Finite Group Databasebeta

← C5×D11×C3⋊D39 #38788263

Subgroups — C5×D11×C3⋊D39 #38788263

Order 25740.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×C3⋊D39C211yesmaximal, characteristic, complemented
3C5×C3⋊D429C211yesmaximal, characteristic, complemented
4C5×D11×D39—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6D11×C3⋊D39C511yesmaximal, characteristic, direct product factor, Hall
7C5×D429—34no—
8C5×C11×D39—34no—
9C3×C5×C13×D11D314yescomplemented
10C5×D11×D13—91noHall
11C3⋊D429C2×C511yescharacteristic, complemented
12C11×C3⋊D39C2×C511yescharacteristic, complemented
13C32×C13×D11C2×C511yescharacteristic, complemented
14C2×C5×C3⋊D39—111nomaximal, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16C5×C3⋊D3×D11—131nomaximal, Hall
17D11×D39—34no—
18C5×D143—91no—
19C5×C13×D11C3⋊D311yescharacteristic, complemented
20C5×C11×D13—91no—
21C32×C11×C13C22×C511yescharacteristic, complemented, Hall
22C2×C32×C5×C13—111no—
23C5×C3⋊D39—111no—
24C5×C3⋊D39D1111yescharacteristic, direct product factor
25C5×C3⋊D33—131no—
26C5×C11×C3⋊D3—131no—
27C32×C5×D11D1311yescharacteristic, complemented
28D429—34no—
29C11×D39—34no—
30C3×C13×D11C5×D314yescomplemented
31C2×C5×D39—334no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33C5×D3×D11—394no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—91noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C2×C3⋊D39—111noHall
38C3×C11×C13C2×C5×D314yescomplemented
39C3⋊D3×D11—131noHall
40C2×C3×C5×C13—114no—
41C5×D39—34no—
42C5×D39—334no—
43C5×D33—394no—
44C5×D3×C11—394no—
45C3×C5×D11D3914yescomplemented
46D143—91no—
47C11×D13—91no—
48C13×D11C5×C3⋊D311yescharacteristic, complemented
49C2×C5×D13—991noHall
50C2×C32×C13—111no—
51C3⋊D39—111no—
52C3⋊D39C5×D1111yescharacteristic, direct product factor
53C2×C5×D11—1171noHall
54C3⋊D33—131no—
55C11×C3⋊D3—131no—
56C32×D11C5×D1311yescharacteristic, complemented
57C3×C5×C13D3×D1114yescomplemented
58C2×C5×C3⋊D3—1431noHall
59C3×C5×C11C2×D3914yescomplemented
60C2×D39—334no—
61C11×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
62D3×D11—394no—
63C2×C5×C13—111no—
64C5×D13—91no—
65C5×D13—991no—
66C32×C13C2×C5×D1111yescharacteristic, complemented, Hall
67C2×C5×C11—1171no—
68C5×D11—1171no—
69C5×D11C3⋊D3911yescharacteristic, direct product factor
70C32×C11C2×C5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—111no—
72C5×C3⋊D3—131no—
73C5×C3⋊D3—1431no—
74C2×C3×C13—114no—
75D39—34no—
76D39—334no—
77D33—394no—
78C3×D11C5×D3914yescomplemented
79D3×C11—394no—
80C5×C13C3⋊D3×D1111yescharacteristic, complemented, Hall
81C2×C5×D3—4294no—
82C5×C11C2×C3⋊D3911yescharacteristic, complemented, Hall
83C2×D13—991noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—1171noHall
86C3×C13C5×D3×D1114yescomplemented
87C2×C3⋊D3—1431noHall
88C3×C11C2×C5×D3914yescomplemented
89C2×C3×C5—114no—
90C5×D3—394no—
91C5×D3—4294no—
92C2×C13—111no—
93D13—91no—
94D13—991no—
95C2×C11—1171no—
96D11—1171no—
97D11C5×C3⋊D3911yescharacteristic, direct product factor
98C22×C5—12871noHall
99C2×C32—111no—
100C3⋊D3—131no—
101C3⋊D3—1431no—
102C3×C5D11×D3914yescomplemented
103C13C5×C3⋊D3×D1111yescharacteristic, complemented, Sylow
104C2×D3—4294no—
105C11C2×C5×C3⋊D3911yescharacteristic, complemented, Sylow
106C2×C5—12871no—
107C2×C5—111no—
108C2×C5—1171no—
109C32C5×D11×D1311yescharacteristic, complemented, Sylow
110C2×C3—114no—
111D3—394no—
112D3—4294no—
113C5D11×C3⋊D3911yescharacteristic, direct product factor, Sylow
114C22—12871noSylow
115C3C5×D11×D3914yescomplemented
116C2—12871no—
117C2—111no—
118C2—1171no—
subgroupG/H
center, hypercenterC5D11×C3⋊D39
commutator, cosocle, hypocenterC32×C11×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×C13×D11C2semidirect
2. C5×C11×C3⋊D39C2semidirect
3. C5×C3⋊D429C2semidirect
5. C32×C5×C11×C13C22semidirect
6. D11×C3⋊D39C5direct (N × H)
9. C3×C5×C13×D11D3semidirect
11. C3⋊D429C2×C5semidirect
12. C11×C3⋊D39C2×C5semidirect
13. C32×C13×D11C2×C5semidirect
15. C3×C5×C11×C13C2×D3semidirect
19. C5×C13×D11C3⋊D3semidirect
21. C32×C11×C13C22×C5semidirect
24. C5×C3⋊D39D11direct (N × H)
27. C32×C5×D11D13semidirect
30. C3×C13×D11C5×D3semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13C2×C5×D3semidirect
45. C3×C5×D11D39semidirect
48. C13×D11C5×C3⋊D3semidirect
52. C3⋊D39C5×D11direct (N × H)
56. C32×D11C5×D13semidirect
57. C3×C5×C13D3×D11semidirect
59. C3×C5×C11C2×D39semidirect
61. C11×C13C2×C5×C3⋊D3semidirect
66. C32×C13C2×C5×D11semidirect
69. C5×D11C3⋊D39direct (N × H)
70. C32×C11C2×C5×D13semidirect
78. C3×D11C5×D39semidirect
80. C5×C13C3⋊D3×D11semidirect
82. C5×C11C2×C3⋊D39semidirect
84. C32×C5D11×D13semidirect
86. C3×C13C5×D3×D11semidirect
88. C3×C11C2×C5×D39semidirect
97. D11C5×C3⋊D39direct (N × H)
102. C3×C5D11×D39semidirect
103. C13C5×C3⋊D3×D11semidirect
105. C11C2×C5×C3⋊D39semidirect
109. C32C5×D11×D13semidirect
113. C5D11×C3⋊D39direct (N × H)
115. C3C5×D11×D39semidirect

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×C3⋊D392
C5×C3⋊D4292
C5×D11×D393
D11×C3⋊D395
C2×C5×C3⋊D3911
C5×C3⋊D3×D1113