Finite Group Databasebeta

← (C103⋊C3)⋊#1039 #44525439

Subgroups — (C103⋊C3)⋊#1039 #44525439

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C52×C103⋊C3C211yesmaximal, characteristic
2C103⋊#1039C311yesmaximal, characteristic, complemented, Hall
3C52×C103⋊C3C411yescharacteristic, complemented, Hall
4(C103⋊C3)⋊Dic5—56nomaximal
5C2×C52×C103C2×C311yescharacteristic
6C2×C5×C103⋊C3D516yes—
7C52×C103C3×C411yescharacteristic, complemented, Hall
8Dic515—56no—
9C5×C103⋊C3Dic516yescomplemented
10(C103⋊C3)⋊C4—251noHall
11C2×C5×C103C3×D516yes—
12C2×C103⋊C3C5⋊D511yescharacteristic
13C5×C103C3×Dic516yescomplemented
14Dic103—251noHall
15C103⋊C3#103911yescharacteristic, complemented, Hall
16C3×#1039—1031nomaximal, Hall
17C2×C103C3×C5⋊D511yescharacteristic
18C2×C3×C52—1031no—
19C103C3×#103911yescharacteristic, complemented, Sylow
20#1039—1031noHall
21C3×C52—1031noHall
22C3×Dic5—5156no—
23C2×C52D103⋊C311yescharacteristic
24C2×C3×C5—1036no—
25C52(C103⋊C3)⋊C411yescharacteristic, complemented, Sylow
26Dic5—5156no—
27C3×C5—1036no—
28C3×C4—25751noHall
29C2×C5C5⋊(D103⋊C3)16yes—
30C2×C3—1031no—
31C5(C103⋊C3)⋊Dic516yescomplemented
32C4—25751noSylow
33C3—1031noSylow
34C2C5⋊(C5⋊(D103⋊C3))11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C5⋊(C5⋊(D103⋊C3))
commutator, hypocenterC52×C103C3×C4
Fitting, socle, cosocleC2×C52×C103C2×C3
prime radicalC2×C52×C103⋊C3C2
LCSG ▷ C52×C103
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C103⋊#1039C3semidirect
3. C52×C103⋊C3C4semidirect
7. C52×C103C3×C4semidirect
9. C5×C103⋊C3Dic5semidirect
13. C5×C103C3×Dic5semidirect
15. C103⋊C3#1039semidirect
19. C103C3×#1039semidirect
25. C52(C103⋊C3)⋊C4semidirect
31. C5(C103⋊C3)⋊Dic5semidirect

Maximal subgroups

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

subgroupindex
C2×C52×C103⋊C32
C103⋊#10393
(C103⋊C3)⋊Dic55
C3×#1039103