Finite Group Databasebeta

← C5×C3⋊D3×D143 #38788264

Subgroups — C5×C3⋊D3×D143 #38788264

Order 25740.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×C3⋊D429C211yesmaximal, characteristic, complemented
4C5×D3×D143—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C3⋊D3×D143C511yesmaximal, characteristic, direct product factor, Hall
7C5×D429—34no—
8C5×D3×C11×C13—34no—
9C3×C5×D143D314yescomplemented
10C2×C5×D143—91noHall
11C3⋊D429C2×C511yescharacteristic, complemented
12C11×C13×C3⋊D3C2×C511yescharacteristic, complemented
13C32×D143C2×C511yescharacteristic, complemented
14C5×C3⋊D3×D13—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C5×C3⋊D3×D11—131nomaximal, Hall
17D3×D143—34no—
18C2×C5×C11×C13—91no—
19C5×D143—91no—
20C5×D143C3⋊D311yescharacteristic, direct product factor
21C32×C11×C13C22×C511yescharacteristic, complemented, Hall
22C5×C3⋊D39—111no—
23C5×C13×C3⋊D3D1111yescharacteristic, complemented
24C32×C5×D13—111no—
25C5×C3⋊D33—131no—
26C5×C11×C3⋊D3D1311yescharacteristic, complemented
27C32×C5×D11—131no—
28D429—34no—
29D3×C11×C13—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
35C2×D143—91noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13—111noHall
38C3×C11×C13C2×C5×D314yescomplemented
39C3⋊D3×D11—131noHall
40C5×D39—334no—
41C5×D3×C13—34no—
42C3×C5×D13—114no—
43C5×D33—394no—
44C5×D3×C11—34no—
45C3×C5×D11—134no—
46C2×C11×C13—91no—
47D143—91no—
48D143C5×C3⋊D311yescharacteristic, direct product factor
49C2×C5×D13—991noHall
50C3⋊D39—111no—
51C13×C3⋊D3C5×D1111yescharacteristic, complemented
52C32×D13—111no—
53C2×C5×D11—1171noHall
54C3⋊D33—131no—
55C11×C3⋊D3C5×D1311yescharacteristic, complemented
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—91no—
64C5×D13—111no—
65C5×D13—991no—
66C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68C5×D11—131no—
69C5×D11—1171no—
70C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—1431no—
72C5×C3⋊D3—1431no—
73C5×C3⋊D3D14311yescharacteristic, direct product factor
74D39—334no—
75C3×D13—114no—
76D3×C13—34no—
77D33—394no—
78C3×D11—134no—
79D3×C11—34no—
80C5×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
81C2×C5×D3—4294no—
82C5×C11C3⋊D3×D1311yescharacteristic, complemented, Hall
83C2×D13—991noHall
84C32×C5C2×D14311yescharacteristic, complemented, Hall
85C2×D11—1171noHall
86C3×C13C5×D3×D1114yescomplemented
87C2×C3⋊D3—1431noHall
88C3×C11C5×D3×D1314yescomplemented
89C2×C3×C5—1434no—
90C5×D3—34no—
91C5×D3—4294no—
92C2×C13—91no—
93D13—111no—
94D13—991no—
95C2×C11—91no—
96D11—131no—
97D11—1171no—
98C22×C5—12871noHall
99C2×C32—1431no—
100C3⋊D3—1431no—
101C3⋊D3C5×D14311yescharacteristic, direct product factor
102C3×C5D3×D14314yescomplemented
103C13C5×C3⋊D3×D1111yescharacteristic, complemented, Sylow
104C2×D3—4294no—
105C11C5×C3⋊D3×D1311yescharacteristic, complemented, Sylow
106C2×C5—12871no—
107C2×C5—91no—
108C2×C5—1431no—
109C32C2×C5×D14311yescharacteristic, complemented, Sylow
110C2×C3—1434no—
111D3—34no—
112D3—4294no—
113C5C3⋊D3×D14311yescharacteristic, direct product factor, Sylow
114C22—12871noSylow
115C3C5×D3×D14314yescomplemented
116C2—12871no—
117C2—91no—
118C2—1431no—
subgroupG/H
center, hypercenterC5C3⋊D3×D143
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×C13×C3⋊D3C2semidirect
3. C5×C3⋊D429C2semidirect
5. C32×C5×C11×C13C22semidirect
6. C3⋊D3×D143C5direct (N × H)
9. C3×C5×D143D3semidirect
11. C3⋊D429C2×C5semidirect
12. C11×C13×C3⋊D3C2×C5semidirect
13. C32×D143C2×C5semidirect
15. C3×C5×C11×C13C2×D3semidirect
20. C5×D143C3⋊D3direct (N × H)
21. C32×C11×C13C22×C5semidirect
23. C5×C13×C3⋊D3D11semidirect
26. C5×C11×C3⋊D3D13semidirect
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
48. D143C5×C3⋊D3direct (N × H)
51. C13×C3⋊D3C5×D11semidirect
55. C11×C3⋊D3C5×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
73. C5×C3⋊D3D143direct (N × H)
80. C5×C13C3⋊D3×D11semidirect
82. C5×C11C3⋊D3×D13semidirect
84. C32×C5C2×D143semidirect
86. C3×C13C5×D3×D11semidirect
88. C3×C11C5×D3×D13semidirect
101. C3⋊D3C5×D143direct (N × H)
102. C3×C5D3×D143semidirect
103. C13C5×C3⋊D3×D11semidirect
105. C11C5×C3⋊D3×D13semidirect
109. C32C2×C5×D143semidirect
113. C5C3⋊D3×D143direct (N × H)
115. C3C5×D3×D143semidirect

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×C13×C3⋊D32
C5×C3⋊D4292
C5×D3×D1433
C3⋊D3×D1435
C5×C3⋊D3×D1311
C5×C3⋊D3×D1113