Finite Group Databasebeta

← C5×ΓL(1,𝔽8)×D143 #44473281

Subgroups — C5×ΓL(1,𝔽8)×D143 #44473281

Order 30030.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C13×ΓL(1,𝔽8)C211yesmaximal, characteristic, complemented, Hall
2C5×C7×D143C311yesmaximal, characteristic, complemented, Hall
3ΓL(1,𝔽8)×D143C511yesmaximal, characteristic, direct product factor, Hall
4C5×C7×C11×C13C2×C311yescharacteristic, complemented, Hall
5C3×C5×D143—71nomaximal, Hall
6C11×C13×ΓL(1,𝔽8)C2×C511yescharacteristic, complemented, Hall
7C5×ΓL(1,𝔽8)×D13—111nomaximal, Hall
8C5×ΓL(1,𝔽8)×D11—131nomaximal, Hall
9C3×C5×C11×C13—71noHall
10C7×D143C3×C511yescharacteristic, complemented, Hall
11C5×D143ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
12C5×C13×ΓL(1,𝔽8)D1111yescharacteristic, complemented, Hall
13C5×C11×ΓL(1,𝔽8)D1311yescharacteristic, complemented, Hall
14C7×C11×C13C2×C3×C511yescharacteristic, complemented, Hall
15C5×C7×D13—111noHall
16C3×D143—71noHall
17C5×C7×D11—131noHall
18C5×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
19ΓL(1,𝔽8)×D13—111noHall
20ΓL(1,𝔽8)×D11—131noHall
21C5×C7×C13C3×D1111yescharacteristic, complemented, Hall
22C3×C11×C13—71noHall
23C3×C5×D13—771noHall
24C5×C7×C11C3×D1311yescharacteristic, complemented, Hall
25C3×C5×D11—911noHall
26D143C5×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
27C13×ΓL(1,𝔽8)C5×D1111yescharacteristic, complemented, Hall
28C11×ΓL(1,𝔽8)C5×D1311yescharacteristic, complemented, Hall
29C2×C5×ΓL(1,𝔽8)—1431noHall
30C3×C5×C13—71noHall
31C7×D13—111noHall
32C3×C5×C11—71noHall
33C7×D11—131noHall
34C11×C13C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
35C5×D13—111noHall
36C5×D11—131noHall
37C5×ΓL(1,𝔽8)D14311yescharacteristic, direct product factor, Hall
38C7×C13C3×C5×D1111yescharacteristic, complemented, Hall
39C3×D13—771noHall
40C7×C11C3×C5×D1311yescharacteristic, complemented, Hall
41C2×C5×C7—1431noHall
42C3×D11—911noHall
43C5×C13ΓL(1,𝔽8)×D1111yescharacteristic, complemented, Hall
44C5×C11ΓL(1,𝔽8)×D1311yescharacteristic, complemented, Hall
45C2×ΓL(1,𝔽8)—1431noHall
46C3×C13—71noHall
47C5×C7C3×D14311yescharacteristic, complemented, Hall
48C3×C11—71noHall
49C2×C3×C5—10011noHall
50D13—111noHall
51D11—131noHall
52ΓL(1,𝔽8)C5×D14311yescharacteristic, direct product factor, Hall
53C3×C5—71noHall
54C2×C7—1431noHall
55C13C5×ΓL(1,𝔽8)×D1111yescharacteristic, complemented, Sylow
56C11C5×ΓL(1,𝔽8)×D1311yescharacteristic, complemented, Sylow
57C2×C5—1431noHall
58C7C3×C5×D14311yescharacteristic, complemented, Sylow
59C2×C3—10011noHall
60C5ΓL(1,𝔽8)×D14311yescharacteristic, direct product factor, Sylow
61C3—71noSylow
62C2—1431noSylow
subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D143
commutator, cosocle, hypocenterC7×C11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C11×C13×ΓL(1,𝔽8)C2semidirect
2. C5×C7×D143C3semidirect
3. ΓL(1,𝔽8)×D143C5direct (N × H)
4. C5×C7×C11×C13C2×C3semidirect
6. C11×C13×ΓL(1,𝔽8)C2×C5semidirect
10. C7×D143C3×C5semidirect
11. C5×D143ΓL(1,𝔽8)direct (N × H)
12. C5×C13×ΓL(1,𝔽8)D11semidirect
13. C5×C11×ΓL(1,𝔽8)D13semidirect
14. C7×C11×C13C2×C3×C5semidirect
18. C5×C11×C13C2×ΓL(1,𝔽8)semidirect
21. C5×C7×C13C3×D11semidirect
24. C5×C7×C11C3×D13semidirect
26. D143C5×ΓL(1,𝔽8)direct (N × H)
27. C13×ΓL(1,𝔽8)C5×D11semidirect
28. C11×ΓL(1,𝔽8)C5×D13semidirect
34. C11×C13C2×C5×ΓL(1,𝔽8)semidirect
37. C5×ΓL(1,𝔽8)D143direct (N × H)
38. C7×C13C3×C5×D11semidirect
40. C7×C11C3×C5×D13semidirect
43. C5×C13ΓL(1,𝔽8)×D11semidirect
44. C5×C11ΓL(1,𝔽8)×D13semidirect
47. C5×C7C3×D143semidirect
52. ΓL(1,𝔽8)C5×D143direct (N × H)
55. C13C5×ΓL(1,𝔽8)×D11semidirect
56. C11C5×ΓL(1,𝔽8)×D13semidirect
58. C7C3×C5×D143semidirect
60. C5ΓL(1,𝔽8)×D143direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C13×ΓL(1,𝔽8)2
C5×C7×D1433
ΓL(1,𝔽8)×D1435
C3×C5×D1437
C5×ΓL(1,𝔽8)×D1311
C5×ΓL(1,𝔽8)×D1113