Finite Group Databasebeta

← D5×#942 #11755083

Subgroups — D5×#942 #11755083

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×D5C211yesmaximal, characteristic, complemented
2D5×#235C211yesmaximal, characteristic
3#91831C211yesmaximal, characteristic, complemented
4C5×#942C211yesmaximal, characteristic, complemented
5#91515C212yesmaximal, complemented
6#91513C212yesmaximal, complemented
7D5×#216C212yesmaximal, complemented
8D5×#215C212yesmaximal, complemented
9#91315C211yesmaximal, characteristic, complemented
10#91309C211yesmaximal, characteristic, complemented
11D5×#208C211yesmaximal, characteristic, complemented
12D5×#137—31nomaximal, Hall
13C2×C3×C5×Q8C2211yescharacteristic, complemented
14#6817C2211yescharacteristic
15C5×#235C2211yescharacteristic
16C3×Q8×D5—21no—
17C3×Q8×D5—21no—
18C3×Q8×D5C2212yes—
19C3×Q8×D5C2212yescomplemented
20C2×C3×C4×D5—21no—
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×Dic10—21no—
23C2×C3×Dic10C2211yescharacteristic, complemented
24D5×#67—21no—
25#6782—21no—
26D5×D12C2211yescharacteristic
27C4×D3×D5—21no—
28#6773C2211yescharacteristic
29#6772C2211yescharacteristic
30#6771—21no—
31D5×Dic6C2211yescharacteristic
32#6718C2212yescomplemented
33#6717C2212yescomplemented
34#6710C2211yescharacteristic, complemented
35C5×#216C2212yescomplemented
36C5×#215C2212yescomplemented
37C5×#208C2211yescharacteristic, complemented
38#6662C2212yescomplemented
39#6661C2212yescomplemented
40#6658C2212yescomplemented
41#6656C2212yescomplemented
42#6649C2212yescomplemented
43D5×C3⋊C8C2212yes—
44C2×#942—51nomaximal, Hall
45D5×#41—31no—
46C2×Q8×D5D311yescharacteristic, complemented
47C5×#137—31no—
48#4097—31no—
49#4088—31no—
50#4064—32no—
51D5×Q16—32no—
52#4061—32no—
53D5×SD16—32no—
54#4055—31no—
55D5×M16—31no—
56C22×C3×D5D411yescharacteristic
57C2×D3×D5—21no—
58C3×C5×Q8—21no—
59C3×C5×Q8C2312yes—
60C2×C3×C4×C5—21no—
61C2×C3×C4×C5C2311yescharacteristic
62#1220—21no—
63D60C2311yescharacteristic
64C4×D15—21no—
65Dic30C2311yescharacteristic
66C5×#67—21no—
67C5×D12C2311yescharacteristic
68C4×C5×D3—21no—
69C5×Dic6C2311yescharacteristic
70C2×C3×Dic5—21no—
71C2×C3×Dic5D411yescharacteristic
72C3×C4×D5—22no—
73C3×C4×D5—22no—
74C3×C4×D5D411yescharacteristic
75C3×C4×D5D411yescharacteristic
76C3×C4×D5C2311yescharacteristic
77C3×C4×D5C2311yescharacteristic
78C3×Dic10—21no—
79C3×Dic10—22no—
80C3×Dic10—22no—
81C3×Dic10C2312yes—
82#1204—21no—
83#1203—21no—
84#1202—21no—
85#1201—21no—
86#1200—21no—
87D3×Dic5—21no—
88D5×Dic3—21no—
89C3⋊#168C2312yes—
90C5×C3⋊C8C2312yes—
91C22×C3×Q8—51no—
92C2×#235—51no—
93C2×#216—52no—
94#942—51no—
95#942—51no—
96#942—52no—
97#942—52no—
98#942—51no—
99#942D511yescharacteristic, direct product factor
100C2×#215—52no—
101C2×#208—51no—
102C5×#41—31no—
103C2×C5×Q8C2×D311yescharacteristic, complemented
104#713—31no—
105Q8×D5—21no—
106Q8×D5—21no—
107Q8×D5—31no—
108Q8×D5C2×D312yes—
109Q8×D5C2×D312yescomplemented
110#711—31no—
111#711—61no—
112D4×D5—31no—
113D4×D5—61no—
114#709—31no—
115#709—61no—
116C2×C4×D5—21no—
117C2×C4×D5—61no—
118C2×C4×D5C2×D311yescharacteristic
119C2×Dic10—21no—
120C2×Dic10C2×D311yescharacteristic, complemented
121C5×Q16—32no—
122C5×SD16—32no—
123C5×M16—31no—
124#689—32no—
125#689—32no—
126#688—32no—
127#687—32no—
128#681—31no—
129Dic20—32no—
130#677—32no—
131#676—32no—
132C8×D5—32no—
133C2×#137—151noSylow
134C22×C3×C5C2×D411yescharacteristic
135C2×D15—21no—
136C2×C5×D3—21no—
137C2×C3×D5—22no—
138C2×C3×D5C2×D411yescharacteristic
139C2×C3×D5C2×D411yescharacteristic
140D3×D5—42no—
141C3×C4×C5—22no—
142C3×C4×C5C2×D411yescharacteristic
143C3×C4×C5C2411yescharacteristic
144Dic15—21no—
145C3×Dic5—22no—
146C3×Dic5C2×D411yescharacteristic
147C3×Dic5C2×D411yescharacteristic
148C5×Dic3—21no—
149C2×C3×Q8—52no—
150C2×C3×Q8—52no—
151C2×C3×Q8—51no—
152C2×C3×Q8—101no—
153C2×C3×Q8—101no—
154C2×C3×Q8—101no—
155C2×C3×Q8C2×D511yescharacteristic, complemented
156C22×C3×C4—51no—
157C22×C3×C4—101no—
158C2×#67—101no—
159#235—51no—
160#235—51no—
161#235—51no—
162#235—101no—
163#235—101no—
164#235C2×D511yescharacteristic
165C2×D12—51no—
166C2×C4×D3—101no—
167C2×Dic6—51no—
168#216—52no—
169#216—52no—
170#216—52no—
171#216C2×D512yescomplemented
172#215—52no—
173#215—52no—
174#215—52no—
175#215C2×D512yescomplemented
176#208—51no—
177#208—52no—
178#208C2×D511yescharacteristic, complemented
179C2×C3⋊C8—52no—
180C22×D5—61no—
181C22×D5#6711yescharacteristic
182C5×Q8—21no—
183C5×Q8—31no—
184C5×Q8C22×D312yes—
185C5×D4—31no—
186C5×D4—61no—
187C2×C4×C5—21no—
188C2×C4×C5—61no—
189C2×C4×C5C22×D311yescharacteristic
190C22⋊D5—61no—
191C22⋊D5—61no—
192C22⋊D5—61no—
193C2×Dic5—21no—
194C2×Dic5—61no—
195C2×Dic5#6711yescharacteristic
196D20—31no—
197D20—61no—
198C4×D5—22no—
199C4×D5—22no—
200C4×D5—61no—
201C4×D5—61no—
202C4×D5—61no—
203C4×D5#6711yescharacteristic
204C4×D5#6711yescharacteristic
205C4×D5C22×D311yescharacteristic
206C4×D5C22×D311yescharacteristic
207Dic10—21no—
208Dic10—22no—
209Dic10—22no—
210Dic10—31no—
211Dic10—61no—
212Dic10C22×D312yes—
213C5×C8—32no—
214#168—32no—
215C2×#41—151no—
216C22×Q8—51no—
217#137—31no—
218#137—151no—
219#137—152no—
220#137—152no—
221#137—151no—
222#137—151no—
223C2×Q16—152no—
224C2×SD16—152no—
225C2×M16—151no—
226C2×C3×C5—21no—
227C2×C3×C5C22×D411yescharacteristic
228D15—41no—
229C3×D5—21no—
230C3×D5#13712yescomplemented
231C5×D3—41no—
232C23×C3—51no—
233C22×D3—101no—
234C3×Q8—21no—
235C3×Q8—52no—
236C3×Q8—102no—
237C3×Q8—102no—
238C3×Q8—101no—
239C3×Q8C22×D512yes—
240C2×C3×C4—21no—
241C2×C3×C4—51no—
242C2×C3×C4—51no—
243C2×C3×C4—51no—
244C2×C3×C4—51no—
245C2×C3×C4—51no—
246C2×C3×C4—102no—
247C2×C3×C4—102no—
248C2×C3×C4—101no—
249C2×C3×C4C22×D511yescharacteristic
250#67—21no—
251#67—101no—
252#67—101no—
253#67—101no—
254C2×Dic3—101no—
255D12—51no—
256D12—101no—
257D12C22×D511yescharacteristic
258C4×D3—21no—
259C4×D3—101no—
260C4×D3—101no—
261C4×D3—101no—
262Dic6—51no—
263Dic6—101no—
264Dic6C22×D511yescharacteristic
265C3⋊C8—52no—
266C3⋊C8C22×D512yes—
267C22×C5—61no—
268C22×C5C2×#6711yescharacteristic
269C2×D5—22no—
270C2×D5—61no—
271C2×D5—122no—
272C2×D5C2×#6711yescharacteristic
273C2×D5C2×#6711yescharacteristic
274C4×C5—22no—
275C4×C5—61no—
276C4×C5C2×#6711yescharacteristic
277C4×C5C23×D311yescharacteristic
278Dic5—22no—
279Dic5—61no—
280Dic5C2×#6711yescharacteristic
281Dic5C2×#6711yescharacteristic
282#41—31no—
283#41—151no—
284#41—151no—
285#41—151no—
286#41—301no—
287#41—301no—
288C2×Q8—52no—
289C2×Q8—52no—
290C2×Q8—51no—
291C2×Q8—101no—
292C2×Q8—101no—
293C2×Q8—101no—
294C2×Q8—151no—
295C2×Q8D3×D511yescharacteristic, complemented
296C2×D4—151no—
297C2×D4—301no—
298C22×C4—51no—
299C22×C4—101no—
300C22×C4—301no—
301Q16—32no—
302Q16—152no—
303Q16—152no—
304Q16—152no—
305SD16—32no—
306SD16—152no—
307SD16—152no—
308SD16—152no—
309M16—31no—
310M16—152no—
311M16—151no—
312C2×C8—152no—
313C3×C5C2×#13711yescharacteristic, complemented, Hall
314C22×C3—51no—
315C22×C3—51no—
316C22×C3—102no—
317C22×C3D4×D511yescharacteristic
318C2×D3—21no—
319C2×D3—101no—
320C2×D3—202no—
321C3×C4—22no—
322C3×C4—51no—
323C3×C4—51no—
324C3×C4—102no—
325C3×C4D4×D511yescharacteristic
326C3×C4C23×D511yescharacteristic
327Dic3—21no—
328Dic3—101no—
329C2×C5—21no—
330C2×C5—121no—
331C2×C5C22×#6711yescharacteristic
332D5—21no—
333D5—121no—
334D5#94212yesdirect product factor
335C23—51no—
336C23—301no—
337Q8—21no—
338Q8—31no—
339Q8—52no—
340Q8—102no—
341Q8—102no—
342Q8—101no—
343Q8—151no—
344Q8—301no—
345Q8C2×D3×D512yes—
346D4—31no—
347D4—61no—
348D4—151no—
349D4—301no—
350D4—301no—
351D4—301no—
352D4—301no—
353C2×C4—21no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—61no—
360C2×C4—102no—
361C2×C4—102no—
362C2×C4—101no—
363C2×C4—301no—
364C2×C4—301no—
365C2×C4—301no—
366C2×C4—301no—
367C2×C4C2×D3×D511yescharacteristic
368C8—32no—
369C8—152no—
370C2×C3—21no—
371C2×C3—52no—
372C2×C3—101no—
373C2×C3C2×D4×D511yescharacteristic
374D3—41no—
375D3—201no—
376C5C2×#94211yescharacteristic, complemented, Sylow
377C22—51no—
378C22—51no—
379C22—61no—
380C22—102no—
381C22—301no—
382C22—602no—
383C22D5×#6711yescharacteristic
384C4—22no—
385C4—51no—
386C4—51no—
387C4—61no—
388C4—102no—
389C4—301no—
390C4D5×#6711yescharacteristic
391C4C22×D3×D511yescharacteristic
392C3D5×#13711yescharacteristic, complemented, Sylow
393C2—21no—
394C2—52no—
395C2—101no—
396C2—121no—
397C2—601no—
398C2C2×D5×#6711yescharacteristic
subgroupG/H
centerC2C2×D5×#67
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×Q8C22
socleC2×C3×C5C22×D4
prime radicalD5×#235C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5C2×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×D5C2semidirect
3. #91831C2semidirect
4. C5×#942C2semidirect
5. #91515C2semidirect
6. #91513C2semidirect
7. D5×#216C2semidirect
8. D5×#215C2semidirect
9. #91315C2semidirect
10. #91309C2semidirect
11. D5×#208C2semidirect
13. C2×C3×C5×Q8C22semidirect
19. C3×Q8×D5C22semidirect
23. C2×C3×Dic10C22semidirect
32. #6718C22semidirect
33. #6717C22semidirect
34. #6710C22semidirect
35. C5×#216C22semidirect
36. C5×#215C22semidirect
37. C5×#208C22semidirect
38. #6662C22semidirect
39. #6661C22semidirect
40. #6658C22semidirect
41. #6656C22semidirect
42. #6649C22semidirect
46. C2×Q8×D5D3semidirect
99. #942D5direct (N × H)
103. C2×C5×Q8C2×D3semidirect
109. Q8×D5C2×D3semidirect
120. C2×Dic10C2×D3semidirect
155. C2×C3×Q8C2×D5semidirect
171. #216C2×D5semidirect
175. #215C2×D5semidirect
178. #208C2×D5semidirect
230. C3×D5#137semidirect
295. C2×Q8D3×D5semidirect
313. C3×C5C2×#137semidirect
334. D5#942direct (N × H)
376. C5C2×#942semidirect
392. C3D5×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×D52
D5×#2352
#918312
C5×#9422
#915152
#915132
D5×#2162
D5×#2152
#913152
#913092
D5×#2082
D5×#1373
C2×#9425