Finite Group Databasebeta

← C49×C3⋊(C3⋊(C5⋊D5)) #36347712

Subgroups — C49×C3⋊(C3⋊(C5⋊D5)) #36347712

Order 22050.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C49C211yesmaximal, characteristic, complemented, Hall
2C49×C3⋊(C5⋊D5)—34nomaximal
3C49×C3⋊D15—56nomaximal
4C3×C52×C49D314yescomplemented
5C7×C3⋊(C3⋊(C5⋊D5))C711yesmaximal, characteristic
6C49×C5⋊D5—91noHall
7C32×C5×C49D516yescomplemented
8C32×C52×C7C2×C711yescharacteristic
9D15×C49—1524no—
10C52×C49C3⋊D311yescharacteristic, complemented, Hall
11C7×C3⋊(C5⋊D5)—34no—
12C3⋊D3×C49—251noHall
13C3×C5×C49D15124yescomplemented
14C7×C3⋊D15—56no—
15C3×C52×C7D3×C714yes—
16D5×C49—456no—
17C3⋊(C3⋊(C5⋊D5))C4911yescharacteristic, direct product factor, Hall
18C32×C49C5⋊D511yescharacteristic, complemented, Hall
19C7×C5⋊D5—91no—
20C32×C5×C7C7×D516yes—
21D3×C49—754no—
22C5×C49C3⋊D1516yescomplemented
23C32×C52C2×C4911yescharacteristic, complemented, Hall
24C7×D15—1524no—
25C52×C7C7×C3⋊D311yescharacteristic
26C3⋊(C5⋊D5)—34no—
27C3×C49C3⋊(C5⋊D5)14yescomplemented
28C7×C3⋊D3—251no—
29C3×C5×C7C7×D15124yes—
30C2×C49—2251noHall
31C3⋊D15—56no—
32C3×C52D3×C4914yescomplemented
33C7×D5—456no—
34C32×C7C7×C5⋊D511yescharacteristic
35C5⋊D5—91noHall
36C49C3⋊(C3⋊(C5⋊D5))11yescharacteristic, direct product factor, Sylow
37C32×C5D5×C4916yescomplemented
38D3×C7—754no—
39C5×C7C7×C3⋊D1516yes—
40D15—1524no—
41C52C3⋊D3×C4911yescharacteristic, complemented, Sylow
42C3×C7C7×C3⋊(C5⋊D5)14yes—
43C3⋊D3—251noHall
44C3×C5D15×C49124yescomplemented
45C2×C7—2251no—
46D5—456no—
47C32C49×C5⋊D511yescharacteristic, complemented, Sylow
48C7C7×C3⋊(C3⋊(C5⋊D5))11yescharacteristic
49D3—754no—
50C5C49×C3⋊D1516yescomplemented
51C3C49×C3⋊(C5⋊D5)14yescomplemented
52C2—2251noSylow
subgroupG/H
center, hypercenterC49C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C2×C49
FrattiniC7C7×C3⋊(C3⋊(C5⋊D5))
FittingC32×C52×C49C2
socle, cosocleC32×C52×C7C2×C7
prime radicalC7×C3⋊(C3⋊(C5⋊D5))C7
LCSG ▷ C32×C52
UCSC1 ◁ C49

Complements

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

NH ≅ G/Ntype
1. C32×C52×C49C2semidirect
4. C3×C52×C49D3semidirect
7. C32×C5×C49D5semidirect
10. C52×C49C3⋊D3semidirect
13. C3×C5×C49D15semidirect
17. C3⋊(C3⋊(C5⋊D5))C49direct (N × H)
18. C32×C49C5⋊D5semidirect
22. C5×C49C3⋊D15semidirect
23. C32×C52C2×C49semidirect
27. C3×C49C3⋊(C5⋊D5)semidirect
32. C3×C52D3×C49semidirect
36. C49C3⋊(C3⋊(C5⋊D5))direct (N × H)
37. C32×C5D5×C49semidirect
41. C52C3⋊D3×C49semidirect
44. C3×C5D15×C49semidirect
47. C32C49×C5⋊D5semidirect
50. C5C49×C3⋊D15semidirect
51. C3C49×C3⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C492
C49×C3⋊(C5⋊D5)3
C49×C3⋊D155
C7×C3⋊(C3⋊(C5⋊D5))7