Finite Group Databasebeta

← C5×D3×(C31⋊C3)⋊C5 #28358451

Subgroups — C5×D3×(C31⋊C3)⋊C5 #28358451

Order 13950.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×(C31⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2C5×D3×ΓL(1,𝔽32)C311yesmaximal, characteristic, complemented
3C2×C5×(C31⋊C3)⋊C5—31nomaximal
4C5×D3×C31⋊C3C511yesmaximal, characteristic, complemented
5D3×(C31⋊C3)⋊C5C515yesmaximal, direct product factor
6C3×C5×ΓL(1,𝔽32)C2×C311yescharacteristic, complemented
7C5×(C31⋊C3)⋊C5—21no—
8C5×(C31⋊C3)⋊C5D311yescharacteristic, direct product factor
9C2×C5×ΓL(1,𝔽32)—31noHall
10C3×C5×C31⋊C3C2×C511yescharacteristic, complemented
11C3×(C31⋊C3)⋊C5C2×C515yescomplemented
12C5×D3×C31C3×C511yescharacteristic, complemented
13C2×C5×C31⋊C3—31no—
14D3×ΓL(1,𝔽32)C3×C515yescomplemented
15C2×(C31⋊C3)⋊C5—35no—
16C5×ΓL(1,𝔽32)C3×D311yescharacteristic, complemented, Hall
17D3×C31⋊C3C5211yescharacteristic, complemented, Hall
18C3×C5×C31C2×C3×C511yescharacteristic, complemented
19C5×C31⋊C3—21no—
20C5×C31⋊C3C5×D311yescharacteristic, complemented
21C3×ΓL(1,𝔽32)C2×C3×C515yescomplemented
22(C31⋊C3)⋊C5—25no—
23(C31⋊C3)⋊C5C5×D315yesdirect product factor
24C3×C52×D3—311nomaximal, Hall
25C2×C5×C31—31no—
26C2×ΓL(1,𝔽32)—35no—
27C3×C31⋊C3C2×C5211yescharacteristic, complemented, Hall
28C32×C52—311noHall
29D3×C31C3×C5211yescharacteristic, complemented
30C2×C31⋊C3—31no—
31C5×C31C3×C5×D311yescharacteristic, complemented
32ΓL(1,𝔽32)C3×C5×D315yescomplemented
33C2×C3×C52—931no—
34C52×D3—311no—
35C3×C31C2×C3×C5211yescharacteristic, complemented
36C31⋊C3—21no—
37C31⋊C3C52×D311yescharacteristic, complemented
38C3×C5×D3—315no—
39C3×C5×D3—311no—
40C3×C52—311no—
41C3×C52—311no—
42C3×C52—621no—
43C2×C31—31noHall
44C2×C52—931noHall
45C32×C5—315no—
46C32×C5—311no—
47C31C3×C52×D311yescharacteristic, complemented, Sylow
48C2×C3×C5—931no—
49C2×C3×C5—935no—
50C5×D3—315no—
51C5×D3(C31⋊C3)⋊C511yescharacteristic, direct product factor
52C52—311noSylow
53C3×D3—311noHall
54C3×C5—315no—
55C3×C5—311no—
56C3×C5—315no—
57C3×C5—625no—
58C3×C5—621no—
59C3×C5C2×(C31⋊C3)⋊C511yescharacteristic, complemented
60C2×C5—31no—
61C2×C5—935no—
62C32—311noSylow
63C2×C3—931no—
64D3C5×(C31⋊C3)⋊C511yescharacteristic, direct product factor
65C5—315no—
66C5D3×(C31⋊C3)⋊C511yescharacteristic, direct product factor
67C3—311no—
68C3—621no—
69C3C2×C5×(C31⋊C3)⋊C511yescharacteristic, complemented
70C2—31noSylow
subgroupG/H
center, hypercenterC5D3×(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC3×C31C2×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C31C2×C3×C5
LCSG ▷ C3×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×(C31⋊C3)⋊C5C2semidirect
2. C5×D3×ΓL(1,𝔽32)C3semidirect
4. C5×D3×C31⋊C3C5semidirect
5. D3×(C31⋊C3)⋊C5C5direct (N × H)
6. C3×C5×ΓL(1,𝔽32)C2×C3semidirect
8. C5×(C31⋊C3)⋊C5D3direct (N × H)
10. C3×C5×C31⋊C3C2×C5semidirect
11. C3×(C31⋊C3)⋊C5C2×C5semidirect
12. C5×D3×C31C3×C5semidirect
14. D3×ΓL(1,𝔽32)C3×C5semidirect
16. C5×ΓL(1,𝔽32)C3×D3semidirect
17. D3×C31⋊C3C52semidirect
18. C3×C5×C31C2×C3×C5semidirect
20. C5×C31⋊C3C5×D3semidirect
21. C3×ΓL(1,𝔽32)C2×C3×C5semidirect
23. (C31⋊C3)⋊C5C5×D3direct (N × H)
27. C3×C31⋊C3C2×C52semidirect
29. D3×C31C3×C52semidirect
31. C5×C31C3×C5×D3semidirect
32. ΓL(1,𝔽32)C3×C5×D3semidirect
35. C3×C31C2×C3×C52semidirect
37. C31⋊C3C52×D3semidirect
47. C31C3×C52×D3semidirect
51. C5×D3(C31⋊C3)⋊C5direct (N × H)
59. C3×C5C2×(C31⋊C3)⋊C5semidirect
64. D3C5×(C31⋊C3)⋊C5direct (N × H)
66. C5D3×(C31⋊C3)⋊C5direct (N × H)
69. C3C2×C5×(C31⋊C3)⋊C5semidirect

Maximal subgroups

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

subgroupindex
C3×C5×(C31⋊C3)⋊C52
C5×D3×ΓL(1,𝔽32)3
C2×C5×(C31⋊C3)⋊C53
C5×D3×C31⋊C35
D3×(C31⋊C3)⋊C55
C3×C52×D331