Finite Group Databasebeta

← C2×#91480 #11754694

Subgroups — C2×#91480 #11754694

Order 960.

596 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 144 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×C5×#237C211yesmaximal, characteristic, complemented
2C2×D3×D20C211yesmaximal, characteristic, complemented
3C2×#6715C211yesmaximal, characteristic, complemented
4C2×C3×#686C211yesmaximal, characteristic, complemented
5#91480C218yesmaximal, direct product factor
6C2×#6660C211yesmaximal, characteristic, complemented
7C2×#6655C211yesmaximal, characteristic, complemented
8C2×#6650C211yesmaximal, characteristic, complemented
9C2×#4095—31nomaximal, Hall
10C22×D3×D5—21no—
11C2×C3×C5×D4C2211yescharacteristic, complemented
12C2×D60C2211yescharacteristic
13C2×C5×#67—21no—
14C22×C5×Dic3—21no—
15C5×#237—22no—
16C5×#237C2214yescomplemented
17C2×C4×C5×D3C2211yescharacteristic
18C2×C5×Dic6C2211yescharacteristic, complemented
19C2×C3×D20C2211yescharacteristic
20C2×#1202—21no—
21D3×D20—22no—
22D3×D20C2214yescomplemented
23#6715C2214yescomplemented
24C2×C3⋊#168C2211yescharacteristic, complemented
25C3×#686C2214yescomplemented
26C2×C3×#168C2211yescharacteristic, complemented
27#6660C2214yescomplemented
28#6655C2214yescomplemented
29#6650C2214yescomplemented
30C2×#911—51nomaximal, Hall
31C2×C5×#41—31no—
32C22×D20—31no—
33#4095—38no—
34C2×#688—31no—
35C2×#688—31no—
36C2×#686—31no—
37C2×#686D311yescharacteristic, complemented
38C2×#681—31no—
39C23×C3×C5—21no—
40C22×D15—21no—
41C22×C5×D3D411yescharacteristic
42C22×C3×D5—21no—
43C2×D3×D5—24no—
44C2×D3×D5—44no—
45C3×C5×D4—21no—
46C3×C5×D4C2312yescomplemented
47C2×C3×C4×C5C2311yescharacteristic
48D60—21no—
49D60C2312yes—
50C5×#67—24no—
51C2×C5×Dic3—21no—
52C2×C5×Dic3—24no—
53C2×C5×Dic3D411yescharacteristic
54C4×C5×D3D412yes—
55C4×C5×D3C2312yes—
56C5×Dic6—21no—
57C5×Dic6C2312yescomplemented
58C3×D20—21no—
59C3×D20C2312yes—
60#1202—24no—
61C3⋊#168C2312yescomplemented
62C3×#168C2312yescomplemented
63C2×#237D511yescharacteristic, complemented
64C2×D3×D4—51no—
65C2×C3×D8—51no—
66C2×#214—51no—
67C2×#213—51no—
68#911—58no—
69C2×#204—51no—
70C2×ΓL(1,𝔽25)—51no—
71C23×D5—61no—
72C5×#41—34no—
73C5×#41—62no—
74C2×C5×Q8—31no—
75C2×C5×D4—61no—
76C2×C5×D4C2×D311yescharacteristic, complemented
77C22×C4×C5—31no—
78C22×C4×C5—61no—
79C2×D20—31no—
80C2×D20—34no—
81C2×D20—62no—
82C2×D20—61no—
83C2×D20C2×D311yescharacteristic
84#688—34no—
85#688—34no—
86#686—34no—
87#686C2×D314yescomplemented
88#681—34no—
89C2×#168—31no—
90C2×#168C2×D311yescharacteristic, complemented
91C2×AGL(1,ℤ/8)—151noSylow
92C22×C3×C5—22no—
93C22×C3×C5—42no—
94C22×C3×C5C2×D411yescharacteristic
95C2×D15—22no—
96C2×D15—42no—
97C2×C5×D3—22no—
98C2×C5×D3C2×D412yes—
99C2×C3×D5—22no—
100C2×C3×D5—42no—
101D3×D5—48no—
102C3×C4×C5C2×D411yescharacteristic
103C3×C4×C5C2411yescharacteristic
104C5×Dic3—22no—
105C5×Dic3C2×D412yes—
106C23×D3—101no—
107C2×C3×D4—51no—
108C2×C3×D4C2×D511yescharacteristic, complemented
109C2×#67—21no—
110C2×#67—101no—
111C22×Dic3—21no—
112#237—22no—
113#237C2×D514yescomplemented
114D3×D4—54no—
115D3×D4—102no—
116C2×D12—51no—
117C2×C4×D3C2×D511yescharacteristic
118C2×Dic6C2×D511yescharacteristic, complemented
119C3×D8—54no—
120C2×C3×C8—51no—
121#214—54no—
122#213—54no—
123C2×C3⋊C8—51no—
124#204—54no—
125ΓL(1,𝔽25)—54no—
126C23×C5—21no—
127C23×C5—31no—
128C22×D5—21no—
129C22×D5—64no—
130C22×D5—61no—
131C22×D5—124no—
132C5×Q8—32no—
133C5×Q8—61no—
134C5×D4—21no—
135C5×D4—64no—
136C5×D4C22×D312yescomplemented
137C2×C4×C5—31no—
138C2×C4×C5—32no—
139C2×C4×C5—32no—
140C2×C4×C5—64no—
141C2×C4×C5—61no—
142C2×C4×C5C22×D311yescharacteristic
143D20—21no—
144D20—32no—
145D20—64no—
146D20—61no—
147D20C22×D312yes—
148#168—32no—
149#168C22×D312yescomplemented
150C2×#41—31no—
151C22×D4—151no—
152AGL(1,ℤ/8)—158no—
153C2×SD16—151no—
154C2×SD16—151no—
155C2×D8—51no—
156C2×D8—151no—
157C2×M16—151no—
158C2×C3×C5—42no—
159C2×C3×C5AGL(1,ℤ/8)12yescomplemented
160C2×C3×C5C22×D411yescharacteristic
161D15—42no—
162C3×D5—42no—
163C5×D3—22no—
164C23×C3—21no—
165C23×C3—101no—
166C22×D3—101no—
167C22×D3—104no—
168C22×D3—204no—
169C22×D3C22⋊D511yescharacteristic
170C3×D4—21no—
171C3×D4—52no—
172C3×D4—101no—
173C3×D4C22×D512yescomplemented
174C2×C3×C4C22×D511yescharacteristic
175#67—24no—
176#67—104no—
177C2×Dic3—21no—
178C2×Dic3—24no—
179C2×Dic3C22⋊D511yescharacteristic
180D12—52no—
181D12—101no—
182C4×D3C22⋊D512yes—
183C4×D3C22×D512yes—
184Dic6—21no—
185Dic6C22×D512yescomplemented
186C3×C8—52no—
187C3⋊C8—52no—
188C22×C5—22no—
189C22×C5—32no—
190C22×C5—42no—
191C22×C5—62no—
192C22×C5D3×D411yescharacteristic
193C2×D5—22no—
194C2×D5—42no—
195C2×D5—62no—
196C2×D5—128no—
197C2×D5—122no—
198C4×C5—32no—
199C4×C5—62no—
200C4×C5D3×D411yescharacteristic
201C4×C5C23×D311yescharacteristic
202C24—301no—
203#41—34no—
204#41—62no—
205C2×Q8—31no—
206C2×D4—51no—
207C2×D4—61no—
208C2×D4—154no—
209C2×D4—151no—
210C2×D4—302no—
211C2×D4—301no—
212C2×D4D3×D511yescharacteristic, complemented
213C22×C4—31no—
214C22×C4—61no—
215SD16—154no—
216SD16—154no—
217D8—54no—
218D8—154no—
219M16—154no—
220C2×C8—51no—
221C2×C8—151no—
222C3×C5C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
223C22×C3—22no—
224C22×C3—42no—
225C22×C3—102no—
226C22×C3—202no—
227C22×C3C2×C22⋊D511yescharacteristic
228C2×D3—22no—
229C2×D3—102no—
230C2×D3—208no—
231C2×D3—202no—
232C2×D3C2×C22⋊D512yes—
233C3×C4C2×C22⋊D511yescharacteristic
234C3×C4C23×D511yescharacteristic
235Dic3—22no—
236Dic3C2×C22⋊D512yes—
237C2×C5—42no—
238C2×C5—62no—
239C2×C5#91112yescomplemented
240C2×C5C2×D3×D411yescharacteristic
241D5—42no—
242D5—122no—
243C23—21no—
244C23—31no—
245C23—101no—
246C23—304no—
247C23—301no—
248C23—604no—
249Q8—32no—
250Q8—61no—
251D4—21no—
252D4—52no—
253D4—64no—
254D4—101no—
255D4—152no—
256D4—304no—
257D4—301no—
258D4C2×D3×D512yescomplemented
259C2×C4—31no—
260C2×C4—32no—
261C2×C4—32no—
262C2×C4—64no—
263C2×C4—61no—
264C2×C4C2×D3×D511yescharacteristic
265C8—52no—
266C8—152no—
267C2×C3—42no—
268C2×C3—202no—
269C2×C3#409512yescomplemented
270C2×C3C22×C22⋊D511yescharacteristic
271D3—22no—
272D3—202no—
273C5C2×#91111yescharacteristic, complemented, Sylow
274C22—22no—
275C22—32no—
276C22—42no—
277C22—62no—
278C22—102no—
279C22—202no—
280C22—302no—
281C22—608no—
282C22—602no—
283C22D3×C22⋊D511yescharacteristic
284C4—32no—
285C4—62no—
286C4D3×C22⋊D511yescharacteristic
287C4C22×D3×D511yescharacteristic
288C3C2×#409511yescharacteristic, complemented, Sylow
289C2—42no—
290C2—62no—
291C2—202no—
292C2—602no—
293C2#9148012yesdirect product factor
294C2C2×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC22D3×C22⋊D5
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×D4C22
socleC22×C3×C5C2×D4
hypercenterC2×D4D3×D5
hypocenterC3×C5C2×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#237C2semidirect
2. C2×D3×D20C2semidirect
3. C2×#6715C2semidirect
4. C2×C3×#686C2semidirect
5. #91480C2direct (N × H)
6. C2×#6660C2semidirect
7. C2×#6655C2semidirect
8. C2×#6650C2semidirect
11. C2×C3×C5×D4C22semidirect
16. C5×#237C22semidirect
18. C2×C5×Dic6C22semidirect
22. D3×D20C22semidirect
23. #6715C22semidirect
24. C2×C3⋊#168C22semidirect
25. C3×#686C22semidirect
26. C2×C3×#168C22semidirect
27. #6660C22semidirect
28. #6655C22semidirect
29. #6650C22semidirect
37. C2×#686D3semidirect
46. C3×C5×D4C23semidirect
57. C5×Dic6C23semidirect
61. C3⋊#168C23semidirect
62. C3×#168C23semidirect
63. C2×#237D5semidirect
76. C2×C5×D4C2×D3semidirect
87. #686C2×D3semidirect
90. C2×#168C2×D3semidirect
108. C2×C3×D4C2×D5semidirect
113. #237C2×D5semidirect
118. C2×Dic6C2×D5semidirect
136. C5×D4C22×D3semidirect
149. #168C22×D3semidirect
159. C2×C3×C5AGL(1,ℤ/8)semidirect
173. C3×D4C22×D5semidirect
185. Dic6C22×D5semidirect
212. C2×D4D3×D5semidirect
222. C3×C5C2×AGL(1,ℤ/8)semidirect
239. C2×C5#911semidirect
258. D4C2×D3×D5semidirect
269. C2×C3#4095semidirect
273. C5C2×#911semidirect
288. C3C2×#4095semidirect
293. C2#91480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#2372
C2×D3×D202
C2×#67152
C2×C3×#6862
#914802
C2×#66602
C2×#66552
C2×#66502
C2×#40953
C2×#9115