Finite Group Databasebeta

← C3⋊(C7⋊(C13⋊AGL(1,𝔽11))) #44473271

Subgroups — C3⋊(C7⋊(C13⋊AGL(1,𝔽11))) #44473271

Order 30030.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C13×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C7⋊(C13⋊AGL(1,𝔽11))—31nomaximal, Hall
3D3003C511yesmaximal, characteristic, complemented, Hall
4C7×C13×C11⋊C5D311yescharacteristic, complemented, Hall
5C3⋊(C13⋊AGL(1,𝔽11))—71nomaximal, Hall
6C3×C7×C11×C13C2×C511yescharacteristic, complemented, Hall
7C5×D273—111nomaximal, Hall
8C3⋊(C7⋊AGL(1,𝔽11))—131nomaximal, Hall
9C3×C13×C11⋊C5D711yescharacteristic, complemented, Hall
10D1001—31noHall
11C13⋊AGL(1,𝔽11)—211noHall
12C3×C5×C7×C13—111noHall
13C3×C7×C11⋊C5D1311yescharacteristic, complemented, Hall
14C7×C11×C13C5×D311yescharacteristic, complemented, Hall
15C5×D91—331noHall
16D429—71noHall
17C7⋊AGL(1,𝔽11)—391noHall
18C13×C11⋊C5D2111yescharacteristic, complemented, Hall
19D273—111noHall
20D231—131noHall
21C5×C7×C13—111noHall
22C3×C11×C13C5×D711yescharacteristic, complemented, Hall
23C5×D39—771noHall
24C7×C11⋊C5D3911yescharacteristic, complemented, Hall
25C3⋊AGL(1,𝔽11)—911noHall
26D143—211noHall
27C3×C7×C13AGL(1,𝔽11)11yescharacteristic, complemented, Hall
28C3×C7×C11C5×D1311yescharacteristic, complemented, Hall
29C5×D21—1431noHall
30C3×C5×C13—111noHall
31D91—331noHall
32C3×C11⋊C5D9111yescharacteristic, complemented, Hall
33D77—391noHall
34C11×C13C5×D2111yescharacteristic, complemented, Hall
35C5×D13—2311noHall
36AGL(1,𝔽11)—2731noHall
37C3×C5×C7—111noHall
38C7×C13C3⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
39D39—771noHall
40C7×C11C5×D3911yescharacteristic, complemented, Hall
41C5×D7—4291noHall
42D33—911noHall
43C5×C13—111noHall
44C11⋊C5D27311yescharacteristic, complemented, Hall
45D21—1431noHall
46C3×C13C7⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
47C5×C7—111noHall
48C3×C11C5×D9111yescharacteristic, complemented, Hall
49C5×D3—10011noHall
50D13—2311noHall
51D11—2731noHall
52C3×C7C13⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
53C3×C5—111noHall
54D7—4291noHall
55C13C3⋊(C7⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
56C11C5×D27311yescharacteristic, complemented, Sylow
57C2×C5—30031noHall
58C7C3⋊(C13⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
59D3—10011noHall
60C5—111noSylow
61C3C7⋊(C13⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
62C2—30031noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C2×C5
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×C11⋊C5C2semidirect
3. D3003C5semidirect
4. C7×C13×C11⋊C5D3semidirect
6. C3×C7×C11×C13C2×C5semidirect
9. C3×C13×C11⋊C5D7semidirect
13. C3×C7×C11⋊C5D13semidirect
14. C7×C11×C13C5×D3semidirect
18. C13×C11⋊C5D21semidirect
22. C3×C11×C13C5×D7semidirect
24. C7×C11⋊C5D39semidirect
27. C3×C7×C13AGL(1,𝔽11)semidirect
28. C3×C7×C11C5×D13semidirect
32. C3×C11⋊C5D91semidirect
34. C11×C13C5×D21semidirect
38. C7×C13C3⋊AGL(1,𝔽11)semidirect
40. C7×C11C5×D39semidirect
44. C11⋊C5D273semidirect
46. C3×C13C7⋊AGL(1,𝔽11)semidirect
48. C3×C11C5×D91semidirect
52. C3×C7C13⋊AGL(1,𝔽11)semidirect
55. C13C3⋊(C7⋊AGL(1,𝔽11))semidirect
56. C11C5×D273semidirect
58. C7C3⋊(C13⋊AGL(1,𝔽11))semidirect
61. C3C7⋊(C13⋊AGL(1,𝔽11))semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×C11⋊C52
C7⋊(C13⋊AGL(1,𝔽11))3
D30035
C3⋊(C13⋊AGL(1,𝔽11))7
C5×D27311
C3⋊(C7⋊AGL(1,𝔽11))13