Finite Group Databasebeta

← C11×D19⋊(C52⋊C3) #44535488

Subgroups — C11×D19⋊(C52⋊C3) #44535488

Order 31350.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C19⋊(C52⋊C3)C211yesmaximal, characteristic, complemented, Hall
2C52×C11×D19C311yesmaximal, characteristic, complemented, Hall
3C52×C11×C19C2×C311yescharacteristic, complemented, Hall
4D19⋊(C52⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
5C5×C11×D19—32no—
6C2×C11×C52⋊C3—191nomaximal, Hall
7C19⋊(C52⋊C3)C2×C1111yescharacteristic, complemented, Hall
8C11×D19⋊C3—251nomaximal, Hall
9C5×C11×C19—32no—
10C52×D19C3×C1111yescharacteristic, complemented, Hall
11C11×C52⋊C3—191noHall
12C11×C19⋊C3—251noHall
13C2×C52×C11—191noHall
14C52×C19C2×C3×C1111yescharacteristic, complemented, Hall
15C11×D19C52⋊C311yescharacteristic, complemented, Hall
16C52×C11D19⋊C311yescharacteristic, complemented, Hall
17C11×C19C2×C52⋊C311yescharacteristic, complemented, Hall
18C5×D19—32no—
19C2×C52⋊C3—191noHall
20D19⋊C3—251noHall
21C2×C5×C11—572no—
22C5×C19—32no—
23C52⋊C3—191noHall
24C2×C3×C11—4751noHall
25C19⋊C3—251noHall
26C5×C11—32no—
27C2×C52—191noHall
28D19C11×C52⋊C311yescharacteristic, complemented, Hall
29C3×C11—4751noHall
30C52C11×D19⋊C311yescharacteristic, complemented, Sylow
31C2×C11—191noHall
32C19C2×C11×C52⋊C311yescharacteristic, complemented, Sylow
33C11D19⋊(C52⋊C3)11yescharacteristic, direct product factor, Sylow
34C2×C5—572no—
35C2×C3—4751noHall
36C5—32no—
37C3—4751noSylow
38C2—191noSylow
subgroupG/H
center, hypercenterC11D19⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C19C2×C3×C11
FrattiniC1G
Fitting, socleC52×C11×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C19⋊(C52⋊C3)C2semidirect
2. C52×C11×D19C3semidirect
3. C52×C11×C19C2×C3semidirect
4. D19⋊(C52⋊C3)C11direct (N × H)
7. C19⋊(C52⋊C3)C2×C11semidirect
10. C52×D19C3×C11semidirect
14. C52×C19C2×C3×C11semidirect
15. C11×D19C52⋊C3semidirect
16. C52×C11D19⋊C3semidirect
17. C11×C19C2×C52⋊C3semidirect
28. D19C11×C52⋊C3semidirect
30. C52C11×D19⋊C3semidirect
32. C19C2×C11×C52⋊C3semidirect
33. C11D19⋊(C52⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C19⋊(C52⋊C3)2
C52×C11×D193
D19⋊(C52⋊C3)11
C2×C11×C52⋊C319
C11×D19⋊C325