Finite Group Databasebeta

← C5×C3⋊(C17⋊(D13⋊C3)) #34091049

Subgroups — C5×C3⋊(C17⋊(D13⋊C3)) #34091049

Order 19890.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C17×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5×C17⋊(D13⋊C3)—31nomaximal
3C5×D663C311yesmaximal, characteristic, complemented
4C3⋊(C17⋊(D13⋊C3))C511yesmaximal, characteristic, direct product factor, Hall
5C5×C17×C13⋊C3—21no—
6C5×C17×C13⋊C3D311yescharacteristic, complemented
7C3×C5×C13×C17C2×C311yescharacteristic, complemented
8C5×D221—31noHall
9C3×C17×C13⋊C3C2×C511yescharacteristic, complemented, Hall
10C3×C5×D51—131nomaximal, Hall
11D663C3×C511yescharacteristic, complemented
12C17⋊(D13⋊C3)—31no—
13C5×C3⋊(D13⋊C3)—171nomaximal, Hall
14C5×C13×C17C3×D311yescharacteristic, complemented, Hall
15C32×C5×C17—131noHall
16C3×C13×C17C2×C3×C511yescharacteristic, complemented
17C17×C13⋊C3—21no—
18C17×C13⋊C3C5×D311yescharacteristic, complemented
19C3×C5×C13⋊C3D1711yescharacteristic, complemented, Hall
20C5×D51—131no—
21C3×C5×D17—391no—
22D221—31noHall
23C5×D39—171no—
24C5×D13⋊C3—511no—
25C3×D51—131noHall
26C3×C5×C17—131no—
27C3×C5×C17—261no—
28C3×C5×C17D13⋊C311yescharacteristic, complemented
29C3⋊(D13⋊C3)—171noHall
30C13×C17C3×C5×D311yescharacteristic, complemented, Hall
31C3×C5×C13C3×D1711yescharacteristic, complemented
32C5×C13⋊C3—21no—
33C5×C13⋊C3D5111yescharacteristic, complemented
34C5×D17—391noHall
35C32×C17—131noHall
36C5×D13—511noHall
37C3×C13⋊C3C5×D1711yescharacteristic, complemented, Hall
38D51—131no—
39C3×D17—391no—
40C3×C5×D3—2211noHall
41C5×C17C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
42D39—171no—
43D13⋊C3—511no—
44C5×C13C3×D5111yescharacteristic, complemented, Hall
45C3×C17—131no—
46C3×C17—261no—
47C3×C17C5×D13⋊C311yescharacteristic, complemented
48C32×C5—131noHall
49C3×C13C3×C5×D1711yescharacteristic, complemented
50C13⋊C3—21no—
51C13⋊C3C5×D5111yescharacteristic, complemented
52D17—391noHall
53C2×C3×C5—6631no—
54C5×D3—2211no—
55D13—511noHall
56C3×D3—2211noHall
57C17C5×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
58C3×C5—131no—
59C3×C5—261no—
60C3×C5C17⋊(D13⋊C3)11yescharacteristic, complemented
61C13C3×C5×D5111yescharacteristic, complemented, Sylow
62C2×C5—6631noHall
63C32—131noSylow
64C2×C3—6631no—
65D3—2211no—
66C5C3⋊(C17⋊(D13⋊C3))11yescharacteristic, direct product factor, Sylow
67C3—131no—
68C3—261no—
69C3C5×C17⋊(D13⋊C3)11yescharacteristic, complemented
70C2—6631noSylow
subgroupG/H
center, hypercenterC5C3⋊(C17⋊(D13⋊C3))
commutator, cosocle, hypocenterC3×C13×C17C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C17C2×C3
LCSG ▷ C3×C13×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C17×C13⋊C3C2semidirect
3. C5×D663C3semidirect
4. C3⋊(C17⋊(D13⋊C3))C5direct (N × H)
6. C5×C17×C13⋊C3D3semidirect
7. C3×C5×C13×C17C2×C3semidirect
9. C3×C17×C13⋊C3C2×C5semidirect
11. D663C3×C5semidirect
14. C5×C13×C17C3×D3semidirect
16. C3×C13×C17C2×C3×C5semidirect
18. C17×C13⋊C3C5×D3semidirect
19. C3×C5×C13⋊C3D17semidirect
28. C3×C5×C17D13⋊C3semidirect
30. C13×C17C3×C5×D3semidirect
31. C3×C5×C13C3×D17semidirect
33. C5×C13⋊C3D51semidirect
37. C3×C13⋊C3C5×D17semidirect
41. C5×C17C3⋊(D13⋊C3)semidirect
44. C5×C13C3×D51semidirect
47. C3×C17C5×D13⋊C3semidirect
49. C3×C13C3×C5×D17semidirect
51. C13⋊C3C5×D51semidirect
57. C17C5×C3⋊(D13⋊C3)semidirect
60. C3×C5C17⋊(D13⋊C3)semidirect
61. C13C3×C5×D51semidirect
66. C5C3⋊(C17⋊(D13⋊C3))direct (N × H)
69. C3C5×C17⋊(D13⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C17×C13⋊C32
C5×C17⋊(D13⋊C3)3
C5×D6633
C3⋊(C17⋊(D13⋊C3))5
C3×C5×D5113
C5×C3⋊(D13⋊C3)17