Finite Group Databasebeta

← D5×C11×C13×C3⋊D3 #38788282

Subgroups — D5×C11×C13×C3⋊D3 #38788282

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×D5×C11×C13C211yesmaximal, characteristic, complemented
2C5×C11×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C11×C13×C3⋊D15C211yesmaximal, characteristic, complemented
4D3×D5×C11×C13—34nomaximal
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C11×C13×C3⋊D3—51nomaximal, Hall
7C11×C13×D15—34no—
8C5×D3×C11×C13—34no—
9C3×D5×C11×C13D314yescomplemented
10C2×D5×C11×C13—91noHall
11C11×C13×C3⋊D3—51no—
12C11×C13×C3⋊D3D511yescharacteristic, direct product factor
13C2×C32×C11×C13—51no—
14D5×C13×C3⋊D3C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D314yescomplemented
16D5×C11×C3⋊D3C1311yesmaximal, characteristic, direct product factor, Hall
17C2×D3×C11×C13—154no—
18C2×C5×C11×C13—91no—
19D5×C11×C13—91no—
20D5×C11×C13C3⋊D311yescharacteristic, direct product factor
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C13×C3⋊D15C2×C1111yescharacteristic, complemented
23C5×C13×C3⋊D3C2×C1111yescharacteristic, complemented
24C32×D5×C13C2×C1111yescharacteristic, complemented
25C11×C3⋊D15C2×C1311yescharacteristic, complemented
26C5×C11×C3⋊D3C2×C1311yescharacteristic, complemented
27C32×D5×C11C2×C1311yescharacteristic, complemented
28C2×C3×C11×C13—54no—
29D3×C11×C13—34no—
30D3×C11×C13—154no—
31D3×D5×C13—34no—
32C5×C11×C13C2×C3⋊D311yescharacteristic, complemented, Hall
33D3×D5×C11—34no—
34C32×C5×C13C22×C1111yescharacteristic, complemented, Hall
35C22×C11×C13—451noHall
36C32×C5×C11C22×C1311yescharacteristic, complemented, Hall
37C2×C13×C3⋊D3—51noHall
38C3×C11×C13D3×D514yescomplemented
39C2×C11×C3⋊D3—51noHall
40C13×D15—34no—
41C5×D3×C13—34no—
42C3×D5×C13D3×C1114yescomplemented
43C11×D15—34no—
44C5×D3×C11—34no—
45C3×D5×C11D3×C1314yescomplemented
46C2×C11×C13—51no—
47C2×C11×C13—91no—
48C2×C11×C13—451no—
49C2×D5×C13—91noHall
50C2×C32×C13—51no—
51C13×C3⋊D3—51no—
52C13×C3⋊D3D5×C1111yescharacteristic, direct product factor
53C2×D5×C11—91noHall
54C2×C32×C11—51no—
55C11×C3⋊D3—51no—
56C11×C3⋊D3D5×C1311yescharacteristic, direct product factor
57C3×C5×C13C2×D3×C1114yescomplemented
58D5×C3⋊D3C11×C1311yescharacteristic, direct product factor, Hall
59C3×C5×C11C2×D3×C1314yescomplemented
60C2×D3×C13—154no—
61C11×C13D5×C3⋊D311yescharacteristic, direct product factor, Hall
62C2×D3×C11—154no—
63C2×C5×C13—91no—
64D5×C13—91no—
65D5×C13C11×C3⋊D311yescharacteristic, direct product factor
66C32×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68D5×C11—91no—
69D5×C11C13×C3⋊D311yescharacteristic, direct product factor
70C32×C11C2×D5×C1311yescharacteristic, complemented, Hall
71C3⋊D15C2×C11×C1311yescharacteristic, complemented
72C5×C3⋊D3C2×C11×C1311yescharacteristic, complemented
73C32×D5C2×C11×C1311yescharacteristic, complemented
74C2×C3×C13—54no—
75D3×C13—34no—
76D3×C13—154no—
77C2×C3×C11—54no—
78D3×C11—34no—
79D3×C11—154no—
80C5×C13C2×C11×C3⋊D311yescharacteristic, complemented, Hall
81D3×D5—34no—
82C5×C11C2×C13×C3⋊D311yescharacteristic, complemented, Hall
83C22×C13—451noHall
84C32×C5C22×C11×C1311yescharacteristic, complemented, Hall
85C22×C11—451noHall
86C3×C13D3×D5×C1114yescomplemented
87C2×C3⋊D3—51noHall
88C3×C11D3×D5×C1314yescomplemented
89D15—34no—
90C3×D5D3×C11×C1314yescomplemented
91C5×D3—34no—
92C2×C13—51no—
93C2×C13—91no—
94C2×C13—451no—
95C2×C11—51no—
96C2×C11—91no—
97C2×C11—451no—
98C2×D5—91noHall
99C2×C32—51no—
100C3⋊D3—51no—
101C3⋊D3D5×C11×C1311yescharacteristic, direct product factor
102C3×C5C2×D3×C11×C1314yescomplemented
103C13D5×C11×C3⋊D311yescharacteristic, direct product factor, Sylow
104C2×D3—154no—
105C11D5×C13×C3⋊D311yescharacteristic, direct product factor, Sylow
106C2×C5—91no—
107D5—91no—
108D5C11×C13×C3⋊D311yescharacteristic, direct product factor
109C32C2×D5×C11×C1311yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—34no—
112D3—154no—
113C5C2×C11×C13×C3⋊D311yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×D5×C11×C1314yescomplemented
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC11×C13D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C22×C11×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C5
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C32×D5×C11×C13C2semidirect
2. C5×C11×C13×C3⋊D3C2semidirect
3. C11×C13×C3⋊D15C2semidirect
5. C32×C5×C11×C13C22semidirect
9. C3×D5×C11×C13D3semidirect
12. C11×C13×C3⋊D3D5direct (N × H)
14. D5×C13×C3⋊D3C11direct (N × H)
15. C3×C5×C11×C13C2×D3semidirect
16. D5×C11×C3⋊D3C13direct (N × H)
20. D5×C11×C13C3⋊D3direct (N × H)
21. C32×C11×C13C2×D5semidirect
22. C13×C3⋊D15C2×C11semidirect
23. C5×C13×C3⋊D3C2×C11semidirect
24. C32×D5×C13C2×C11semidirect
25. C11×C3⋊D15C2×C13semidirect
26. C5×C11×C3⋊D3C2×C13semidirect
27. C32×D5×C11C2×C13semidirect
32. C5×C11×C13C2×C3⋊D3semidirect
34. C32×C5×C13C22×C11semidirect
36. C32×C5×C11C22×C13semidirect
38. C3×C11×C13D3×D5semidirect
42. C3×D5×C13D3×C11semidirect
45. C3×D5×C11D3×C13semidirect
52. C13×C3⋊D3D5×C11direct (N × H)
56. C11×C3⋊D3D5×C13direct (N × H)
57. C3×C5×C13C2×D3×C11semidirect
58. D5×C3⋊D3C11×C13direct (N × H)
59. C3×C5×C11C2×D3×C13semidirect
61. C11×C13D5×C3⋊D3direct (N × H)
65. D5×C13C11×C3⋊D3direct (N × H)
66. C32×C13C2×D5×C11semidirect
69. D5×C11C13×C3⋊D3direct (N × H)
70. C32×C11C2×D5×C13semidirect
71. C3⋊D15C2×C11×C13semidirect
72. C5×C3⋊D3C2×C11×C13semidirect
73. C32×D5C2×C11×C13semidirect
80. C5×C13C2×C11×C3⋊D3semidirect
82. C5×C11C2×C13×C3⋊D3semidirect
84. C32×C5C22×C11×C13semidirect
86. C3×C13D3×D5×C11semidirect
88. C3×C11D3×D5×C13semidirect
90. C3×D5D3×C11×C13semidirect
101. C3⋊D3D5×C11×C13direct (N × H)
102. C3×C5C2×D3×C11×C13semidirect
103. C13D5×C11×C3⋊D3direct (N × H)
105. C11D5×C13×C3⋊D3direct (N × H)
108. D5C11×C13×C3⋊D3direct (N × H)
109. C32C2×D5×C11×C13semidirect
113. C5C2×C11×C13×C3⋊D3semidirect
115. C3D3×D5×C11×C13semidirect

Maximal subgroups

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

subgroupindex
C32×D5×C11×C132
C5×C11×C13×C3⋊D32
C11×C13×C3⋊D152
D3×D5×C11×C133
C2×C11×C13×C3⋊D35
D5×C13×C3⋊D311
D5×C11×C3⋊D313