Finite Group Databasebeta

← C3⋊(C3⋊(Dic131⋊C5)) #37556068

Subgroups — C3⋊(C3⋊(Dic131⋊C5)) #37556068

Order 23580.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C131⋊C5C211yesmaximal, characteristic
2C3⋊(Dic131⋊C5)—34nomaximal
3C32×C131⋊C5C411yescharacteristic, complemented, Hall
4C3⋊Dic393C511yesmaximal, characteristic, complemented, Hall
5C2×C3×C131⋊C5D314yes—
6Dic131⋊C5—91noHall
7C2×C32×C131C2×C511yescharacteristic
8C3×C131⋊C5Dic314yescomplemented
9Dic393—34no—
10C2×C131⋊C5C3⋊D311yescharacteristic
11C32×C131C4×C511yescharacteristic, complemented, Hall
12C2×C3×C131C5×D314yes—
13C131⋊C5C3⋊Dic311yescharacteristic, complemented, Hall
14Dic131—91noHall
15C3×C131C5×Dic314yescomplemented
16C2×C131C5×C3⋊D311yescharacteristic
17C5×C3⋊Dic3—1311nomaximal, Hall
18C131C5×C3⋊Dic311yescharacteristic, complemented, Sylow
19C2×C32×C5—1311no—
20C5×Dic3—3934no—
21C32×C5—1311noHall
22C3⋊Dic3—6551noHall
23C2×C3×C5—1314no—
24C4×C5—11791noHall
25C2×C32D131⋊C511yescharacteristic
26C3×C5—1314no—
27Dic3—19654no—
28C2×C5—1311no—
29C32Dic131⋊C511yescharacteristic, complemented, Sylow
30C2×C3C3⋊(D131⋊C5)14yes—
31C5—1311noSylow
32C4—58951noSylow
33C3C3⋊(Dic131⋊C5)14yescomplemented
34C2C3⋊(C3⋊(D131⋊C5))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊(C3⋊(D131⋊C5))
commutator, hypocenterC32×C131C4×C5
Fitting, socle, cosocleC2×C32×C131C2×C5
prime radicalC2×C32×C131⋊C5C2
LCSG ▷ C32×C131
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C32×C131⋊C5C4semidirect
4. C3⋊Dic393C5semidirect
8. C3×C131⋊C5Dic3semidirect
11. C32×C131C4×C5semidirect
13. C131⋊C5C3⋊Dic3semidirect
15. C3×C131C5×Dic3semidirect
18. C131C5×C3⋊Dic3semidirect
29. C32Dic131⋊C5semidirect
33. C3C3⋊(Dic131⋊C5)semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C131⋊C52
C3⋊(Dic131⋊C5)3
C3⋊Dic3935
C5×C3⋊Dic3131