Finite Group Databasebeta

← C5×C11⋊(D97⋊C3) #44544979

Subgroups — C5×C11⋊(D97⋊C3) #44544979

Order 32010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C97⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5×D1067C311yesmaximal, characteristic, complemented, Hall
3C11⋊(D97⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
4C5×C11×C97C2×C311yescharacteristic, complemented, Hall
5C11×C97⋊C3C2×C511yescharacteristic, complemented, Hall
6C5×D97⋊C3—111nomaximal, Hall
7D1067C3×C511yescharacteristic, complemented, Hall
8C5×C97⋊C3D1111yescharacteristic, complemented, Hall
9C11×C97C2×C3×C511yescharacteristic, complemented, Hall
10C5×D97—111noHall
11D97⋊C3—111noHall
12C5×C97C3×D1111yescharacteristic, complemented, Hall
13C3×C5×D11—971nomaximal, Hall
14C97⋊C3C5×D1111yescharacteristic, complemented, Hall
15D97—111noHall
16C3×C5×C11—971noHall
17C5×D11—971noHall
18C97C3×C5×D1111yescharacteristic, complemented, Sylow
19C3×D11—971noHall
20C5×C11D97⋊C311yescharacteristic, complemented, Hall
21C3×C11—971noHall
22C2×C3×C5—10671noHall
23D11—971noHall
24C3×C5—971noHall
25C11C5×D97⋊C311yescharacteristic, complemented, Sylow
26C2×C5—10671noHall
27C2×C3—10671noHall
28C5C11⋊(D97⋊C3)11yescharacteristic, direct product factor, Sylow
29C3—971noSylow
30C2—10671noSylow
subgroupG/H
center, hypercenterC5C11⋊(D97⋊C3)
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C97C2×C3
LCSG ▷ C11×C97
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C11×C97⋊C3C2semidirect
2. C5×D1067C3semidirect
3. C11⋊(D97⋊C3)C5direct (N × H)
4. C5×C11×C97C2×C3semidirect
5. C11×C97⋊C3C2×C5semidirect
7. D1067C3×C5semidirect
8. C5×C97⋊C3D11semidirect
9. C11×C97C2×C3×C5semidirect
12. C5×C97C3×D11semidirect
14. C97⋊C3C5×D11semidirect
18. C97C3×C5×D11semidirect
20. C5×C11D97⋊C3semidirect
25. C11C5×D97⋊C3semidirect
28. C5C11⋊(D97⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C97⋊C32
C5×D10673
C11⋊(D97⋊C3)5
C5×D97⋊C311
C3×C5×D1197