Finite Group Databasebeta

← C22×C3×#10597244 #20300081

Subgroups — C22×C3×#10597244 #20300081

Order 7260.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#10597244C213yesmaximal, direct product factor
2C22×#10597244C311yesmaximal, characteristic, direct product factor, Hall
3C3×#10597244C2211yescharacteristic, direct product factor, Hall
4C22×C3×C112C511yesmaximal, characteristic, complemented, Hall
5C2×#10597244C2×C313yesdirect product factor
6C2×C3×C112C2×C513yescomplemented
7C22×C3×C11⋊C5—112nomaximal
8#10597244C22×C311yescharacteristic, direct product factor, Hall
9C22×C112C3×C511yescharacteristic, complemented, Hall
10C3×C112C22×C511yescharacteristic, complemented, Hall
11C2×C3×C11⋊C5—116no—
12C2×C112C2×C3×C513yescomplemented
13C22×C11⋊C5—112no—
14C3×C11⋊C5—112no—
15C22×C3×C11—52no—
16C22×C3×C11C11⋊C512yescomplemented
17C112C22×C3×C511yescharacteristic, complemented, Sylow
18C2×C11⋊C5—116no—
19C2×C3×C11—56no—
20C2×C3×C11C2×C11⋊C516yescomplemented
21C22×C3×C5—1211noHall
22C11⋊C5—112no—
23C22×C11—52no—
24C22×C11C3×C11⋊C512yescomplemented
25C3×C11—52no—
26C3×C11C22×C11⋊C512yescomplemented
27C2×C3×C5—1213no—
28C2×C11—56no—
29C2×C11C2×C3×C11⋊C516yescomplemented
30C22×C5—1211noHall
31C3×C5—1211noHall
32C22×C3#1059724411yescharacteristic, direct product factor, Hall
33C11—52no—
34C11C22×C3×C11⋊C512yescomplemented
35C2×C5—1213no—
36C2×C3C2×#1059724413yesdirect product factor
37C5—1211noSylow
38C22C3×#1059724411yescharacteristic, direct product factor, Sylow
39C3C22×#1059724411yescharacteristic, direct product factor, Sylow
40C2C2×C3×#1059724413yesdirect product factor
subgroupG/H
center, hypercenterC22×C3#10597244
commutator, hypocenterC112C22×C3×C5
FrattiniC1G
Fitting, socleC22×C3×C112C5
LCSG ▷ C112
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#10597244C2direct (N × H)
2. C22×#10597244C3direct (N × H)
3. C3×#10597244C22direct (N × H)
4. C22×C3×C112C5semidirect
5. C2×#10597244C2×C3direct (N × H)
6. C2×C3×C112C2×C5semidirect
8. #10597244C22×C3direct (N × H)
9. C22×C112C3×C5semidirect
10. C3×C112C22×C5semidirect
12. C2×C112C2×C3×C5semidirect
16. C22×C3×C11C11⋊C5semidirect
17. C112C22×C3×C5semidirect
20. C2×C3×C11C2×C11⋊C5semidirect
24. C22×C11C3×C11⋊C5semidirect
26. C3×C11C22×C11⋊C5semidirect
29. C2×C11C2×C3×C11⋊C5semidirect
32. C22×C3#10597244direct (N × H)
34. C11C22×C3×C11⋊C5semidirect
36. C2×C3C2×#10597244direct (N × H)
38. C22C3×#10597244direct (N × H)
39. C3C22×#10597244direct (N × H)
40. C2C2×C3×#10597244direct (N × H)