Finite Group Databasebeta

← D143⋊(C3⋊D15) #38788281

Subgroups — D143⋊(C3⋊D15) #38788281

Order 25740.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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
2C11×C3⋊D195C211yesmaximal, characteristic, complemented
3C13×C3⋊D165C211yesmaximal, characteristic, complemented
4D143⋊D15—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6D143⋊(C3⋊D3)—51nomaximal, Hall
7C13×D165—34no—
8C11×D195—34no—
9C3×C5×D143D314yescomplemented
10D55⋊D13—91noHall
11C13×C3⋊D33—51no—
12C11×C3⋊D39—51no—
13C32×D143D511yescharacteristic, complemented
14D13×C3⋊D15—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D11×C3⋊D15—131nomaximal, Hall
17D33⋊D13—154no—
18C13×D55—91no—
19C11×D65—91no—
20C5×D143C3⋊D311yescharacteristic, complemented
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C3⋊D195D1111yescharacteristic, complemented
23C13×C3⋊D15—111no—
24C32×C5×D13—111no—
25C3⋊D165D1311yescharacteristic, complemented
26C11×C3⋊D15—131no—
27C32×C5×D11—131no—
28C13×D33—154no—
29C11×D39—154no—
30C3×D143D1514yescomplemented
31D13×D15—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D11×D15—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—451noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—551noHall
38C3×C11×C13C2×D1514yescomplemented
39C3⋊D3×D11—651noHall
40D195—34no—
41C13×D15—334no—
42C3×C5×D13—114no—
43D165—34no—
44C11×D15—394no—
45C3×C5×D11—134no—
46D143C3⋊D1511yescharacteristic, complemented
47C11×D13—451no—
48C13×D11—451no—
49D5×D13—991noHall
50C3⋊D39—51no—
51C13×C3⋊D3—551no—
52C32×D13—111no—
53D5×D11—1171noHall
54C3⋊D33—51no—
55C11×C3⋊D3—651no—
56C32×D11—131no—
57C3×C5×C13D3×D1114yescomplemented
58C2×C3⋊D15—1431noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—1654no—
61C11×C13C2×C3⋊D1511yescharacteristic, complemented, Hall
62D3×D11—1954no—
63D65—91no—
64C5×D13—111no—
65D5×C13—991no—
66C32×C13D5×D1111yescharacteristic, complemented, Hall
67D55—91no—
68C5×D11—131no—
69D5×C11—1171no—
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—1431no—
72C3⋊D15—111no—
73C3⋊D15—131no—
74D39—154no—
75C3×D13—114no—
76D3×C13—1654no—
77D33—154no—
78C3×D11—134no—
79D3×C11—1954no—
80C5×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
81C2×D15—4294no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—4951noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—5851noHall
86C3×C13D11×D1514yescomplemented
87C2×C3⋊D3—7151noHall
88C3×C11D13×D1514yescomplemented
89C2×C3×C5—1434no—
90D15—334no—
91D15—394no—
92C2×C13—4951no—
93D13—111no—
94D13—451no—
95C2×C11—5851no—
96D11—131no—
97D11—451no—
98C2×D5—12871noHall
99C2×C32—1431no—
100C3⋊D3—551no—
101C3⋊D3—651no—
102C3×C5D33⋊D1314yescomplemented
103C13D11×C3⋊D1511yescharacteristic, complemented, Sylow
104C2×D3—21454no—
105C11D13×C3⋊D1511yescharacteristic, complemented, Sylow
106C2×C5—1431no—
107D5—991no—
108D5—1171no—
109C32D55⋊D1311yescharacteristic, complemented, Sylow
110C2×C3—1434no—
111D3—1654no—
112D3—1954no—
113C5D143⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
114C22—64351noSylow
115C3D143⋊D1514yescomplemented
116C2—5851no—
117C2—1431no—
118C2—4951no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C13C22
LCSG ▷ C32×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5×D143C2semidirect
2. C11×C3⋊D195C2semidirect
3. C13×C3⋊D165C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×C5×D143D3semidirect
13. C32×D143D5semidirect
15. C3×C5×C11×C13C2×D3semidirect
20. C5×D143C3⋊D3semidirect
21. C32×C11×C13C2×D5semidirect
22. C3⋊D195D11semidirect
25. C3⋊D165D13semidirect
30. C3×D143D15semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13C2×D15semidirect
46. D143C3⋊D15semidirect
57. C3×C5×C13D3×D11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13C2×C3⋊D15semidirect
66. C32×C13D5×D11semidirect
70. C32×C11D5×D13semidirect
80. C5×C13C3⋊D3×D11semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5D11×D13semidirect
86. C3×C13D11×D15semidirect
88. C3×C11D13×D15semidirect
102. C3×C5D33⋊D13semidirect
103. C13D11×C3⋊D15semidirect
105. C11D13×C3⋊D15semidirect
109. C32D55⋊D13semidirect
113. C5D143⋊(C3⋊D3)semidirect
115. C3D143⋊D15semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D1432
C11×C3⋊D1952
C13×C3⋊D1652
D143⋊D153
D143⋊(C3⋊D3)5
D13×C3⋊D1511
D11×C3⋊D1513