Finite Group Databasebeta

← C2×C3⋊(C3⋊(C5⋊D35)) #20263156

Subgroups — C2×C3⋊(C3⋊(C5⋊D35)) #20263156

Order 6300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊(C3⋊(C5⋊D35))C212yesmaximal, direct product factor
2C2×C32×C52×C7C211yesmaximal, characteristic, complemented
3C2×C3⋊(C5⋊D35)—34nomaximal
4C32×C52×C7C2211yescharacteristic, complemented, Hall
5C2×C3⋊D105—56nomaximal
6C2×C3×C52×C7D314yescomplemented
7C3⋊(C5⋊D35)—38no—
8C2×C3⋊(C3⋊(C5⋊D5))—71nomaximal, Hall
9C2×C5⋊D35—91noHall
10C2×C32×C5×C7D516yescomplemented
11C3⋊D105—512no—
12C3×C52×C7C2×D314yescomplemented
13C2×C32×C52D711yescharacteristic, complemented
14C3⋊(C3⋊(C5⋊D5))—72no—
15C2×D105—1524no—
16C2×C52×C7C3⋊D311yescharacteristic, complemented
17C5⋊D35—92no—
18C32×C5×C7C2×D516yescomplemented
19C2×C3⋊(C5⋊D5)—214no—
20C2×C3⋊D21—251noHall
21C32×C52C2×D711yescharacteristic, complemented, Hall
22C2×C3×C5×C7D15124yescomplemented
23D105—1548no—
24C2×C3⋊D15—356no—
25C52×C7C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×C3×C52D2114yescomplemented
27C3⋊(C5⋊D5)—218no—
28C2×D35—456no—
29C2×C32×C7C5⋊D511yescharacteristic, complemented
30C3⋊D21—252no—
31C3×C5×C7C2×D15124yescomplemented
32C2×C5⋊D5—631noHall
33C2×C32×C5D3516yescomplemented
34C3⋊D15—3512no—
35C2×D21—754no—
36C3×C52C2×D2114yescomplemented
37C2×C5×C7C3⋊D1516yescomplemented
38D35—4512no—
39C32×C7C2×C5⋊D511yescharacteristic, complemented, Hall
40C2×D15—10524no—
41C2×C52C3⋊D2111yescharacteristic, complemented
42C5⋊D5—632no—
43C32×C5C2×D3516yescomplemented
44C2×C3×C7C3⋊(C5⋊D5)14yescomplemented
45D21—758no—
46C2×C3⋊D3—1751noHall
47C5×C7C2×C3⋊D1516yescomplemented
48C2×C3×C5D105124yescomplemented
49D15—10548no—
50C2×D7—2251noHall
51C52C2×C3⋊D2111yescharacteristic, complemented, Sylow
52C3×C7C2×C3⋊(C5⋊D5)14yescomplemented
53C2×D5—3156no—
54C2×C32C5⋊D3511yescharacteristic, complemented
55C3⋊D3—1752no—
56C3×C5C2×D105124yescomplemented
57C2×C7C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented
58D7—2252no—
59C2×D3—5254no—
60C2×C5C3⋊D10516yescomplemented
61D5—31512no—
62C32C2×C5⋊D3511yescharacteristic, complemented, Sylow
63C7C2×C3⋊(C3⋊(C5⋊D5))11yescharacteristic, complemented, Sylow
64C2×C3C3⋊(C5⋊D35)14yescomplemented
65D3—5258no—
66C5C2×C3⋊D10516yescomplemented
67C22—15751noSylow
68C3C2×C3⋊(C5⋊D35)14yescomplemented
69C2—15752no—
70C2C3⋊(C3⋊(C5⋊D35))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C5⋊D35))
commutator, hypocenterC32×C52×C7C22
FrattiniC1G
Fitting, socleC2×C32×C52×C7C2
LCSG ▷ C32×C52×C7
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊(C5⋊D35))C2direct (N × H)
2. C2×C32×C52×C7C2semidirect
4. C32×C52×C7C22semidirect
6. C2×C3×C52×C7D3semidirect
10. C2×C32×C5×C7D5semidirect
12. C3×C52×C7C2×D3semidirect
13. C2×C32×C52D7semidirect
16. C2×C52×C7C3⋊D3semidirect
18. C32×C5×C7C2×D5semidirect
21. C32×C52C2×D7semidirect
22. C2×C3×C5×C7D15semidirect
25. C52×C7C2×C3⋊D3semidirect
26. C2×C3×C52D21semidirect
29. C2×C32×C7C5⋊D5semidirect
31. C3×C5×C7C2×D15semidirect
33. C2×C32×C5D35semidirect
36. C3×C52C2×D21semidirect
37. C2×C5×C7C3⋊D15semidirect
39. C32×C7C2×C5⋊D5semidirect
41. C2×C52C3⋊D21semidirect
43. C32×C5C2×D35semidirect
44. C2×C3×C7C3⋊(C5⋊D5)semidirect
47. C5×C7C2×C3⋊D15semidirect
48. C2×C3×C5D105semidirect
51. C52C2×C3⋊D21semidirect
52. C3×C7C2×C3⋊(C5⋊D5)semidirect
54. C2×C32C5⋊D35semidirect
56. C3×C5C2×D105semidirect
57. C2×C7C3⋊(C3⋊(C5⋊D5))semidirect
60. C2×C5C3⋊D105semidirect
62. C32C2×C5⋊D35semidirect
63. C7C2×C3⋊(C3⋊(C5⋊D5))semidirect
64. C2×C3C3⋊(C5⋊D35)semidirect
66. C5C2×C3⋊D105semidirect
68. C3C2×C3⋊(C5⋊D35)semidirect
70. C2C3⋊(C3⋊(C5⋊D35))direct (N × H)