Finite Group Databasebeta

← C3⋊(C5⋊(C23⋊(D13⋊C3))) #41002111

Subgroups — C3⋊(C5⋊(C23⋊(D13⋊C3))) #41002111

Order 26910.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C23×C13⋊C3C211yesmaximal, characteristic, complemented, Hall
2C5⋊(C23⋊(D13⋊C3))—31nomaximal
3D4485C311yesmaximal, characteristic, complemented
4C3⋊(C23⋊(D13⋊C3))—51nomaximal, Hall
5C5×C23×C13⋊C3—21no—
6C5×C23×C13⋊C3D311yescharacteristic, complemented
7C3×C5×C13×C23C2×C311yescharacteristic, complemented
8D1495—31noHall
9C3×C23×C13⋊C3D511yescharacteristic, complemented, Hall
10C3×D345—131nomaximal, Hall
11D897—51no—
12C23⋊(D13⋊C3)—151no—
13C5×C13×C23C3×D311yescharacteristic, complemented, Hall
14C3⋊(C5⋊(D13⋊C3))—231nomaximal, Hall
15C32×C5×C23—261noHall
16C3×C13×C23C3×D511yescharacteristic, complemented
17C23×C13⋊C3—21no—
18C23×C13⋊C3D1511yescharacteristic, complemented
19D345—131no—
20C3×D115—391no—
21D299—151noHall
22C3×C5×C13⋊C3D2311yescharacteristic, complemented, Hall
23C3×D69—651noHall
24D195—231no—
25C5⋊(D13⋊C3)—691no—
26C3×C5×C23—261no—
27C3×C5×C23—261no—
28C3×C5×C23D13⋊C311yescharacteristic, complemented
29C13×C23C3×D1511yescharacteristic, complemented, Hall
30C3⋊(D13⋊C3)—1151noHall
31D115—391noHall
32C32×C23—131noHall
33C3×C5×C13C3×D2311yescharacteristic, complemented
34C5×C13⋊C3—21no—
35C5×C13⋊C3D6911yescharacteristic, complemented
36D69—651no—
37C3×D23—1951no—
38D65—691noHall
39C3×C13⋊C3D11511yescharacteristic, complemented, Hall
40C5×C23C3⋊(D13⋊C3)11yescharacteristic, complemented, Hall
41C3×D15—2991noHall
42D39—1151no—
43D13⋊C3—3451no—
44C3×C23—261no—
45C3×C23—261no—
46C3×C23C5⋊(D13⋊C3)11yescharacteristic, complemented
47C5×C13C3×D6911yescharacteristic, complemented, Hall
48D23—1951noHall
49C32×C5—261noHall
50C3×C13C3×D11511yescharacteristic, complemented
51C13⋊C3—21no—
52C13⋊C3D34511yescharacteristic, complemented
53D15—2991no—
54C3×D5—8971no—
55D13—3451noHall
56C23C3⋊(C5⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
57C3×D3—14951noHall
58C3×C5—261no—
59C3×C5—261no—
60C3×C5C23⋊(D13⋊C3)11yescharacteristic, complemented
61C13C3×D34511yescharacteristic, complemented, Sylow
62D5—8971noHall
63C32—261noSylow
64C2×C3—44851no—
65D3—14951no—
66C5C3⋊(C23⋊(D13⋊C3))11yescharacteristic, complemented, Sylow
67C3—261no—
68C3—261no—
69C3C5⋊(C23⋊(D13⋊C3))11yescharacteristic, complemented
70C2—44851noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C23C2×C3
LCSG ▷ C3×C5×C13×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×C23×C13⋊C3C2semidirect
3. D4485C3semidirect
6. C5×C23×C13⋊C3D3semidirect
7. C3×C5×C13×C23C2×C3semidirect
9. C3×C23×C13⋊C3D5semidirect
13. C5×C13×C23C3×D3semidirect
16. C3×C13×C23C3×D5semidirect
18. C23×C13⋊C3D15semidirect
22. C3×C5×C13⋊C3D23semidirect
28. C3×C5×C23D13⋊C3semidirect
29. C13×C23C3×D15semidirect
33. C3×C5×C13C3×D23semidirect
35. C5×C13⋊C3D69semidirect
39. C3×C13⋊C3D115semidirect
40. C5×C23C3⋊(D13⋊C3)semidirect
46. C3×C23C5⋊(D13⋊C3)semidirect
47. C5×C13C3×D69semidirect
50. C3×C13C3×D115semidirect
52. C13⋊C3D345semidirect
56. C23C3⋊(C5⋊(D13⋊C3))semidirect
60. C3×C5C23⋊(D13⋊C3)semidirect
61. C13C3×D345semidirect
66. C5C3⋊(C23⋊(D13⋊C3))semidirect
69. C3C5⋊(C23⋊(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×C23×C13⋊C32
C5⋊(C23⋊(D13⋊C3))3
D44853
C3⋊(C23⋊(D13⋊C3))5
C3×D34513
C3⋊(C5⋊(D13⋊C3))23