Finite Group Databasebeta

← D13⋊C3×D165 #38788094

Subgroups — D13⋊C3×D165 #38788094

Order 25740.

176 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 47 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
1C13⋊C3×D165C211yesmaximal, characteristic, complemented
2C3⋊(C5⋊(C11⋊(D13⋊C3)))C211yesmaximal, characteristic, complemented
3C3×C5×C11×D13⋊C3C211yesmaximal, characteristic, complemented
4D13×D165C311yesmaximal, characteristic, complemented
5D13⋊C3×D55—31nomaximal
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7D33×D13⋊C3—51nomaximal, Hall
8C5⋊(C11⋊(D13⋊C3))—31no—
9C13⋊C3×D55—31no—
10C5×C11×D13⋊C3—21no—
11C5×C11×D13⋊C3D311yescharacteristic, complemented
12D2145C2×C311yescharacteristic, complemented
13C13×D165C2×C311yescharacteristic, complemented
14C3×C5×C11×D13C2×C311yescharacteristic, complemented
15D13×D55—31noHall
16C13⋊C3×D33—51no—
17C3⋊(C11⋊(D13⋊C3))—51no—
18C3×C11×D13⋊C3D511yescharacteristic, complemented
19D15×D13⋊C3—111nomaximal, Hall
20C5×C11×C13⋊C3—21no—
21C5×C11×C13⋊C3C2×D311yescharacteristic, complemented
22C3×C5×C11×C13C22×C311yescharacteristic, complemented
23C2×C3×D165—131nomaximal, Hall
24D13×D33—51no—
25D11×D13⋊C3—151no—
26D715—31no—
27C13×D55—31no—
28C5×C11×D13C3×D311yescharacteristic, complemented
29C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
30C3⋊(C5⋊(D13⋊C3))—111no—
31D15×C13⋊C3—111no—
32C3×C5×D13⋊C3D1111yescharacteristic, complemented
33C2×C32×C5×C11—131no—
34C3×D165—131no—
35C3×D165—261no—
36D429—51no—
37C13×D33—51no—
38C3×C11×D13C3×D511yescharacteristic, complemented
39C11⋊(D13⋊C3)—151no—
40D11×C13⋊C3—151no—
41C11×D13⋊C3—21no—
42C11×D13⋊C3D1511yescharacteristic, complemented
43D13×D15—111no—
44D5×D13⋊C3—331no—
45C5×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
46C2×D165—131no—
47C2×C3×D55—391no—
48C3×C5×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
49D11×D13—151noHall
50C32×C5×C11—261noHall
51D3×D13⋊C3—551noHall
52C3×C11×C13C2×C3×D511yescharacteristic, complemented
53C11×C13⋊C3—21no—
54C11×C13⋊C3C2×D1511yescharacteristic, complemented
55C2×C3×D33—651noHall
56D195—111no—
57C13×D15—111no—
58C3×C5×D13C3×D1111yescharacteristic, complemented
59C5⋊(D13⋊C3)—331no—
60D5×C13⋊C3—331no—
61C5×D13⋊C3—21no—
62C5×D13⋊C3D3311yescharacteristic, complemented
63C2×C3×C5×C11—131no—
64C2×C3×C5×C11—131no—
65C2×C3×C5×C11—261no—
66D165—131no—
67D165D13⋊C311yescharacteristic, direct product factor
68C3×D55—391no—
69C3×D55—781no—
70D143—151no—
71C11×D13C3×D1511yescharacteristic, complemented
72C13×D11—151no—
73D5×D13—331noHall
74C3⋊(D13⋊C3)—551no—
75D3×C13⋊C3—551no—
76C3×D13⋊C3D5511yescharacteristic, complemented
77C2×D55—391noHall
78C2×C32×C11—131no—
79C3×D33—651no—
80C3×D33—651no—
81C3×C5×C13C2×C3×D1111yescharacteristic, complemented
82C5×C13⋊C3—21no—
83C5×C13⋊C3C2×D3311yescharacteristic, complemented
84C2×C3×D15—1431noHall
85C3×C5×C11—261no—
86C3×C5×C11—521no—
87C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
88D3×D13—551no—
89C2×D13⋊C3—1651no—
90C11×C13C2×C3×D1511yescharacteristic, complemented, Hall
91C2×D33—651no—
92C2×C3×D11—1951no—
93D65—331no—
94C5×D13C3×D3311yescharacteristic, complemented
95D5×C13—331no—
96C3×C13⋊C3C2×D5511yescharacteristic, complemented, Hall
97C2×C5×C11—131no—
98D55—31no—
99D55—391no—
100C32×C11—131noHall
101C2×C32×C5—131no—
102C3×D15—1431no—
103C3×D15—1431no—
104D39—551no—
105C3×D13C3×D5511yescharacteristic, complemented
106D3×C13—551no—
107C2×C13⋊C3—1651no—
108D13⋊C3—21no—
109D13⋊C3—1651no—
110D13⋊C3D16511yescharacteristic, direct product factor
111C2×C3×C11—131no—
112C2×C3×C11—131no—
113C2×C3×C11—261no—
114D33—51no—
115D33—651no—
116C3×D11—3901no—
117C3×D11—1951no—
118C5×C13C2×C3×D3311yescharacteristic, complemented, Hall
119C2×D15—1431no—
120C2×C3×D5—4291no—
121C5×C11D3×D13⋊C311yescharacteristic, complemented, Hall
122C2×D13—1651noHall
123C32×C5—131noHall
124C2×D11—1951noHall
125C3×C13C2×C3×D5511yescharacteristic, complemented
126C13⋊C3—21no—
127C13⋊C3C2×D16511yescharacteristic, complemented
128C2×C3×D3—7151noHall
129C3×C11—261no—
130C3×C11—261no—
131C3×C11D5×D13⋊C311yescharacteristic, complemented
132C2×C3×C5—131no—
133C2×C3×C5—131no—
134C2×C3×C5—261no—
135D15—111no—
136D15—1431no—
137C3×D5—8581no—
138C3×D5—4291no—
139C2×C13—1651no—
140D13—1651no—
141D13C3×D16511yescharacteristic, complemented
142C2×C11—131no—
143D11—151no—
144D11—1951no—
145C2×D5—4291noHall
146C2×C32—131no—
147C3×D3—14301no—
148C3×D3—7151no—
149C3×C5—261no—
150C3×C5—521no—
151C3×C5D11×D13⋊C311yescharacteristic, complemented
152C13C2×C3×D16511yescharacteristic, complemented, Sylow
153C22×C3—21451no—
154C2×D3—7151no—
155C11D15×D13⋊C311yescharacteristic, complemented, Sylow
156C2×C5—131no—
157D5—331no—
158D5—4291no—
159C32—261noSylow
160C2×C3—131no—
161C2×C3—131no—
162C2×C3—261no—
163C2×C3—21451no—
164C2×C3—42901no—
165D3—551no—
166D3—7151no—
167C5D33×D13⋊C311yescharacteristic, complemented, Sylow
168C22—21451noSylow
169C3—261no—
170C3—521no—
171C3D13⋊C3×D5511yescharacteristic, complemented
172C2—131no—
173C2—21451no—
174C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C13C22×C3
LCSG ▷ C3×C5×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×D165C2semidirect
2. C3⋊(C5⋊(C11⋊(D13⋊C3)))C2semidirect
3. C3×C5×C11×D13⋊C3C2semidirect
4. D13×D165C3semidirect
6. C3×C5×C11×C13⋊C3C22semidirect
11. C5×C11×D13⋊C3D3semidirect
12. D2145C2×C3semidirect
13. C13×D165C2×C3semidirect
14. C3×C5×C11×D13C2×C3semidirect
18. C3×C11×D13⋊C3D5semidirect
21. C5×C11×C13⋊C3C2×D3semidirect
22. C3×C5×C11×C13C22×C3semidirect
28. C5×C11×D13C3×D3semidirect
29. C3×C11×C13⋊C3C2×D5semidirect
32. C3×C5×D13⋊C3D11semidirect
38. C3×C11×D13C3×D5semidirect
42. C11×D13⋊C3D15semidirect
45. C5×C11×C13C2×C3×D3semidirect
48. C3×C5×C13⋊C3C2×D11semidirect
52. C3×C11×C13C2×C3×D5semidirect
54. C11×C13⋊C3C2×D15semidirect
58. C3×C5×D13C3×D11semidirect
62. C5×D13⋊C3D33semidirect
67. D165D13⋊C3direct (N × H)
71. C11×D13C3×D15semidirect
76. C3×D13⋊C3D55semidirect
81. C3×C5×C13C2×C3×D11semidirect
83. C5×C13⋊C3C2×D33semidirect
87. C3×C5×C11C2×D13⋊C3semidirect
90. C11×C13C2×C3×D15semidirect
94. C5×D13C3×D33semidirect
96. C3×C13⋊C3C2×D55semidirect
105. C3×D13C3×D55semidirect
110. D13⋊C3D165direct (N × H)
118. C5×C13C2×C3×D33semidirect
121. C5×C11D3×D13⋊C3semidirect
125. C3×C13C2×C3×D55semidirect
127. C13⋊C3C2×D165semidirect
131. C3×C11D5×D13⋊C3semidirect
141. D13C3×D165semidirect
151. C3×C5D11×D13⋊C3semidirect
152. C13C2×C3×D165semidirect
155. C11D15×D13⋊C3semidirect
167. C5D33×D13⋊C3semidirect
171. C3D13⋊C3×D55semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D1652
C3⋊(C5⋊(C11⋊(D13⋊C3)))2
C3×C5×C11×D13⋊C32
D13×D1653
D13⋊C3×D553
D33×D13⋊C35
D15×D13⋊C311
C2×C3×D16513