Finite Group Databasebeta

← C17×C11⋊((C5⋊D5)⋊C3) #43242525

Subgroups — C17×C11⋊((C5⋊D5)⋊C3) #43242525

Order 28050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C17×C52⋊C3C211yesmaximal, characteristic, complemented, Hall
2C17×C5⋊D55C311yesmaximal, characteristic, complemented, Hall
3C52×C11×C17C2×C311yescharacteristic, complemented, Hall
4C17×(C5⋊D5)⋊C3—111nomaximal, Hall
5C17×D55—152no—
6C11⋊((C5⋊D5)⋊C3)C1711yesmaximal, characteristic, direct product factor, Hall
7C17×C52⋊C3D1111yescharacteristic, complemented, Hall
8C3×C17×D11—251nomaximal, Hall
9C5×C11×C17—32no—
10C17×C5⋊D5—111noHall
11C11×C52⋊C3C2×C1711yescharacteristic, complemented, Hall
12C3×C11×C17—251noHall
13C5⋊D55C3×C1711yescharacteristic, complemented, Hall
14C52×C17C3×D1111yescharacteristic, complemented, Hall
15C17×D11—251noHall
16C52×C11C2×C3×C1711yescharacteristic, complemented, Hall
17C11×C17(C5⋊D5)⋊C311yescharacteristic, complemented, Hall
18D5×C17—1652no—
19(C5⋊D5)⋊C3—111noHall
20D55—152no—
21C2×C3×C17—2751noHall
22C5×C17—32no—
23C52⋊C3C17×D1111yescharacteristic, complemented, Hall
24C3×D11—251noHall
25C5×C11—32no—
26C3×C17—251noHall
27C5⋊D5—111noHall
28C2×C17—2751noHall
29C3×C11—251noHall
30C52C3×C17×D1111yescharacteristic, complemented, Sylow
31D11—251noHall
32C17C11⋊((C5⋊D5)⋊C3)11yescharacteristic, direct product factor, Sylow
33C11C17×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
34D5—1652no—
35C2×C3—2751noHall
36C5—32no—
37C3—251noSylow
38C2—2751noSylow
subgroupG/H
center, hypercenterC17C11⋊((C5⋊D5)⋊C3)
commutator, cosocle, hypocenterC52×C11C2×C3×C17
FrattiniC1G
Fitting, socleC52×C11×C17C2×C3
LCSG ▷ C52×C11
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C11×C17×C52⋊C3C2semidirect
2. C17×C5⋊D55C3semidirect
3. C52×C11×C17C2×C3semidirect
6. C11⋊((C5⋊D5)⋊C3)C17direct (N × H)
7. C17×C52⋊C3D11semidirect
11. C11×C52⋊C3C2×C17semidirect
13. C5⋊D55C3×C17semidirect
14. C52×C17C3×D11semidirect
16. C52×C11C2×C3×C17semidirect
17. C11×C17(C5⋊D5)⋊C3semidirect
23. C52⋊C3C17×D11semidirect
30. C52C3×C17×D11semidirect
32. C17C11⋊((C5⋊D5)⋊C3)direct (N × H)
33. C11C17×(C5⋊D5)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×C17×C52⋊C32
C17×C5⋊D553
C17×(C5⋊D5)⋊C311
C11⋊((C5⋊D5)⋊C3)17
C3×C17×D1125