Finite Group Databasebeta

← C11⋊C5×D309 #46800935

Subgroups — C11⋊C5×D309 #46800935

Order 33990.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C11⋊C5×C103C211yesmaximal, characteristic, complemented, Hall
2C11⋊C5×D103—31nomaximal, Hall
3C11×D309C511yesmaximal, characteristic, complemented, Hall
4C11⋊C5×C103D311yescharacteristic, complemented, Hall
5C3×C11×C103C2×C511yescharacteristic, complemented, Hall
6C5×D309—111nomaximal, Hall
7C11×D103—31noHall
8C3×C5×C103—111noHall
9C11×C103C5×D311yescharacteristic, complemented, Hall
10C5×D103—331noHall
11D309C11⋊C511yescharacteristic, direct product factor, Hall
12C5×C103—111noHall
13D3×C11⋊C5—1031nomaximal, Hall
14C3×C103C2×C11⋊C511yescharacteristic, complemented, Hall
15D103—31noHall
16C3×C11⋊C5D10311yescharacteristic, complemented, Hall
17C2×C11⋊C5—3091noHall
18C103D3×C11⋊C511yescharacteristic, complemented, Sylow
19D3×C11—1031noHall
20C11⋊C5D30911yescharacteristic, direct product factor, Hall
21C3×C11C5×D10311yescharacteristic, complemented, Hall
22C5×D3—11331noHall
23C2×C11—3091noHall
24C3×C5—111noHall
25C11C5×D30911yescharacteristic, complemented, Sylow
26C2×C5—33991noHall
27D3—1031noHall
28C5—111noSylow
29C3C11⋊C5×D10311yescharacteristic, complemented, Sylow
30C2—3091noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C103C2×C5
LCSG ▷ C3×C11×C103
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C11⋊C5×C103C2semidirect
3. C11×D309C5semidirect
4. C11⋊C5×C103D3semidirect
5. C3×C11×C103C2×C5semidirect
9. C11×C103C5×D3semidirect
11. D309C11⋊C5direct (N × H)
14. C3×C103C2×C11⋊C5semidirect
16. C3×C11⋊C5D103semidirect
18. C103D3×C11⋊C5semidirect
20. C11⋊C5D309direct (N × H)
21. C3×C11C5×D103semidirect
25. C11C5×D309semidirect
29. C3C11⋊C5×D103semidirect

Maximal subgroups

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

subgroupindex
C3×C11⋊C5×C1032
C11⋊C5×D1033
C11×D3095
C5×D30911
D3×C11⋊C5103