Finite Group Databasebeta

← C5×#13097589 #22547607

Subgroups — C5×#13097589 #22547607

Order 7980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#87705C211yesmaximal, characteristic
2C5×Dic133C311yesmaximal, characteristic, complemented, Hall
3C5×#87705C411yescharacteristic, complemented, Hall
4#13097589C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C7×C19C2×C311yescharacteristic
6C5×(C19⋊C3)⋊C4—71nomaximal, Hall
7C2×#87705C2×C511yescharacteristic
8C5×C7×C19C3×C411yescharacteristic, complemented, Hall
9C2×C5×C19⋊C3—71no—
10Dic133C3×C511yescharacteristic, complemented, Hall
11C5×ΓL(1,𝔽8)⋊C4—191nomaximal, Hall
12#87705C4×C511yescharacteristic, complemented, Hall
13C5×Dic19—71noHall
14C5×C19⋊C3—71noHall
15C2×C7×C19C2×C3×C511yescharacteristic
16(C19⋊C3)⋊C4—71noHall
17C2×C5×ΓL(1,𝔽8)—191no—
18C2×C5×C19AGL(1,𝔽7)11yescharacteristic
19C5×Dic7—191noHall
20C7×C19C3×C4×C511yescharacteristic, complemented, Hall
21C2×C19⋊C3—71no—
22C5×ΓL(1,𝔽8)—191noHall
23C5×C19ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Hall
24ΓL(1,𝔽8)⋊C4—191noHall
25Dic19—71noHall
26C2×C5×C7D19⋊C311yescharacteristic
27C3×C4×C5—1331noHall
28C19⋊C3—71noHall
29C2×ΓL(1,𝔽8)—191no—
30C2×C19C5×AGL(1,𝔽7)11yescharacteristic
31C5×C7(C19⋊C3)⋊C411yescharacteristic, complemented, Hall
32C2×C3×C5—1331no—
33Dic7—191noHall
34ΓL(1,𝔽8)—191noHall
35C4×C5—1331noHall
36C19C5×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented, Sylow
37C3×C5—1331noHall
38C2×C7C5×D19⋊C311yescharacteristic
39C3×C4—1331noHall
40C2×C5#1171632811yescharacteristic
41C7C5×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
42C2×C3—1331no—
43C5#1309758911yescharacteristic, direct product factor, Sylow
44C4—1331noSylow
45C3—1331noSylow
46C2C5×#1171632811yescharacteristic
subgroupG/H
center, hypercenterC2×C5#11716328
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C5×#11716328
Fitting, socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×Dic133C3semidirect
3. C5×#87705C4semidirect
4. #13097589C5direct (N × H)
8. C5×C7×C19C3×C4semidirect
10. Dic133C3×C5semidirect
12. #87705C4×C5semidirect
20. C7×C19C3×C4×C5semidirect
23. C5×C19ΓL(1,𝔽8)⋊C4semidirect
31. C5×C7(C19⋊C3)⋊C4semidirect
36. C19C5×ΓL(1,𝔽8)⋊C4semidirect
41. C7C5×(C19⋊C3)⋊C4semidirect
43. C5#13097589direct (N × H)