Finite Group Databasebeta

← C3×C11×D15×C31 #44501878

Subgroups — C3×C11×D15×C31 #44501878

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×C11×C31C211yesmaximal, characteristic, complemented, Hall
2C11×D15×C31C311yesmaximal, characteristic, direct product factor
3C3×D5×C11×C31—31nomaximal
4C3×D3×C11×C31—51nomaximal, Hall
5C3×C5×C11×C31—21no—
6C3×C5×C11×C31D311yescharacteristic, complemented
7C3×C5×C11×C31C2×C311yescharacteristic, complemented
8D5×C11×C31—31noHall
9C32×C11×C31D511yescharacteristic, complemented, Hall
10C3×D15×C31C1111yesmaximal, characteristic, direct product factor, Hall
11D3×C11×C31—51no—
12C2×C3×C11×C31—151no—
13C5×C11×C31C3×D311yescharacteristic, complemented, Hall
14C32×C5×C31C2×C1111yescharacteristic, complemented, Hall
15C3×C11×C31—21no—
16C3×C11×C31C3×D511yescharacteristic, complemented
17C3×C11×C31D1511yescharacteristic, direct product factor
18C3×C11×D15C3111yesmaximal, characteristic, direct product factor, Hall
19D15×C31C3×C1111yescharacteristic, direct product factor
20C3×D5×C31—31no—
21C2×C11×C31—151noHall
22C3×D3×C31—51noHall
23C32×C5×C11C2×C3111yescharacteristic, complemented, Hall
24C3×C5×C31—21no—
25C3×C5×C31D3×C1111yescharacteristic, complemented
26C3×C5×C31C2×C3×C1111yescharacteristic, complemented
27C11×C31C3×D1511yescharacteristic, direct product factor, Hall
28C11×D15C3×C3111yescharacteristic, direct product factor
29C3×D5×C11—31no—
30D5×C31—31noHall
31C32×C31D5×C1111yescharacteristic, complemented, Hall
32C3×D3×C11—51noHall
33C2×C3×C31—151no—
34D3×C31—51no—
35C3×C5×C11—21no—
36C3×C5×C11D3×C3111yescharacteristic, complemented
37C3×C5×C11C2×C3×C3111yescharacteristic, complemented
38C5×C31C3×D3×C1111yescharacteristic, complemented, Hall
39D5×C11—31noHall
40C32×C11D5×C3111yescharacteristic, complemented, Hall
41C3×C31—21no—
42C3×C31C3×D5×C1111yescharacteristic, complemented
43C3×C31C11×D1511yescharacteristic, direct product factor
44C3×D15C11×C3111yescharacteristic, direct product factor, Hall
45C2×C3×C11—151no—
46D3×C11—51no—
47C2×C31—151noHall
48C5×C11C3×D3×C3111yescharacteristic, complemented, Hall
49C32×C5C2×C11×C3111yescharacteristic, complemented, Hall
50C3×C11—21no—
51C3×C11C3×D5×C3111yescharacteristic, complemented
52C3×C11D15×C3111yescharacteristic, direct product factor
53C31C3×C11×D1511yescharacteristic, direct product factor, Sylow
54D15C3×C11×C3111yescharacteristic, direct product factor
55C3×D5—31no—
56C2×C11—151noHall
57C3×D3—51noHall
58C3×C5—21no—
59C3×C5C2×C3×C11×C3111yescharacteristic, complemented
60C3×C5D3×C11×C3111yescharacteristic, complemented
61C11C3×D15×C3111yescharacteristic, direct product factor, Sylow
62D5—31noHall
63C32D5×C11×C3111yescharacteristic, complemented, Sylow
64C2×C3—151no—
65D3—51no—
66C5C3×D3×C11×C3111yescharacteristic, complemented, Sylow
67C3—21no—
68C3C3×D5×C11×C3111yescharacteristic, complemented
69C3C11×D15×C3111yescharacteristic, direct product factor
70C2—151noSylow
subgroupG/H
center, hypercenterC3×C11×C31D15
commutator, cosocle, hypocenterC3×C5C2×C3×C11×C31
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C5
UCSC1 ◁ C3×C11×C31

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×C31C2semidirect
2. C11×D15×C31C3direct (N × H)
6. C3×C5×C11×C31D3semidirect
7. C3×C5×C11×C31C2×C3semidirect
9. C32×C11×C31D5semidirect
10. C3×D15×C31C11direct (N × H)
13. C5×C11×C31C3×D3semidirect
14. C32×C5×C31C2×C11semidirect
16. C3×C11×C31C3×D5semidirect
17. C3×C11×C31D15direct (N × H)
18. C3×C11×D15C31direct (N × H)
19. D15×C31C3×C11direct (N × H)
23. C32×C5×C11C2×C31semidirect
25. C3×C5×C31D3×C11semidirect
26. C3×C5×C31C2×C3×C11semidirect
27. C11×C31C3×D15direct (N × H)
28. C11×D15C3×C31direct (N × H)
31. C32×C31D5×C11semidirect
36. C3×C5×C11D3×C31semidirect
37. C3×C5×C11C2×C3×C31semidirect
38. C5×C31C3×D3×C11semidirect
40. C32×C11D5×C31semidirect
42. C3×C31C3×D5×C11semidirect
43. C3×C31C11×D15direct (N × H)
44. C3×D15C11×C31direct (N × H)
48. C5×C11C3×D3×C31semidirect
49. C32×C5C2×C11×C31semidirect
51. C3×C11C3×D5×C31semidirect
52. C3×C11D15×C31direct (N × H)
53. C31C3×C11×D15direct (N × H)
54. D15C3×C11×C31direct (N × H)
59. C3×C5C2×C3×C11×C31semidirect
60. C3×C5D3×C11×C31semidirect
61. C11C3×D15×C31direct (N × H)
63. C32D5×C11×C31semidirect
66. C5C3×D3×C11×C31semidirect
68. C3C3×D5×C11×C31semidirect
69. C3C11×D15×C31direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×C11×C312
C11×D15×C313
C3×D5×C11×C313
C3×D3×C11×C315
C3×D15×C3111
C3×C11×D1531