C49C5×C11direct (N × H)
17. C2×C5×C11C2×C49direct (N × H)
18. C2×C49C2×C5×C11direct (N × H)
21. C5×C11C22×C49direct (N × H)
22. C49C22×C5×C11direct (N × H)
23. C22×C11C5×C49direct (N × H)
26. C2×C11C2×C5×C49direct (N × H)
27. C22×C5C11×C49direct (N × H)
29. C11C22×C5×C49direct (N × H)
30. C2×C5C2×C11×C49direct (N × H)
32. C5C22×C11×C49direct (N × H)
33. C22C5×C11×C49direct (N × H)
34. C2C2×C5×C11×C49direct (N × H)