Finite Group Databasebeta

← C2×C3⋊D3×D20 #13089269

Subgroups — C2×C3⋊D3×D20 #13089269

Order 1440.

1416 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 240 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
1C22×D5×C3⋊D3C212yesmaximal, complemented
2C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
3C2×C4×C5×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C32×D20C211yesmaximal, characteristic, complemented
5C2×#67139C212yesmaximal, complemented
6C3⋊D3×D20C218yesmaximal, direct product factor
7C2×D3×D20—34nomaximal
8C22×C3⋊D15C2212yescomplemented
9C22×C5×C3⋊D3C2211yescharacteristic
10C22×C32×D5C2212yescomplemented
11C2×D5×C3⋊D3—28no—
12C2×D5×C3⋊D3C2218yescomplemented
13C2×C32×C4×C5C2211yescharacteristic, complemented
14C4⋊(C3⋊D15)C2214yescomplemented
15C2×C5×C3⋊Dic3C2211yescharacteristic, complemented
16C4×C5×C3⋊D3C2214yescomplemented
17C32×D20C2214yescomplemented
18#67139C2218yescomplemented
19C2×D4×C3⋊D3—51nomaximal, Hall
20C22×D3×D5—38no—
21C2×D60—34no—
22C2×C4×C5×D3—34no—
23C2×C3×D20D314yescomplemented
24C2×#1202—38no—
25D3×D20—332no—
26C22×C32×C5C2311yescharacteristic
27C2×C3⋊D15—24no—
28C2×C3⋊D15C2314yescomplemented
29C2×C5×C3⋊D3D414yescomplemented
30C2×C5×C3⋊D3C2312yes—
31C2×C32×D5—24no—
32C2×C32×D5C2314yescomplemented
33D5×C3⋊D3—216no—
34C32×C4×C5C2312yescomplemented
35C5×C3⋊Dic3C2312yescomplemented
36C22×D20—91noHall
37C23×C3⋊D3—52no—
38C2×C32×D4—51no—
39C2×#638—52no—
40D4×C3⋊D3—58no—
41C2×C4⋊(C3⋊D3)—51no—
42C2×C4×C3⋊D3D511yescharacteristic, complemented
43C22×D15—38no—
44C22×C5×D3—34no—
45C22×C3×D5C2×D318yescomplemented
46C2×D3×D5—332no—
47C2×D3×D5—632no—
48C2×C3×C4×C5C2×D314yescomplemented
49D60—316no—
50C2×C5×Dic3—34no—
51C4×C5×D3—316no—
52C3×D20C2×D3116yescomplemented
53#1202—332no—
54C2×D3×D4—154no—
55C2×C32×C5C2×D412yescomplemented
56C2×C32×C5C2411yescharacteristic
57C3⋊D15—24no—
58C5×C3⋊D3C2×D414yescomplemented
59C32×D5—24no—
60C23×D5—92no—
61C22×C4×C5—91no—
62C2×D20—92no—
63C2×D20—91no—
64C2×D20—98no—
65C2×D20C3⋊D311yescharacteristic, direct product factor
66C23×C32—52no—
67C22×C3⋊D3—52no—
68C22×C3⋊D3—58no—
69C22×C3⋊D3—108no—
70C22×C3⋊D3C2×D511yescharacteristic
71C32×D4—54no—
72C2×C32×C4C2×D511yescharacteristic, complemented
73#638—58no—
74C2×C3⋊Dic3C2×D511yescharacteristic, complemented
75C4⋊(C3⋊D3)—54no—
76C4×C3⋊D3C2×D514yescomplemented
77C22×C3×C5C22×D314yes—
78C2×D15—316no—
79C2×D15—616no—
80C2×C5×D3—316no—
81C2×C5×D3—38no—
82C2×C3×D5—216no—
83C2×C3×D5C22×D3116yescomplemented
84D3×D5—664no—
85C3×C4×C5C22×D318yescomplemented
86C5×Dic3—38no—
87C23×D3—158no—
88C2×C3×D4—54no—
89C2×#67—158no—
90D3×D4—1532no—
91C2×D12—154no—
92C2×C4×D3—34no—
93C32×C5C22×D411yescharacteristic, complemented, Hall
94C23×C5—91no—
95C22×D5—92no—
96C22×D5—98no—
97C22×D5—188no—
98C22×D5C2×C3⋊D312yescomplemented
99C2×C4×C5—91no—
100C2×C4×C5—94no—
101C2×C4×C5C2×C3⋊D311yescharacteristic, complemented
102D20—98no—
103D20—94no—
104D20C2×C3⋊D314yesdirect product factor
105C22×C32—54no—
106C22×C32—104no—
107C22×C32C22×D511yescharacteristic
108C2×C3⋊D3—54no—
109C2×C3⋊D3—104no—
110C2×C3⋊D3—1016no—
111C2×C3⋊D3D2014yesdirect product factor
112C2×C3⋊D3C22×D512yes—
113C32×C4C22×D512yescomplemented
114C3⋊Dic3C22×D512yescomplemented
115C22×D4—451noSylow
116C2×C3×C5D3×D418yescomplemented
117C2×C3×C5C23×D314yes—
118D15—616no—
119C3×D5—216no—
120C5×D3—316no—
121C23×C3—58no—
122C22×D3—34no—
123C22×D3—1532no—
124C22×D3—158no—
125C22×D3—3032no—
126C3×D4—516no—
127C2×C3×C4D3×D514yescomplemented
128#67—1532no—
129C2×Dic3—34no—
130D12—1516no—
131C4×D3—316no—
132C22×C5—92no—
133C22×C5—94no—
134C22×C5C22×C3⋊D311yescharacteristic
135C2×D5—24no—
136C2×D5—94no—
137C2×D5—1816no—
138C2×D5—184no—
139C2×D5C22×C3⋊D314yescomplemented
140C4×C5—92no—
141C4×C5C22×C3⋊D312yescomplemented
142C2×C32—104no—
143C2×C32C2×D2012yescomplemented
144C2×C32C23×D511yescharacteristic
145C3⋊D3—104no—
146C3⋊D3C2×D2014yesdirect product factor
147C24—452no—
148C2×D4—51no—
149C2×D4—458no—
150C2×D4—452no—
151C2×D4—451no—
152C22×C4—91no—
153C3×C5C2×D3×D414yescomplemented
154C22×C3—516no—
155C22×C3—1016no—
156C22×C3C2×D3×D514yes—
157C2×D3—316no—
158C2×D3—38no—
159C2×D3—1516no—
160C2×D3—3064no—
161C2×D3—3016no—
162C3×C4C2×D3×D518yescomplemented
163Dic3—38no—
164C2×C5—94no—
165C2×C5D4×C3⋊D312yescomplemented
166C2×C5C23×C3⋊D311yescharacteristic
167D5—24no—
168D5—184no—
169C32C22×D2011yescharacteristic, complemented, Sylow
170C23—52no—
171C23—91no—
172C23—458no—
173C23—452no—
174C23—908no—
175D4—54no—
176D4—458no—
177D4—454no—
178C2×C4—91no—
179C2×C4—94no—
180C2×C4D5×C3⋊D311yescharacteristic, complemented
181C2×C3—1016no—
182C2×C3D3×D2018yescomplemented
183C2×C3C22×D3×D514yes—
184D3—316no—
185D3—3016no—
186C5C2×D4×C3⋊D311yescharacteristic, complemented, Sylow
187C22—54no—
188C22—92no—
189C22—94no—
190C22—104no—
191C22—454no—
192C22—9016no—
193C22—904no—
194C22C2×D5×C3⋊D311yescharacteristic
195C4—92no—
196C4C2×D5×C3⋊D312yescomplemented
197C3C2×D3×D2014yescomplemented
198C2—94no—
199C2—104no—
200C2—904no—
201C2C3⋊D3×D2012yesdirect product factor
202C2C22×D5×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D5×C3⋊D3
commutator, cosocleC2×C32×C5C24
FrattiniC2C22×D5×C3⋊D3
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×C3⋊D3C2semidirect
2. C2×C4⋊(C3⋊D15)C2semidirect
3. C2×C4×C5×C3⋊D3C2semidirect
4. C2×C32×D20C2semidirect
5. C2×#67139C2semidirect
6. C3⋊D3×D20C2direct (N × H)
8. C22×C3⋊D15C22semidirect
10. C22×C32×D5C22semidirect
12. C2×D5×C3⋊D3C22semidirect
13. C2×C32×C4×C5C22semidirect
14. C4⋊(C3⋊D15)C22semidirect
15. C2×C5×C3⋊Dic3C22semidirect
16. C4×C5×C3⋊D3C22semidirect
17. C32×D20C22semidirect
18. #67139C22semidirect
23. C2×C3×D20D3semidirect
28. C2×C3⋊D15C23semidirect
29. C2×C5×C3⋊D3D4semidirect
32. C2×C32×D5C23semidirect
34. C32×C4×C5C23semidirect
35. C5×C3⋊Dic3C23semidirect
42. C2×C4×C3⋊D3D5semidirect
45. C22×C3×D5C2×D3semidirect
48. C2×C3×C4×C5C2×D3semidirect
52. C3×D20C2×D3semidirect
55. C2×C32×C5C2×D4semidirect
58. C5×C3⋊D3C2×D4semidirect
65. C2×D20C3⋊D3direct (N × H)
72. C2×C32×C4C2×D5semidirect
74. C2×C3⋊Dic3C2×D5semidirect
76. C4×C3⋊D3C2×D5semidirect
83. C2×C3×D5C22×D3semidirect
85. C3×C4×C5C22×D3semidirect
93. C32×C5C22×D4semidirect
98. C22×D5C2×C3⋊D3semidirect
101. C2×C4×C5C2×C3⋊D3semidirect
104. D20C2×C3⋊D3direct (N × H)
111. C2×C3⋊D3D20direct (N × H)
113. C32×C4C22×D5semidirect
114. C3⋊Dic3C22×D5semidirect
116. C2×C3×C5D3×D4semidirect
127. C2×C3×C4D3×D5semidirect
139. C2×D5C22×C3⋊D3semidirect
141. C4×C5C22×C3⋊D3semidirect
143. C2×C32C2×D20semidirect
146. C3⋊D3C2×D20direct (N × H)
153. C3×C5C2×D3×D4semidirect
162. C3×C4C2×D3×D5semidirect
165. C2×C5D4×C3⋊D3semidirect
169. C32C22×D20semidirect
180. C2×C4D5×C3⋊D3semidirect
182. C2×C3D3×D20semidirect
186. C5C2×D4×C3⋊D3semidirect
196. C4C2×D5×C3⋊D3semidirect
197. C3C2×D3×D20semidirect
201. C2C3⋊D3×D20direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C3⋊D32
C2×C4⋊(C3⋊D15)2
C2×C4×C5×C3⋊D32
C2×C32×D202
C2×#671392
C3⋊D3×D202
C2×D3×D203
C2×D4×C3⋊D35