Finite Group Databasebeta

← AGL(1,𝔽5)×#13133721 #46802084

Subgroups — AGL(1,𝔽5)×#13133721 #46802084

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#13133721C211yesmaximal, characteristic
2C5×#13133721C411yescharacteristic, complemented, Hall
3C11×AGL(1,𝔽5)×C31C511yesmaximal, characteristic, complemented
4C4×#13133721—51nomaximal
5D5×C11×C31C2×C511yescharacteristic
6C2×#13133721—51no—
7AGL(1,𝔽5)×ΓL(1,𝔽32)—111nomaximal, Hall
8C5×C11×C31C4×C511yescharacteristic, complemented
9#13133721—41no—
10#13133721AGL(1,𝔽5)11yescharacteristic, direct product factor
11D5×ΓL(1,𝔽32)—111no—
12C4×C11×C31—51noHall
13AGL(1,𝔽5)×C11⋊C5—311nomaximal, Hall
14C5×ΓL(1,𝔽32)—111noHall
15C2×C11×C31—51no—
16AGL(1,𝔽5)×C31C11⋊C511yescharacteristic, complemented
17C4×ΓL(1,𝔽32)—551no—
18D5×C11⋊C5—311no—
19C11×C31C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20D5×C31C2×C11⋊C511yescharacteristic
21C2×ΓL(1,𝔽32)—551no—
22C5×C11⋊C5—311noHall
23C11×AGL(1,𝔽5)ΓL(1,𝔽32)11yescharacteristic, complemented
24C4×C11⋊C5—1551no—
25C5×C31C4×C11⋊C511yescharacteristic, complemented
26ΓL(1,𝔽32)—111no—
27ΓL(1,𝔽32)—441no—
28C4×C31—51noHall
29D5×C11C2×ΓL(1,𝔽32)11yescharacteristic
30C2×C11⋊C5—1551no—
31C5×AGL(1,𝔽5)—3411noHall
32C2×C31—51no—
33C5×C11C4×ΓL(1,𝔽32)11yescharacteristic, complemented
34C11⋊C5—311no—
35C11⋊C5—1241no—
36C5×D5—3411no—
37C4×C11—51noHall
38C31AGL(1,𝔽5)×C11⋊C511yescharacteristic, complemented, Sylow
39C52—3411noSylow
40C2×C11—51no—
41AGL(1,𝔽5)#1313372111yescharacteristic, direct product factor
42C4×C5—17051no—
43C11AGL(1,𝔽5)×ΓL(1,𝔽32)11yescharacteristic, complemented, Sylow
44C2×C5—17051no—
45D5C2×#1313372111yescharacteristic
46C5—13641no—
47C5—3411no—
48C5C4×#1313372111yescharacteristic, complemented
49C4—51noSylow
50C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C31C4×C5
prime radicalD5×#13133721C2
cosocleD5×C11×C31C2×C5
LCSG ▷ C5×C11×C31
UCSC1

Complements

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

NH ≅ G/Ntype
2. C5×#13133721C4semidirect
3. C11×AGL(1,𝔽5)×C31C5semidirect
8. C5×C11×C31C4×C5semidirect
10. #13133721AGL(1,𝔽5)direct (N × H)
16. AGL(1,𝔽5)×C31C11⋊C5semidirect
19. C11×C31C5×AGL(1,𝔽5)semidirect
23. C11×AGL(1,𝔽5)ΓL(1,𝔽32)semidirect
25. C5×C31C4×C11⋊C5semidirect
33. C5×C11C4×ΓL(1,𝔽32)semidirect
38. C31AGL(1,𝔽5)×C11⋊C5semidirect
41. AGL(1,𝔽5)#13133721direct (N × H)
43. C11AGL(1,𝔽5)×ΓL(1,𝔽32)semidirect
48. C5C4×#13133721semidirect

Maximal subgroups

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

subgroupindex
D5×#131337212
C11×AGL(1,𝔽5)×C315
C4×#131337215
AGL(1,𝔽5)×ΓL(1,𝔽32)11
AGL(1,𝔽5)×C11⋊C531