Finite Group Databasebeta

← C23×C4×C11⋊C5 #13183323

Subgroups — C23×C4×C11⋊C5 #13183323

Order 1760.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C11⋊C5C211yesmaximal, characteristic
2C22×C4×C11⋊C5C2114yesmaximal, direct product factor
3C23×C11⋊C5C418yesdirect product factor
4C23×C11⋊C5C2217yes—
5C2×C4×C11⋊C5C22128yesdirect product factor
6C23×C4×C11C511yesmaximal, characteristic, complemented, Hall
7C22×C11⋊C5C2×C4128yesdirect product factor
8C22×C11⋊C5C2317yes—
9C4×C11⋊C5C2318yesdirect product factor
10C24×C11C2×C511yescharacteristic
11C22×C4×C11C2×C5114yescomplemented
12C23×C4×C5—111nomaximal, Hall
13C2×C11⋊C5C22×C4114yesdirect product factor
14C2×C11⋊C5C2411yescharacteristic
15C23×C11C4×C518yescomplemented
16C23×C11C22×C517yes—
17C2×C4×C11C22×C5128yescomplemented
18C24×C5—111no—
19C22×C4×C5—1114no—
20C11⋊C5C23×C411yescharacteristic, direct product factor, Hall
21C22×C11C2×C4×C5128yescomplemented
22C22×C11C23×C517yes—
23C4×C11C23×C518yescomplemented
24C23×C5—118no—
25C23×C5—117no—
26C2×C4×C5—1128no—
27C23×C4C11⋊C511yescharacteristic, direct product factor, Sylow
28C2×C11C22×C4×C5114yescomplemented
29C2×C11C24×C511yescharacteristic
30C22×C5—1128no—
31C22×C5—117no—
32C4×C5—118no—
33C24C2×C11⋊C511yescharacteristic
34C22×C4C2×C11⋊C5114yesdirect product factor
35C11C23×C4×C511yescharacteristic, complemented, Sylow
36C2×C5—1114no—
37C2×C5—111no—
38C23C4×C11⋊C518yesdirect product factor
39C23C22×C11⋊C517yes—
40C2×C4C22×C11⋊C5128yesdirect product factor
41C5—111noSylow
42C22C2×C4×C11⋊C5128yesdirect product factor
43C22C23×C11⋊C517yes—
44C4C23×C11⋊C518yesdirect product factor
45C2C22×C4×C11⋊C5114yesdirect product factor
46C2C24×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC23×C4C11⋊C5
commutator, hypocenterC11C23×C4×C5
FrattiniC2C24×C11⋊C5
FittingC23×C4×C11C5
socleC24×C11C2×C5
prime radicalC24×C11⋊C5C2
cosocleC2×C11C24×C5
LCSG ▷ C11
UCSC1 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C11⋊C5C2direct (N × H)
3. C23×C11⋊C5C4direct (N × H)
5. C2×C4×C11⋊C5C22direct (N × H)
6. C23×C4×C11C5semidirect
7. C22×C11⋊C5C2×C4direct (N × H)
9. C4×C11⋊C5C23direct (N × H)
11. C22×C4×C11C2×C5semidirect
13. C2×C11⋊C5C22×C4direct (N × H)
15. C23×C11C4×C5semidirect
17. C2×C4×C11C22×C5semidirect
20. C11⋊C5C23×C4direct (N × H)
21. C22×C11C2×C4×C5semidirect
23. C4×C11C23×C5semidirect
27. C23×C4C11⋊C5direct (N × H)
28. C2×C11C22×C4×C5semidirect
34. C22×C4C2×C11⋊C5direct (N × H)
35. C11C23×C4×C5semidirect
38. C23C4×C11⋊C5direct (N × H)
40. C2×C4C22×C11⋊C5direct (N × H)
42. C22C2×C4×C11⋊C5direct (N × H)
44. C4C23×C11⋊C5direct (N × H)
45. C2C22×C4×C11⋊C5direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C24×C11⋊C52
C22×C4×C11⋊C52
C23×C4×C115
C23×C4×C511