Finite Group Databasebeta

← C5×C11×C3⋊D3×D13 #38788259

Subgroups — C5×C11×C3⋊D3×D13 #38788259

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×C11×D13C211yesmaximal, characteristic, complemented
2C5×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×C11×C3⋊D39C211yesmaximal, characteristic, complemented
4C5×D3×C11×D13—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C11×C3⋊D3×D13C511yesmaximal, characteristic, direct product factor, Hall
7C5×C11×D39—34no—
8C5×D3×C11×C13—34no—
9C3×C5×C11×D13D314yescomplemented
10C2×C5×C11×D13—91noHall
11C11×C3⋊D39C2×C511yescharacteristic, complemented
12C11×C13×C3⋊D3C2×C511yescharacteristic, complemented
13C32×C11×D13C2×C511yescharacteristic, complemented
14C5×C3⋊D3×D13C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C2×C5×C11×C3⋊D3—131nomaximal, Hall
17D3×C11×D13—34no—
18C2×C5×C11×C13—91no—
19C5×C11×D13—91no—
20C5×C11×D13C3⋊D311yescharacteristic, direct product factor
21C32×C11×C13C22×C511yescharacteristic, complemented, Hall
22C5×C3⋊D39C2×C1111yescharacteristic, complemented
23C5×C13×C3⋊D3C2×C1111yescharacteristic, complemented
24C32×C5×D13C2×C1111yescharacteristic, complemented
25C2×C32×C5×C11—131no—
26C5×C11×C3⋊D3—131no—
27C5×C11×C3⋊D3D1311yescharacteristic, direct product factor
28C11×D39—34no—
29D3×C11×C13—34no—
30C3×C11×D13C5×D314yescomplemented
31C5×D3×D13—34no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C2×C5×D3×C11—394no—
34C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
35C2×C11×D13—91noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C3⋊D3×D13C5×C1111yescharacteristic, direct product factor, Hall
38C3×C11×C13C2×C5×D314yescomplemented
39C2×C11×C3⋊D3—131noHall
40C5×D39—34no—
41C5×D3×C13—34no—
42C3×C5×D13D3×C1114yescomplemented
43C2×C3×C5×C11—134no—
44C5×D3×C11—34no—
45C5×D3×C11—394no—
46C2×C11×C13—91no—
47C11×D13—91no—
48C11×D13C5×C3⋊D311yescharacteristic, direct product factor
49C2×C5×D13—91noHall
50C3⋊D39C2×C5×C1111yescharacteristic, complemented
51C13×C3⋊D3C2×C5×C1111yescharacteristic, complemented
52C32×D13C2×C5×C1111yescharacteristic, complemented
53C22×C5×C11—1171noHall
54C2×C32×C11—131no—
55C11×C3⋊D3—131no—
56C11×C3⋊D3C5×D1311yescharacteristic, direct product factor
57C3×C5×C13C2×D3×C1114yescomplemented
58C2×C5×C3⋊D3—131noHall
59C3×C5×C11D3×D1314yescomplemented
60D3×D13—34no—
61C11×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
62C2×D3×C11—394no—
63C2×C5×C13—91no—
64C5×D13—91no—
65C5×D13C11×C3⋊D311yescharacteristic, direct product factor
66C32×C13C22×C5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68C2×C5×C11—131no—
69C2×C5×C11—1171no—
70C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—131no—
72C5×C3⋊D3—131no—
73C5×C3⋊D3C11×D1311yescharacteristic, direct product factor
74D39—34no—
75C3×D13C5×D3×C1114yescomplemented
76D3×C13—34no—
77C2×C3×C11—134no—
78D3×C11—34no—
79D3×C11—394no—
80C5×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
81C2×C5×D3—394no—
82C5×C11C3⋊D3×D1311yescharacteristic, direct product factor, Hall
83C2×D13—91noHall
84C32×C5C2×C11×D1311yescharacteristic, complemented, Hall
85C22×C11—1171noHall
86C3×C13C2×C5×D3×C1114yescomplemented
87C2×C3⋊D3—131noHall
88C3×C11C5×D3×D1314yescomplemented
89C2×C3×C5—134no—
90C5×D3—34no—
91C5×D3—394no—
92C2×C13—91no—
93D13—91no—
94D13C5×C11×C3⋊D311yescharacteristic, direct product factor
95C2×C11—91no—
96C2×C11—131no—
97C2×C11—1171no—
98C22×C5—1171noHall
99C2×C32—131no—
100C3⋊D3—131no—
101C3⋊D3C5×C11×D1311yescharacteristic, direct product factor
102C3×C5D3×C11×D1314yescomplemented
103C13C2×C5×C11×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—394no—
105C11C5×C3⋊D3×D1311yescharacteristic, direct product factor, Sylow
106C2×C5—91no—
107C2×C5—131no—
108C2×C5—1171no—
109C32C2×C5×C11×D1311yescharacteristic, complemented, Sylow
110C2×C3—134no—
111D3—34no—
112D3—394no—
113C5C11×C3⋊D3×D1311yescharacteristic, direct product factor, Sylow
114C22—1171noSylow
115C3C5×D3×C11×D1314yescomplemented
116C2—91no—
117C2—131no—
118C2—1171no—
subgroupG/H
center, hypercenterC5×C11C3⋊D3×D13
commutator, cosocle, hypocenterC32×C13C22×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C13
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C32×C5×C11×D13C2semidirect
2. C5×C11×C13×C3⋊D3C2semidirect
3. C5×C11×C3⋊D39C2semidirect
5. C32×C5×C11×C13C22semidirect
6. C11×C3⋊D3×D13C5direct (N × H)
9. C3×C5×C11×D13D3semidirect
11. C11×C3⋊D39C2×C5semidirect
12. C11×C13×C3⋊D3C2×C5semidirect
13. C32×C11×D13C2×C5semidirect
14. C5×C3⋊D3×D13C11direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
20. C5×C11×D13C3⋊D3direct (N × H)
21. C32×C11×C13C22×C5semidirect
22. C5×C3⋊D39C2×C11semidirect
23. C5×C13×C3⋊D3C2×C11semidirect
24. C32×C5×D13C2×C11semidirect
27. C5×C11×C3⋊D3D13direct (N × H)
30. C3×C11×D13C5×D3semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C22×C11semidirect
36. C32×C5×C11C2×D13semidirect
37. C3⋊D3×D13C5×C11direct (N × H)
38. C3×C11×C13C2×C5×D3semidirect
42. C3×C5×D13D3×C11semidirect
48. C11×D13C5×C3⋊D3direct (N × H)
50. C3⋊D39C2×C5×C11semidirect
51. C13×C3⋊D3C2×C5×C11semidirect
52. C32×D13C2×C5×C11semidirect
56. C11×C3⋊D3C5×D13direct (N × H)
57. C3×C5×C13C2×D3×C11semidirect
59. C3×C5×C11D3×D13semidirect
61. C11×C13C2×C5×C3⋊D3semidirect
65. C5×D13C11×C3⋊D3direct (N × H)
66. C32×C13C22×C5×C11semidirect
70. C32×C11C2×C5×D13semidirect
73. C5×C3⋊D3C11×D13direct (N × H)
75. C3×D13C5×D3×C11semidirect
80. C5×C13C2×C11×C3⋊D3semidirect
82. C5×C11C3⋊D3×D13direct (N × H)
84. C32×C5C2×C11×D13semidirect
86. C3×C13C2×C5×D3×C11semidirect
88. C3×C11C5×D3×D13semidirect
94. D13C5×C11×C3⋊D3direct (N × H)
101. C3⋊D3C5×C11×D13direct (N × H)
102. C3×C5D3×C11×D13semidirect
103. C13C2×C5×C11×C3⋊D3semidirect
105. C11C5×C3⋊D3×D13direct (N × H)
109. C32C2×C5×C11×D13semidirect
113. C5C11×C3⋊D3×D13direct (N × H)
115. C3C5×D3×C11×D13semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C11×D132
C5×C11×C13×C3⋊D32
C5×C11×C3⋊D392
C5×D3×C11×D133
C11×C3⋊D3×D135
C5×C3⋊D3×D1311
C2×C5×C11×C3⋊D313