Finite Group Databasebeta

← C5×C72×C11×A4 #44568925

Subgroups — C5×C72×C11×A4 #44568925

Order 32340.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C72×C11C311yesmaximal, characteristic, complemented, Hall
2C3×C5×C72×C11—41nomaximal, Hall
3C72×C11×A4C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C72×C11—31no—
5C5×C7×C11×A4C718yesmaximal, direct product factor
6C5×C72×A4C1111yesmaximal, characteristic, direct product factor, Hall
7C5×C72×C11A411yescharacteristic, direct product factor, Hall
8C22×C72×C11C3×C511yescharacteristic, complemented, Hall
9C3×C72×C11—41noHall
10C22×C5×C7×C11C3×C718yescomplemented
11C3×C5×C7×C11—48no—
12C2×C72×C11—31no—
13C22×C5×C72C3×C1111yescharacteristic, complemented, Hall
14C7×C11×A4C5×C718yesdirect product factor
15C2×C5×C7×C11—38no—
16C3×C5×C72—41noHall
17C5×C11×A4C7211yescharacteristic, direct product factor, Hall
18C72×A4C5×C1111yescharacteristic, direct product factor, Hall
19C72×C11C5×A411yescharacteristic, direct product factor, Hall
20C2×C5×C72—31no—
21C5×C7×A4C7×C1118yesdirect product factor
22C5×C7×C11C7×A418yesdirect product factor
23C22×C7×C11C3×C5×C718yescomplemented
24C5×C72C11×A411yescharacteristic, direct product factor, Hall
25C3×C7×C11—48no—
26C22×C5×C11C3×C7211yescharacteristic, complemented, Hall
27C22×C72C3×C5×C1111yescharacteristic, complemented, Hall
28C3×C5×C11—41noHall
29C2×C7×C11—38no—
30C3×C72—41noHall
31C22×C5×C7C3×C7×C1118yescomplemented
32C11×A4C5×C7211yescharacteristic, direct product factor, Hall
33C2×C5×C11—31no—
34C3×C5×C7—48no—
35C2×C72—31no—
36C7×A4C5×C7×C1118yesdirect product factor
37C7×C11C5×C7×A418yesdirect product factor
38C2×C5×C7—38no—
39C5×A4C72×C1111yescharacteristic, direct product factor, Hall
40C5×C11C72×A411yescharacteristic, direct product factor, Hall
41C72C5×C11×A411yescharacteristic, direct product factor, Sylow
42C22×C11C3×C5×C7211yescharacteristic, complemented, Hall
43C5×C7C7×C11×A418yesdirect product factor
44C3×C11—41noHall
45C22×C7C3×C5×C7×C1118yescomplemented
46C2×C11—31no—
47C3×C7—48no—
48C22×C5C3×C72×C1111yescharacteristic, complemented, Hall
49C3×C5—41noHall
50C2×C7—38no—
51A4C5×C72×C1111yescharacteristic, direct product factor, Hall
52C11C5×C72×A411yescharacteristic, direct product factor, Sylow
53C2×C5—31no—
54C7C5×C7×C11×A418yesdirect product factor
55C5C72×C11×A411yescharacteristic, direct product factor, Sylow
56C22C3×C5×C72×C1111yescharacteristic, complemented, Sylow
57C3—41noSylow
58C2—31no—
subgroupG/H
center, hypercenterC5×C72×C11A4
commutator, cosocle, hypocenterC22C3×C5×C72×C11
FrattiniC1G
Fitting, socleC22×C5×C72×C11C3
LCSG ▷ C22
UCSC1 ◁ C5×C72×C11

Complements

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

NH ≅ G/Ntype
1. C22×C5×C72×C11C3semidirect
3. C72×C11×A4C5direct (N × H)
5. C5×C7×C11×A4C7direct (N × H)
6. C5×C72×A4C11direct (N × H)
7. C5×C72×C11A4direct (N × H)
8. C22×C72×C11C3×C5semidirect
10. C22×C5×C7×C11C3×C7semidirect
13. C22×C5×C72C3×C11semidirect
14. C7×C11×A4C5×C7direct (N × H)
17. C5×C11×A4C72direct (N × H)
18. C72×A4C5×C11direct (N × H)
19. C72×C11C5×A4direct (N × H)
21. C5×C7×A4C7×C11direct (N × H)
22. C5×C7×C11C7×A4direct (N × H)
23. C22×C7×C11C3×C5×C7semidirect
24. C5×C72C11×A4direct (N × H)
26. C22×C5×C11C3×C72semidirect
27. C22×C72C3×C5×C11semidirect
31. C22×C5×C7C3×C7×C11semidirect
32. C11×A4C5×C72direct (N × H)
36. C7×A4C5×C7×C11direct (N × H)
37. C7×C11C5×C7×A4direct (N × H)
39. C5×A4C72×C11direct (N × H)
40. C5×C11C72×A4direct (N × H)
41. C72C5×C11×A4direct (N × H)
42. C22×C11C3×C5×C72semidirect
43. C5×C7C7×C11×A4direct (N × H)
45. C22×C7C3×C5×C7×C11semidirect
48. C22×C5C3×C72×C11semidirect
51. A4C5×C72×C11direct (N × H)
52. C11C5×C72×A4direct (N × H)
54. C7C5×C7×C11×A4direct (N × H)
55. C5C72×C11×A4direct (N × H)
56. C22C3×C5×C72×C11semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C72×C113
C3×C5×C72×C114
C72×C11×A45
C5×C7×C11×A47
C5×C72×A411