Finite Group Databasebeta

← C5×C11×C3⋊D93 #44501883

Subgroups — C5×C11×C3⋊D93 #44501883

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×C31C211yesmaximal, characteristic, complemented, Hall
2C5×C11×D93—34nomaximal
3C11×C3⋊D93C511yesmaximal, characteristic, direct product factor, Hall
4C3×C5×C11×C31D314yescomplemented
5C5×C11×D31—91noHall
6C32×C11×C31C2×C511yescharacteristic, complemented, Hall
7C5×C3⋊D93C1111yesmaximal, characteristic, direct product factor, Hall
8C11×D93—34no—
9C5×C11×C31C3⋊D311yescharacteristic, complemented, Hall
10C32×C5×C31C2×C1111yescharacteristic, complemented, Hall
11C3×C11×C31C5×D314yescomplemented
12C5×C11×C3⋊D3—311nomaximal, Hall
13C5×D93—34no—
14C11×D31—91noHall
15C3⋊D93C5×C1111yescharacteristic, direct product factor, Hall
16C32×C5×C11D3111yescharacteristic, complemented, Hall
17C3×C5×C31D3×C1114yescomplemented
18C11×C31C5×C3⋊D311yescharacteristic, complemented, Hall
19C5×D3×C11—934no—
20C5×D31—91noHall
21C32×C31C2×C5×C1111yescharacteristic, complemented, Hall
22C11×C3⋊D3—311noHall
23D93—34no—
24C3×C5×C11D9314yescomplemented
25C5×C31C11×C3⋊D311yescharacteristic, complemented, Hall
26C2×C5×C11—2791noHall
27C32×C11C5×D3111yescharacteristic, complemented, Hall
28C3×C31C5×D3×C1114yescomplemented
29C5×C3⋊D3—311noHall
30D3×C11—934no—
31D31—91noHall
32C5×C11C3⋊D9311yescharacteristic, direct product factor, Hall
33C32×C5C11×D3111yescharacteristic, complemented, Hall
34C3×C11C5×D9314yescomplemented
35C31C5×C11×C3⋊D311yescharacteristic, complemented, Sylow
36C5×D3—934no—
37C2×C11—2791noHall
38C3⋊D3—311noHall
39C3×C5C11×D9314yescomplemented
40C11C5×C3⋊D9311yescharacteristic, direct product factor, Sylow
41C2×C5—2791noHall
42C32C5×C11×D3111yescharacteristic, complemented, Sylow
43D3—934no—
44C5C11×C3⋊D9311yescharacteristic, direct product factor, Sylow
45C3C5×C11×D9314yescomplemented
46C2—2791noSylow
subgroupG/H
center, hypercenterC5×C11C3⋊D93
commutator, cosocle, hypocenterC32×C31C2×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C32×C31
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×C31C2semidirect
3. C11×C3⋊D93C5direct (N × H)
4. C3×C5×C11×C31D3semidirect
6. C32×C11×C31C2×C5semidirect
7. C5×C3⋊D93C11direct (N × H)
9. C5×C11×C31C3⋊D3semidirect
10. C32×C5×C31C2×C11semidirect
11. C3×C11×C31C5×D3semidirect
15. C3⋊D93C5×C11direct (N × H)
16. C32×C5×C11D31semidirect
17. C3×C5×C31D3×C11semidirect
18. C11×C31C5×C3⋊D3semidirect
21. C32×C31C2×C5×C11semidirect
24. C3×C5×C11D93semidirect
25. C5×C31C11×C3⋊D3semidirect
27. C32×C11C5×D31semidirect
28. C3×C31C5×D3×C11semidirect
32. C5×C11C3⋊D93direct (N × H)
33. C32×C5C11×D31semidirect
34. C3×C11C5×D93semidirect
35. C31C5×C11×C3⋊D3semidirect
39. C3×C5C11×D93semidirect
40. C11C5×C3⋊D93direct (N × H)
42. C32C5×C11×D31semidirect
44. C5C11×C3⋊D93direct (N × H)
45. C3C5×C11×D93semidirect

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×C11×D933
C11×C3⋊D935
C5×C3⋊D9311
C5×C11×C3⋊D331