Finite Group Databasebeta

← C11×(C43⋊C3)⋊Dic5 #43248784

Subgroups — C11×(C43⋊C3)⋊Dic5 #43248784

Order 28380.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×C43⋊C3C211yesmaximal, characteristic
2C11×Dic215C311yesmaximal, characteristic, complemented, Hall
3C5×C11×C43⋊C3C411yescharacteristic, complemented, Hall
4C11×(C43⋊C3)⋊C4—51nomaximal, Hall
5C2×C5×C11×C43C2×C311yescharacteristic
6C2×C11×C43⋊C3D511yescharacteristic
7(C43⋊C3)⋊Dic5C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C11×C43C3×C411yescharacteristic, complemented, Hall
9C11×Dic43—51noHall
10C11×C43⋊C3Dic511yescharacteristic, complemented, Hall
11C2×C5×C43⋊C3C2×C1111yescharacteristic
12C2×C11×C43C3×D511yescharacteristic
13Dic215C3×C1111yescharacteristic, complemented, Hall
14C3×C11×Dic5—431nomaximal, Hall
15C5×C43⋊C3C4×C1111yescharacteristic, complemented, Hall
16(C43⋊C3)⋊C4—51noHall
17C11×C43C3×Dic511yescharacteristic, complemented, Hall
18C2×C5×C43C2×C3×C1111yescharacteristic
19C2×C3×C5×C11—431no—
20C2×C43⋊C3D5×C1111yescharacteristic
21C11×Dic5—431noHall
22C5×C43C3×C4×C1111yescharacteristic, complemented, Hall
23Dic43—51noHall
24C3×C5×C11—431noHall
25C3×C4×C11—2151noHall
26C43⋊C3C11×Dic511yescharacteristic, complemented, Hall
27C2×C5×C11D43⋊C311yescharacteristic
28C2×C43C3×D5×C1111yescharacteristic
29C2×C3×C11—431no—
30C3×Dic5—431noHall
31C5×C11(C43⋊C3)⋊C411yescharacteristic, complemented, Hall
32C4×C11—2151noHall
33C43C3×C11×Dic511yescharacteristic, complemented, Sylow
34C3×C11—431noHall
35C2×C3×C5—431no—
36C2×C11C5⋊(D43⋊C3)11yescharacteristic
37Dic5—431noHall
38C3×C5—431noHall
39C3×C4—2151noHall
40C11(C43⋊C3)⋊Dic511yescharacteristic, direct product factor, Sylow
41C2×C5C11×D43⋊C311yescharacteristic
42C2×C3—431no—
43C5C11×(C43⋊C3)⋊C411yescharacteristic, complemented, Sylow
44C4—2151noSylow
45C3—431noSylow
46C2C11×C5⋊(D43⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC2×C11C5⋊(D43⋊C3)
commutator, hypocenterC5×C43C3×C4×C11
FrattiniC2C11×C5⋊(D43⋊C3)
Fitting, socleC2×C5×C11×C43C2×C3
prime radicalC2×C5×C11×C43⋊C3C2
cosocleC2×C5×C43C2×C3×C11
LCSG ▷ C5×C43
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
2. C11×Dic215C3semidirect
3. C5×C11×C43⋊C3C4semidirect
7. (C43⋊C3)⋊Dic5C11direct (N × H)
8. C5×C11×C43C3×C4semidirect
10. C11×C43⋊C3Dic5semidirect
13. Dic215C3×C11semidirect
15. C5×C43⋊C3C4×C11semidirect
17. C11×C43C3×Dic5semidirect
22. C5×C43C3×C4×C11semidirect
26. C43⋊C3C11×Dic5semidirect
31. C5×C11(C43⋊C3)⋊C4semidirect
33. C43C3×C11×Dic5semidirect
40. C11(C43⋊C3)⋊Dic5direct (N × H)
43. C5C11×(C43⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C11×C43⋊C32
C11×Dic2153
C11×(C43⋊C3)⋊C45
(C43⋊C3)⋊Dic511
C3×C11×Dic543