Finite Group Databasebeta

← C2×C5×C11×C3⋊D51 #46778210

Subgroups — C2×C5×C11×C3⋊D51 #46778210

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C3⋊D51C212yesmaximal, direct product factor
2C2×C32×C5×C11×C17C211yesmaximal, characteristic, complemented
3C2×C5×C11×D51—34nomaximal
4C32×C5×C11×C17C2211yescharacteristic, complemented, Hall
5C2×C11×C3⋊D51C511yesmaximal, characteristic, direct product factor, Hall
6C5×C11×D51—38no—
7C2×C3×C5×C11×C17D314yescomplemented
8C2×C5×C11×D17—91noHall
9C11×C3⋊D51C2×C512yesdirect product factor
10C2×C32×C11×C17C2×C511yescharacteristic, complemented
11C2×C5×C3⋊D51C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C17C2×D314yescomplemented
13C2×C11×D51—34no—
14C2×C5×C11×C3⋊D3—171nomaximal, Hall
15C2×C5×C11×C17C3⋊D311yescharacteristic, complemented
16C5×C11×D17—92no—
17C32×C11×C17C22×C511yescharacteristic, complemented, Hall
18C2×C32×C5×C17C2×C1111yescharacteristic, complemented
19C5×C3⋊D51C2×C1112yesdirect product factor
20C2×C3×C11×C17C5×D314yescomplemented
21C11×D51—38no—
22C2×C5×D51—34no—
23C2×C32×C5×C11D1711yescharacteristic, complemented
24C5×C11×C3⋊D3—172no—
25C5×C11×C17C2×C3⋊D311yescharacteristic, complemented, Hall
26C32×C5×C17C22×C1111yescharacteristic, complemented, Hall
27C2×C11×D17—91noHall
28C2×C5×D3×C11—514no—
29C2×C3⋊D51C5×C1111yescharacteristic, direct product factor, Hall
30C3×C11×C17C2×C5×D314yescomplemented
31C2×C3×C5×C17D3×C1114yescomplemented
32C5×D51—38no—
33C32×C5×C11C2×D1711yescharacteristic, complemented, Hall
34C2×C11×C3⋊D3—171noHall
35C2×C11×C17C5×C3⋊D311yescharacteristic, complemented
36C11×D17—92no—
37C2×C5×D17—91noHall
38C2×C3×C5×C11D5114yescomplemented
39C5×D3×C11—518no—
40C2×C32×C17C2×C5×C1111yescharacteristic, complemented
41C3⋊D51C2×C5×C1112yesdirect product factor
42C3×C5×C17C2×D3×C1114yescomplemented
43C22×C5×C11—1531noHall
44C2×D51—34no—
45C2×C32×C11C5×D1711yescharacteristic, complemented
46C11×C3⋊D3—172no—
47C11×C17C2×C5×C3⋊D311yescharacteristic, complemented, Hall
48C2×C5×C3⋊D3—171noHall
49C2×C5×C17C11×C3⋊D311yescharacteristic, complemented
50C5×D17—92no—
51C3×C5×C11C2×D5114yescomplemented
52C32×C17C22×C5×C1111yescharacteristic, complemented, Hall
53C2×D3×C11—514no—
54C2×C5×C11—1532no—
55C2×C5×C11C3⋊D5111yescharacteristic, direct product factor
56C2×C3×C17C5×D3×C1114yescomplemented
57D51—38no—
58C32×C11C2×C5×D1711yescharacteristic, complemented, Hall
59C2×C32×C5C11×D1711yescharacteristic, complemented
60C5×C3⋊D3—172no—
61C5×C17C2×C11×C3⋊D311yescharacteristic, complemented, Hall
62C2×D17—91noHall
63C2×C3×C11C5×D5114yescomplemented
64D3×C11—518no—
65C2×C5×D3—514no—
66C5×C11C2×C3⋊D5111yescharacteristic, direct product factor, Hall
67C3×C17C2×C5×D3×C1114yescomplemented
68C32×C5C2×C11×D1711yescharacteristic, complemented, Hall
69C22×C11—1531noHall
70C2×C3⋊D3—171noHall
71C2×C17C5×C11×C3⋊D311yescharacteristic, complemented
72D17—92no—
73C3×C11C2×C5×D5114yescomplemented
74C2×C3×C5C11×D5114yescomplemented
75C5×D3—518no—
76C2×C11—1532no—
77C2×C11C5×C3⋊D5111yescharacteristic, direct product factor
78C22×C5—1531noHall
79C2×C32C5×C11×D1711yescharacteristic, complemented
80C3⋊D3—172no—
81C17C2×C5×C11×C3⋊D311yescharacteristic, complemented, Sylow
82C3×C5C2×C11×D5114yescomplemented
83C2×D3—514no—
84C11C2×C5×C3⋊D5111yescharacteristic, direct product factor, Sylow
85C2×C5—1532no—
86C2×C5C11×C3⋊D5111yescharacteristic, direct product factor
87C32C2×C5×C11×D1711yescharacteristic, complemented, Sylow
88C2×C3C5×C11×D5114yescomplemented
89D3—518no—
90C5C2×C11×C3⋊D5111yescharacteristic, direct product factor, Sylow
91C22—1531noSylow
92C3C2×C5×C11×D5114yescomplemented
93C2—1532no—
94C2C5×C11×C3⋊D5111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C11C3⋊D51
commutator, cosocle, hypocenterC32×C17C22×C5×C11
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C32×C17
UCSC1 ◁ C2×C5×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×C3⋊D51C2direct (N × H)
2. C2×C32×C5×C11×C17C2semidirect
4. C32×C5×C11×C17C22semidirect
5. C2×C11×C3⋊D51C5direct (N × H)
7. C2×C3×C5×C11×C17D3semidirect
9. C11×C3⋊D51C2×C5direct (N × H)
10. C2×C32×C11×C17C2×C5semidirect
11. C2×C5×C3⋊D51C11direct (N × H)
12. C3×C5×C11×C17C2×D3semidirect
15. C2×C5×C11×C17C3⋊D3semidirect
17. C32×C11×C17C22×C5semidirect
18. C2×C32×C5×C17C2×C11semidirect
19. C5×C3⋊D51C2×C11direct (N × H)
20. C2×C3×C11×C17C5×D3semidirect
23. C2×C32×C5×C11D17semidirect
25. C5×C11×C17C2×C3⋊D3semidirect
26. C32×C5×C17C22×C11semidirect
29. C2×C3⋊D51C5×C11direct (N × H)
30. C3×C11×C17C2×C5×D3semidirect
31. C2×C3×C5×C17D3×C11semidirect
33. C32×C5×C11C2×D17semidirect
35. C2×C11×C17C5×C3⋊D3semidirect
38. C2×C3×C5×C11D51semidirect
40. C2×C32×C17C2×C5×C11semidirect
41. C3⋊D51C2×C5×C11direct (N × H)
42. C3×C5×C17C2×D3×C11semidirect
45. C2×C32×C11C5×D17semidirect
47. C11×C17C2×C5×C3⋊D3semidirect
49. C2×C5×C17C11×C3⋊D3semidirect
51. C3×C5×C11C2×D51semidirect
52. C32×C17C22×C5×C11semidirect
55. C2×C5×C11C3⋊D51direct (N × H)
56. C2×C3×C17C5×D3×C11semidirect
58. C32×C11C2×C5×D17semidirect
59. C2×C32×C5C11×D17semidirect
61. C5×C17C2×C11×C3⋊D3semidirect
63. C2×C3×C11C5×D51semidirect
66. C5×C11C2×C3⋊D51direct (N × H)
67. C3×C17C2×C5×D3×C11semidirect
68. C32×C5C2×C11×D17semidirect
71. C2×C17C5×C11×C3⋊D3semidirect
73. C3×C11C2×C5×D51semidirect
74. C2×C3×C5C11×D51semidirect
77. C2×C11C5×C3⋊D51direct (N × H)
79. C2×C32C5×C11×D17semidirect
81. C17C2×C5×C11×C3⋊D3semidirect
82. C3×C5C2×C11×D51semidirect
84. C11C2×C5×C3⋊D51direct (N × H)
86. C2×C5C11×C3⋊D51direct (N × H)
87. C32C2×C5×C11×D17semidirect
88. C2×C3C5×C11×D51semidirect
90. C5C2×C11×C3⋊D51direct (N × H)
92. C3C2×C5×C11×D51semidirect
94. C2C5×C11×C3⋊D51direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C3⋊D512
C2×C32×C5×C11×C172
C2×C5×C11×D513
C2×C11×C3⋊D515
C2×C5×C3⋊D5111
C2×C5×C11×C3⋊D317