Finite Group Databasebeta

← C5×C11×C3⋊D3×C31 #44501882

Subgroups — C5×C11×C3⋊D3×C31 #44501882

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×C31C211yesmaximal, characteristic, complemented, Hall
2C5×D3×C11×C31—34nomaximal
3C11×C3⋊D3×C31C511yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C11×C31D314yescomplemented
5C2×C5×C11×C31—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C5×C3⋊D3×C31C1111yesmaximal, characteristic, direct product factor, Hall
8D3×C11×C31—34no—
9C5×C11×C31C3⋊D311yescharacteristic, direct product factor, Hall
10C32×C5×C31C2×C1111yescharacteristic, complemented, Hall
11C3×C11×C31C5×D314yescomplemented
12C5×C11×C3⋊D3C3111yesmaximal, characteristic, direct product factor, Hall
13C5×D3×C31—34no—
14C2×C11×C31—91noHall
15C3⋊D3×C31C5×C1111yescharacteristic, direct product factor, Hall
16C32×C5×C11C2×C3111yescharacteristic, complemented, Hall
17C3×C5×C31D3×C1114yescomplemented
18C11×C31C5×C3⋊D311yescharacteristic, direct product factor, Hall
19C5×D3×C11—34no—
20C2×C5×C31—91noHall
21C32×C31C2×C5×C1111yescharacteristic, complemented, Hall
22C11×C3⋊D3C5×C3111yescharacteristic, direct product factor, Hall
23D3×C31—34no—
24C3×C5×C11D3×C3114yescomplemented
25C5×C31C11×C3⋊D311yescharacteristic, direct product factor, Hall
26C2×C5×C11—91noHall
27C32×C11C2×C5×C3111yescharacteristic, complemented, Hall
28C3×C31C5×D3×C1114yescomplemented
29C5×C3⋊D3C11×C3111yescharacteristic, direct product factor, Hall
30D3×C11—34no—
31C2×C31—91noHall
32C5×C11C3⋊D3×C3111yescharacteristic, direct product factor, Hall
33C32×C5C2×C11×C3111yescharacteristic, complemented, Hall
34C3×C11C5×D3×C3114yescomplemented
35C31C5×C11×C3⋊D311yescharacteristic, direct product factor, Sylow
36C5×D3—34no—
37C2×C11—91noHall
38C3⋊D3C5×C11×C3111yescharacteristic, direct product factor, Hall
39C3×C5D3×C11×C3114yescomplemented
40C11C5×C3⋊D3×C3111yescharacteristic, direct product factor, Sylow
41C2×C5—91noHall
42C32C2×C5×C11×C3111yescharacteristic, complemented, Sylow
43D3—34no—
44C5C11×C3⋊D3×C3111yescharacteristic, direct product factor, Sylow
45C3C5×D3×C11×C3114yescomplemented
46C2—91noSylow
subgroupG/H
center, hypercenterC5×C11×C31C3⋊D3
commutator, cosocle, hypocenterC32C2×C5×C11×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C32
UCSC1 ◁ C5×C11×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×C31C2semidirect
3. C11×C3⋊D3×C31C5direct (N × H)
4. C3×C5×C11×C31D3semidirect
6. C32×C11×C31C2×C5semidirect
7. C5×C3⋊D3×C31C11direct (N × H)
9. C5×C11×C31C3⋊D3direct (N × H)
10. C32×C5×C31C2×C11semidirect
11. C3×C11×C31C5×D3semidirect
12. C5×C11×C3⋊D3C31direct (N × H)
15. C3⋊D3×C31C5×C11direct (N × H)
16. C32×C5×C11C2×C31semidirect
17. C3×C5×C31D3×C11semidirect
18. C11×C31C5×C3⋊D3direct (N × H)
21. C32×C31C2×C5×C11semidirect
22. C11×C3⋊D3C5×C31direct (N × H)
24. C3×C5×C11D3×C31semidirect
25. C5×C31C11×C3⋊D3direct (N × H)
27. C32×C11C2×C5×C31semidirect
28. C3×C31C5×D3×C11semidirect
29. C5×C3⋊D3C11×C31direct (N × H)
32. C5×C11C3⋊D3×C31direct (N × H)
33. C32×C5C2×C11×C31semidirect
34. C3×C11C5×D3×C31semidirect
35. C31C5×C11×C3⋊D3direct (N × H)
38. C3⋊D3C5×C11×C31direct (N × H)
39. C3×C5D3×C11×C31semidirect
40. C11C5×C3⋊D3×C31direct (N × H)
42. C32C2×C5×C11×C31semidirect
44. C5C11×C3⋊D3×C31direct (N × H)
45. C3C5×D3×C11×C31semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×C312
C5×D3×C11×C313
C11×C3⋊D3×C315
C5×C3⋊D3×C3111
C5×C11×C3⋊D331