Finite Group Databasebeta

← C22×C5×C4⋊(C3⋊D3) #13089490

Subgroups — C22×C5×C4⋊(C3⋊D3) #13089490

Order 1440.

1416 conjugacy classes of subgroups; only the 426 normal subgroups are shown.

normal subgroups only

This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 426 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C3⋊D3C212yesmaximal, complemented
2C22×C32×C4×C5C211yesmaximal, characteristic, complemented
3C2×C5×C4⋊(C3⋊D3)C2112yesmaximal, direct product factor
4C22×C5×D12—34nomaximal
5C23×C32×C5C2211yescharacteristic
6C22×C5×C3⋊D3—28no—
7C22×C5×C3⋊D3C22112yescomplemented
8C2×C32×C4×C5C2216yescomplemented
9C5×C4⋊(C3⋊D3)C22116yesdirect product factor
10C22×C4⋊(C3⋊D3)C511yesmaximal, characteristic, direct product factor, Hall
11C23×C5×D3—38no—
12C22×C3×C4×C5D314yescomplemented
13C2×C5×D12—348no—
14C22×C32×C5D414yescomplemented
15C22×C32×C5C2313yes—
16C2×C5×C3⋊D3—224no—
17C2×C5×C3⋊D3C2318yescomplemented
18C32×C4×C5C2314yescomplemented
19C22×C5×D4—91noHall
20C23×C3⋊D3C2×C512yescomplemented
21C22×C32×C4C2×C511yescharacteristic, complemented
22C2×C4⋊(C3⋊D3)C2×C5112yesdirect product factor
23C23×C3×C5C2×D314yes—
24C22×C5×D3—348no—
25C22×C5×D3—632no—
26C2×C3×C4×C5C2×D3124yescomplemented
27C5×D12—364no—
28C22×D12—34no—
29C2×C32×C5C2×D416yescomplemented
30C2×C32×C5C2411yescharacteristic
31C5×C3⋊D3—28no—
32C24×C5—92no—
33C2×C5×D4—912no—
34C22×C4×C5C3⋊D311yescharacteristic, complemented
35C23×C32C22×C511yescharacteristic
36C22×C3⋊D3—28no—
37C22×C3⋊D3C22×C5112yescomplemented
38C2×C32×C4C22×C516yescomplemented
39C4⋊(C3⋊D3)C22×C5116yesdirect product factor
40C22×C3×C5D12116yescomplemented
41C22×C3×C5C22×D3112yes—
42C2×C5×D3—332no—
43C2×C5×D3—696no—
44C3×C4×C5C22×D3116yescomplemented
45C23×D3—38no—
46C22×C3×C4C5×D314yescomplemented
47C2×D12—348no—
48C32×C5C22×D411yescharacteristic, complemented, Hall
49C23×C5—912no—
50C23×C5—188no—
51C23×C5C2×C3⋊D311yescharacteristic
52C5×D4—916no—
53C2×C4×C5C2×C3⋊D316yescomplemented
54C22×C32C5×D414yescomplemented
55C22×C32C23×C513yes—
56C2×C3⋊D3—224no—
57C2×C3⋊D3C23×C518yescomplemented
58C32×C4C23×C514yescomplemented
59C22×D4—91noSylow
60C2×C3×C5C2×D12124yescomplemented
61C2×C3×C5C23×D314yes—
62C5×D3—632no—
63C23×C3C2×C5×D314yes—
64C22×D3—348no—
65C22×D3—632no—
66C2×C3×C4C2×C5×D3124yescomplemented
67D12—364no—
68C22×C5—98no—
69C22×C5—1824no—
70C22×C5C4⋊(C3⋊D3)14yesdirect product factor
71C22×C5C22×C3⋊D313yes—
72C4×C5C22×C3⋊D314yescomplemented
73C2×C32C2×C5×D416yescomplemented
74C2×C32C24×C511yescharacteristic
75C3⋊D3—28no—
76C24—92no—
77C2×D4—912no—
78C22×C4C5×C3⋊D311yescharacteristic, complemented
79C3×C5C22×D1214yescomplemented
80C22×C3C5×D12116yescomplemented
81C22×C3C22×C5×D3112yes—
82C2×D3—332no—
83C2×D3—696no—
84C3×C4C22×C5×D3116yescomplemented
85C2×C5—188no—
86C2×C5C2×C4⋊(C3⋊D3)16yesdirect product factor
87C2×C5C23×C3⋊D311yescharacteristic
88C32C22×C5×D411yescharacteristic, complemented, Sylow
89C23—912no—
90C23—188no—
91C23C2×C5×C3⋊D311yescharacteristic
92D4—916no—
93C2×C4C2×C5×C3⋊D316yescomplemented
94C2×C3C2×C5×D12124yescomplemented
95C2×C3C23×C5×D314yes—
96D3—632no—
97C5C22×C4⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
98C22—98no—
99C22—1824no—
100C22C5×C4⋊(C3⋊D3)14yesdirect product factor
101C22C22×C5×C3⋊D313yes—
102C4C22×C5×C3⋊D314yescomplemented
103C3C22×C5×D1214yescomplemented
104C2—188no—
105C2C2×C5×C4⋊(C3⋊D3)16yesdirect product factor
106C2C23×C5×C3⋊D311yescharacteristic
subgroupG/H
centerC23×C5C2×C3⋊D3
commutator, cosocleC2×C32C24×C5
FrattiniC2C23×C5×C3⋊D3
FittingC22×C32×C4×C5C2
socleC23×C32×C5C22
hypercenterC22×C4×C5C3⋊D3
hypocenterC32C22×C5×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

Complements

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

NH ≅ G/Ntype
1. C23×C5×C3⋊D3C2semidirect
2. C22×C32×C4×C5C2semidirect
3. C2×C5×C4⋊(C3⋊D3)C2direct (N × H)
7. C22×C5×C3⋊D3C22semidirect
8. C2×C32×C4×C5C22semidirect
9. C5×C4⋊(C3⋊D3)C22direct (N × H)
10. C22×C4⋊(C3⋊D3)C5direct (N × H)
12. C22×C3×C4×C5D3semidirect
14. C22×C32×C5D4semidirect
17. C2×C5×C3⋊D3C23semidirect
18. C32×C4×C5C23semidirect
20. C23×C3⋊D3C2×C5semidirect
21. C22×C32×C4C2×C5semidirect
22. C2×C4⋊(C3⋊D3)C2×C5direct (N × H)
26. C2×C3×C4×C5C2×D3semidirect
29. C2×C32×C5C2×D4semidirect
34. C22×C4×C5C3⋊D3semidirect
37. C22×C3⋊D3C22×C5semidirect
38. C2×C32×C4C22×C5semidirect
39. C4⋊(C3⋊D3)C22×C5direct (N × H)
40. C22×C3×C5D12semidirect
44. C3×C4×C5C22×D3semidirect
46. C22×C3×C4C5×D3semidirect
48. C32×C5C22×D4semidirect
53. C2×C4×C5C2×C3⋊D3semidirect
54. C22×C32C5×D4semidirect
57. C2×C3⋊D3C23×C5semidirect
58. C32×C4C23×C5semidirect
60. C2×C3×C5C2×D12semidirect
66. C2×C3×C4C2×C5×D3semidirect
70. C22×C5C4⋊(C3⋊D3)direct (N × H)
72. C4×C5C22×C3⋊D3semidirect
73. C2×C32C2×C5×D4semidirect
78. C22×C4C5×C3⋊D3semidirect
79. C3×C5C22×D12semidirect
80. C22×C3C5×D12semidirect
84. C3×C4C22×C5×D3semidirect
86. C2×C5C2×C4⋊(C3⋊D3)direct (N × H)
88. C32C22×C5×D4semidirect
93. C2×C4C2×C5×C3⋊D3semidirect
94. C2×C3C2×C5×D12semidirect
97. C5C22×C4⋊(C3⋊D3)direct (N × H)
100. C22C5×C4⋊(C3⋊D3)direct (N × H)
102. C4C22×C5×C3⋊D3semidirect
103. C3C22×C5×D12semidirect
105. C2C2×C5×C4⋊(C3⋊D3)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C22×C32×C4×C52
C2×C5×C4⋊(C3⋊D3)2
C22×C5×D123
C22×C4⋊(C3⋊D3)5