Finite Group Databasebeta

← C2×C11×C13×C3⋊D15 #38788320

Subgroups — C2×C11×C13×C3⋊D15 #38788320

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×C13×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C5×C11×C13C211yesmaximal, characteristic, complemented
3C2×C11×C13×D15—34nomaximal
4C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
5C2×C11×C13×C3⋊D3—51nomaximal, Hall
6C11×C13×D15—38no—
7C2×C3×C5×C11×C13D314yescomplemented
8C2×D5×C11×C13—91noHall
9C11×C13×C3⋊D3—52no—
10C2×C32×C11×C13D511yescharacteristic, complemented
11C2×C13×C3⋊D15C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C13C2×D314yescomplemented
13C2×C11×C3⋊D15C1311yesmaximal, characteristic, direct product factor, Hall
14C2×D3×C11×C13—154no—
15C2×C5×C11×C13C3⋊D311yescharacteristic, complemented
16D5×C11×C13—92no—
17C32×C11×C13C2×D511yescharacteristic, complemented, Hall
18C2×C32×C5×C13C2×C1111yescharacteristic, complemented
19C13×C3⋊D15C2×C1112yesdirect product factor
20C2×C32×C5×C11C2×C1311yescharacteristic, complemented
21C11×C3⋊D15C2×C1312yesdirect product factor
22C2×C3×C11×C13D1514yescomplemented
23D3×C11×C13—158no—
24C2×C13×D15—34no—
25C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
26C2×C11×D15—34no—
27C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
28C22×C11×C13—451noHall
29C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
30C2×C13×C3⋊D3—51noHall
31C3×C11×C13C2×D1514yescomplemented
32C2×C11×C3⋊D3—51noHall
33C2×C3×C5×C13D3×C1114yescomplemented
34C13×D15—38no—
35C2×C3×C5×C11D3×C1314yescomplemented
36C11×D15—38no—
37C2×C11×C13—452no—
38C2×C11×C13C3⋊D1511yescharacteristic, direct product factor
39C2×D5×C13—91noHall
40C2×C32×C13D5×C1111yescharacteristic, complemented
41C13×C3⋊D3—52no—
42C2×D5×C11—91noHall
43C2×C32×C11D5×C1311yescharacteristic, complemented
44C11×C3⋊D3—52no—
45C3×C5×C13C2×D3×C1114yescomplemented
46C2×C3⋊D15C11×C1311yescharacteristic, direct product factor, Hall
47C3×C5×C11C2×D3×C1314yescomplemented
48C2×D3×C13—154no—
49C11×C13C2×C3⋊D1511yescharacteristic, direct product factor, Hall
50C2×D3×C11—154no—
51C2×C5×C13C11×C3⋊D311yescharacteristic, complemented
52D5×C13—92no—
53C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
54C2×C5×C11C13×C3⋊D311yescharacteristic, complemented
55D5×C11—92no—
56C32×C11C2×D5×C1311yescharacteristic, complemented, Hall
57C2×C32×C5C2×C11×C1311yescharacteristic, complemented
58C3⋊D15C2×C11×C1312yesdirect product factor
59C2×C3×C13C11×D1514yescomplemented
60D3×C13—158no—
61C2×C3×C11C13×D1514yescomplemented
62D3×C11—158no—
63C5×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
64C2×D15—34no—
65C5×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
66C22×C13—451noHall
67C32×C5C22×C11×C1311yescharacteristic, complemented, Hall
68C22×C11—451noHall
69C3×C13C2×C11×D1514yescomplemented
70C2×C3⋊D3—51noHall
71C3×C11C2×C13×D1514yescomplemented
72C2×C3×C5D3×C11×C1314yescomplemented
73D15—38no—
74C2×C13—452no—
75C2×C13C11×C3⋊D1511yescharacteristic, direct product factor
76C2×C11—452no—
77C2×C11C13×C3⋊D1511yescharacteristic, direct product factor
78C2×D5—91noHall
79C2×C32D5×C11×C1311yescharacteristic, complemented
80C3⋊D3—52no—
81C3×C5C2×D3×C11×C1314yescomplemented
82C13C2×C11×C3⋊D1511yescharacteristic, direct product factor, Sylow
83C2×D3—154no—
84C11C2×C13×C3⋊D1511yescharacteristic, direct product factor, Sylow
85C2×C5C11×C13×C3⋊D311yescharacteristic, complemented
86D5—92no—
87C32C2×D5×C11×C1311yescharacteristic, complemented, Sylow
88C2×C3C11×C13×D1514yescomplemented
89D3—158no—
90C5C2×C11×C13×C3⋊D311yescharacteristic, complemented, Sylow
91C22—451noSylow
92C3C2×C11×C13×D1514yescomplemented
93C2—452no—
94C2C11×C13×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C11×C13C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C11×C13
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C13C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C11×C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×C3⋊D15C2direct (N × H)
2. C2×C32×C5×C11×C13C2semidirect
4. C32×C5×C11×C13C22semidirect
7. C2×C3×C5×C11×C13D3semidirect
10. C2×C32×C11×C13D5semidirect
11. C2×C13×C3⋊D15C11direct (N × H)
12. C3×C5×C11×C13C2×D3semidirect
13. C2×C11×C3⋊D15C13direct (N × H)
15. C2×C5×C11×C13C3⋊D3semidirect
17. C32×C11×C13C2×D5semidirect
18. C2×C32×C5×C13C2×C11semidirect
19. C13×C3⋊D15C2×C11direct (N × H)
20. C2×C32×C5×C11C2×C13semidirect
21. C11×C3⋊D15C2×C13direct (N × H)
22. C2×C3×C11×C13D15semidirect
25. C5×C11×C13C2×C3⋊D3semidirect
27. C32×C5×C13C22×C11semidirect
29. C32×C5×C11C22×C13semidirect
31. C3×C11×C13C2×D15semidirect
33. C2×C3×C5×C13D3×C11semidirect
35. C2×C3×C5×C11D3×C13semidirect
38. C2×C11×C13C3⋊D15direct (N × H)
40. C2×C32×C13D5×C11semidirect
43. C2×C32×C11D5×C13semidirect
45. C3×C5×C13C2×D3×C11semidirect
46. C2×C3⋊D15C11×C13direct (N × H)
47. C3×C5×C11C2×D3×C13semidirect
49. C11×C13C2×C3⋊D15direct (N × H)
51. C2×C5×C13C11×C3⋊D3semidirect
53. C32×C13C2×D5×C11semidirect
54. C2×C5×C11C13×C3⋊D3semidirect
56. C32×C11C2×D5×C13semidirect
57. C2×C32×C5C2×C11×C13semidirect
58. C3⋊D15C2×C11×C13direct (N × H)
59. C2×C3×C13C11×D15semidirect
61. C2×C3×C11C13×D15semidirect
63. C5×C13C2×C11×C3⋊D3semidirect
65. C5×C11C2×C13×C3⋊D3semidirect
67. C32×C5C22×C11×C13semidirect
69. C3×C13C2×C11×D15semidirect
71. C3×C11C2×C13×D15semidirect
72. C2×C3×C5D3×C11×C13semidirect
75. C2×C13C11×C3⋊D15direct (N × H)
77. C2×C11C13×C3⋊D15direct (N × H)
79. C2×C32D5×C11×C13semidirect
81. C3×C5C2×D3×C11×C13semidirect
82. C13C2×C11×C3⋊D15direct (N × H)
84. C11C2×C13×C3⋊D15direct (N × H)
85. C2×C5C11×C13×C3⋊D3semidirect
87. C32C2×D5×C11×C13semidirect
88. C2×C3C11×C13×D15semidirect
90. C5C2×C11×C13×C3⋊D3semidirect
92. C3C2×C11×C13×D15semidirect
94. C2C11×C13×C3⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C11×C13×C3⋊D152
C2×C32×C5×C11×C132
C2×C11×C13×D153
C2×C11×C13×C3⋊D35
C2×C13×C3⋊D1511
C2×C11×C3⋊D1513