Finite Group Databasebeta

← C5×C13×C3⋊D3×D11 #38788262

Subgroups — C5×C13×C3⋊D3×D11 #38788262

Order 25740.

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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×C13×D11C211yesmaximal, characteristic, complemented
2C5×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×C13×C3⋊D33C211yesmaximal, characteristic, complemented
4C5×D3×C13×D11—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C13×C3⋊D3×D11C511yesmaximal, characteristic, direct product factor, Hall
7C5×C13×D33—34no—
8C5×D3×C11×C13—34no—
9C3×C5×C13×D11D314yescomplemented
10C2×C5×C13×D11—91noHall
11C13×C3⋊D33C2×C511yescharacteristic, complemented
12C11×C13×C3⋊D3C2×C511yescharacteristic, complemented
13C32×C13×D11C2×C511yescharacteristic, complemented
14C2×C5×C13×C3⋊D3—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C5×C3⋊D3×D11C1311yesmaximal, characteristic, direct product factor, Hall
17D3×C13×D11—34no—
18C2×C5×C11×C13—91no—
19C5×C13×D11—91no—
20C5×C13×D11C3⋊D311yescharacteristic, direct product factor
21C32×C11×C13C22×C511yescharacteristic, complemented, Hall
22C2×C32×C5×C13—111no—
23C5×C13×C3⋊D3—111no—
24C5×C13×C3⋊D3D1111yescharacteristic, direct product factor
25C5×C3⋊D33C2×C1311yescharacteristic, complemented
26C5×C11×C3⋊D3C2×C1311yescharacteristic, complemented
27C32×C5×D11C2×C1311yescharacteristic, complemented
28C13×D33—34no—
29D3×C11×C13—34no—
30C3×C13×D11C5×D314yescomplemented
31C2×C5×D3×C13—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C5×D3×D11—34no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35C2×C13×D11—91noHall
36C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
37C2×C13×C3⋊D3—111noHall
38C3×C11×C13C2×C5×D314yescomplemented
39C3⋊D3×D11C5×C1311yescharacteristic, direct product factor, Hall
40C2×C3×C5×C13—114no—
41C5×D3×C13—34no—
42C5×D3×C13—334no—
43C5×D33—34no—
44C5×D3×C11—34no—
45C3×C5×D11D3×C1314yescomplemented
46C2×C11×C13—91no—
47C13×D11—91no—
48C13×D11C5×C3⋊D311yescharacteristic, direct product factor
49C22×C5×C13—991noHall
50C2×C32×C13—111no—
51C13×C3⋊D3—111no—
52C13×C3⋊D3C5×D1111yescharacteristic, direct product factor
53C2×C5×D11—91noHall
54C3⋊D33C2×C5×C1311yescharacteristic, complemented
55C11×C3⋊D3C2×C5×C1311yescharacteristic, complemented
56C32×D11C2×C5×C1311yescharacteristic, complemented
57C3×C5×C13D3×D1114yescomplemented
58C2×C5×C3⋊D3—111noHall
59C3×C5×C11C2×D3×C1314yescomplemented
60C2×D3×C13—334no—
61C11×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
62D3×D11—34no—
63C2×C5×C13—91no—
64C2×C5×C13—111no—
65C2×C5×C13—991no—
66C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68C5×D11—91no—
69C5×D11C13×C3⋊D311yescharacteristic, direct product factor
70C32×C11C22×C5×C1311yescharacteristic, complemented, Hall
71C2×C32×C5—111no—
72C5×C3⋊D3—111no—
73C5×C3⋊D3C13×D1111yescharacteristic, direct product factor
74C2×C3×C13—114no—
75D3×C13—34no—
76D3×C13—334no—
77D33—34no—
78C3×D11C5×D3×C1314yescomplemented
79D3×C11—34no—
80C5×C13C3⋊D3×D1111yescharacteristic, direct product factor, Hall
81C2×C5×D3—334no—
82C5×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
83C22×C13—991noHall
84C32×C5C2×C13×D1111yescharacteristic, complemented, Hall
85C2×D11—91noHall
86C3×C13C5×D3×D1114yescomplemented
87C2×C3⋊D3—111noHall
88C3×C11C2×C5×D3×C1314yescomplemented
89C2×C3×C5—114no—
90C5×D3—34no—
91C5×D3—334no—
92C2×C13—91no—
93C2×C13—111no—
94C2×C13—991no—
95C2×C11—91no—
96D11—91no—
97D11C5×C13×C3⋊D311yescharacteristic, direct product factor
98C22×C5—991noHall
99C2×C32—111no—
100C3⋊D3—111no—
101C3⋊D3C5×C13×D1111yescharacteristic, direct product factor
102C3×C5D3×C13×D1114yescomplemented
103C13C5×C3⋊D3×D1111yescharacteristic, direct product factor, Sylow
104C2×D3—334no—
105C11C2×C5×C13×C3⋊D311yescharacteristic, complemented, Sylow
106C2×C5—91no—
107C2×C5—111no—
108C2×C5—991no—
109C32C2×C5×C13×D1111yescharacteristic, complemented, Sylow
110C2×C3—114no—
111D3—34no—
112D3—334no—
113C5C13×C3⋊D3×D1111yescharacteristic, direct product factor, Sylow
114C22—991noSylow
115C3C5×D3×C13×D1114yescomplemented
116C2—91no—
117C2—111no—
118C2—991no—
subgroupG/H
center, hypercenterC5×C13C3⋊D3×D11
commutator, cosocle, hypocenterC32×C11C22×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11
UCSC1 ◁ C5×C13

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D11C2semidirect
2. C5×C11×C13×C3⋊D3C2semidirect
3. C5×C13×C3⋊D33C2semidirect
5. C32×C5×C11×C13C22semidirect
6. C13×C3⋊D3×D11C5direct (N × H)
9. C3×C5×C13×D11D3semidirect
11. C13×C3⋊D33C2×C5semidirect
12. C11×C13×C3⋊D3C2×C5semidirect
13. C32×C13×D11C2×C5semidirect
15. C3×C5×C11×C13C2×D3semidirect
16. C5×C3⋊D3×D11C13direct (N × H)
20. C5×C13×D11C3⋊D3direct (N × H)
21. C32×C11×C13C22×C5semidirect
24. C5×C13×C3⋊D3D11direct (N × H)
25. C5×C3⋊D33C2×C13semidirect
26. C5×C11×C3⋊D3C2×C13semidirect
27. C32×C5×D11C2×C13semidirect
30. C3×C13×D11C5×D3semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C22×C13semidirect
38. C3×C11×C13C2×C5×D3semidirect
39. C3⋊D3×D11C5×C13direct (N × H)
45. C3×C5×D11D3×C13semidirect
48. C13×D11C5×C3⋊D3direct (N × H)
52. C13×C3⋊D3C5×D11direct (N × H)
54. C3⋊D33C2×C5×C13semidirect
55. C11×C3⋊D3C2×C5×C13semidirect
56. C32×D11C2×C5×C13semidirect
57. C3×C5×C13D3×D11semidirect
59. C3×C5×C11C2×D3×C13semidirect
61. C11×C13C2×C5×C3⋊D3semidirect
66. C32×C13C2×C5×D11semidirect
69. C5×D11C13×C3⋊D3direct (N × H)
70. C32×C11C22×C5×C13semidirect
73. C5×C3⋊D3C13×D11direct (N × H)
78. C3×D11C5×D3×C13semidirect
80. C5×C13C3⋊D3×D11direct (N × H)
82. C5×C11C2×C13×C3⋊D3semidirect
84. C32×C5C2×C13×D11semidirect
86. C3×C13C5×D3×D11semidirect
88. C3×C11C2×C5×D3×C13semidirect
97. D11C5×C13×C3⋊D3direct (N × H)
101. C3⋊D3C5×C13×D11direct (N × H)
102. C3×C5D3×C13×D11semidirect
103. C13C5×C3⋊D3×D11direct (N × H)
105. C11C2×C5×C13×C3⋊D3semidirect
109. C32C2×C5×C13×D11semidirect
113. C5C13×C3⋊D3×D11direct (N × H)
115. C3C5×D3×C13×D11semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C13×D112
C5×C11×C13×C3⋊D32
C5×C13×C3⋊D332
C5×D3×C13×D113
C13×C3⋊D3×D115
C2×C5×C13×C3⋊D311
C5×C3⋊D3×D1113