Finite Group Databasebeta

← C5×C11×D97⋊C3 #44544977

Subgroups — C5×C11×D97⋊C3 #44544977

Order 32010.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C97⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5×C11×D97C311yesmaximal, characteristic, complemented, Hall
3C11×D97⋊C3C511yesmaximal, characteristic, direct product factor, Hall
4C5×C11×C97C2×C311yescharacteristic, complemented, Hall
5C11×C97⋊C3C2×C511yescharacteristic, complemented, Hall
6C5×D97⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
7C11×D97C3×C511yescharacteristic, complemented, Hall
8C5×C97⋊C3C2×C1111yescharacteristic, complemented, Hall
9C11×C97C2×C3×C511yescharacteristic, complemented, Hall
10C5×D97C3×C1111yescharacteristic, complemented, Hall
11D97⋊C3C5×C1111yescharacteristic, direct product factor, Hall
12C5×C97C2×C3×C1111yescharacteristic, complemented, Hall
13C2×C3×C5×C11—971nomaximal, Hall
14C97⋊C3C2×C5×C1111yescharacteristic, complemented, Hall
15D97C3×C5×C1111yescharacteristic, complemented, Hall
16C3×C5×C11—971noHall
17C2×C5×C11—971noHall
18C97C2×C3×C5×C1111yescharacteristic, complemented, Sylow
19C2×C3×C11—971noHall
20C5×C11D97⋊C311yescharacteristic, direct product factor, Hall
21C3×C11—971noHall
22C2×C3×C5—971noHall
23C2×C11—971noHall
24C3×C5—971noHall
25C11C5×D97⋊C311yescharacteristic, direct product factor, Sylow
26C2×C5—971noHall
27C2×C3—971noHall
28C5C11×D97⋊C311yescharacteristic, direct product factor, Sylow
29C3—971noSylow
30C2—971noSylow
subgroupG/H
center, hypercenterC5×C11D97⋊C3
commutator, cosocle, hypocenterC97C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C97C2×C3
LCSG ▷ C97
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×C97⋊C3C2semidirect
2. C5×C11×D97C3semidirect
3. C11×D97⋊C3C5direct (N × H)
4. C5×C11×C97C2×C3semidirect
5. C11×C97⋊C3C2×C5semidirect
6. C5×D97⋊C3C11direct (N × H)
7. C11×D97C3×C5semidirect
8. C5×C97⋊C3C2×C11semidirect
9. C11×C97C2×C3×C5semidirect
10. C5×D97C3×C11semidirect
11. D97⋊C3C5×C11direct (N × H)
12. C5×C97C2×C3×C11semidirect
14. C97⋊C3C2×C5×C11semidirect
15. D97C3×C5×C11semidirect
18. C97C2×C3×C5×C11semidirect
20. C5×C11D97⋊C3direct (N × H)
25. C11C5×D97⋊C3direct (N × H)
28. C5C11×D97⋊C3direct (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×C11×D973
C11×D97⋊C35
C5×D97⋊C311
C2×C3×C5×C1197