Finite Group Databasebeta

← C13×C11⋊((C5⋊D5)⋊C3) #36339751

Subgroups — C13×C11⋊((C5⋊D5)⋊C3) #36339751

Order 21450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C13×C52⋊C3C211yesmaximal, characteristic, complemented, Hall
2C13×C5⋊D55C311yesmaximal, characteristic, complemented, Hall
3C52×C11×C13C2×C311yescharacteristic, complemented, Hall
4C13×(C5⋊D5)⋊C3—111nomaximal, Hall
5C11⋊((C5⋊D5)⋊C3)C1311yesmaximal, characteristic, direct product factor, Hall
6C13×D55—152no—
7C13×C52⋊C3D1111yescharacteristic, complemented, Hall
8C3×C13×D11—251nomaximal, Hall
9C11×C52⋊C3C2×C1311yescharacteristic, complemented, Hall
10C5×C11×C13—32no—
11C13×C5⋊D5—111noHall
12C5⋊D55C3×C1311yescharacteristic, complemented, Hall
13C3×C11×C13—251noHall
14C52×C13C3×D1111yescharacteristic, complemented, Hall
15C13×D11—251noHall
16C52×C11C2×C3×C1311yescharacteristic, complemented, Hall
17(C5⋊D5)⋊C3—111noHall
18C11×C13(C5⋊D5)⋊C311yescharacteristic, complemented, Hall
19D5×C13—1652no—
20D55—152no—
21C2×C3×C13—2751noHall
22C52⋊C3C13×D1111yescharacteristic, complemented, Hall
23C3×D11—251noHall
24C5×C13—32no—
25C5×C11—32no—
26C5⋊D5—111noHall
27C3×C13—251noHall
28C3×C11—251noHall
29C2×C13—2751noHall
30C52C3×C13×D1111yescharacteristic, complemented, Sylow
31D11—251noHall
32C13C11⋊((C5⋊D5)⋊C3)11yescharacteristic, direct product factor, Sylow
33C11C13×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
34D5—1652no—
35C2×C3—2751noHall
36C5—32no—
37C3—251noSylow
38C2—2751noSylow
subgroupG/H
center, hypercenterC13C11⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C11C2×C3×C13
FrattiniC1G
Fitting, socleC52×C11×C13C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×C52⋊C3C2semidirect
2. C13×C5⋊D55C3semidirect
3. C52×C11×C13C2×C3semidirect
5. C11⋊((C5⋊D5)⋊C3)C13direct (N × H)
7. C13×C52⋊C3D11semidirect
9. C11×C52⋊C3C2×C13semidirect
12. C5⋊D55C3×C13semidirect
14. C52×C13C3×D11semidirect
16. C52×C11C2×C3×C13semidirect
18. C11×C13(C5⋊D5)⋊C3semidirect
22. C52⋊C3C13×D11semidirect
30. C52C3×C13×D11semidirect
32. C13C11⋊((C5⋊D5)⋊C3)direct (N × H)
33. C11C13×(C5⋊D5)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×C13×C52⋊C32
C13×C5⋊D553
C13×(C5⋊D5)⋊C311
C11⋊((C5⋊D5)⋊C3)13
C3×C13×D1125