Finite Group Databasebeta

← C2×C13⋊C3×D165 #38788141

Subgroups — C2×C13⋊C3×D165 #38788141

Order 25740.

176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×C3×C5×C11×C13⋊C3C211yesmaximal, characteristic, complemented
2C13⋊C3×D165C212yesmaximal, direct product factor
3C2×C13×D165C311yesmaximal, characteristic, complemented
4C2×C13⋊C3×D55—31nomaximal
5C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C13⋊C3×D33—51nomaximal, Hall
7C13⋊C3×D55—32no—
8C13×D165C2×C312yescomplemented
9C2×C5×C11×C13⋊C3—21no—
10C2×C5×C11×C13⋊C3D311yescharacteristic, complemented
11C2×C3×C5×C11×C13C2×C311yescharacteristic, complemented
12C2×C13×D55—31noHall
13C2×C3×C11×C13⋊C3D511yescharacteristic, complemented
14C13⋊C3×D33—52no—
15C2×D15×C13⋊C3—111nomaximal, Hall
16C5×C11×C13⋊C3—21no—
17C5×C11×C13⋊C3C2×D311yescharacteristic, complemented
18C3×C5×C11×C13C22×C311yescharacteristic, complemented
19C2×C3×D165—131nomaximal, Hall
20C2×C13×D33—51no—
21C2×D11×C13⋊C3—151no—
22C2×C5×C11×C13C3×D311yescharacteristic, complemented
23C13×D55—32no—
24C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
25C2×C3×C5×C13⋊C3D1111yescharacteristic, complemented
26D15×C13⋊C3—112no—
27C2×C32×C5×C11—131no—
28C3×D165—132no—
29C2×C3×C11×C13C3×D511yescharacteristic, complemented
30C13×D33—52no—
31C2×C11×C13⋊C3—21no—
32C2×C11×C13⋊C3D1511yescharacteristic, complemented
33D11×C13⋊C3—152no—
34C2×C13×D15—111no—
35C2×D5×C13⋊C3—331no—
36C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
37C2×D165C13⋊C311yescharacteristic, direct product factor
38C2×C3×D55—391no—
39C3×C5×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
40C2×C13×D11—151noHall
41C32×C5×C11—131noHall
42C2×D3×C13⋊C3—551noHall
43C3×C11×C13C2×C3×D511yescharacteristic, complemented
44C11×C13⋊C3—21no—
45C11×C13⋊C3C2×D1511yescharacteristic, complemented
46C2×C3×D33—651noHall
47C2×C3×C5×C13C3×D1111yescharacteristic, complemented
48C13×D15—112no—
49C2×C5×C13⋊C3—21no—
50C2×C5×C13⋊C3D3311yescharacteristic, complemented
51D5×C13⋊C3—332no—
52C2×C3×C5×C11—131no—
53C2×C3×C5×C11—261no—
54C2×C3×C5×C11C2×C13⋊C311yescharacteristic, complemented
55D165C2×C13⋊C312yesdirect product factor
56C3×D55—392no—
57C2×C11×C13C3×D1511yescharacteristic, complemented
58C13×D11—152no—
59C2×D5×C13—331noHall
60C2×C3×C13⋊C3D5511yescharacteristic, complemented
61D3×C13⋊C3—552no—
62C2×D55—31noHall
63C2×C32×C11—131no—
64C3×D33—652no—
65C3×C5×C13C2×C3×D1111yescharacteristic, complemented
66C5×C13⋊C3—21no—
67C5×C13⋊C3C2×D3311yescharacteristic, complemented
68C2×C3×D15—1431noHall
69C3×C5×C11—131no—
70C3×C5×C11—261no—
71C3×C5×C11C22×C13⋊C311yescharacteristic, complemented
72C2×D3×C13—551no—
73C22×C13⋊C3—1651no—
74C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
75C2×D33—51no—
76C2×C3×D11—1951no—
77C2×C5×C13C3×D3311yescharacteristic, complemented
78D5×C13—332no—
79C3×C13⋊C3C2×D5511yescharacteristic, complemented, Hall
80C2×C5×C11D3×C13⋊C311yescharacteristic, complemented
81D55—32no—
82C32×C11—131noHall
83C2×C32×C5—131no—
84C3×D15—1432no—
85C2×C3×C13C3×D5511yescharacteristic, complemented
86D3×C13—552no—
87C2×C13⋊C3—21no—
88C2×C13⋊C3—1652no—
89C2×C13⋊C3D16511yescharacteristic, direct product factor
90C2×C3×C11—131no—
91C2×C3×C11—261no—
92C2×C3×C11D5×C13⋊C311yescharacteristic, complemented
93D33—52no—
94C3×D11—1952no—
95C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
96C2×D15—111no—
97C2×C3×D5—4291no—
98C5×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
99C22×C13—1651noHall
100C32×C5—131noHall
101C2×D11—151noHall
102C3×C13C2×C3×D5511yescharacteristic, complemented
103C13⋊C3—21no—
104C13⋊C3C2×D16511yescharacteristic, direct product factor
105C2×C3×D3—7151noHall
106C3×C11—131no—
107C3×C11—261no—
108C3×C11C2×D5×C13⋊C311yescharacteristic, complemented
109C2×C3×C5—131no—
110C2×C3×C5—261no—
111C2×C3×C5D11×C13⋊C311yescharacteristic, complemented
112D15—112no—
113C3×D5—4292no—
114C2×C13—1652no—
115C2×C13C3×D16511yescharacteristic, complemented
116C2×C11D15×C13⋊C311yescharacteristic, complemented
117D11—152no—
118C2×D5—331noHall
119C2×C32—131no—
120C3×D3—7152no—
121C3×C5—131no—
122C3×C5—261no—
123C3×C5C2×D11×C13⋊C311yescharacteristic, complemented
124C13C2×C3×D16511yescharacteristic, complemented, Sylow
125C22×C3—21451no—
126C2×D3—551no—
127C11C2×D15×C13⋊C311yescharacteristic, complemented, Sylow
128C2×C5C13⋊C3×D3311yescharacteristic, complemented
129D5—332no—
130C32—131noSylow
131C2×C3—131no—
132C2×C3—261no—
133C2×C3—21452no—
134C2×C3C13⋊C3×D5511yescharacteristic, complemented
135D3—552no—
136C5C2×C13⋊C3×D3311yescharacteristic, complemented, Sylow
137C22—1651noSylow
138C3—131no—
139C3—261no—
140C3C2×C13⋊C3×D5511yescharacteristic, complemented
141C2—1652no—
142C2C13⋊C3×D16511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C13⋊C3×D165
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2×C3
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C11×C13⋊C3C2semidirect
2. C13⋊C3×D165C2direct (N × H)
3. C2×C13×D165C3semidirect
5. C3×C5×C11×C13⋊C3C22semidirect
8. C13×D165C2×C3semidirect
10. C2×C5×C11×C13⋊C3D3semidirect
11. C2×C3×C5×C11×C13C2×C3semidirect
13. C2×C3×C11×C13⋊C3D5semidirect
17. C5×C11×C13⋊C3C2×D3semidirect
18. C3×C5×C11×C13C22×C3semidirect
22. C2×C5×C11×C13C3×D3semidirect
24. C3×C11×C13⋊C3C2×D5semidirect
25. C2×C3×C5×C13⋊C3D11semidirect
29. C2×C3×C11×C13C3×D5semidirect
32. C2×C11×C13⋊C3D15semidirect
36. C5×C11×C13C2×C3×D3semidirect
37. C2×D165C13⋊C3direct (N × H)
39. C3×C5×C13⋊C3C2×D11semidirect
43. C3×C11×C13C2×C3×D5semidirect
45. C11×C13⋊C3C2×D15semidirect
47. C2×C3×C5×C13C3×D11semidirect
50. C2×C5×C13⋊C3D33semidirect
54. C2×C3×C5×C11C2×C13⋊C3semidirect
55. D165C2×C13⋊C3direct (N × H)
57. C2×C11×C13C3×D15semidirect
60. C2×C3×C13⋊C3D55semidirect
65. C3×C5×C13C2×C3×D11semidirect
67. C5×C13⋊C3C2×D33semidirect
71. C3×C5×C11C22×C13⋊C3semidirect
74. C11×C13C2×C3×D15semidirect
77. C2×C5×C13C3×D33semidirect
79. C3×C13⋊C3C2×D55semidirect
80. C2×C5×C11D3×C13⋊C3semidirect
85. C2×C3×C13C3×D55semidirect
89. C2×C13⋊C3D165direct (N × H)
92. C2×C3×C11D5×C13⋊C3semidirect
95. C5×C13C2×C3×D33semidirect
98. C5×C11C2×D3×C13⋊C3semidirect
102. C3×C13C2×C3×D55semidirect
104. C13⋊C3C2×D165direct (N × H)
108. C3×C11C2×D5×C13⋊C3semidirect
111. C2×C3×C5D11×C13⋊C3semidirect
115. C2×C13C3×D165semidirect
116. C2×C11D15×C13⋊C3semidirect
123. C3×C5C2×D11×C13⋊C3semidirect
124. C13C2×C3×D165semidirect
127. C11C2×D15×C13⋊C3semidirect
128. C2×C5C13⋊C3×D33semidirect
134. C2×C3C13⋊C3×D55semidirect
136. C5C2×C13⋊C3×D33semidirect
140. C3C2×C13⋊C3×D55semidirect
142. C2C13⋊C3×D165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C11×C13⋊C32
C13⋊C3×D1652
C2×C13×D1653
C2×C13⋊C3×D553
C2×C13⋊C3×D335
C2×D15×C13⋊C311
C2×C3×D16513