Finite Group Databasebeta

← #11754028

Subgroups — #11754028

Order 960.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#709C211yesmaximal, characteristic, complemented
2C2×#6769C211yesmaximal, characteristic, complemented
3#91797C211yesmaximal, characteristic, complemented
4C5×D3×M16C211yesmaximal, characteristic, complemented
5C3×#4055C211yesmaximal, characteristic, complemented
6#91315C211yesmaximal, characteristic, complemented
7#91301C211yesmaximal, characteristic, complemented
8#91275C212yesmaximal, complemented
9#91272C212yesmaximal, complemented
10#91263C212yesmaximal, complemented
11#91253C212yesmaximal, complemented
12#66082—31nomaximal, Hall
13#6817C2211yescharacteristic
14C2×D60C2211yescharacteristic, complemented
15C2×C4×C5×D3C2211yescharacteristic
16C3×#709C2211yescharacteristic
17C2×C3×Dic10C2211yescharacteristic, complemented
18D3×C22⋊D5—21no—
19C2×#1203—21no—
20C2×#1200—21no—
21#6779—21no—
22D3×D20C2211yescharacteristic, complemented
23C4×D3×D5—21no—
24#6771—21no—
25#6769—21no—
26#6769—21no—
27#6769C2212yes—
28#6769C2212yescomplemented
29#6769C2211yescharacteristic, complemented
30D3×Dic10C2211yescharacteristic, complemented
31#6765C2211yescharacteristic, complemented
32C3×C5×M16C2211yescharacteristic, complemented
33D120C2212yescomplemented
34#6706C2212yescomplemented
35C5×#208C2211yescharacteristic, complemented
36C5×ΓL(1,𝔽25)C2212yescomplemented
37C5×D3×C8C2212yescomplemented
38C3×Dic20C2212yescomplemented
39C3×#677C2212yescomplemented
40#6662C2212yescomplemented
41#6658C2212yescomplemented
42#6658C2212yescomplemented
43#6653C2212yescomplemented
44#5777—51nomaximal, Hall
45C2×#709—31no—
46C2×#709—31no—
47C2×C5×M16—31no—
48#4055—31no—
49#4055—32no—
50#4055D311yescharacteristic, complemented
51#4054—31no—
52#4054—31no—
53#4054—32no—
54#4050—32no—
55#4050—32no—
56C22×D15—21no—
57C22×C5×D3D411yescharacteristic
58C2×D3×D5—21no—
59C2×C3×C4×C5C2311yescharacteristic
60#1220—21no—
61D60—21no—
62D60C2311yescharacteristic
63D60C2312yes—
64C4×D15—21no—
65Dic30C2311yescharacteristic
66C2×C5×Dic3D411yescharacteristic
67C4×C5×D3D411yescharacteristic
68C4×C5×D3D411yescharacteristic
69C4×C5×D3C2311yescharacteristic
70C4×C5×D3C2311yescharacteristic
71C3×C22⋊D5—21no—
72C2×C3×Dic5—21no—
73C3×D20C2311yescharacteristic
74C3×C4×D5—21no—
75C3×Dic10—21no—
76C3×Dic10C2311yescharacteristic
77C3×Dic10C2312yes—
78#1204—21no—
79#1203—22no—
80#1203—22no—
81#1203—21no—
82#1202—21no—
83#1201—21no—
84#1200—22no—
85#1200—22no—
86#1200—21no—
87D3×Dic5—21no—
88D5×Dic3—21no—
89C3×C5×C8C2312yes—
90C5×C3⋊C8C2312yes—
91D3×#41—51no—
92C2×#239—51no—
93C3×#137—51no—
94#949—51no—
95#942—51no—
96#919—52no—
97#918—52no—
98#916—52no—
99#914—52no—
100#908—51no—
101D3×M16D511yescharacteristic, complemented
102C22×C4×C5—31no—
103C2×C22⋊D5—61no—
104C2×C22⋊D5—61no—
105#709—31no—
106#709—31no—
107#709—32no—
108#709—31no—
109#709—32no—
110#709—61no—
111#709—61no—
112#709—61no—
113#709—61no—
114#709C2×D311yescharacteristic
115C2×D20—31no—
116C2×D20—31no—
117C2×C4×D5—61no—
118C2×C4×D5—61no—
119C2×Dic10—31no—
120C2×Dic10C2×D311yescharacteristic, complemented
121C5×M16—31no—
122C5×M16—32no—
123C5×M16C2×D311yescharacteristic, complemented
124C2×C5×C8—32no—
125Dic20—32no—
126Dic20C2×D312yescomplemented
127D40—32no—
128D40—32no—
129#677—32no—
130#677—32no—
131#677—32no—
132#677C2×D312yescomplemented
133#575—151noSylow
134C22×C3×C5C2×D411yescharacteristic
135C2×D15—22no—
136C2×D15—21no—
137C2×D15—42no—
138C2×C5×D3—41no—
139C2×C5×D3C2×D411yescharacteristic
140C2×C5×D3C2×D411yescharacteristic
141C2×C3×D5—21no—
142D3×D5—42no—
143C3×C4×C5C2×D411yescharacteristic
144C3×C4×C5C2411yescharacteristic
145Dic15—21no—
146C3×Dic5—21no—
147C3×Dic5—22no—
148C5×Dic3C2×D411yescharacteristic
149C5×Dic3C2×D411yescharacteristic
150C3×#41—51no—
151C2×C3×Q8—51no—
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—51no—
163#235—101no—
164C2×D12—51no—
165C2×D12—101no—
166C2×C4×D3—101no—
167C2×C4×D3—101no—
168C2×C4×D3C2×D511yescharacteristic
169C3×Q16—52no—
170C3×SD16—52no—
171C3×M16C2×D511yescharacteristic, complemented
172#216—52no—
173#215—52no—
174#215—52no—
175#213—52no—
176#208C2×D511yescharacteristic, complemented
177D24—52no—
178#204—52no—
179ΓL(1,𝔽25)C2×D512yescomplemented
180D3×C8C2×D512yescomplemented
181C23×C5—31no—
182C22×D5—61no—
183C22×D5—61no—
184C2×C4×C5—31no—
185C2×C4×C5—31no—
186C2×C4×C5—31no—
187C2×C4×C5—31no—
188C2×C4×C5—31no—
189C2×C4×C5C22×D311yescharacteristic
190C22⋊D5—21no—
191C22⋊D5—62no—
192C22⋊D5—62no—
193C22⋊D5—61no—
194C22⋊D5—61no—
195C22⋊D5—61no—
196C2×Dic5—21no—
197C2×Dic5—61no—
198D20—31no—
199D20—32no—
200D20—61no—
201D20—61no—
202D20C22×D311yescharacteristic
203C4×D5—21no—
204C4×D5—62no—
205C4×D5—62no—
206C4×D5—61no—
207C4×D5—61no—
208C4×D5—61no—
209Dic10—21no—
210Dic10—31no—
211Dic10—61no—
212Dic10C22×D311yescharacteristic
213Dic10C22×D312yes—
214C5×C8—32no—
215C5×C8C22×D312yes—
216C2×#41—151no—
217C2×#41—151no—
218#137—51no—
219#137—152no—
220#137—151no—
221AGL(1,ℤ/8)—152no—
222AGL(1,ℤ/8)—151no—
223AGL(1,ℤ/8)—151no—
224#135—152no—
225#135—152no—
226C2×M16—31no—
227C2×C3×C5—21no—
228C2×C3×C5C22×D411yescharacteristic
229D15—41no—
230D15—42no—
231C3×D5—41no—
232C5×D3—21no—
233C5×D3—21no—
234C22×D3—101no—
235C22×D3—101no—
236C22×D3D2011yescharacteristic
237C3×Q8—51no—
238C3×Q8—52no—
239C3×Q8—101no—
240C3×D4—51no—
241C3×D4—101no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4C22×D511yescharacteristic
245#67—101no—
246#67—101no—
247#67—101no—
248C2×Dic3—101no—
249C2×Dic3D2011yescharacteristic
250D12—52no—
251D12—51no—
252D12—102no—
253D12—102no—
254D12—101no—
255D12—101no—
256C4×D3—101no—
257C4×D3—101no—
258C4×D3—101no—
259C4×D3—102no—
260C4×D3—102no—
261C4×D3D2011yescharacteristic
262C4×D3D2011yescharacteristic
263C4×D3C22×D511yescharacteristic
264C4×D3C22×D511yescharacteristic
265Dic6—51no—
266Dic6—101no—
267C3×C8C22×D512yes—
268C3⋊C8C22×D512yes—
269C22×C5—31no—
270C22×C5—31no—
271C22×C5—121no—
272C22×C5D3×D411yescharacteristic
273C2×D5—21no—
274C2×D5—62no—
275C2×D5—61no—
276C2×D5—122no—
277C2×D5—122no—
278C4×C5—31no—
279C4×C5—31no—
280C4×C5D3×D411yescharacteristic
281C4×C5C23×D311yescharacteristic
282Dic5—22no—
283Dic5—21no—
284Dic5—61no—
285#41—51no—
286#41—151no—
287#41—152no—
288#41—151no—
289#41—152no—
290#41—151no—
291#41—301no—
292#41—301no—
293#41—301no—
294#41—301no—
295C2×Q8—51no—
296C2×Q8—151no—
297C2×D4—151no—
298C2×D4—151no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—31no—
302C22×C4—301no—
303C22×C4—301no—
304Q16—52no—
305Q16—152no—
306SD16—52no—
307SD16—152no—
308SD16—152no—
309SD16—152no—
310D8—152no—
311D8—152no—
312M16—31no—
313M16—32no—
314M16D3×D511yescharacteristic, complemented
315C2×C8—32no—
316C3×C5#57511yescharacteristic, complemented, Hall
317C22×C3—101no—
318C22×C3C2×D2011yescharacteristic
319C2×D3—41no—
320C2×D3—102no—
321C2×D3—101no—
322C2×D3—202no—
323C2×D3—202no—
324C2×D3C2×D2011yescharacteristic
325C2×D3C2×D2011yescharacteristic
326C3×C4—101no—
327C3×C4—102no—
328C3×C4C2×D2011yescharacteristic
329C3×C4C23×D511yescharacteristic
330Dic3—101no—
331Dic3C2×D2011yescharacteristic
332Dic3C2×D2011yescharacteristic
333C2×C5—21no—
334C2×C5—61no—
335C2×C5—61no—
336C2×C5C2×D3×D411yescharacteristic
337D5—41no—
338D5—121no—
339D5—122no—
340C23—31no—
341C23—301no—
342C23—301no—
343Q8—52no—
344Q8—51no—
345Q8—101no—
346Q8—151no—
347Q8—301no—
348D4—51no—
349D4—101no—
350D4—152no—
351D4—151no—
352D4—301no—
353D4—301no—
354D4—302no—
355D4—302no—
356D4—301no—
357D4—301no—
358D4—301no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—101no—
365C2×C4—101no—
366C2×C4—301no—
367C2×C4—302no—
368C2×C4—302no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—301no—
372C2×C4C2×D3×D511yescharacteristic
373C8—32no—
374C8C2×D3×D512yes—
375C2×C3—21no—
376C2×C3—201no—
377C2×C3C22×D2011yescharacteristic
378D3—21no—
379D3—21no—
380D3—202no—
381D3—201no—
382C5#577711yescharacteristic, complemented, Sylow
383C22—31no—
384C22—31no—
385C22—101no—
386C22—121no—
387C22—302no—
388C22—301no—
389C22—602no—
390C22—602no—
391C22D3×D2011yescharacteristic
392C4—31no—
393C4—31no—
394C4—101no—
395C4—102no—
396C4—301no—
397C4D3×D2011yescharacteristic
398C4C22×D3×D511yescharacteristic
399C3#6608211yescharacteristic, complemented, Sylow
400C2—21no—
401C2—61no—
402C2—61no—
403C2—201no—
404C2—602no—
405C2—601no—
406C2C2×D3×D2011yescharacteristic
subgroupG/H
centerC2C2×D3×D20
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC3×C5×M16C22
socleC2×C3×C5C22×D4
hypercenterM16D3×D5
hypocenterC3×C5#575
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
1. D3×#709C2semidirect
2. C2×#6769C2semidirect
3. #91797C2semidirect
4. C5×D3×M16C2semidirect
5. C3×#4055C2semidirect
6. #91315C2semidirect
7. #91301C2semidirect
8. #91275C2semidirect
9. #91272C2semidirect
10. #91263C2semidirect
11. #91253C2semidirect
14. C2×D60C22semidirect
17. C2×C3×Dic10C22semidirect
22. D3×D20C22semidirect
28. #6769C22semidirect
29. #6769C22semidirect
30. D3×Dic10C22semidirect
31. #6765C22semidirect
32. C3×C5×M16C22semidirect
33. D120C22semidirect
34. #6706C22semidirect
35. C5×#208C22semidirect
36. C5×ΓL(1,𝔽25)C22semidirect
37. C5×D3×C8C22semidirect
38. C3×Dic20C22semidirect
39. C3×#677C22semidirect
40. #6662C22semidirect
41. #6658C22semidirect
42. #6658C22semidirect
43. #6653C22semidirect
50. #4055D3semidirect
101. D3×M16D5semidirect
120. C2×Dic10C2×D3semidirect
123. C5×M16C2×D3semidirect
126. Dic20C2×D3semidirect
132. #677C2×D3semidirect
171. C3×M16C2×D5semidirect
176. #208C2×D5semidirect
179. ΓL(1,𝔽25)C2×D5semidirect
180. D3×C8C2×D5semidirect
314. M16D3×D5semidirect
316. C3×C5#575semidirect
382. C5#5777semidirect
399. C3#66082semidirect

Maximal subgroups

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

subgroupindex
D3×#7092
C2×#67692
#917972
C5×D3×M162
C3×#40552
#913152
#913012
#912752
#912722
#912632
#912532
#660823
#57775