Finite Group Databasebeta

← C5×C17⋊(D7⋊C9) #24924205

Subgroups — C5×C17⋊(D7⋊C9) #24924205

Order 10710.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C17×C7⋊C9C211yesmaximal, characteristic, complemented, Hall
2C3×C5×D119C311yesmaximal, characteristic
3C17⋊(D7⋊C9)C511yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C7×C17C2×C311yescharacteristic
5C5×C9×D17—71nomaximal, Hall
6C5×D119C911yescharacteristic, complemented, Hall
7C17×C7⋊C9C2×C511yescharacteristic, complemented, Hall
8C5×C9×C17—71noHall
9C3×D119C3×C511yescharacteristic
10C5×D7⋊C9—171nomaximal, Hall
11C5×C7×C17C2×C911yescharacteristic, complemented, Hall
12C3×C5×D17—71no—
13C3×C7×C17C2×C3×C511yescharacteristic
14C5×C7⋊C9D1711yescharacteristic, complemented, Hall
15C9×D17—71noHall
16C3×C5×C17AGL(1,𝔽7)11yescharacteristic
17D119C5×C911yescharacteristic, complemented, Hall
18C3×C5×D7—171no—
19C5×D17—71noHall
20C9×C17—71noHall
21D7⋊C9—171noHall
22C7×C17C2×C5×C911yescharacteristic, complemented, Hall
23C3×C5×C7C3×D1711yescharacteristic
24C3×D17—71no—
25C2×C5×C9—1191noHall
26C5×C17D7⋊C911yescharacteristic, complemented, Hall
27C5×D7—171noHall
28C7⋊C9C5×D1711yescharacteristic, complemented, Hall
29C3×C17C5×AGL(1,𝔽7)11yescharacteristic
30C5×C9—71noHall
31C3×D7—171no—
32C5×C7C9×D1711yescharacteristic, complemented, Hall
33D17—71noHall
34C2×C3×C5—1191no—
35C3×C7C3×C5×D1711yescharacteristic
36C2×C9—1191noHall
37C17C5×D7⋊C911yescharacteristic, complemented, Sylow
38C3×C5C17⋊AGL(1,𝔽7)11yescharacteristic
39D7—171noHall
40C2×C5—1191noHall
41C9—71noSylow
42C7C5×C9×D1711yescharacteristic, complemented, Sylow
43C2×C3—1191no—
44C5C17⋊(D7⋊C9)11yescharacteristic, direct product factor, Sylow
45C3C5×C17⋊AGL(1,𝔽7)11yescharacteristic
46C2—1191noSylow
subgroupG/H
center, hypercenterC3×C5C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C2×C5×C9
FrattiniC3C5×C17⋊AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C17C2×C3
prime radicalC3×C5×D119C3
cosocleC3×C7×C17C2×C3×C5
LCSG ▷ C7×C17
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C5×C17×C7⋊C9C2semidirect
3. C17⋊(D7⋊C9)C5direct (N × H)
6. C5×D119C9semidirect
7. C17×C7⋊C9C2×C5semidirect
11. C5×C7×C17C2×C9semidirect
14. C5×C7⋊C9D17semidirect
17. D119C5×C9semidirect
22. C7×C17C2×C5×C9semidirect
26. C5×C17D7⋊C9semidirect
28. C7⋊C9C5×D17semidirect
32. C5×C7C9×D17semidirect
37. C17C5×D7⋊C9semidirect
42. C7C5×C9×D17semidirect
44. C5C17⋊(D7⋊C9)direct (N × H)