Finite Group Databasebeta

← C7⋊C9×D85 #24924207

Subgroups — C7⋊C9×D85 #24924207

Order 10710.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C17×C7⋊C9C211yesmaximal, characteristic, complemented, Hall
2C3×C7×D85C311yesmaximal, characteristic
3D17×C7⋊C9—51nomaximal, Hall
4C3×C5×C7×C17C2×C311yescharacteristic
5C9×D85—71nomaximal, Hall
6C7×D85C911yescharacteristic, complemented, Hall
7C17×C7⋊C9D511yescharacteristic, complemented, Hall
8C5×C9×C17—71noHall
9C3×C7×D17—51no—
10D5×C7⋊C9—171nomaximal, Hall
11C5×C7×C17C2×C911yescharacteristic, complemented, Hall
12C3×D85ΓL(1,𝔽8)11yescharacteristic
13C3×C7×C17C3×D511yescharacteristic
14C5×C7⋊C9D1711yescharacteristic, complemented, Hall
15C9×D17—351noHall
16C3×C5×C17C2×ΓL(1,𝔽8)11yescharacteristic
17C7×D17—51noHall
18C3×C7×D5—171no—
19D85C7⋊C911yescharacteristic, direct product factor, Hall
20C9×C17—71noHall
21C2×C7⋊C9—851noHall
22C7×C17C9×D511yescharacteristic, complemented, Hall
23C3×C5×C7C3×D1711yescharacteristic
24C3×D17—51no—
25C9×D5—1191noHall
26C5×C17C2×C7⋊C911yescharacteristic, complemented, Hall
27C7×D5—171noHall
28C7⋊C9D8511yescharacteristic, direct product factor, Hall
29C3×C17D5×ΓL(1,𝔽8)11yescharacteristic
30C5×C9—71noHall
31C2×C3×C7—851no—
32C5×C7C9×D1711yescharacteristic, complemented, Hall
33D17—51noHall
34C3×D5—171no—
35C3×C7C3×D8511yescharacteristic
36C2×C9—5951noHall
37C17D5×C7⋊C911yescharacteristic, complemented, Sylow
38C3×C5ΓL(1,𝔽8)×D1711yescharacteristic
39C2×C7—851noHall
40D5—171noHall
41C9—71noSylow
42C7C9×D8511yescharacteristic, complemented, Sylow
43C2×C3—851no—
44C5D17×C7⋊C911yescharacteristic, complemented, Sylow
45C3ΓL(1,𝔽8)×D8511yescharacteristic
46C2—851noSylow
subgroupG/H
center, Frattini, hypercenterC3ΓL(1,𝔽8)×D85
commutator, hypocenterC5×C7×C17C2×C9
Fitting, socle, cosocleC3×C5×C7×C17C2×C3
prime radicalC3×C7×D85C3
LCSG ▷ C5×C7×C17
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C5×C17×C7⋊C9C2semidirect
6. C7×D85C9semidirect
7. C17×C7⋊C9D5semidirect
11. C5×C7×C17C2×C9semidirect
14. C5×C7⋊C9D17semidirect
19. D85C7⋊C9direct (N × H)
22. C7×C17C9×D5semidirect
26. C5×C17C2×C7⋊C9semidirect
28. C7⋊C9D85direct (N × H)
32. C5×C7C9×D17semidirect
37. C17D5×C7⋊C9semidirect
42. C7C9×D85semidirect
44. C5D17×C7⋊C9semidirect