Finite Group Databasebeta

← (C11⋊C5)⋊(C31⋊AGL(1,𝔽5)) #46802078

Subgroups — (C11⋊C5)⋊(C31⋊AGL(1,𝔽5)) #46802078

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
3C11⋊(C31⋊AGL(1,𝔽5))C511yesmaximal, characteristic, complemented
4(C11⋊C5)⋊Dic31—51nomaximal
5D5×C11×C31C2×C511yescharacteristic
6C2×C31×C11⋊C5—51no—
7C5×C31⋊AGL(1,𝔽5)—111nomaximal, Hall
8C5×C11×C31C4×C511yescharacteristic, complemented
9C31×C11⋊C5—41no—
10C31×C11⋊C5AGL(1,𝔽5)11yescharacteristic, complemented
11C5×D5×C31—111no—
12Dic341—51noHall
13(C11⋊C5)⋊AGL(1,𝔽5)—311nomaximal, Hall
14C52×C31—111noHall
15C2×C11×C31—51no—
16C31⋊AGL(1,𝔽5)—111no—
17C5×Dic31—551no—
18D5×C11⋊C5D3111yescharacteristic
19C11×C31C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
20C2×C5×C31—551no—
21D5×C31AGL(1,𝔽11)11yescharacteristic
22C5×C11⋊C5Dic3111yescharacteristic, complemented, Hall
23C11⋊AGL(1,𝔽5)—311no—
24Dic11⋊C5—1551no—
25C5×C31—111no—
26C5×C31—441no—
27C5×C31Dic11⋊C511yescharacteristic, complemented
28Dic31—551noHall
29D5×C11C5×D3111yescharacteristic
30C2×C11⋊C5—51no—
31C5×AGL(1,𝔽5)—3411noHall
32C2×C31—51no—
33C5×C11C5×Dic3111yescharacteristic, complemented
34C11⋊C5—41no—
35C11⋊C5C31⋊AGL(1,𝔽5)11yescharacteristic, complemented
36C5×D5—111no—
37Dic11—1551noHall
38C31(C11⋊C5)⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
39C52—111noSylow
40C2×C11—51no—
41AGL(1,𝔽5)—3411no—
42C4×C5—17051no—
43C11C5×C31⋊AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
44C2×C5—551no—
45D5(C11⋊C5)⋊D3111yescharacteristic
46C5—111no—
47C5—441no—
48C5(C11⋊C5)⋊Dic3111yescharacteristic, complemented
49C4—17051noSylow
50C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C31C4×C5
prime radicalD5×C31×C11⋊C5C2
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×C31×C11⋊C5C4semidirect
3. C11⋊(C31⋊AGL(1,𝔽5))C5semidirect
8. C5×C11×C31C4×C5semidirect
10. C31×C11⋊C5AGL(1,𝔽5)semidirect
19. C11×C31C5×AGL(1,𝔽5)semidirect
22. C5×C11⋊C5Dic31semidirect
27. C5×C31Dic11⋊C5semidirect
33. C5×C11C5×Dic31semidirect
35. C11⋊C5C31⋊AGL(1,𝔽5)semidirect
38. C31(C11⋊C5)⋊AGL(1,𝔽5)semidirect
43. C11C5×C31⋊AGL(1,𝔽5)semidirect
48. C5(C11⋊C5)⋊Dic31semidirect

Maximal subgroups

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

subgroupindex
D5×C31×C11⋊C52
C11⋊(C31⋊AGL(1,𝔽5))5
(C11⋊C5)⋊Dic315
C5×C31⋊AGL(1,𝔽5)11
(C11⋊C5)⋊AGL(1,𝔽5)31