Finite Group Databasebeta

← C7×C3⋊(C3⋊(D41⋊C5)) #38788949

Subgroups — C7×C3⋊(C3⋊(D41⋊C5)) #38788949

Order 25830.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C41⋊C5C211yesmaximal, characteristic, complemented, Hall
2C7×C3⋊(D41⋊C5)—34nomaximal
3C7×C3⋊D123C511yesmaximal, characteristic, complemented, Hall
4C3×C7×C41⋊C5D314yescomplemented
5C3⋊(C3⋊(D41⋊C5))C711yesmaximal, characteristic, direct product factor, Hall
6C7×D41⋊C5—91noHall
7C32×C7×C41C2×C511yescharacteristic, complemented, Hall
8C32×C41⋊C5C2×C711yescharacteristic, complemented, Hall
9C7×D123—34no—
10C7×C41⋊C5C3⋊D311yescharacteristic, complemented, Hall
11C3⋊(D41⋊C5)—34no—
12C3×C7×C41C5×D314yescomplemented
13C3⋊D123C5×C711yescharacteristic, complemented, Hall
14C5×C7×C3⋊D3—411nomaximal, Hall
15C3×C41⋊C5D3×C714yescomplemented
16C7×D41—91noHall
17D41⋊C5—91noHall
18C32×C41C2×C5×C711yescharacteristic, complemented, Hall
19C32×C5×C7—411noHall
20C7×C41C5×C3⋊D311yescharacteristic, complemented, Hall
21D123—34no—
22C5×D3×C7—1234no—
23C41⋊C5C7×C3⋊D311yescharacteristic, complemented, Hall
24C7×C3⋊D3—411noHall
25C3×C41C5×D3×C714yescomplemented
26C3×C5×C7—414no—
27C5×C3⋊D3—411noHall
28D41—91noHall
29C2×C5×C7—3691noHall
30C32×C7D41⋊C511yescharacteristic, complemented, Hall
31C32×C5—411noHall
32D3×C7—1234no—
33C41C5×C7×C3⋊D311yescharacteristic, complemented, Sylow
34C5×C7—411noHall
35C5×D3—1234no—
36C3×C7C3⋊(D41⋊C5)14yescomplemented
37C3⋊D3—411noHall
38C3×C5—414no—
39C2×C7—3691noHall
40C2×C5—3691noHall
41C32C7×D41⋊C511yescharacteristic, complemented, Sylow
42C7C3⋊(C3⋊(D41⋊C5))11yescharacteristic, direct product factor, Sylow
43D3—1234no—
44C5—411noSylow
45C3C7×C3⋊(D41⋊C5)14yescomplemented
46C2—3691noSylow
subgroupG/H
center, hypercenterC7C3⋊(C3⋊(D41⋊C5))
commutator, cosocle, hypocenterC32×C41C2×C5×C7
FrattiniC1G
Fitting, socleC32×C7×C41C2×C5
LCSG ▷ C32×C41
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C7×C41⋊C5C2semidirect
3. C7×C3⋊D123C5semidirect
4. C3×C7×C41⋊C5D3semidirect
5. C3⋊(C3⋊(D41⋊C5))C7direct (N × H)
7. C32×C7×C41C2×C5semidirect
8. C32×C41⋊C5C2×C7semidirect
10. C7×C41⋊C5C3⋊D3semidirect
12. C3×C7×C41C5×D3semidirect
13. C3⋊D123C5×C7semidirect
15. C3×C41⋊C5D3×C7semidirect
18. C32×C41C2×C5×C7semidirect
20. C7×C41C5×C3⋊D3semidirect
23. C41⋊C5C7×C3⋊D3semidirect
25. C3×C41C5×D3×C7semidirect
30. C32×C7D41⋊C5semidirect
33. C41C5×C7×C3⋊D3semidirect
36. C3×C7C3⋊(D41⋊C5)semidirect
41. C32C7×D41⋊C5semidirect
42. C7C3⋊(C3⋊(D41⋊C5))direct (N × H)
45. C3C7×C3⋊(D41⋊C5)semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C41⋊C52
C7×C3⋊(D41⋊C5)3
C7×C3⋊D1235
C3⋊(C3⋊(D41⋊C5))7
C5×C7×C3⋊D341