Finite Group Databasebeta

← C2×C3×C11⋊C5×C103 #46800913

Subgroups — C2×C3×C11⋊C5×C103 #46800913

Order 33990.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C103C211yesmaximal, characteristic, direct product factor, Hall
2C2×C11⋊C5×C103C311yesmaximal, characteristic, direct product factor, Hall
3C2×C3×C11×C103C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C103C2×C311yescharacteristic, direct product factor, Hall
5C3×C11×C103C2×C511yescharacteristic, complemented, Hall
6C2×C3×C5×C103—111nomaximal, Hall
7C2×C11×C103C3×C511yescharacteristic, complemented, Hall
8C3×C5×C103—111noHall
9C11×C103C2×C3×C511yescharacteristic, complemented, Hall
10C2×C5×C103—111noHall
11C2×C3×C103C11⋊C511yescharacteristic, direct product factor, Hall
12C5×C103—111noHall
13C2×C3×C11⋊C5C10311yesmaximal, characteristic, direct product factor, Hall
14C3×C103C2×C11⋊C511yescharacteristic, direct product factor, Hall
15C2×C103C3×C11⋊C511yescharacteristic, direct product factor, Hall
16C3×C11⋊C5C2×C10311yescharacteristic, direct product factor, Hall
17C2×C11⋊C5C3×C10311yescharacteristic, direct product factor, Hall
18C103C2×C3×C11⋊C511yescharacteristic, direct product factor, Sylow
19C2×C3×C11C5×C10311yescharacteristic, complemented, Hall
20C11⋊C5C2×C3×C10311yescharacteristic, direct product factor, Hall
21C3×C11C2×C5×C10311yescharacteristic, complemented, Hall
22C2×C3×C5—111noHall
23C2×C11C3×C5×C10311yescharacteristic, complemented, Hall
24C3×C5—111noHall
25C11C2×C3×C5×C10311yescharacteristic, complemented, Sylow
26C2×C5—111noHall
27C2×C3C11⋊C5×C10311yescharacteristic, direct product factor, Hall
28C5—111noSylow
29C3C2×C11⋊C5×C10311yescharacteristic, direct product factor, Sylow
30C2C3×C11⋊C5×C10311yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3×C103C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C103
FrattiniC1G
Fitting, socleC2×C3×C11×C103C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C103

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C103C2direct (N × H)
2. C2×C11⋊C5×C103C3direct (N × H)
3. C2×C3×C11×C103C5semidirect
4. C11⋊C5×C103C2×C3direct (N × H)
5. C3×C11×C103C2×C5semidirect
7. C2×C11×C103C3×C5semidirect
9. C11×C103C2×C3×C5semidirect
11. C2×C3×C103C11⋊C5direct (N × H)
13. C2×C3×C11⋊C5C103direct (N × H)
14. C3×C103C2×C11⋊C5direct (N × H)
15. C2×C103C3×C11⋊C5direct (N × H)
16. C3×C11⋊C5C2×C103direct (N × H)
17. C2×C11⋊C5C3×C103direct (N × H)
18. C103C2×C3×C11⋊C5direct (N × H)
19. C2×C3×C11C5×C103semidirect
20. C11⋊C5C2×C3×C103direct (N × H)
21. C3×C11C2×C5×C103semidirect
23. C2×C11C3×C5×C103semidirect
25. C11C2×C3×C5×C103semidirect
27. C2×C3C11⋊C5×C103direct (N × H)
29. C3C2×C11⋊C5×C103direct (N × H)
30. C2C3×C11⋊C5×C103direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C11⋊C5×C1032
C2×C11⋊C5×C1033
C2×C3×C11×C1035
C2×C3×C5×C10311
C2×C3×C11⋊C5103