Finite Group Databasebeta

← C31×(C11⋊C5)⋊AGL(1,𝔽5) #46802069

Subgroups — C31×(C11⋊C5)⋊AGL(1,𝔽5) #46802069

Order 34100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C31×C11⋊C5C211yesmaximal, characteristic
2C5×C31×C11⋊C5C411yescharacteristic, complemented, Hall
3C31×C11⋊AGL(1,𝔽5)C511yesmaximal, characteristic, complemented
4C31×Dic11⋊C5—51nomaximal
5D5×C11×C31C2×C511yescharacteristic
6C2×C31×C11⋊C5—51no—
7C5×AGL(1,𝔽5)×C31—111nomaximal, Hall
8C5×C11×C31C4×C511yescharacteristic, complemented
9C31×C11⋊C5—41no—
10C31×C11⋊C5AGL(1,𝔽5)11yescharacteristic, complemented
11C5×D5×C31—111no—
12C31×Dic11—51noHall
13(C11⋊C5)⋊AGL(1,𝔽5)C3111yesmaximal, characteristic, direct product factor, Hall
14C52×C31—111noHall
15C2×C11×C31—51no—
16AGL(1,𝔽5)×C31—111no—
17C4×C5×C31—551no—
18D5×C11⋊C5C2×C3111yescharacteristic
19C11×C31C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20C2×C5×C31—551no—
21D5×C31AGL(1,𝔽11)11yescharacteristic
22C5×C11⋊C5C4×C3111yescharacteristic, complemented, Hall
23C11⋊AGL(1,𝔽5)C5×C3111yescharacteristic, complemented
24Dic11⋊C5—51no—
25C5×C31—111no—
26C5×C31—441no—
27C5×C31Dic11⋊C511yescharacteristic, complemented
28C4×C31—551noHall
29D5×C11C2×C5×C3111yescharacteristic
30C2×C11⋊C5—51no—
31C5×AGL(1,𝔽5)—111noHall
32C2×C31—51no—
33C5×C11C4×C5×C3111yescharacteristic, complemented
34C11⋊C5—41no—
35C11⋊C5AGL(1,𝔽5)×C3111yescharacteristic, complemented
36C5×D5—111no—
37Dic11—51noHall
38C31(C11⋊C5)⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
39C52—111noSylow
40C2×C11—51no—
41AGL(1,𝔽5)—111no—
42C4×C5—551no—
43C11C5×AGL(1,𝔽5)×C3111yescharacteristic, complemented, Sylow
44C2×C5—551no—
45D5C31×AGL(1,𝔽11)11yescharacteristic
46C5—111no—
47C5—441no—
48C5C31×Dic11⋊C511yescharacteristic, complemented
49C4—551noSylow
50C2—51no—
subgroupG/H
center, hypercenterC31(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C5×C31
FrattiniC1G
Fitting, socleC5×C11×C31C4×C5
prime radicalD5×C31×C11⋊C5C2
cosocleD5×C11C2×C5×C31
LCSG ▷ C5×C11
UCSC1 ◁ C31

Complements

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

NH ≅ G/Ntype
2. C5×C31×C11⋊C5C4semidirect
3. C31×C11⋊AGL(1,𝔽5)C5semidirect
8. C5×C11×C31C4×C5semidirect
10. C31×C11⋊C5AGL(1,𝔽5)semidirect
13. (C11⋊C5)⋊AGL(1,𝔽5)C31direct (N × H)
19. C11×C31C5×AGL(1,𝔽5)semidirect
22. C5×C11⋊C5C4×C31semidirect
23. C11⋊AGL(1,𝔽5)C5×C31semidirect
27. C5×C31Dic11⋊C5semidirect
33. C5×C11C4×C5×C31semidirect
35. C11⋊C5AGL(1,𝔽5)×C31semidirect
38. C31(C11⋊C5)⋊AGL(1,𝔽5)direct (N × H)
43. C11C5×AGL(1,𝔽5)×C31semidirect
48. C5C31×Dic11⋊C5semidirect

Maximal subgroups

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

subgroupindex
D5×C31×C11⋊C52
C31×C11⋊AGL(1,𝔽5)5
C31×Dic11⋊C55
C5×AGL(1,𝔽5)×C3111
(C11⋊C5)⋊AGL(1,𝔽5)31