Finite Group Databasebeta

← C2×#10624035 #13089013

Subgroups — C2×#10624035 #13089013

Order 1440.

998 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 164 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×D3×D15C212yesmaximal, complemented
2C2×#67157C211yesmaximal, characteristic, complemented
3C2×C5×#625C211yesmaximal, characteristic, complemented
4C2×#67137C211yesmaximal, characteristic, complemented
5C2×C3×#1203C212yesmaximal, complemented
6#10624035C218yesmaximal, direct product factor
7C2×#6790—32nomaximal
8C22×C3⋊D15C2211yescharacteristic
9C22×C3×D15C2212yescomplemented
10C22×C3×C5×D3C2212yescomplemented
11C2×D3×D15—28no—
12C2×D3×D15C2218yescomplemented
13C2×C5×C3⋊Dic3C2211yescharacteristic, complemented
14C2×C32×Dic5C2211yescharacteristic, complemented
15#67157C2214yescomplemented
16C5×#625C2214yescomplemented
17#67137C2214yescomplemented
18C3×#1203C2218yescomplemented
19C2×#3802—51nomaximal, Hall
20C23×D15—32no—
21C22×D3×D5—32no—
22C2×C5×#67—32no—
23C2×C3×C22⋊D5—32no—
24#6790—316no—
25C2×#1203D312yescomplemented
26C2×#1202—32no—
27C2×#1200—32no—
28C2×#1200—61no—
29C22×C32×C5C2311yescharacteristic
30C2×C3⋊D15D414yescomplemented
31C2×C3⋊D15C2312yes—
32C2×C3×D15—24no—
33C2×C3×D15C2314yescomplemented
34C2×C3×C5×D3—24no—
35C2×C3×C5×D3C2314yescomplemented
36D3×D15—216no—
37C5×C3⋊Dic3C2312yescomplemented
38C32×Dic5C2312yescomplemented
39C2×D4×D5—91noHall
40C22×D32—52no—
41C2×C4×C3⋊D3—51no—
42C2×C3×D12—52no—
43C2×#625—51no—
44C2×#625D511yescharacteristic, complemented
45#3802—58no—
46C23×C3×C5—32no—
47C22×D15—32no—
48C22×D15—38no—
49C22×D15—68no—
50C22×D15—61no—
51C22×D15C2×D312yescomplemented
52C22×C5×D3C2×D312yescomplemented
53C22×C3×D5—32no—
54C2×D3×D5—38no—
55C2×D3×D5—68no—
56C5×#67—38no—
57C2×C5×Dic3—32no—
58C2×C5×Dic3—61no—
59C3×C22⋊D5—38no—
60C2×C3×Dic5—21no—
61C2×C3×Dic5C2×D312yescomplemented
62#1203C2×D318yescomplemented
63#1202—38no—
64#1200—38no—
65#1200—64no—
66C2×D3×D4—152no—
67C2×C32×C5C2×D412yescomplemented
68C2×C32×C5C2411yescharacteristic
69C3⋊D15C2×D414yescomplemented
70C3×D15—24no—
71C3×C5×D3—24no—
72C23×D5—92no—
73C2×C5×D4—91no—
74C2×C22⋊D5—32no—
75D4×D5—98no—
76C2×D20—91no—
77C2×C4×D5—91no—
78C22×C3⋊D3—51no—
79C22×C3×D3—52no—
80C22×C3×D3C2×D512yescomplemented
81C2×D32—58no—
82C2×D32—108no—
83C2×C32×C4—51no—
84C2×C3⋊Dic3C2×D511yescharacteristic, complemented
85C4×C3⋊D3—54no—
86C3×D12—58no—
87#625—54no—
88#625C2×D514yescomplemented
89C22×C3×C5—21no—
90C22×C3×C5—34no—
91C22×C3×C5—64no—
92C22×C3×C5C22×D312yes—
93C2×D15—24no—
94C2×D15—38no—
95C2×D15—34no—
96C2×D15—64no—
97C2×D15—62no—
98C2×D15—616no—
99C2×D15C22×D314yescomplemented
100C2×C5×D3—24no—
101C2×C5×D3C22×D314yescomplemented
102C2×C3×D5—34no—
103C2×C3×D5—64no—
104D3×D5—616no—
105C3×Dic5—22no—
106C3×Dic5C22×D314yescomplemented
107C5×Dic3—34no—
108C5×Dic3—62no—
109C23×D3—152no—
110C23×D3—152no—
111C2×C3×D4—152no—
112C2×#67—32no—
113C2×#67—152no—
114D3×D4—1516no—
115C2×D12—52no—
116C2×C4×D3—152no—
117C2×C4×D3—301no—
118C32×C5C22×D411yescharacteristic, complemented, Hall
119C23×C5—32no—
120C22×D5—32no—
121C22×D5—98no—
122C22×D5—91no—
123C22×D5—188no—
124C5×D4—94no—
125C2×C4×C5—91no—
126C22⋊D5—38no—
127C2×Dic5D3211yescharacteristic, complemented
128D20—94no—
129C4×D5—94no—
130C22×C32C22×D511yescharacteristic
131C2×C3⋊D3—54no—
132C2×C3⋊D3—52no—
133C2×C3×D3—24no—
134C2×C3×D3—54no—
135C2×C3×D3—104no—
136C2×C3×D3C22×D514yescomplemented
137D32—1016no—
138C32×C4—52no—
139C3⋊Dic3C22×D512yescomplemented
140C22×D4—451noSylow
141C2×C3×C5—21no—
142C2×C3×C5—22no—
143C2×C3×C5—64no—
144C2×C3×C5D3×D414yescomplemented
145C2×C3×C5C23×D312yes—
146D15—24no—
147D15—38no—
148D15—64no—
149C3×D5—64no—
150C5×D3—24no—
151C23×C3—32no—
152C23×C3—152no—
153C22×D3—52no—
154C22×D3—158no—
155C22×D3—152no—
156C22×D3—158no—
157C22×D3—301no—
158C22×D3—308no—
159C22×D3—308no—
160C22×D3D3×D512yescomplemented
161C3×D4—158no—
162C2×C3×C4—52no—
163C2×C3×C4—101no—
164#67—38no—
165#67—158no—
166C2×Dic3—32no—
167C2×Dic3—61no—
168D12—58no—
169C4×D3—158no—
170C4×D3—304no—
171C22×C5—34no—
172C22×C5—64no—
173C22×C5C2×D3211yescharacteristic
174C2×D5—34no—
175C2×D5—64no—
176C2×D5—92no—
177C2×D5—94no—
178C2×D5—1816no—
179C4×C5—92no—
180Dic5C2×D3212yescomplemented
181C2×C32D4×D512yescomplemented
182C2×C32C23×D511yescharacteristic
183C3⋊D3—54no—
184C3×D3—24no—
185C3×D3—104no—
186C24—452no—
187C2×D4—91no—
188C2×D4—152no—
189C2×D4—451no—
190C2×D4—458no—
191C22×C4—451no—
192C3×C5—21no—
193C3×C5C2×D3×D412yescomplemented
194C22×C3—21no—
195C22×C3—34no—
196C22×C3—64no—
197C22×C3—154no—
198C22×C3—304no—
199C22×C3C2×D3×D512yes—
200C2×D3—24no—
201C2×D3—54no—
202C2×D3—104no—
203C2×D3—158no—
204C2×D3—154no—
205C2×D3—302no—
206C2×D3—304no—
207C2×D3—3016no—
208C2×D3—3016no—
209C2×D3C2×D3×D514yescomplemented
210C3×C4—54no—
211C3×C4—102no—
212Dic3—34no—
213Dic3—62no—
214C2×C5—64no—
215C2×C5#380212yescomplemented
216C2×C5C22×D3211yescharacteristic
217D5—64no—
218D5—94no—
219C32C2×D4×D511yescharacteristic, complemented, Sylow
220C23—32no—
221C23—152no—
222C23—458no—
223C23—451no—
224C23—908no—
225D4—94no—
226D4—158no—
227D4—454no—
228C2×C4—51no—
229C2×C4—91no—
230C2×C4—454no—
231C2×C3—22no—
232C2×C3—21no—
233C2×C3—64no—
234C2×C3—304no—
235C2×C3#679014yescomplemented
236C2×C3C22×D3×D512yes—
237D3—24no—
238D3—104no—
239D3—158no—
240D3—304no—
241C5C2×#380211yescharacteristic, complemented, Sylow
242C22—34no—
243C22—64no—
244C22—154no—
245C22—304no—
246C22—454no—
247C22—452no—
248C22—9016no—
249C22D32×D511yescharacteristic
250C4—52no—
251C4—92no—
252C3—21no—
253C3C2×#679012yescomplemented
254C2—64no—
255C2—304no—
256C2—454no—
257C2#1062403512yesdirect product factor
258C2C2×D32×D511yescharacteristic
subgroupG/H
center, hypercenterC22D32×D5
commutator, cosocleC2×C32×C5C24
FrattiniC2C2×D32×D5
Fitting, socleC22×C32×C5C23
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×D3×D15C2semidirect
2. C2×#67157C2semidirect
3. C2×C5×#625C2semidirect
4. C2×#67137C2semidirect
5. C2×C3×#1203C2semidirect
6. #10624035C2direct (N × H)
9. C22×C3×D15C22semidirect
10. C22×C3×C5×D3C22semidirect
12. C2×D3×D15C22semidirect
13. C2×C5×C3⋊Dic3C22semidirect
14. C2×C32×Dic5C22semidirect
15. #67157C22semidirect
16. C5×#625C22semidirect
17. #67137C22semidirect
18. C3×#1203C22semidirect
25. C2×#1203D3semidirect
30. C2×C3⋊D15D4semidirect
33. C2×C3×D15C23semidirect
35. C2×C3×C5×D3C23semidirect
37. C5×C3⋊Dic3C23semidirect
38. C32×Dic5C23semidirect
44. C2×#625D5semidirect
51. C22×D15C2×D3semidirect
52. C22×C5×D3C2×D3semidirect
61. C2×C3×Dic5C2×D3semidirect
62. #1203C2×D3semidirect
67. C2×C32×C5C2×D4semidirect
69. C3⋊D15C2×D4semidirect
80. C22×C3×D3C2×D5semidirect
84. C2×C3⋊Dic3C2×D5semidirect
88. #625C2×D5semidirect
99. C2×D15C22×D3semidirect
101. C2×C5×D3C22×D3semidirect
106. C3×Dic5C22×D3semidirect
118. C32×C5C22×D4semidirect
127. C2×Dic5D32semidirect
136. C2×C3×D3C22×D5semidirect
139. C3⋊Dic3C22×D5semidirect
144. C2×C3×C5D3×D4semidirect
160. C22×D3D3×D5semidirect
180. Dic5C2×D32semidirect
181. C2×C32D4×D5semidirect
193. C3×C5C2×D3×D4semidirect
209. C2×D3C2×D3×D5semidirect
215. C2×C5#3802semidirect
219. C32C2×D4×D5semidirect
235. C2×C3#6790semidirect
241. C5C2×#3802semidirect
253. C3C2×#6790semidirect
257. C2#10624035direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×#671572
C2×C5×#6252
C2×#671372
C2×C3×#12032
#106240352
C2×#67903
C2×#38025