Finite Group Databasebeta

← C2×C11×C23×C11⋊C5 #42123734

Subgroups — C2×C11×C23×C11⋊C5 #42123734

Order 27830.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C23×C11⋊C5C211yesmaximal, characteristic, direct product factor, Hall
2C2×C112×C23C511yesmaximal, characteristic, complemented, Hall
3C112×C23C2×C511yescharacteristic, complemented, Hall
4C2×C23×C11⋊C5C1111yesmaximal, characteristic, direct product factor
5C2×C5×C11×C23—111nomaximal
6C5×C11×C23—111no—
7C23×C11⋊C5C2×C1111yescharacteristic, direct product factor
8C2×C11×C11⋊C5C2311yesmaximal, characteristic, direct product factor, Hall
9C11×C11⋊C5C2×C2311yescharacteristic, direct product factor, Hall
10C2×C11×C23—52no—
11C2×C11×C23C11⋊C511yescharacteristic, direct product factor
12C2×C11×C23C5×C1111yescharacteristic, complemented
13C11×C23—52no—
14C11×C23C2×C11⋊C511yescharacteristic, direct product factor
15C11×C23C2×C5×C1111yescharacteristic, complemented
16C2×C112C5×C2311yescharacteristic, complemented, Hall
17C2×C5×C23—111noHall
18C112C2×C5×C2311yescharacteristic, complemented, Sylow
19C5×C23—111noHall
20C2×C5×C11—111no—
21C2×C11⋊C5C11×C2311yescharacteristic, direct product factor
22C5×C11—111no—
23C11⋊C5C2×C11×C2311yescharacteristic, direct product factor
24C2×C23C11×C11⋊C511yescharacteristic, direct product factor, Hall
25C23C2×C11×C11⋊C511yescharacteristic, direct product factor, Sylow
26C2×C11—52no—
27C2×C11C23×C11⋊C511yescharacteristic, direct product factor
28C2×C11C5×C11×C2311yescharacteristic, complemented
29C11—52no—
30C11C2×C5×C11×C2311yescharacteristic, complemented
31C11C2×C23×C11⋊C511yescharacteristic, direct product factor
32C2×C5—111noHall
33C5—111noSylow
34C2C11×C23×C11⋊C511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C11×C23C11⋊C5
commutator, cosocle, hypocenterC11C2×C5×C11×C23
FrattiniC1G
Fitting, socleC2×C112×C23C5
LCSG ▷ C11
UCSC1 ◁ C2×C11×C23

Complements

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

NH ≅ G/Ntype
1. C11×C23×C11⋊C5C2direct (N × H)
2. C2×C112×C23C5semidirect
3. C112×C23C2×C5semidirect
4. C2×C23×C11⋊C5C11direct (N × H)
7. C23×C11⋊C5C2×C11direct (N × H)
8. C2×C11×C11⋊C5C23direct (N × H)
9. C11×C11⋊C5C2×C23direct (N × H)
11. C2×C11×C23C11⋊C5direct (N × H)
12. C2×C11×C23C5×C11semidirect
14. C11×C23C2×C11⋊C5direct (N × H)
15. C11×C23C2×C5×C11semidirect
16. C2×C112C5×C23semidirect
18. C112C2×C5×C23semidirect
21. C2×C11⋊C5C11×C23direct (N × H)
23. C11⋊C5C2×C11×C23direct (N × H)
24. C2×C23C11×C11⋊C5direct (N × H)
25. C23C2×C11×C11⋊C5direct (N × H)
27. C2×C11C23×C11⋊C5direct (N × H)
28. C2×C11C5×C11×C23semidirect
30. C11C2×C5×C11×C23semidirect
31. C11C2×C23×C11⋊C5direct (N × H)
34. C2C11×C23×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C23×C11⋊C52
C2×C112×C235
C2×C23×C11⋊C511
C2×C5×C11×C2311
C2×C11×C11⋊C523