Finite Group Databasebeta

← C5×C31×C22⋊(C13⋊C3) #37563992

Subgroups — C5×C31×C22⋊(C13⋊C3) #37563992

Order 24180.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C13×C31C311yesmaximal, characteristic, complemented, Hall
2C5×C31×C13⋊C3—41nomaximal, Hall
3C31×C22⋊(C13⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C13×C31—31no—
5C5×C13×C31A411yescharacteristic, complemented, Hall
6C5×A4×C31—131nomaximal, Hall
7C22×C13×C31C3×C511yescharacteristic, complemented, Hall
8C31×C13⋊C3—41noHall
9C2×C13×C31—31no—
10C5×C22⋊(C13⋊C3)C3111yesmaximal, characteristic, direct product factor, Hall
11C22×C5×C31C13⋊C311yescharacteristic, complemented, Hall
12C3×C5×C31—521noHall
13C13×C31C5×A411yescharacteristic, complemented, Hall
14A4×C31—131noHall
15C2×C5×C31—31no—
16C22×C5×C13C3×C3111yescharacteristic, complemented, Hall
17C5×C13⋊C3—41noHall
18C22⋊(C13⋊C3)C5×C3111yescharacteristic, direct product factor, Hall
19C5×C31C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Hall
20C2×C5×C13—31no—
21C22×C31C5×C13⋊C311yescharacteristic, complemented, Hall
22C3×C31—521noHall
23C5×C13A4×C3111yescharacteristic, complemented, Hall
24C2×C31—31no—
25C5×A4—131noHall
26C22×C13C3×C5×C3111yescharacteristic, complemented, Hall
27C13⋊C3—41noHall
28C31C5×C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Sylow
29C2×C13—31no—
30C22×C5C31×C13⋊C311yescharacteristic, complemented, Hall
31C3×C5—521noHall
32C13C5×A4×C3111yescharacteristic, complemented, Sylow
33A4—131noHall
34C2×C5—31no—
35C5C31×C22⋊(C13⋊C3)11yescharacteristic, direct product factor, Sylow
36C22C5×C31×C13⋊C311yescharacteristic, complemented, Sylow
37C3—521noSylow
38C2—31no—
subgroupG/H
center, hypercenterC5×C31C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C5×C31
FrattiniC1G
Fitting, socleC22×C5×C13×C31C3
LCSG ▷ C22×C13
UCSC1 ◁ C5×C31

Complements

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

NH ≅ G/Ntype
1. C22×C5×C13×C31C3semidirect
3. C31×C22⋊(C13⋊C3)C5direct (N × H)
5. C5×C13×C31A4semidirect
7. C22×C13×C31C3×C5semidirect
10. C5×C22⋊(C13⋊C3)C31direct (N × H)
11. C22×C5×C31C13⋊C3semidirect
13. C13×C31C5×A4semidirect
16. C22×C5×C13C3×C31semidirect
18. C22⋊(C13⋊C3)C5×C31direct (N × H)
19. C5×C31C22⋊(C13⋊C3)direct (N × H)
21. C22×C31C5×C13⋊C3semidirect
23. C5×C13A4×C31semidirect
26. C22×C13C3×C5×C31semidirect
28. C31C5×C22⋊(C13⋊C3)direct (N × H)
30. C22×C5C31×C13⋊C3semidirect
32. C13C5×A4×C31semidirect
35. C5C31×C22⋊(C13⋊C3)direct (N × H)
36. C22C5×C31×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C13×C313
C5×C31×C13⋊C34
C31×C22⋊(C13⋊C3)5
C5×A4×C3113
C5×C22⋊(C13⋊C3)31