Finite Group Databasebeta

← AGL(1,𝔽5)×C169⋊C3 #23778357

Subgroups — AGL(1,𝔽5)×C169⋊C3 #23778357

Order 10140.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C169⋊C3C211yesmaximal, characteristic
2AGL(1,𝔽5)×C169C311yesmaximal, characteristic, complemented, Hall
3C5×C169⋊C3C411yescharacteristic, complemented, Hall
4C4×C169⋊C3—51nomaximal, Hall
5D5×C169C2×C311yescharacteristic
6C2×C169⋊C3—51no—
7C5×C169C3×C411yescharacteristic, complemented, Hall
8AGL(1,𝔽5)×C13⋊C3—131nomaximal
9C4×C169—51noHall
10C169⋊C3AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
11D5×C13⋊C3—131no—
12C2×C169—51no—
13C13×AGL(1,𝔽5)C13⋊C311yescharacteristic
14C5×C13⋊C3—131no—
15C169C3×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
16C4×C13⋊C3—651no—
17D5×C13C2×C13⋊C311yescharacteristic
18C2×C13⋊C3—651no—
19C5×C13C4×C13⋊C311yescharacteristic
20C3×AGL(1,𝔽5)—1691noHall
21C4×C13—51no—
22C13⋊C3—131no—
23C3×D5—1691no—
24C2×C13—51no—
25AGL(1,𝔽5)C169⋊C311yescharacteristic, direct product factor, Hall
26C3×C5—1691noHall
27C13AGL(1,𝔽5)×C13⋊C311yescharacteristic
28C3×C4—8451noHall
29D5C2×C169⋊C311yescharacteristic
30C2×C3—8451no—
31C5C4×C169⋊C311yescharacteristic, complemented, Sylow
32C4—51noSylow
33C3—1691noSylow
34C2—51no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C169C3×C4
FrattiniC13AGL(1,𝔽5)×C13⋊C3
socleC5×C13C4×C13⋊C3
prime radicalD5×C169⋊C3C2
cosocleD5×C169C2×C3
LCSG ▷ C5×C169
UCSC1

Complements

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

NH ≅ G/Ntype
2. AGL(1,𝔽5)×C169C3semidirect
3. C5×C169⋊C3C4semidirect
7. C5×C169C3×C4semidirect
10. C169⋊C3AGL(1,𝔽5)direct (N × H)
15. C169C3×AGL(1,𝔽5)semidirect
25. AGL(1,𝔽5)C169⋊C3direct (N × H)
31. C5C4×C169⋊C3semidirect