Finite Group Databasebeta

← #11755096

Subgroups — #11755096

Order 960.

524 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 128 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×#6821C211yesmaximal, characteristic, complemented
2#92016C211yesmaximal, characteristic, complemented
3C5×#942C211yesmaximal, characteristic, complemented
4C3×#4088C211yesmaximal, characteristic, complemented
5#91523C212yesmaximal, complemented
6#91521C212yesmaximal, complemented
7#91512C212yesmaximal, complemented
8#91506C212yesmaximal, complemented
9#91305C211yesmaximal, characteristic, complemented
10#91301C211yesmaximal, characteristic, complemented
11#91292C211yesmaximal, characteristic, complemented
12#66111—31nomaximal, Hall
13C2×C3×C5×Q8C2211yescharacteristic, complemented
14#6821—21no—
15#6821—21no—
16#6821C2212yes—
17#6821C2212yescomplemented
18C2×D60—21no—
19C2×D60C2211yescharacteristic, complemented
20C2×C4×D15—21no—
21C2×C4×D15C2211yescharacteristic
22C5×#235C2211yescharacteristic
23C3×#709C2211yescharacteristic
24#6790—21no—
25#6780—21no—
26#6777C2211yescharacteristic, complemented
27C4×D3×D5—21no—
28#6771—21no—
29D15⋊Q8C2211yescharacteristic, complemented
30#6768C2211yescharacteristic, complemented
31#6766C2211yescharacteristic, complemented
32C5×#216C2212yescomplemented
33C5×#215C2212yescomplemented
34C5×#208C2211yescharacteristic, complemented
35C3×#689C2212yescomplemented
36C3×#688C2212yescomplemented
37C3×#681C2211yescharacteristic, complemented
38#6660C2212yescomplemented
39#6658C2212yescomplemented
40#6654C2212yescomplemented
41#6653C2212yescomplemented
42#6651C2212yescomplemented
43#6648C2212yescomplemented
44#5777—51nomaximal, Hall
45D5×#41—31no—
46C2×#713—31no—
47C5×#137—31no—
48#4095—31no—
49#4088D311yescharacteristic, complemented
50#4065—32no—
51#4064—32no—
52#4062—32no—
53#4060—32no—
54#4054—31no—
55D5×M16—31no—
56C22×D15—21no—
57C22×D15D411yescharacteristic
58C2×D3×D5—21no—
59C3×C5×Q8—21no—
60C3×C5×Q8C2312yes—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5C2311yescharacteristic
63C2×Dic15D411yescharacteristic
64D60—22no—
65D60—22no—
66D60—21no—
67D60C2312yes—
68C4×D15—22no—
69C4×D15—22no—
70C4×D15D411yescharacteristic
71C4×D15D411yescharacteristic
72C4×D15C2311yescharacteristic
73C4×D15C2311yescharacteristic
74C5×#67—21no—
75C5×D12C2311yescharacteristic
76C4×C5×D3—21no—
77C5×Dic6C2311yescharacteristic
78C3×C22⋊D5—21no—
79C3×D20C2311yescharacteristic
80C3×C4×D5—21no—
81C3×Dic10C2311yescharacteristic
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—
91D3×#41—51no—
92C2×#239—51no—
93C3×#137—51no—
94#949—51no—
95#942D511yescharacteristic, complemented
96#919—52no—
97#918—52no—
98#916—52no—
99#914—52no—
100#908—51no—
101D3×M16—51no—
102C5×#41—31no—
103C2×C5×Q8C2×D311yescharacteristic, complemented
104#713—32no—
105#713—32no—
106#713—31no—
107#713—61no—
108#713—61no—
109Q8×D5—31no—
110#711—31no—
111#711—61no—
112D4×D5—31no—
113D4×D5—61no—
114#709—61no—
115#709C2×D311yescharacteristic
116C2×D20—31no—
117C2×D20—61no—
118C2×C4×D5—31no—
119C2×C4×D5—61no—
120C2×C4×D5—61no—
121C5×Q16—32no—
122C5×SD16—32no—
123C5×M16—31no—
124#689C2×D312yescomplemented
125#688—32no—
126#688C2×D312yescomplemented
127#686—32no—
128#681C2×D311yescharacteristic, complemented
129D40—32no—
130#677—32no—
131#676—32no—
132C8×D5—32no—
133#575—151noSylow
134C22×C3×C5C2×D411yescharacteristic
135C2×D15—22no—
136C2×D15—41no—
137C2×D15—42no—
138C2×D15C2×D411yescharacteristic
139C2×D15C2×D411yescharacteristic
140C2×C5×D3—21no—
141C2×C3×D5—21no—
142D3×D5—42no—
143C3×C4×C5—22no—
144C3×C4×C5C2×D411yescharacteristic
145C3×C4×C5C2411yescharacteristic
146Dic15C2×D411yescharacteristic
147Dic15C2×D411yescharacteristic
148C3×Dic5—21no—
149C5×Dic3—21no—
150C3×#41—51no—
151C2×C3×Q8C2×D511yescharacteristic, complemented
152#239—52no—
153#239—52no—
154#239—51no—
155#239—101no—
156#239—101no—
157D3×Q8—51no—
158#237—51no—
159#237—101no—
160D3×D4—51no—
161D3×D4—101no—
162#235—101no—
163#235C2×D511yescharacteristic
164C2×D12—51no—
165C2×D12—101no—
166C2×C4×D3—51no—
167C2×C4×D3—101no—
168C2×C4×D3—101no—
169C3×Q16—52no—
170C3×SD16—52no—
171C3×M16—51no—
172#216C2×D512yescomplemented
173#215—52no—
174#215C2×D512yescomplemented
175#213—52no—
176#208C2×D511yescharacteristic, complemented
177D24—52no—
178#204—52no—
179ΓL(1,𝔽25)—52no—
180D3×C8—52no—
181C22×D5—31no—
182C22×D5—61no—
183C22×D5—61no—
184C5×Q8—21no—
185C5×Q8—31no—
186C5×Q8C22×D312yes—
187C5×D4—31no—
188C5×D4—61no—
189C2×C4×C5—21no—
190C2×C4×C5—61no—
191C2×C4×C5C22×D311yescharacteristic
192C22⋊D5—21no—
193C22⋊D5—61no—
194C22⋊D5—61no—
195C2×Dic5—31no—
196C2×Dic5—61no—
197D20—32no—
198D20—62no—
199D20—62no—
200D20—61no—
201D20—61no—
202D20C22×D311yescharacteristic
203C4×D5—21no—
204C4×D5—31no—
205C4×D5—31no—
206C4×D5—31no—
207C4×D5—31no—
208C4×D5—61no—
209C4×D5—62no—
210C4×D5—62no—
211C4×D5—61no—
212Dic10—61no—
213Dic10C22×D311yescharacteristic
214C5×C8—32no—
215#168C22×D312yes—
216C2×#41—151no—
217C2×#41—151no—
218#137—31no—
219#137—51no—
220#137—152no—
221AGL(1,ℤ/8)—151no—
222AGL(1,ℤ/8)—151no—
223AGL(1,ℤ/8)—152no—
224#135—152no—
225#135—152no—
226C2×M16—151no—
227C2×C3×C5—21no—
228C2×C3×C5C22×D411yescharacteristic
229D15—21no—
230D15—21no—
231D15—42no—
232C3×D5—41no—
233C5×D3—41no—
234C22×D3—51no—
235C22×D3—101no—
236C22×D3—101no—
237C3×Q8—21no—
238C3×Q8—51no—
239C3×Q8C22×D512yes—
240C3×D4—51no—
241C3×D4—101no—
242C2×C3×C4—21no—
243C2×C3×C4—101no—
244C2×C3×C4C22×D511yescharacteristic
245#67—21no—
246#67—101no—
247#67—101no—
248C2×Dic3—51no—
249C2×Dic3—101no—
250D12—52no—
251D12—102no—
252D12—102no—
253D12—101no—
254D12—101no—
255D12C22×D511yescharacteristic
256C4×D3—21no—
257C4×D3—51no—
258C4×D3—51no—
259C4×D3—51no—
260C4×D3—51no—
261C4×D3—101no—
262C4×D3—102no—
263C4×D3—102no—
264C4×D3—101no—
265Dic6—101no—
266Dic6C22×D511yescharacteristic
267C3×C8—52no—
268C3⋊C8C22×D512yes—
269C22×C5—61no—
270C22×C5D3×D411yescharacteristic
271C2×D5—21no—
272C2×D5—31no—
273C2×D5—31no—
274C2×D5—62no—
275C2×D5—122no—
276C2×D5—121no—
277C2×D5—122no—
278C4×C5—22no—
279C4×C5—61no—
280C4×C5D3×D411yescharacteristic
281C4×C5C23×D311yescharacteristic
282Dic5—21no—
283Dic5—31no—
284Dic5—31no—
285#41—31no—
286#41—51no—
287#41—151no—
288#41—151no—
289#41—152no—
290#41—152no—
291#41—301no—
292#41—301no—
293#41—301no—
294#41—301no—
295C2×Q8—151no—
296C2×Q8D3×D511yescharacteristic, complemented
297C2×D4—151no—
298C2×D4—151no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—151no—
302C22×C4—301no—
303C22×C4—301no—
304Q16—32no—
305Q16—52no—
306SD16—32no—
307SD16—52no—
308SD16—152no—
309SD16—152no—
310D8—152no—
311D8—152no—
312M16—31no—
313M16—51no—
314M16—152no—
315C2×C8—152no—
316C3×C5#57511yescharacteristic, complemented, Hall
317C22×C3—101no—
318C22×C3D4×D511yescharacteristic
319C2×D3—21no—
320C2×D3—51no—
321C2×D3—51no—
322C2×D3—102no—
323C2×D3—202no—
324C2×D3—201no—
325C2×D3—202no—
326C3×C4—22no—
327C3×C4—101no—
328C3×C4D4×D511yescharacteristic
329C3×C4C23×D511yescharacteristic
330Dic3—21no—
331Dic3—51no—
332Dic3—51no—
333C2×C5—21no—
334C2×C5—121no—
335C2×C5C2×D3×D411yescharacteristic
336D5—41no—
337D5—61no—
338D5—61no—
339D5—122no—
340C23—151no—
341C23—301no—
342C23—301no—
343Q8—21no—
344Q8—31no—
345Q8—51no—
346Q8—301no—
347Q8C2×D3×D512yes—
348D4—31no—
349D4—51no—
350D4—61no—
351D4—101no—
352D4—152no—
353D4—302no—
354D4—302no—
355D4—301no—
356D4—301no—
357D4—301no—
358D4—301no—
359C2×C4—21no—
360C2×C4—61no—
361C2×C4—101no—
362C2×C4—151no—
363C2×C4—151no—
364C2×C4—151no—
365C2×C4—151no—
366C2×C4—151no—
367C2×C4—302no—
368C2×C4—302no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—301no—
372C2×C4C2×D3×D511yescharacteristic
373C8—32no—
374C8—52no—
375C2×C3—21no—
376C2×C3—201no—
377C2×C3C2×D4×D511yescharacteristic
378D3—41no—
379D3—101no—
380D3—101no—
381D3—202no—
382C5#577711yescharacteristic, complemented, Sylow
383C22—61no—
384C22—101no—
385C22—151no—
386C22—151no—
387C22—302no—
388C22—601no—
389C22—602no—
390C22—602no—
391C22#679011yescharacteristic
392C4—22no—
393C4—61no—
394C4—101no—
395C4—151no—
396C4—151no—
397C4#679011yescharacteristic
398C4C22×D3×D511yescharacteristic
399C3#6611111yescharacteristic, complemented, Sylow
400C2—21no—
401C2—121no—
402C2—201no—
403C2—301no—
404C2—301no—
405C2—602no—
406C2C2×#679011yescharacteristic
subgroupG/H
centerC2C2×#6790
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×Q8C22
socleC2×C3×C5C22×D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#575
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×#6821C2semidirect
2. #92016C2semidirect
3. C5×#942C2semidirect
4. C3×#4088C2semidirect
5. #91523C2semidirect
6. #91521C2semidirect
7. #91512C2semidirect
8. #91506C2semidirect
9. #91305C2semidirect
10. #91301C2semidirect
11. #91292C2semidirect
13. C2×C3×C5×Q8C22semidirect
17. #6821C22semidirect
19. C2×D60C22semidirect
26. #6777C22semidirect
29. D15⋊Q8C22semidirect
30. #6768C22semidirect
31. #6766C22semidirect
32. C5×#216C22semidirect
33. C5×#215C22semidirect
34. C5×#208C22semidirect
35. C3×#689C22semidirect
36. C3×#688C22semidirect
37. C3×#681C22semidirect
38. #6660C22semidirect
39. #6658C22semidirect
40. #6654C22semidirect
41. #6653C22semidirect
42. #6651C22semidirect
43. #6648C22semidirect
49. #4088D3semidirect
95. #942D5semidirect
103. C2×C5×Q8C2×D3semidirect
124. #689C2×D3semidirect
126. #688C2×D3semidirect
128. #681C2×D3semidirect
151. C2×C3×Q8C2×D5semidirect
172. #216C2×D5semidirect
174. #215C2×D5semidirect
176. #208C2×D5semidirect
296. C2×Q8D3×D5semidirect
316. C3×C5#575semidirect
382. C5#5777semidirect
399. C3#66111semidirect

Maximal subgroups

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

subgroupindex
C2×#68212
#920162
C5×#9422
C3×#40882
#915232
#915212
#915122
#915062
#913052
#913012
#912922
#661113
#57775