Finite Group Databasebeta

← C5×D143⋊(C3⋊D3) #38788265

Subgroups — C5×D143⋊(C3⋊D3) #38788265

Order 25740.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C32×C5×D143C211yesmaximal, characteristic, complemented
2C5×C11×C3⋊D39C211yesmaximal, characteristic, complemented
3C5×C13×C3⋊D33C211yesmaximal, characteristic, complemented
4C5×D33⋊D13—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6D143⋊(C3⋊D3)C511yesmaximal, characteristic, direct product factor, Hall
7C5×C13×D33—34no—
8C5×C11×D39—34no—
9C3×C5×D143D314yescomplemented
10C5×D11×D13—91noHall
11C13×C3⋊D33C2×C511yescharacteristic, complemented
12C11×C3⋊D39C2×C511yescharacteristic, complemented
13C32×D143C2×C511yescharacteristic, complemented
14C5×C3⋊D3×D13—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C5×C3⋊D3×D11—131nomaximal, Hall
17D33⋊D13—34no—
18C5×D143C3⋊D311yescharacteristic, complemented
19C5×C13×D11—91no—
20C5×C11×D13—91no—
21C32×C11×C13C22×C511yescharacteristic, complemented, Hall
22C5×C3⋊D39D1111yescharacteristic, complemented
23C5×C13×C3⋊D3—111no—
24C32×C5×D13—111no—
25C5×C3⋊D33D1311yescharacteristic, complemented
26C5×C11×C3⋊D3—131no—
27C32×C5×D11—131no—
28C13×D33—34no—
29C11×D39—34no—
30C3×D143C5×D314yescomplemented
31C5×D3×D13—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C5×D3×D11—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—91noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—111noHall
38C3×C11×C13C2×C5×D314yescomplemented
39C3⋊D3×D11—131noHall
40C5×D39—34no—
41C5×D3×C13—334no—
42C3×C5×D13—114no—
43C5×D33—34no—
44C5×D3×C11—394no—
45C3×C5×D11—134no—
46D143C5×C3⋊D311yescharacteristic, complemented
47C11×D13—91no—
48C13×D11—91no—
49C2×C5×D13—991noHall
50C3⋊D39C5×D1111yescharacteristic, complemented
51C13×C3⋊D3—111no—
52C32×D13—111no—
53C2×C5×D11—1171noHall
54C3⋊D33C5×D1311yescharacteristic, complemented
55C11×C3⋊D3—131no—
56C32×D11—131no—
57C3×C5×C13D3×D1114yescomplemented
58C2×C5×C3⋊D3—1431noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—334no—
61C11×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
62D3×D11—394no—
63C2×C5×C13—991no—
64C5×D13—91no—
65C5×D13—111no—
66C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
67C2×C5×C11—1171no—
68C5×D11—91no—
69C5×D11—131no—
70C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—1431no—
72C5×C3⋊D3—111no—
73C5×C3⋊D3—131no—
74D39—34no—
75C3×D13—114no—
76D3×C13—334no—
77D33—34no—
78C3×D11—134no—
79D3×C11—394no—
80C5×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
81C2×C5×D3—4294no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—991noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—1171noHall
86C3×C13C5×D3×D1114yescomplemented
87C2×C3⋊D3—1431noHall
88C3×C11C5×D3×D1314yescomplemented
89C2×C3×C5—1434no—
90C5×D3—334no—
91C5×D3—394no—
92C2×C13—991no—
93D13—91no—
94D13—111no—
95C2×C11—1171no—
96D11—91no—
97D11—131no—
98C22×C5—12871noHall
99C2×C32—1431no—
100C3⋊D3—111no—
101C3⋊D3—131no—
102C3×C5D33⋊D1314yescomplemented
103C13C5×C3⋊D3×D1111yescharacteristic, complemented, Sylow
104C2×D3—4294no—
105C11C5×C3⋊D3×D1311yescharacteristic, complemented, Sylow
106C2×C5—991no—
107C2×C5—1171no—
108C2×C5—1431no—
109C32C5×D11×D1311yescharacteristic, complemented, Sylow
110C2×C3—1434no—
111D3—334no—
112D3—394no—
113C5D143⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
114C22—12871noSylow
115C3C5×D33⋊D1314yescomplemented
116C2—991no—
117C2—1171no—
118C2—1431no—
subgroupG/H
center, hypercenterC5D143⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D143C2semidirect
2. C5×C11×C3⋊D39C2semidirect
3. C5×C13×C3⋊D33C2semidirect
5. C32×C5×C11×C13C22semidirect
6. D143⋊(C3⋊D3)C5direct (N × H)
9. C3×C5×D143D3semidirect
11. C13×C3⋊D33C2×C5semidirect
12. C11×C3⋊D39C2×C5semidirect
13. C32×D143C2×C5semidirect
15. C3×C5×C11×C13C2×D3semidirect
18. C5×D143C3⋊D3semidirect
21. C32×C11×C13C22×C5semidirect
22. C5×C3⋊D39D11semidirect
25. C5×C3⋊D33D13semidirect
30. C3×D143C5×D3semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13C2×C5×D3semidirect
46. D143C5×C3⋊D3semidirect
50. C3⋊D39C5×D11semidirect
54. C3⋊D33C5×D13semidirect
57. C3×C5×C13D3×D11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13C2×C5×C3⋊D3semidirect
66. C32×C13C2×C5×D11semidirect
70. C32×C11C2×C5×D13semidirect
80. C5×C13C3⋊D3×D11semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5D11×D13semidirect
86. C3×C13C5×D3×D11semidirect
88. C3×C11C5×D3×D13semidirect
102. C3×C5D33⋊D13semidirect
103. C13C5×C3⋊D3×D11semidirect
105. C11C5×C3⋊D3×D13semidirect
109. C32C5×D11×D13semidirect
113. C5D143⋊(C3⋊D3)direct (N × H)
115. C3C5×D33⋊D13semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1432
C5×C11×C3⋊D392
C5×C13×C3⋊D332
C5×D33⋊D133
D143⋊(C3⋊D3)5
C5×C3⋊D3×D1311
C5×C3⋊D3×D1113