Finite Group Databasebeta

← C2×C13×C3⋊D3×C11⋊C5 #38788124

Subgroups — C2×C13×C3⋊D3×C11⋊C5 #38788124

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C13×C11⋊C5C211yesmaximal, characteristic, complemented
2C13×C3⋊D3×C11⋊C5C212yesmaximal, direct product factor
3C2×D3×C13×C11⋊C5—34nomaximal
4C32×C13×C11⋊C5C2211yescharacteristic, complemented, Hall
5C2×C11×C13×C3⋊D3C511yesmaximal, characteristic, complemented, Hall
6D3×C13×C11⋊C5—38no—
7C2×C3×C13×C11⋊C5D314yescomplemented
8C22×C13×C11⋊C5—91noHall
9C11×C13×C3⋊D3C2×C512yescomplemented
10C2×C32×C11×C13C2×C511yescharacteristic, complemented
11C2×C5×C13×C3⋊D3—111nomaximal, Hall
12C3×C13×C11⋊C5C2×D314yescomplemented
13C2×C3⋊D3×C11⋊C5C1311yesmaximal, characteristic, direct product factor, Hall
14C2×D3×C11×C13—34no—
15C2×C13×C11⋊C5—92no—
16C2×C13×C11⋊C5C3⋊D311yescharacteristic, direct product factor
17C32×C11×C13C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C13—111no—
19C5×C13×C3⋊D3—112no—
20C2×C32×C11⋊C5C2×C1311yescharacteristic, complemented
21C3⋊D3×C11⋊C5C2×C1312yesdirect product factor
22C2×C3×C11×C13C5×D314yescomplemented
23D3×C11×C13—38no—
24C2×C5×D3×C13—334no—
25C13×C11⋊C5C2×C3⋊D311yescharacteristic, direct product factor, Hall
26C2×D3×C11⋊C5—34no—
27C32×C5×C13—111noHall
28C22×C11×C13—91noHall
29C32×C11⋊C5C22×C1311yescharacteristic, complemented, Hall
30C2×C13×C3⋊D3C11⋊C511yescharacteristic, direct product factor, Hall
31C3×C11×C13C2×C5×D314yescomplemented
32C2×C11×C3⋊D3C5×C1311yescharacteristic, complemented, Hall
33C2×C3×C5×C13—114no—
34C5×D3×C13—338no—
35C2×C3×C11⋊C5D3×C1314yescomplemented
36D3×C11⋊C5—38no—
37C2×C11×C13—92no—
38C2×C11×C13C5×C3⋊D311yescharacteristic, complemented
39C22×C5×C13—991noHall
40C2×C32×C13C2×C11⋊C511yescharacteristic, complemented
41C13×C3⋊D3C2×C11⋊C512yesdirect product factor
42C22×C11⋊C5—91noHall
43C2×C32×C11C2×C5×C1311yescharacteristic, complemented
44C11×C3⋊D3C2×C5×C1312yescomplemented
45C3×C5×C13—114no—
46C2×C5×C3⋊D3—111noHall
47C3×C11⋊C5C2×D3×C1314yescomplemented
48C2×D3×C13—34no—
49C11×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
50C2×D3×C11—34no—
51C2×C5×C13—111no—
52C2×C5×C13—992no—
53C32×C13C22×C11⋊C511yescharacteristic, complemented, Hall
54C2×C11⋊C5—92no—
55C2×C11⋊C5C13×C3⋊D311yescharacteristic, direct product factor
56C32×C11C22×C5×C1311yescharacteristic, complemented, Hall
57C2×C32×C5—111no—
58C5×C3⋊D3—112no—
59C2×C3×C13D3×C11⋊C514yescomplemented
60D3×C13—38no—
61C2×C3×C11C5×D3×C1314yescomplemented
62D3×C11—38no—
63C5×C13—111noHall
64C2×C5×D3—334no—
65C11⋊C5C2×C13×C3⋊D311yescharacteristic, direct product factor, Hall
66C22×C13—91noHall
67C32×C5—111noHall
68C22×C11—91noHall
69C3×C13C2×D3×C11⋊C514yescomplemented
70C2×C3⋊D3C13×C11⋊C511yescharacteristic, direct product factor, Hall
71C3×C11C2×C5×D3×C1314yescomplemented
72C2×C3×C5—114no—
73C5×D3—338no—
74C2×C13—92no—
75C2×C13C3⋊D3×C11⋊C511yescharacteristic, direct product factor
76C2×C11—92no—
77C2×C11C5×C13×C3⋊D311yescharacteristic, complemented
78C22×C5—991noHall
79C2×C32C2×C13×C11⋊C511yescharacteristic, complemented
80C3⋊D3C2×C13×C11⋊C512yesdirect product factor
81C3×C5—114no—
82C13C2×C3⋊D3×C11⋊C511yescharacteristic, direct product factor, Sylow
83C2×D3—34no—
84C11C2×C5×C13×C3⋊D311yescharacteristic, complemented, Sylow
85C2×C5—111no—
86C2×C5—992no—
87C32C22×C13×C11⋊C511yescharacteristic, complemented, Sylow
88C2×C3D3×C13×C11⋊C514yescomplemented
89D3—38no—
90C5—111noSylow
91C22—91noSylow
92C3C2×D3×C13×C11⋊C514yescomplemented
93C2—92no—
94C2C13×C3⋊D3×C11⋊C511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C13C3⋊D3×C11⋊C5
commutator, cosocle, hypocenterC32×C11C22×C5×C13
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C2×C13

Complements

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

NH ≅ G/Ntype
1. C2×C32×C13×C11⋊C5C2semidirect
2. C13×C3⋊D3×C11⋊C5C2direct (N × H)
4. C32×C13×C11⋊C5C22semidirect
5. C2×C11×C13×C3⋊D3C5semidirect
7. C2×C3×C13×C11⋊C5D3semidirect
9. C11×C13×C3⋊D3C2×C5semidirect
10. C2×C32×C11×C13C2×C5semidirect
12. C3×C13×C11⋊C5C2×D3semidirect
13. C2×C3⋊D3×C11⋊C5C13direct (N × H)
16. C2×C13×C11⋊C5C3⋊D3direct (N × H)
17. C32×C11×C13C22×C5semidirect
20. C2×C32×C11⋊C5C2×C13semidirect
21. C3⋊D3×C11⋊C5C2×C13direct (N × H)
22. C2×C3×C11×C13C5×D3semidirect
25. C13×C11⋊C5C2×C3⋊D3direct (N × H)
29. C32×C11⋊C5C22×C13semidirect
30. C2×C13×C3⋊D3C11⋊C5direct (N × H)
31. C3×C11×C13C2×C5×D3semidirect
32. C2×C11×C3⋊D3C5×C13semidirect
35. C2×C3×C11⋊C5D3×C13semidirect
38. C2×C11×C13C5×C3⋊D3semidirect
40. C2×C32×C13C2×C11⋊C5semidirect
41. C13×C3⋊D3C2×C11⋊C5direct (N × H)
43. C2×C32×C11C2×C5×C13semidirect
44. C11×C3⋊D3C2×C5×C13semidirect
47. C3×C11⋊C5C2×D3×C13semidirect
49. C11×C13C2×C5×C3⋊D3semidirect
53. C32×C13C22×C11⋊C5semidirect
55. C2×C11⋊C5C13×C3⋊D3direct (N × H)
56. C32×C11C22×C5×C13semidirect
59. C2×C3×C13D3×C11⋊C5semidirect
61. C2×C3×C11C5×D3×C13semidirect
65. C11⋊C5C2×C13×C3⋊D3direct (N × H)
69. C3×C13C2×D3×C11⋊C5semidirect
70. C2×C3⋊D3C13×C11⋊C5direct (N × H)
71. C3×C11C2×C5×D3×C13semidirect
75. C2×C13C3⋊D3×C11⋊C5direct (N × H)
77. C2×C11C5×C13×C3⋊D3semidirect
79. C2×C32C2×C13×C11⋊C5semidirect
80. C3⋊D3C2×C13×C11⋊C5direct (N × H)
82. C13C2×C3⋊D3×C11⋊C5direct (N × H)
84. C11C2×C5×C13×C3⋊D3semidirect
87. C32C22×C13×C11⋊C5semidirect
88. C2×C3D3×C13×C11⋊C5semidirect
92. C3C2×D3×C13×C11⋊C5semidirect
94. C2C13×C3⋊D3×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C13×C11⋊C52
C13×C3⋊D3×C11⋊C52
C2×D3×C13×C11⋊C53
C2×C11×C13×C3⋊D35
C2×C5×C13×C3⋊D311
C2×C3⋊D3×C11⋊C513