Finite Group Databasebeta

← D5×C11×C31⋊C9 #44501708

Subgroups — D5×C11×C31⋊C9 #44501708

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C31⋊C9C211yesmaximal, characteristic, complemented, Hall
2C3×D5×C11×C31C311yesmaximal, characteristic
3C2×C11×C31⋊C9—51nomaximal, Hall
4C3×C5×C11×C31C2×C311yescharacteristic
5D5×C11×C31C911yescharacteristic, complemented, Hall
6C11×C31⋊C9D511yescharacteristic, direct product factor, Hall
7D5×C31⋊C9C1111yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C11×C31—51no—
9C5×C11×C31C2×C911yescharacteristic, complemented, Hall
10C5×C31⋊C9C2×C1111yescharacteristic, complemented, Hall
11C3×C11×C31C3×D511yescharacteristic
12C9×D5×C11—311nomaximal, Hall
13C3×D5×C31C3×C1111yescharacteristic
14C2×C11×C31—51noHall
15C2×C31⋊C9—51noHall
16C5×C9×C11—311noHall
17C3×C5×C31C2×C3×C1111yescharacteristic
18C11×C31C9×D511yescharacteristic, complemented, Hall
19C3×D5×C11C31⋊C311yescharacteristic
20D5×C31C9×C1111yescharacteristic, complemented, Hall
21C31⋊C9D5×C1111yescharacteristic, direct product factor, Hall
22C2×C9×C11—1551noHall
23C2×C3×C31—51no—
24C3×C5×C11C2×C31⋊C311yescharacteristic
25C5×C31C2×C9×C1111yescharacteristic, complemented, Hall
26D5×C11C31⋊C911yescharacteristic, direct product factor, Hall
27C9×C11—311noHall
28C3×C31C3×D5×C1111yescharacteristic
29C9×D5—311noHall
30C2×C3×C11—51no—
31C2×C31—51noHall
32C5×C11C2×C31⋊C911yescharacteristic, complemented, Hall
33C5×C9—311noHall
34C3×C11D5×C31⋊C311yescharacteristic
35C31C9×D5×C1111yescharacteristic, complemented, Sylow
36C3×D5C11×C31⋊C311yescharacteristic
37C2×C11—51noHall
38C2×C9—1551noHall
39C3×C5C2×C11×C31⋊C311yescharacteristic
40C11D5×C31⋊C911yescharacteristic, direct product factor, Sylow
41D5C11×C31⋊C911yescharacteristic, direct product factor, Hall
42C9—311noSylow
43C2×C3—51no—
44C5C2×C11×C31⋊C911yescharacteristic, complemented, Sylow
45C3D5×C11×C31⋊C311yescharacteristic
46C2—51noSylow
subgroupG/H
center, hypercenterC3×C11D5×C31⋊C3
commutator, hypocenterC5×C31C2×C9×C11
FrattiniC3D5×C11×C31⋊C3
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×D5×C11×C31C3
cosocleC3×C5×C31C2×C3×C11
LCSG ▷ C5×C31
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×C31⋊C9C2semidirect
5. D5×C11×C31C9semidirect
6. C11×C31⋊C9D5direct (N × H)
7. D5×C31⋊C9C11direct (N × H)
9. C5×C11×C31C2×C9semidirect
10. C5×C31⋊C9C2×C11semidirect
18. C11×C31C9×D5semidirect
20. D5×C31C9×C11semidirect
21. C31⋊C9D5×C11direct (N × H)
25. C5×C31C2×C9×C11semidirect
26. D5×C11C31⋊C9direct (N × H)
32. C5×C11C2×C31⋊C9semidirect
35. C31C9×D5×C11semidirect
40. C11D5×C31⋊C9direct (N × H)
41. D5C11×C31⋊C9direct (N × H)
44. C5C2×C11×C31⋊C9semidirect

Maximal subgroups

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

subgroupindex
C5×C11×C31⋊C92
C3×D5×C11×C313
C2×C11×C31⋊C95
D5×C31⋊C911
C9×D5×C1131