Finite Group Databasebeta

← C22×C3×C5×C11⋊C5 #15693179

Subgroups — C22×C3×C5×C11⋊C5 #15693179

Order 3300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C11⋊C5C213yesmaximal, direct product factor
2C22×C5×C11⋊C5C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C11⋊C5C2211yescharacteristic, direct product factor, Hall
4C22×C3×C5×C11C511yesmaximal, characteristic, complemented
5C22×C3×C11⋊C5C515yesmaximal, direct product factor
6C2×C5×C11⋊C5C2×C313yesdirect product factor
7C2×C3×C5×C11C2×C513yescomplemented
8C2×C3×C11⋊C5C2×C5115yesdirect product factor
9C22×C3×C52—111nomaximal, Hall
10C5×C11⋊C5C22×C311yescharacteristic, direct product factor, Hall
11C22×C5×C11C3×C511yescharacteristic, complemented
12C22×C11⋊C5C3×C515yesdirect product factor
13C3×C5×C11C22×C511yescharacteristic, complemented
14C3×C11⋊C5C22×C515yesdirect product factor
15C2×C3×C52—113no—
16C22×C3×C11C5211yescharacteristic, complemented, Hall
17C2×C5×C11C2×C3×C513yescomplemented
18C2×C11⋊C5C2×C3×C5115yesdirect product factor
19C22×C52—111noHall
20C3×C52—111noHall
21C2×C3×C11C2×C5213yescomplemented
22C22×C3×C5—115no—
23C22×C3×C5C11⋊C511yescharacteristic, direct product factor
24C5×C11C22×C3×C511yescharacteristic, complemented
25C11⋊C5C22×C3×C515yesdirect product factor
26C2×C52—113no—
27C22×C11C3×C5211yescharacteristic, complemented, Hall
28C3×C11C22×C5211yescharacteristic, complemented, Hall
29C2×C3×C5—1115no—
30C2×C3×C5C2×C11⋊C513yesdirect product factor
31C52—111noSylow
32C2×C11C2×C3×C5213yescomplemented
33C22×C5—115no—
34C22×C5C3×C11⋊C511yescharacteristic, direct product factor
35C3×C5—115no—
36C3×C5C22×C11⋊C511yescharacteristic, direct product factor
37C22×C3C5×C11⋊C511yescharacteristic, direct product factor, Hall
38C11C22×C3×C5211yescharacteristic, complemented, Sylow
39C2×C5—1115no—
40C2×C5C2×C3×C11⋊C513yesdirect product factor
41C2×C3C2×C5×C11⋊C513yesdirect product factor
42C5—115no—
43C5C22×C3×C11⋊C511yescharacteristic, direct product factor
44C22C3×C5×C11⋊C511yescharacteristic, direct product factor, Sylow
45C3C22×C5×C11⋊C511yescharacteristic, direct product factor, Sylow
46C2C2×C3×C5×C11⋊C513yesdirect product factor
subgroupG/H
center, hypercenterC22×C3×C5C11⋊C5
commutator, cosocle, hypocenterC11C22×C3×C52
FrattiniC1G
Fitting, socleC22×C3×C5×C11C5
LCSG ▷ C11
UCSC1 ◁ C22×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C11⋊C5C2direct (N × H)
2. C22×C5×C11⋊C5C3direct (N × H)
3. C3×C5×C11⋊C5C22direct (N × H)
4. C22×C3×C5×C11C5semidirect
5. C22×C3×C11⋊C5C5direct (N × H)
6. C2×C5×C11⋊C5C2×C3direct (N × H)
7. C2×C3×C5×C11C2×C5semidirect
8. C2×C3×C11⋊C5C2×C5direct (N × H)
10. C5×C11⋊C5C22×C3direct (N × H)
11. C22×C5×C11C3×C5semidirect
12. C22×C11⋊C5C3×C5direct (N × H)
13. C3×C5×C11C22×C5semidirect
14. C3×C11⋊C5C22×C5direct (N × H)
16. C22×C3×C11C52semidirect
17. C2×C5×C11C2×C3×C5semidirect
18. C2×C11⋊C5C2×C3×C5direct (N × H)
21. C2×C3×C11C2×C52semidirect
23. C22×C3×C5C11⋊C5direct (N × H)
24. C5×C11C22×C3×C5semidirect
25. C11⋊C5C22×C3×C5direct (N × H)
27. C22×C11C3×C52semidirect
28. C3×C11C22×C52semidirect
30. C2×C3×C5C2×C11⋊C5direct (N × H)
32. C2×C11C2×C3×C52semidirect
34. C22×C5C3×C11⋊C5direct (N × H)
36. C3×C5C22×C11⋊C5direct (N × H)
37. C22×C3C5×C11⋊C5direct (N × H)
38. C11C22×C3×C52semidirect
40. C2×C5C2×C3×C11⋊C5direct (N × H)
41. C2×C3C2×C5×C11⋊C5direct (N × H)
43. C5C22×C3×C11⋊C5direct (N × H)
44. C22C3×C5×C11⋊C5direct (N × H)
45. C3C22×C5×C11⋊C5direct (N × H)
46. C2C2×C3×C5×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11⋊C52
C22×C5×C11⋊C53
C22×C3×C5×C115
C22×C3×C11⋊C55
C22×C3×C5211