Finite Group Databasebeta

← C3×C11×C47⋊AGL(1,𝔽5) #44526641

Subgroups — C3×C11×C47⋊AGL(1,𝔽5) #44526641

Order 31020.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C11×C47C211yesmaximal, characteristic
2C11×C47⋊AGL(1,𝔽5)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C11×C47C411yescharacteristic, complemented, Hall
4C3×C11×Dic47—51nomaximal, Hall
5D5×C11×C47C2×C311yescharacteristic
6C2×C3×C11×C47—51no—
7C3×C47⋊AGL(1,𝔽5)C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C47C3×C411yescharacteristic, complemented, Hall
9C11×Dic47—51noHall
10C3×C11×C47AGL(1,𝔽5)11yescharacteristic, complemented, Hall
11C3×D5×C47C2×C1111yescharacteristic
12C2×C11×C47—51no—
13C47⋊AGL(1,𝔽5)C3×C1111yescharacteristic, direct product factor, Hall
14C3×C5×C47C4×C1111yescharacteristic, complemented, Hall
15C3×C11×AGL(1,𝔽5)—471nomaximal, Hall
16C3×Dic47—51noHall
17C11×C47C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
18D5×C47C2×C3×C1111yescharacteristic
19C3×D5×C11D4711yescharacteristic
20C2×C3×C47—51no—
21C5×C47C3×C4×C1111yescharacteristic, complemented, Hall
22C11×AGL(1,𝔽5)—471noHall
23Dic47—51noHall
24C3×C5×C11Dic4711yescharacteristic, complemented, Hall
25C3×C47C11×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
26C3×C4×C11—2351noHall
27D5×C11C3×D4711yescharacteristic
28C2×C47—51no—
29C2×C3×C11—51no—
30C3×AGL(1,𝔽5)—471noHall
31C5×C11C3×Dic4711yescharacteristic, complemented, Hall
32C47C3×C11×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
33C4×C11—2351noHall
34C3×C11C47⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
35C3×D5C11×D4711yescharacteristic
36C2×C11—51no—
37AGL(1,𝔽5)—471noHall
38C3×C5C11×Dic4711yescharacteristic, complemented, Hall
39C3×C4—2351noHall
40C11C3×C47⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
41D5C3×C11×D4711yescharacteristic
42C2×C3—51no—
43C5C3×C11×Dic4711yescharacteristic, complemented, Sylow
44C4—2351noSylow
45C3C11×C47⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
46C2—51no—
subgroupG/H
center, hypercenterC3×C11C47⋊AGL(1,𝔽5)
commutator, hypocenterC5×C47C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C47C4
prime radicalC3×D5×C11×C47C2
cosocleD5×C47C2×C3×C11
LCSG ▷ C5×C47
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
2. C11×C47⋊AGL(1,𝔽5)C3direct (N × H)
3. C3×C5×C11×C47C4semidirect
7. C3×C47⋊AGL(1,𝔽5)C11direct (N × H)
8. C5×C11×C47C3×C4semidirect
10. C3×C11×C47AGL(1,𝔽5)semidirect
13. C47⋊AGL(1,𝔽5)C3×C11direct (N × H)
14. C3×C5×C47C4×C11semidirect
17. C11×C47C3×AGL(1,𝔽5)semidirect
21. C5×C47C3×C4×C11semidirect
24. C3×C5×C11Dic47semidirect
25. C3×C47C11×AGL(1,𝔽5)semidirect
31. C5×C11C3×Dic47semidirect
32. C47C3×C11×AGL(1,𝔽5)semidirect
34. C3×C11C47⋊AGL(1,𝔽5)direct (N × H)
38. C3×C5C11×Dic47semidirect
40. C11C3×C47⋊AGL(1,𝔽5)direct (N × H)
43. C5C3×C11×Dic47semidirect
45. C3C11×C47⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×D5×C11×C472
C11×C47⋊AGL(1,𝔽5)3
C3×C11×Dic475
C3×C47⋊AGL(1,𝔽5)11
C3×C11×AGL(1,𝔽5)47