Finite Group Databasebeta

← C2×C3⋊(C3⋊(C5⋊D85)) #29506071

Subgroups — C2×C3⋊(C3⋊(C5⋊D85)) #29506071

Order 15300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C3⋊(C5⋊D85))C212yesmaximal, direct product factor
2C2×C32×C52×C17C211yesmaximal, characteristic, complemented
3C2×C3⋊(C5⋊D85)—34nomaximal
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5C2×C3⋊D255—56nomaximal
6C3⋊(C5⋊D85)—38no—
7C2×C3×C52×C17D314yescomplemented
8C2×C5⋊D85—91noHall
9C2×C32×C5×C17D516yescomplemented
10C3⋊D255—512no—
11C3×C52×C17C2×D314yescomplemented
12C2×D255—1524no—
13C2×C3⋊(C3⋊(C5⋊D5))—171nomaximal, Hall
14C2×C52×C17C3⋊D311yescharacteristic, complemented
15C5⋊D85—92no—
16C32×C5×C17C2×D516yescomplemented
17C2×C3⋊D51—251noHall
18C2×C3×C5×C17D15124yescomplemented
19D255—1548no—
20C2×C32×C52D1711yescharacteristic, complemented
21C3⋊(C3⋊(C5⋊D5))—172no—
22C52×C17C2×C3⋊D311yescharacteristic, complemented, Hall
23C2×D85—456no—
24C2×C32×C17C5⋊D511yescharacteristic, complemented
25C3⋊D51—252no—
26C2×C3⋊(C5⋊D5)—514no—
27C3×C5×C17C2×D15124yescomplemented
28C32×C52C2×D1711yescharacteristic, complemented, Hall
29C2×D51—754no—
30C2×C3⋊D15—856no—
31C2×C5×C17C3⋊D1516yescomplemented
32D85—4512no—
33C32×C17C2×C5⋊D511yescharacteristic, complemented, Hall
34C2×C3×C52D5114yescomplemented
35C3⋊(C5⋊D5)—518no—
36C2×C3×C17C3⋊(C5⋊D5)14yescomplemented
37D51—758no—
38C2×C5⋊D5—1531noHall
39C2×C32×C5D8516yescomplemented
40C3⋊D15—8512no—
41C5×C17C2×C3⋊D1516yescomplemented
42C3×C52C2×D5114yescomplemented
43C2×D17—2251noHall
44C2×D15—25524no—
45C3×C17C2×C3⋊(C5⋊D5)14yescomplemented
46C2×C52C3⋊D5111yescharacteristic, complemented
47C5⋊D5—1532no—
48C32×C5C2×D8516yescomplemented
49C2×C3⋊D3—4251noHall
50C2×C17C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented
51D17—2252no—
52C2×C3×C5D255124yescomplemented
53D15—25548no—
54C52C2×C3⋊D5111yescharacteristic, complemented, Sylow
55C2×D5—7656no—
56C2×C32C5⋊D8511yescharacteristic, complemented
57C3⋊D3—4252no—
58C17C2×C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented, Sylow
59C3×C5C2×D255124yescomplemented
60C2×D3—12754no—
61C2×C5C3⋊D25516yescomplemented
62D5—76512no—
63C32C2×C5⋊D8511yescharacteristic, complemented, Sylow
64C2×C3C3⋊(C5⋊D85)14yescomplemented
65D3—12758no—
66C5C2×C3⋊D25516yescomplemented
67C22—38251noSylow
68C3C2×C3⋊(C5⋊D85)14yescomplemented
69C2—38252no—
70C2C3⋊(C3⋊(C5⋊D85))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C5⋊D85))
commutator, cosocle, hypocenterC32×C52×C17C22
FrattiniC1G
Fitting, socleC2×C32×C52×C17C2
LCSG ▷ C32×C52×C17
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(C5⋊D85))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
14. C2×C52×C17C3⋊D3semidirect
16. C32×C5×C17C2×D5semidirect
18. C2×C3×C5×C17D15semidirect
20. C2×C32×C52D17semidirect
22. C52×C17C2×C3⋊D3semidirect
24. C2×C32×C17C5⋊D5semidirect
27. C3×C5×C17C2×D15semidirect
28. C32×C52C2×D17semidirect
31. C2×C5×C17C3⋊D15semidirect
33. C32×C17C2×C5⋊D5semidirect
34. C2×C3×C52D51semidirect
36. C2×C3×C17C3⋊(C5⋊D5)semidirect
39. C2×C32×C5D85semidirect
41. C5×C17C2×C3⋊D15semidirect
42. C3×C52C2×D51semidirect
45. C3×C17C2×C3⋊(C5⋊D5)semidirect
46. C2×C52C3⋊D51semidirect
48. C32×C5C2×D85semidirect
50. C2×C17C3⋊(C3⋊(C5⋊D5))semidirect
52. C2×C3×C5D255semidirect
54. C52C2×C3⋊D51semidirect
56. C2×C32C5⋊D85semidirect
58. C17C2×C3⋊(C3⋊(C5⋊D5))semidirect
59. C3×C5C2×D255semidirect
61. C2×C5C3⋊D255semidirect
63. C32C2×C5⋊D85semidirect
64. C2×C3C3⋊(C5⋊D85)semidirect
66. C5C2×C3⋊D255semidirect
68. C3C2×C3⋊(C5⋊D85)semidirect
70. C2C3⋊(C3⋊(C5⋊D85))direct (N × H)

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊(C5⋊D85))2
C2×C32×C52×C172
C2×C3⋊(C5⋊D85)3
C2×C3⋊D2555
C2×C3⋊(C3⋊(C5⋊D5))17