Finite Group Databasebeta

← C3×C11×C5⋊(D31⋊C3) #44501848

Subgroups — C3×C11×C5⋊(D31⋊C3) #44501848

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C11×C31⋊C3C211yesmaximal, characteristic, complemented, Hall
2C11×C5⋊(D31⋊C3)C313yesmaximal, direct product factor
3C3×C11×D155C311yesmaximal, characteristic, complemented
4C3×C11×D31⋊C3—51nomaximal, Hall
5C5×C11×C31⋊C3C2×C313yescomplemented
6C3×C5×C11×C31C2×C311yescharacteristic, complemented
7C11×D155C3211yescharacteristic, complemented, Hall
8C3×C11×C31⋊C3D511yescharacteristic, complemented, Hall
9C3×C5⋊(D31⋊C3)C1111yesmaximal, characteristic, direct product factor, Hall
10C11×D31⋊C3—53no—
11C3×C11×D31—51no—
12C5×C11×C31C2×C3211yescharacteristic, complemented, Hall
13C3×C5×C31⋊C3C2×C1111yescharacteristic, complemented, Hall
14C3×C11×C31C3×D511yescharacteristic, complemented
15C11×C31⋊C3C3×D513yescomplemented
16C32×D5×C11—311nomaximal, Hall
17C3×D155C3×C1111yescharacteristic, complemented
18C5⋊(D31⋊C3)C3×C1113yesdirect product factor
19C11×D31—51noHall
20C3×D31⋊C3—51noHall
21C32×C5×C11—311noHall
22C3×C5×C31C2×C3×C1111yescharacteristic, complemented
23C5×C31⋊C3C2×C3×C1113yescomplemented
24C11×C31C32×D511yescharacteristic, complemented, Hall
25C3×D5×C11—313no—
26C3×D5×C11—311no—
27D155C32×C1111yescharacteristic, complemented, Hall
28C3×C31⋊C3D5×C1111yescharacteristic, complemented, Hall
29C2×C32×C11—1551noHall
30C3×D31—51no—
31D31⋊C3—53no—
32C3×C5×C11—313no—
33C3×C5×C11D31⋊C311yescharacteristic, complemented
34C5×C31C2×C32×C1111yescharacteristic, complemented, Hall
35D5×C11—311noHall
36C32×C11—311noHall
37C3×C31C3×D5×C1111yescharacteristic, complemented
38C31⋊C3C3×D5×C1113yescomplemented
39C32×D5—311noHall
40C2×C3×C11—1553no—
41C2×C3×C11—1551no—
42D31—51noHall
43C5×C11C3×D31⋊C311yescharacteristic, complemented, Hall
44C32×C5—311noHall
45C3×C11—313no—
46C3×C11C5⋊(D31⋊C3)11yescharacteristic, direct product factor
47C31C32×D5×C1111yescharacteristic, complemented, Sylow
48C3×D5—313no—
49C3×D5—311no—
50C2×C11—1551noHall
51C2×C32—1551noHall
52C3×C5—313no—
53C3×C5C11×D31⋊C311yescharacteristic, complemented
54C11C3×C5⋊(D31⋊C3)11yescharacteristic, direct product factor, Sylow
55D5—311noHall
56C32—311noSylow
57C2×C3—1553no—
58C2×C3—1551no—
59C5C3×C11×D31⋊C311yescharacteristic, complemented, Sylow
60C3—313no—
61C3C11×C5⋊(D31⋊C3)11yescharacteristic, direct product factor
62C2—1551noSylow
subgroupG/H
center, hypercenterC3×C11C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C32×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×C31⋊C3C2semidirect
2. C11×C5⋊(D31⋊C3)C3direct (N × H)
3. C3×C11×D155C3semidirect
5. C5×C11×C31⋊C3C2×C3semidirect
6. C3×C5×C11×C31C2×C3semidirect
7. C11×D155C32semidirect
8. C3×C11×C31⋊C3D5semidirect
9. C3×C5⋊(D31⋊C3)C11direct (N × H)
12. C5×C11×C31C2×C32semidirect
13. C3×C5×C31⋊C3C2×C11semidirect
14. C3×C11×C31C3×D5semidirect
15. C11×C31⋊C3C3×D5semidirect
17. C3×D155C3×C11semidirect
18. C5⋊(D31⋊C3)C3×C11direct (N × H)
22. C3×C5×C31C2×C3×C11semidirect
23. C5×C31⋊C3C2×C3×C11semidirect
24. C11×C31C32×D5semidirect
27. D155C32×C11semidirect
28. C3×C31⋊C3D5×C11semidirect
33. C3×C5×C11D31⋊C3semidirect
34. C5×C31C2×C32×C11semidirect
37. C3×C31C3×D5×C11semidirect
38. C31⋊C3C3×D5×C11semidirect
43. C5×C11C3×D31⋊C3semidirect
46. C3×C11C5⋊(D31⋊C3)direct (N × H)
47. C31C32×D5×C11semidirect
53. C3×C5C11×D31⋊C3semidirect
54. C11C3×C5⋊(D31⋊C3)direct (N × H)
59. C5C3×C11×D31⋊C3semidirect
61. C3C11×C5⋊(D31⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C11×C31⋊C32
C11×C5⋊(D31⋊C3)3
C3×C11×D1553
C3×C11×D31⋊C35
C3×C5⋊(D31⋊C3)11
C32×D5×C1131