Finite Group Databasebeta

← (C19⋊C3)⋊(C7⋊AGL(1,𝔽5)) #22547643

Subgroups — (C19⋊C3)⋊(C7⋊AGL(1,𝔽5)) #22547643

Order 7980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D5×C19⋊C3C211yesmaximal, characteristic
2C7⋊(C19⋊AGL(1,𝔽5))C311yesmaximal, characteristic, complemented, Hall
3C5×C7×C19⋊C3C411yescharacteristic, complemented, Hall
4(C19⋊C3)⋊Dic7—51nomaximal, Hall
5C7×D5×C19C2×C311yescharacteristic
6(C19⋊C3)⋊AGL(1,𝔽5)—71nomaximal, Hall
7C2×C7×C19⋊C3—51no—
8C5×C7×C19C3×C411yescharacteristic, complemented, Hall
9D5×C19⋊C3D711yescharacteristic
10Dic133—51noHall
11C3×C7⋊AGL(1,𝔽5)—191nomaximal, Hall
12C7×C19⋊C3AGL(1,𝔽5)11yescharacteristic, complemented, Hall
13C19⋊AGL(1,𝔽5)—71noHall
14C5×C19⋊C3Dic711yescharacteristic, complemented, Hall
15C2×C7×C19—51no—
16(C19⋊C3)⋊C4—351noHall
17C3×C7×D5—191no—
18D5×C19C3×D711yescharacteristic
19C7⋊AGL(1,𝔽5)—191noHall
20C7×C19C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
21C2×C19⋊C3—51no—
22C3×C5×C7—191noHall
23C5×C19C3×Dic711yescharacteristic, complemented, Hall
24C3×Dic7—951noHall
25Dic19—351noHall
26C7×D5D19⋊C311yescharacteristic
27C3×AGL(1,𝔽5)—1331noHall
28C19⋊C3C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Hall
29C2×C3×C7—951no—
30C2×C19—51no—
31C5×C7(C19⋊C3)⋊C411yescharacteristic, complemented, Hall
32C3×D5—191no—
33Dic7—951noHall
34C3×C7—191noHall
35AGL(1,𝔽5)—1331noHall
36C19C3×C7⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
37C3×C5—191noHall
38C2×C7—51no—
39C3×C4—6651noHall
40D5(C19⋊C3)⋊D711yescharacteristic
41C7(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
42C2×C3—951no—
43C5(C19⋊C3)⋊Dic711yescharacteristic, complemented, Sylow
44C4—6651noSylow
45C3—191noSylow
46C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C3×C4
LCSG ▷ C5×C7×C19
UCSC1

Complements

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

NH ≅ G/Ntype
2. C7⋊(C19⋊AGL(1,𝔽5))C3semidirect
3. C5×C7×C19⋊C3C4semidirect
8. C5×C7×C19C3×C4semidirect
12. C7×C19⋊C3AGL(1,𝔽5)semidirect
14. C5×C19⋊C3Dic7semidirect
20. C7×C19C3×AGL(1,𝔽5)semidirect
23. C5×C19C3×Dic7semidirect
28. C19⋊C3C7⋊AGL(1,𝔽5)semidirect
31. C5×C7(C19⋊C3)⋊C4semidirect
36. C19C3×C7⋊AGL(1,𝔽5)semidirect
41. C7(C19⋊C3)⋊AGL(1,𝔽5)semidirect
43. C5(C19⋊C3)⋊Dic7semidirect