Finite Group Databasebeta

← C2×C17×C3⋊(C3⋊(C5⋊D5)) #29506072

Subgroups — C2×C17×C3⋊(C3⋊(C5⋊D5)) #29506072

Order 15300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×C3⋊(C3⋊(C5⋊D5))C212yesmaximal, direct product factor
2C2×C32×C52×C17C211yesmaximal, characteristic, complemented
3C2×C17×C3⋊(C5⋊D5)—34nomaximal
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5C2×C17×C3⋊D15—56nomaximal
6C17×C3⋊(C5⋊D5)—38no—
7C2×C3×C52×C17D314yescomplemented
8C2×C17×C5⋊D5—91noHall
9C2×C32×C5×C17D516yescomplemented
10C17×C3⋊D15—512no—
11C3×C52×C17C2×D314yescomplemented
12C2×C17×D15—1524no—
13C2×C3⋊(C3⋊(C5⋊D5))C1711yesmaximal, characteristic, direct product factor, Hall
14C2×C52×C17C3⋊D311yescharacteristic, complemented
15C17×C5⋊D5—92no—
16C32×C5×C17C2×D516yescomplemented
17C2×C17×C3⋊D3—251noHall
18C2×C3×C5×C17D15124yescomplemented
19C17×D15—1548no—
20C2×C32×C52C2×C1711yescharacteristic, complemented
21C3⋊(C3⋊(C5⋊D5))C2×C1712yesdirect product factor
22C52×C17C2×C3⋊D311yescharacteristic, complemented, Hall
23C2×D5×C17—456no—
24C2×C32×C17C5⋊D511yescharacteristic, complemented
25C17×C3⋊D3—252no—
26C2×C3⋊(C5⋊D5)—34no—
27C3×C5×C17C2×D15124yescomplemented
28C32×C52C22×C1711yescharacteristic, complemented, Hall
29C2×D3×C17—754no—
30C2×C3⋊D15—56no—
31C2×C5×C17C3⋊D1516yescomplemented
32D5×C17—4512no—
33C32×C17C2×C5⋊D511yescharacteristic, complemented, Hall
34C2×C3×C52D3×C1714yescomplemented
35C3⋊(C5⋊D5)—38no—
36C2×C3×C17C3⋊(C5⋊D5)14yescomplemented
37D3×C17—758no—
38C2×C5⋊D5—91noHall
39C2×C32×C5D5×C1716yescomplemented
40C3⋊D15—512no—
41C5×C17C2×C3⋊D1516yescomplemented
42C3×C52C2×D3×C1714yescomplemented
43C22×C17—2251noHall
44C2×D15—1524no—
45C3×C17C2×C3⋊(C5⋊D5)14yescomplemented
46C2×C52C17×C3⋊D311yescharacteristic, complemented
47C5⋊D5—92no—
48C32×C5C2×D5×C1716yescomplemented
49C2×C3⋊D3—251noHall
50C2×C17—2252no—
51C2×C17C3⋊(C3⋊(C5⋊D5))11yescharacteristic, direct product factor
52C2×C3×C5C17×D15124yescomplemented
53D15—1548no—
54C52C2×C17×C3⋊D311yescharacteristic, complemented, Sylow
55C2×D5—456no—
56C2×C32C17×C5⋊D511yescharacteristic, complemented
57C3⋊D3—252no—
58C17C2×C3⋊(C3⋊(C5⋊D5))11yescharacteristic, direct product factor, Sylow
59C3×C5C2×C17×D15124yescomplemented
60C2×D3—754no—
61C2×C5C17×C3⋊D1516yescomplemented
62D5—4512no—
63C32C2×C17×C5⋊D511yescharacteristic, complemented, Sylow
64C2×C3C17×C3⋊(C5⋊D5)14yescomplemented
65D3—758no—
66C5C2×C17×C3⋊D1516yescomplemented
67C22—2251noSylow
68C3C2×C17×C3⋊(C5⋊D5)14yescomplemented
69C2—2252no—
70C2C17×C3⋊(C3⋊(C5⋊D5))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C17C3⋊(C3⋊(C5⋊D5))
commutator, cosocle, hypocenterC32×C52C22×C17
FrattiniC1G
Fitting, socleC2×C32×C52×C17C2
LCSG ▷ C32×C52
UCSC1 ◁ C2×C17

Complements

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

NH ≅ G/Ntype
1. C17×C3⋊(C3⋊(C5⋊D5))C2direct (N × H)
2. C2×C32×C52×C17C2semidirect
4. C32×C52×C17C22semidirect
7. C2×C3×C52×C17D3semidirect
9. C2×C32×C5×C17D5semidirect
11. C3×C52×C17C2×D3semidirect
13. C2×C3⋊(C3⋊(C5⋊D5))C17direct (N × H)
14. C2×C52×C17C3⋊D3semidirect
16. C32×C5×C17C2×D5semidirect
18. C2×C3×C5×C17D15semidirect
20. C2×C32×C52C2×C17semidirect
21. C3⋊(C3⋊(C5⋊D5))C2×C17direct (N × H)
22. C52×C17C2×C3⋊D3semidirect
24. C2×C32×C17C5⋊D5semidirect
27. C3×C5×C17C2×D15semidirect
28. C32×C52C22×C17semidirect
31. C2×C5×C17C3⋊D15semidirect
33. C32×C17C2×C5⋊D5semidirect
34. C2×C3×C52D3×C17semidirect
36. C2×C3×C17C3⋊(C5⋊D5)semidirect
39. C2×C32×C5D5×C17semidirect
41. C5×C17C2×C3⋊D15semidirect
42. C3×C52C2×D3×C17semidirect
45. C3×C17C2×C3⋊(C5⋊D5)semidirect
46. C2×C52C17×C3⋊D3semidirect
48. C32×C5C2×D5×C17semidirect
51. C2×C17C3⋊(C3⋊(C5⋊D5))direct (N × H)
52. C2×C3×C5C17×D15semidirect
54. C52C2×C17×C3⋊D3semidirect
56. C2×C32C17×C5⋊D5semidirect
58. C17C2×C3⋊(C3⋊(C5⋊D5))direct (N × H)
59. C3×C5C2×C17×D15semidirect
61. C2×C5C17×C3⋊D15semidirect
63. C32C2×C17×C5⋊D5semidirect
64. C2×C3C17×C3⋊(C5⋊D5)semidirect
66. C5C2×C17×C3⋊D15semidirect
68. C3C2×C17×C3⋊(C5⋊D5)semidirect
70. C2C17×C3⋊(C3⋊(C5⋊D5))direct (N × H)

Maximal subgroups

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

subgroupindex
C17×C3⋊(C3⋊(C5⋊D5))2
C2×C32×C52×C172
C2×C17×C3⋊(C5⋊D5)3
C2×C17×C3⋊D155
C2×C3⋊(C3⋊(C5⋊D5))17