Finite Group Databasebeta

← ΓL(1,𝔽8)×D13×C11⋊C5 #44473333

Subgroups — ΓL(1,𝔽8)×D13×C11⋊C5 #44473333

Order 30030.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C7×D13×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3C11×ΓL(1,𝔽8)×D13C511yesmaximal, characteristic, complemented, Hall
4C7×C13×C11⋊C5C2×C311yescharacteristic, complemented, Hall
5C3×D13×C11⋊C5—71nomaximal, Hall
6C11×C13×ΓL(1,𝔽8)C2×C511yescharacteristic, complemented, Hall
7C5×ΓL(1,𝔽8)×D13—111nomaximal, Hall
8C2×ΓL(1,𝔽8)×C11⋊C5—131nomaximal, Hall
9C3×C13×C11⋊C5—71noHall
10C7×C11×D13C3×C511yescharacteristic, complemented, Hall
11D13×C11⋊C5ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
12C5×C13×ΓL(1,𝔽8)—111noHall
13ΓL(1,𝔽8)×C11⋊C5D1311yescharacteristic, direct product factor, Hall
14C7×C11×C13C2×C3×C511yescharacteristic, complemented, Hall
15C5×C7×D13—111noHall
16C3×C11×D13—71noHall
17C2×C7×C11⋊C5—131noHall
18C13×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
19ΓL(1,𝔽8)×D13C11⋊C511yescharacteristic, direct product factor, Hall
20C2×C11×ΓL(1,𝔽8)—131noHall
21C5×C7×C13—111noHall
22C3×C11×C13—71noHall
23C3×C5×D13—771noHall
24C7×C11⋊C5C3×D1311yescharacteristic, complemented, Hall
25C2×C3×C11⋊C5—911noHall
26C11×D13C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
27C13×ΓL(1,𝔽8)C2×C11⋊C511yescharacteristic, complemented, Hall
28C11×ΓL(1,𝔽8)C5×D1311yescharacteristic, complemented, Hall
29C2×C5×ΓL(1,𝔽8)—1431noHall
30C3×C5×C13—771noHall
31C7×D13C3×C11⋊C511yescharacteristic, complemented, Hall
32C3×C11⋊C5—71noHall
33C2×C7×C11—131noHall
34C11×C13C2×C5×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
35C5×D13—111noHall
36C2×C11⋊C5—131noHall
37C5×ΓL(1,𝔽8)—111noHall
38C7×C13C2×C3×C11⋊C511yescharacteristic, complemented, Hall
39C3×D13—71noHall
40C7×C11C3×C5×D1311yescharacteristic, complemented, Hall
41C2×C5×C7—1431noHall
42C2×C3×C11—911noHall
43C5×C13—111noHall
44C11⋊C5ΓL(1,𝔽8)×D1311yescharacteristic, direct product factor, Hall
45C2×ΓL(1,𝔽8)—131noHall
46C3×C13—71noHall
47C5×C7—111noHall
48C3×C11—71noHall
49C2×C3×C5—10011noHall
50D13ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor, Hall
51C2×C11—131noHall
52ΓL(1,𝔽8)D13×C11⋊C511yescharacteristic, direct product factor, Hall
53C3×C5—771noHall
54C2×C7—131noHall
55C13C2×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, complemented, Sylow
56C11C5×ΓL(1,𝔽8)×D1311yescharacteristic, complemented, Sylow
57C2×C5—1431noHall
58C7C3×D13×C11⋊C511yescharacteristic, complemented, Sylow
59C2×C3—911noHall
60C5—111noSylow
61C3—71noSylow
62C2—131noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C2×C3×C5
LCSG ▷ C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13×ΓL(1,𝔽8)×C11⋊C5C2semidirect
2. C7×D13×C11⋊C5C3semidirect
3. C11×ΓL(1,𝔽8)×D13C5semidirect
4. C7×C13×C11⋊C5C2×C3semidirect
6. C11×C13×ΓL(1,𝔽8)C2×C5semidirect
10. C7×C11×D13C3×C5semidirect
11. D13×C11⋊C5ΓL(1,𝔽8)direct (N × H)
13. ΓL(1,𝔽8)×C11⋊C5D13direct (N × H)
14. C7×C11×C13C2×C3×C5semidirect
18. C13×C11⋊C5C2×ΓL(1,𝔽8)semidirect
19. ΓL(1,𝔽8)×D13C11⋊C5direct (N × H)
24. C7×C11⋊C5C3×D13semidirect
26. C11×D13C5×ΓL(1,𝔽8)semidirect
27. C13×ΓL(1,𝔽8)C2×C11⋊C5semidirect
28. C11×ΓL(1,𝔽8)C5×D13semidirect
31. C7×D13C3×C11⋊C5semidirect
34. C11×C13C2×C5×ΓL(1,𝔽8)semidirect
38. C7×C13C2×C3×C11⋊C5semidirect
40. C7×C11C3×C5×D13semidirect
44. C11⋊C5ΓL(1,𝔽8)×D13direct (N × H)
50. D13ΓL(1,𝔽8)×C11⋊C5direct (N × H)
52. ΓL(1,𝔽8)D13×C11⋊C5direct (N × H)
55. C13C2×ΓL(1,𝔽8)×C11⋊C5semidirect
56. C11C5×ΓL(1,𝔽8)×D13semidirect
58. C7C3×D13×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C13×ΓL(1,𝔽8)×C11⋊C52
C7×D13×C11⋊C53
C11×ΓL(1,𝔽8)×D135
C3×D13×C11⋊C57
C5×ΓL(1,𝔽8)×D1311
C2×ΓL(1,𝔽8)×C11⋊C513