Finite Group Databasebeta

← C32×D55⋊D13 #38788181

Subgroups — C32×D55⋊D13 #38788181

Order 25740.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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×D143C211yesmaximal, characteristic, complemented
2C32×C11×D65C211yesmaximal, characteristic, complemented
3C32×C13×D55C211yesmaximal, characteristic, complemented
4C3×D55⋊D13C314yesmaximal, direct product factor
5C32×C5×C11×C13C2211yescharacteristic, complemented, Hall
6C32×D11×D13—51nomaximal, Hall
7C3×C13×D55C2×C314yescomplemented
8C3×C11×D65C2×C314yescomplemented
9C3×C5×D143C2×C314yescomplemented
10D55⋊D13C3211yescharacteristic, direct product factor, Hall
11C32×D143D511yescharacteristic, complemented
12C32×C13×D11—51no—
13C32×C11×D13—51no—
14C32×D5×D13—111nomaximal, Hall
15C3×C5×C11×C13C22×C314yescomplemented
16C32×D5×D11—131nomaximal, Hall
17C3×D11×D13—54no—
18C13×D55C2×C3211yescharacteristic, complemented
19C11×D65C2×C3211yescharacteristic, complemented
20C5×D143C2×C3211yescharacteristic, complemented
21C32×C11×C13C2×D511yescharacteristic, complemented, Hall
22C32×D65D1111yescharacteristic, complemented
23C32×D5×C13—111no—
24C32×C5×D13—111no—
25C32×D55D1311yescharacteristic, complemented
26C32×D5×C11—131no—
27C32×C5×D11—131no—
28C3×D143C3×D514yescomplemented
29C3×C13×D11—54no—
30C3×C11×D13—54no—
31C3×D5×D13—114no—
32C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
33C3×D5×D11—134no—
34C32×C5×C13C2×D1111yescharacteristic, complemented, Hall
35D11×D13—51noHall
36C32×C5×C11C2×D1311yescharacteristic, complemented, Hall
37C2×C32×D13—551noHall
38C3×C11×C13C2×C3×D514yescomplemented
39C2×C32×D11—651noHall
40C3×D65C3×D1114yescomplemented
41C3×D5×C13—114no—
42C3×C5×D13—114no—
43C3×D55C3×D1314yescomplemented
44C3×D5×C11—134no—
45C3×C5×D11—134no—
46D143C32×D511yescharacteristic, complemented
47C11×D13—51no—
48C13×D11—51no—
49D5×D13—111noHall
50C2×C32×C13—551no—
51C32×D13—51no—
52C32×D13—111no—
53D5×D11—131noHall
54C2×C32×C11—651no—
55C32×D11—51no—
56C32×D11—131no—
57C3×C5×C13C2×C3×D1114yescomplemented
58C2×C32×D5—1431noHall
59C3×C5×C11C2×C3×D1314yescomplemented
60C2×C3×D13—554no—
61C11×C13C2×C32×D511yescharacteristic, complemented, Hall
62C2×C3×D11—654no—
63D65C32×D1111yescharacteristic, complemented
64C5×D13—111no—
65D5×C13—111no—
66C32×C13D5×D1111yescharacteristic, complemented, Hall
67D55C32×D1311yescharacteristic, complemented
68C5×D11—131no—
69D5×C11—131no—
70C32×C11D5×D1311yescharacteristic, complemented, Hall
71C2×C32×C5—1431no—
72C32×D5—111no—
73C32×D5—131no—
74C2×C3×C13—554no—
75C3×D13—54no—
76C3×D13—114no—
77C2×C3×C11—654no—
78C3×D11—54no—
79C3×D11—134no—
80C5×C13C2×C32×D1111yescharacteristic, complemented, Hall
81C2×C3×D5—1434no—
82C5×C11C2×C32×D1311yescharacteristic, complemented, Hall
83C2×D13—551noHall
84C32×C5D11×D1311yescharacteristic, complemented, Hall
85C2×D11—651noHall
86C3×C13C3×D5×D1114yescomplemented
87C22×C32—7151noHall
88C3×C11C3×D5×D1314yescomplemented
89C2×C3×C5—1434no—
90C3×D5—114no—
91C3×D5—134no—
92C2×C13—551no—
93D13—51no—
94D13—111no—
95C2×C11—651no—
96D11—51no—
97D11—131no—
98C2×D5—1431noHall
99C2×C32—551no—
100C2×C32—651no—
101C2×C32—1431no—
102C3×C5C3×D11×D1314yescomplemented
103C13C32×D5×D1111yescharacteristic, complemented, Sylow
104C22×C3—7154no—
105C11C32×D5×D1311yescharacteristic, complemented, Sylow
106C2×C5—1431no—
107D5—111no—
108D5—131no—
109C32D55⋊D1311yescharacteristic, direct product factor, Sylow
110C2×C3—554no—
111C2×C3—654no—
112C2×C3—1434no—
113C5C32×D11×D1311yescharacteristic, complemented, Sylow
114C22—7151noSylow
115C3C3×D55⋊D1314yesdirect product factor
116C2—551no—
117C2—651no—
118C2—1431no—
subgroupG/H
center, hypercenterC32D55⋊D13
commutator, cosocle, hypocenterC5×C11×C13C22×C32
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C5×C11×C13
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5×D143C2semidirect
2. C32×C11×D65C2semidirect
3. C32×C13×D55C2semidirect
4. C3×D55⋊D13C3direct (N × H)
5. C32×C5×C11×C13C22semidirect
7. C3×C13×D55C2×C3semidirect
8. C3×C11×D65C2×C3semidirect
9. C3×C5×D143C2×C3semidirect
10. D55⋊D13C32direct (N × H)
11. C32×D143D5semidirect
15. C3×C5×C11×C13C22×C3semidirect
18. C13×D55C2×C32semidirect
19. C11×D65C2×C32semidirect
20. C5×D143C2×C32semidirect
21. C32×C11×C13C2×D5semidirect
22. C32×D65D11semidirect
25. C32×D55D13semidirect
28. C3×D143C3×D5semidirect
32. C5×C11×C13C22×C32semidirect
34. C32×C5×C13C2×D11semidirect
36. C32×C5×C11C2×D13semidirect
38. C3×C11×C13C2×C3×D5semidirect
40. C3×D65C3×D11semidirect
43. C3×D55C3×D13semidirect
46. D143C32×D5semidirect
57. C3×C5×C13C2×C3×D11semidirect
59. C3×C5×C11C2×C3×D13semidirect
61. C11×C13C2×C32×D5semidirect
63. D65C32×D11semidirect
66. C32×C13D5×D11semidirect
67. D55C32×D13semidirect
70. C32×C11D5×D13semidirect
80. C5×C13C2×C32×D11semidirect
82. C5×C11C2×C32×D13semidirect
84. C32×C5D11×D13semidirect
86. C3×C13C3×D5×D11semidirect
88. C3×C11C3×D5×D13semidirect
102. C3×C5C3×D11×D13semidirect
103. C13C32×D5×D11semidirect
105. C11C32×D5×D13semidirect
109. C32D55⋊D13direct (N × H)
113. C5C32×D11×D13semidirect
115. C3C3×D55⋊D13direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1432
C32×C11×D652
C32×C13×D552
C3×D55⋊D133
C32×D11×D135
C32×D5×D1311
C32×D5×D1113