Finite Group Databasebeta

← #11755344

Subgroups — #11755344

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
1C3×D5×#41C211yesmaximal, characteristic, complemented
2C2×#6773C211yesmaximal, characteristic, complemented
3#91838C211yesmaximal, characteristic, complemented
4C5×#951C211yesmaximal, characteristic, complemented
5#91516C212yesmaximal, complemented
6#91515C212yesmaximal, complemented
7#91492C212yesmaximal, complemented
8#91491C212yesmaximal, complemented
9#91307C211yesmaximal, characteristic, complemented
10#91301C211yesmaximal, characteristic, complemented
11D5×#208C211yesmaximal, characteristic, complemented
12#66111—31nomaximal, Hall
13C3×C5×#41C2211yescharacteristic
14C2×D60C2211yescharacteristic, complemented
15C2×C5×Dic6C2211yescharacteristic, complemented
16C3×#713C2211yescharacteristic, complemented
17C3×Q8×D5C2211yescharacteristic, complemented
18C3×#711—21no—
19C3×#711C2211yescharacteristic, complemented
20C3×D4×D5—21no—
21C3×D4×D5C2211yescharacteristic, complemented
22C3×#709—21no—
23C3×#709C2211yescharacteristic
24C2×C3×C4×D5—21no—
25C2×C3×C4×D5C2211yescharacteristic
26C2×#1202—21no—
27C2×#1200—21no—
28#6773—21no—
29#6773—21no—
30#6773C2212yes—
31#6773C2212yescomplemented
32#6717C2212yescomplemented
33#6715C2212yescomplemented
34#6710C2211yescharacteristic, complemented
35C5×#216C2212yescomplemented
36C5×#214C2212yescomplemented
37C5×#208C2211yescharacteristic, complemented
38#6661C2212yescomplemented
39#6658C2212yescomplemented
40#6655C2212yescomplemented
41#6653C2212yescomplemented
42#6649C2212yescomplemented
43D5×C3⋊C8C2212yescomplemented
44#5822—51nomaximal, Hall
45D5×#41D311yescharacteristic, complemented
46C2×#713—31no—
47C5×#137—31no—
48#4095—31no—
49#4088—31no—
50#4065—32no—
51#4064—32no—
52#4062—32no—
53#4060—32no—
54#4054—31no—
55D5×M16—31no—
56C22×D15—21no—
57C22×C3×D5—21no—
58C22×C3×D5D411yescharacteristic
59C3×C5×Q8C2311yescharacteristic
60C3×C5×D4—21no—
61C3×C5×D4C2311yescharacteristic
62C2×C3×C4×C5—21no—
63C2×C3×C4×C5C2311yescharacteristic
64D60—21no—
65D60C2312yes—
66C2×C5×Dic3—21no—
67C5×Dic6—21no—
68C5×Dic6C2312yes—
69C3×C22⋊D5—21no—
70C3×C22⋊D5—21no—
71C3×C22⋊D5—21no—
72C2×C3×Dic5—21no—
73C2×C3×Dic5D411yescharacteristic
74C3×D20—21no—
75C3×D20C2311yescharacteristic
76C3×C4×D5—21no—
77C3×C4×D5—21no—
78C3×C4×D5—21no—
79C3×C4×D5D411yescharacteristic
80C3×C4×D5D411yescharacteristic
81C3×C4×D5C2311yescharacteristic
82C3×C4×D5C2311yescharacteristic
83C3×Dic10—21no—
84C3×Dic10C2311yescharacteristic
85#1202—22no—
86#1202—22no—
87#1200—22no—
88#1200—22no—
89C3⋊#168C2312yes—
90C5×C3⋊C8C2312yes—
91C2×C3×#41—51no—
92C2×#235—51no—
93#951—51no—
94#951D511yescharacteristic, complemented
95#950—52no—
96#950—52no—
97#949—51no—
98#949—51no—
99#942—52no—
100#932—52no—
101C2×#208—51no—
102C5×#41C2×D311yescharacteristic
103C2×C5×Q8—31no—
104#713—32no—
105#713—32no—
106#713—61no—
107#713—61no—
108#713C2×D311yescharacteristic, complemented
109Q8×D5C2×D311yescharacteristic, complemented
110#711—21no—
111#711C2×D311yescharacteristic, complemented
112D4×D5—21no—
113D4×D5C2×D311yescharacteristic, complemented
114#709—21no—
115#709C2×D311yescharacteristic
116C2×D20—31no—
117C2×D20—61no—
118C2×C4×D5—21no—
119C2×C4×D5—61no—
120C2×C4×D5C2×D311yescharacteristic
121C5×Q16—32no—
122C5×SD16—32no—
123C5×M16—31no—
124#689—32no—
125#688—32no—
126#688—32no—
127#686—32no—
128#681—31no—
129D40—32no—
130#677—32no—
131#676—32no—
132C8×D5—32no—
133#575—151noSylow
134C22×C3×C5—21no—
135C22×C3×C5C2×D411yescharacteristic
136C2×D15—22no—
137C2×D15—42no—
138C2×C3×D5—21no—
139C2×C3×D5—41no—
140C2×C3×D5—42no—
141C2×C3×D5C2×D411yescharacteristic
142C2×C3×D5C2×D411yescharacteristic
143C3×C4×C5—21no—
144C3×C4×C5C2×D411yescharacteristic
145C3×C4×C5C2411yescharacteristic
146C3×Dic5—21no—
147C3×Dic5C2×D411yescharacteristic
148C3×Dic5C2×D411yescharacteristic
149C5×Dic3—22no—
150C3×#41—51no—
151C3×#41—51no—
152C3×#41—51no—
153C3×#41—101no—
154C3×#41—101no—
155C3×#41C2×D511yescharacteristic
156C2×C3×Q8—51no—
157C2×C3×D4—51no—
158C2×C3×D4—101no—
159C22×C3×C4—51no—
160C22×C3×C4—101no—
161C2×#67—101no—
162#235—52no—
163#235—52no—
164#235—101no—
165#235—101no—
166C2×D12—51no—
167C2×C4×D3—101no—
168C2×Dic6C2×D511yescharacteristic, complemented
169#216—52no—
170#216C2×D512yescomplemented
171#215—52no—
172#215—52no—
173#214—52no—
174#214C2×D512yescomplemented
175#213—52no—
176#213—52no—
177#208—51no—
178#208—52no—
179#208C2×D511yescharacteristic, complemented
180C2×C3⋊C8—52no—
181C22×D5—21no—
182C22×D5—61no—
183C22×D5#6711yescharacteristic
184C5×Q8—32no—
185C5×Q8—61no—
186C5×Q8C22×D311yescharacteristic
187C5×D4—21no—
188C5×D4C22×D311yescharacteristic
189C2×C4×C5—21no—
190C2×C4×C5—61no—
191C2×C4×C5C22×D311yescharacteristic
192C22⋊D5—21no—
193C22⋊D5—21no—
194C22⋊D5—21no—
195C2×Dic5—21no—
196C2×Dic5#6711yescharacteristic
197D20—21no—
198D20—32no—
199D20—62no—
200D20—62no—
201D20—61no—
202D20C22×D311yescharacteristic
203C4×D5—21no—
204C4×D5—21no—
205C4×D5—21no—
206C4×D5—62no—
207C4×D5—62no—
208C4×D5#6711yescharacteristic
209C4×D5#6711yescharacteristic
210C4×D5C22×D311yescharacteristic
211C4×D5C22×D311yescharacteristic
212Dic10—21no—
213Dic10C22×D311yescharacteristic
214C5×C8—32no—
215#168—32no—
216C2×#41—51no—
217C2×#41—151no—
218#137—31no—
219#137—152no—
220#137—151no—
221AGL(1,ℤ/8)—151no—
222AGL(1,ℤ/8)—152no—
223AGL(1,ℤ/8)—151no—
224#135—152no—
225#135—152no—
226C2×M16—151no—
227C2×C3×C5—21no—
228C2×C3×C5—41no—
229C2×C3×C5C22×D411yescharacteristic
230D15—42no—
231C3×D5—21no—
232C3×D5—21no—
233C3×D5—41no—
234C23×C3—51no—
235C23×C3—101no—
236C22×D3—101no—
237C3×Q8—51no—
238C3×Q8—101no—
239C3×Q8C22×D511yescharacteristic
240C3×D4—21no—
241C3×D4—51no—
242C3×D4—101no—
243C3×D4—101no—
244C3×D4—101no—
245C3×D4—101no—
246C3×D4C22×D511yescharacteristic
247C2×C3×C4—21no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—51no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—101no—
257C2×C3×C4C22×D511yescharacteristic
258#67—102no—
259#67—102no—
260C2×Dic3—21no—
261D12—52no—
262D12—101no—
263C4×D3—102no—
264C4×D3—102no—
265Dic6—21no—
266Dic6C22×D512yes—
267C3⋊C8—52no—
268C3⋊C8C22×D512yes—
269C22×C5—21no—
270C22×C5C2×#6711yescharacteristic
271C2×D5—21no—
272C2×D5—41no—
273C2×D5—42no—
274C2×D5—62no—
275C2×D5—122no—
276C2×D5C2×#6711yescharacteristic
277C2×D5C2×#6711yescharacteristic
278C4×C5—21no—
279C4×C5—62no—
280C4×C5C2×#6711yescharacteristic
281C4×C5C23×D311yescharacteristic
282Dic5—21no—
283Dic5C2×#6711yescharacteristic
284Dic5C2×#6711yescharacteristic
285#41—51no—
286#41—51no—
287#41—51no—
288#41—101no—
289#41—101no—
290#41—152no—
291#41—152no—
292#41—301no—
293#41—301no—
294#41D3×D511yescharacteristic
295C2×Q8—31no—
296C2×Q8—51no—
297C2×D4—51no—
298C2×D4—101no—
299C2×D4—151no—
300C2×D4—301no—
301C22×C4—51no—
302C22×C4—101no—
303C22×C4—301no—
304Q16—32no—
305Q16—152no—
306SD16—32no—
307SD16—152no—
308SD16—152no—
309SD16—152no—
310D8—152no—
311D8—152no—
312M16—31no—
313M16—152no—
314M16—151no—
315C2×C8—152no—
316C3×C5#57511yescharacteristic, complemented, Hall
317C22×C3—21no—
318C22×C3—51no—
319C22×C3—51no—
320C22×C3—101no—
321C22×C3—201no—
322C22×C3—202no—
323C22×C3D4×D511yescharacteristic
324C2×D3—102no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—51no—
328C3×C4—51no—
329C3×C4—101no—
330C3×C4D4×D511yescharacteristic
331C3×C4C23×D511yescharacteristic
332Dic3—22no—
333C2×C5—21no—
334C2×C5—41no—
335C2×C5C22×#6711yescharacteristic
336D5—21no—
337D5—21no—
338D5—41no—
339D5—122no—
340C23—51no—
341C23—101no—
342C23—301no—
343Q8—32no—
344Q8—51no—
345Q8—61no—
346Q8—101no—
347Q8C2×D3×D511yescharacteristic
348D4—21no—
349D4—51no—
350D4—101no—
351D4—101no—
352D4—101no—
353D4—101no—
354D4—152no—
355D4—302no—
356D4—302no—
357D4—301no—
358D4C2×D3×D511yescharacteristic
359C2×C4—21no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—51no—
364C2×C4—51no—
365C2×C4—61no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—302no—
371C2×C4—302no—
372C2×C4C2×D3×D511yescharacteristic
373C8—32no—
374C8—152no—
375C2×C3—21no—
376C2×C3—41no—
377C2×C3—101no—
378C2×C3—101no—
379C2×C3—201no—
380C2×C3C2×D4×D511yescharacteristic
381D3—202no—
382C5#582211yescharacteristic, complemented, Sylow
383C22—21no—
384C22—51no—
385C22—51no—
386C22—101no—
387C22—201no—
388C22—202no—
389C22—302no—
390C22—602no—
391C22D5×#6711yescharacteristic
392C4—21no—
393C4—51no—
394C4—51no—
395C4—62no—
396C4—101no—
397C4D5×#6711yescharacteristic
398C4C22×D3×D511yescharacteristic
399C3#6611111yescharacteristic, complemented, Sylow
400C2—21no—
401C2—41no—
402C2—101no—
403C2—101no—
404C2—201no—
405C2—602no—
406C2C2×D5×#6711yescharacteristic
subgroupG/H
centerC2C2×D5×#67
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC3×C5×#41C22
socleC2×C3×C5C22×D4
hypercenter#41D3×D5
hypocenterC3×C5#575
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. C3×D5×#41C2semidirect
2. C2×#6773C2semidirect
3. #91838C2semidirect
4. C5×#951C2semidirect
5. #91516C2semidirect
6. #91515C2semidirect
7. #91492C2semidirect
8. #91491C2semidirect
9. #91307C2semidirect
10. #91301C2semidirect
11. D5×#208C2semidirect
14. C2×D60C22semidirect
15. C2×C5×Dic6C22semidirect
16. C3×#713C22semidirect
17. C3×Q8×D5C22semidirect
19. C3×#711C22semidirect
21. C3×D4×D5C22semidirect
31. #6773C22semidirect
32. #6717C22semidirect
33. #6715C22semidirect
34. #6710C22semidirect
35. C5×#216C22semidirect
36. C5×#214C22semidirect
37. C5×#208C22semidirect
38. #6661C22semidirect
39. #6658C22semidirect
40. #6655C22semidirect
41. #6653C22semidirect
42. #6649C22semidirect
43. D5×C3⋊C8C22semidirect
45. D5×#41D3semidirect
94. #951D5semidirect
108. #713C2×D3semidirect
109. Q8×D5C2×D3semidirect
111. #711C2×D3semidirect
113. D4×D5C2×D3semidirect
168. C2×Dic6C2×D5semidirect
170. #216C2×D5semidirect
174. #214C2×D5semidirect
179. #208C2×D5semidirect
316. C3×C5#575semidirect
382. C5#5822semidirect
399. C3#66111semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#412
C2×#67732
#918382
C5×#9512
#915162
#915152
#914922
#914912
#913072
#913012
D5×#2082
#661113
#58225