Finite Group Databasebeta

← #11753853

Subgroups — #11753853

Order 960.

660 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D5C211yesmaximal, characteristic, complemented
2C2×#6766C211yesmaximal, characteristic, complemented
3#91782C211yesmaximal, characteristic, complemented
4C5×#896C211yesmaximal, characteristic, complemented
5C3×#4040C211yesmaximal, characteristic, complemented
6#91476C211yesmaximal, characteristic, complemented
7#91474C211yesmaximal, characteristic, complemented
8#91459C211yesmaximal, characteristic, complemented
9#91454C211yesmaximal, characteristic, complemented
10#91442C211yesmaximal, characteristic, complemented
11#91424C211yesmaximal, characteristic, complemented
12#91406C211yesmaximal, characteristic, complemented
13#91396C211yesmaximal, characteristic, complemented
14#91394C211yesmaximal, characteristic, complemented
15#91348C211yesmaximal, characteristic, complemented
16#65961—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×D60C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic, complemented
21C2×C4×C5×D3C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic, complemented
23C2×C3×D20C2211yescharacteristic
24C2×C3×C4×D5C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic, complemented
29C2×#1201C2211yescharacteristic
30C2×#1200C2211yescharacteristic
31C2×D3×Dic5C2211yescharacteristic
32C2×D5×Dic3C2211yescharacteristic
33C2×D5×Dic3C2211yescharacteristic, complemented
34C4×D3×D5—24no—
35#6766—24no—
36C3×C5×C4⋊C4C2211yescharacteristic, complemented
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic, complemented
39C4×Dic15C2211yescharacteristic, complemented
40C5×(C2×D3)⋊C4C2211yescharacteristic
41C5×(C2×D3)⋊C4C2211yescharacteristic
42C5×Dic3⋊C4C2211yescharacteristic, complemented
43C5×Dic3⋊C4C2211yescharacteristic, complemented
44C3×#685C2211yescharacteristic
45C3×#685C2211yescharacteristic, complemented
46C3×#685C2211yescharacteristic, complemented
47C3×#683C2211yescharacteristic, complemented
48Dic3⋊Dic5C2211yescharacteristic, complemented
49#6669C2211yescharacteristic, complemented
50#6667C2211yescharacteristic
51#6667C2211yescharacteristic, complemented
52#6665C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic, complemented
54#5656—51nomaximal, Hall
55C2×#713—31no—
56C22×C4×D5—31no—
57C5×C22⋊Q8—31no—
58#4092—31no—
59#4076—31no—
60#4041—31no—
61#4040—31no—
62#4040D311yescharacteristic, complemented
63#4039—31no—
64#4039—31no—
65#4038—31no—
66#4028—31no—
67#4028—31no—
68#4027—31no—
69#4027—31no—
70C22×D15C2311yescharacteristic
71C22×D15C2311yescharacteristic
72C22×C5×D3C2311yescharacteristic
73C22×C3×D5C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C2×D3×D5—22no—
76C2×D3×D5—22no—
77C2×D3×D5—22no—
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83D60—22no—
84C4×D15—22no—
85C4×D15—22no—
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C2×C5×Dic3C2311yescharacteristic
89C4×C5×D3—22no—
90C5×Dic6—22no—
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93C3×D20—22no—
94C3×C4×D5—22no—
95#1203—22no—
96#1202—22no—
97#1202—22no—
98#1202—22no—
99#1201—22no—
100#1200—22no—
101D3×Dic5—22no—
102D5×Dic3—22no—
103D5×Dic3D414yescomplemented
104C2×#237—51no—
105C22×C4×D3—51no—
106C3×#123—51no—
107#937—51no—
108#929—51no—
109#896—51no—
110#896D511yescharacteristic, complemented
111#893—51no—
112#893—51no—
113#884—51no—
114#884—51no—
115#882—51no—
116#67⋊C4—51no—
117#67⋊C4—51no—
118#877—51no—
119C23×D5—31no—
120C2×C5×Q8—31no—
121C22×C4×C5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C22×Dic5—31no—
125#713—64no—
126C2×D20—31no—
127C2×D20—31no—
128C2×D20—31no—
129C2×D20—31no—
130C2×D20C2×D311yescharacteristic
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—64no—
137C2×C4×D5C2×D311yescharacteristic
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4C2×D311yescharacteristic, complemented
141C5×C22⋊C4—31no—
142C5×C22⋊C4—31no—
143#685—31no—
144#685—31no—
145#685—31no—
146#685—31no—
147#685—31no—
148#685C2×D311yescharacteristic
149#685C2×D311yescharacteristic, complemented
150#685C2×D311yescharacteristic, complemented
151C4⋊Dic5—31no—
152#683—31no—
153#683C2×D311yescharacteristic, complemented
154C4×Dic5—31no—
155C4×Dic5—31no—
156#525—151noSylow
157C22×C3×C5C2411yescharacteristic
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C2×D15#4112yescomplemented
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166C2×C5×D3#4112yescomplemented
167C2×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5C2×D412yes—
173D3×D5—28no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177Dic15—21no—
178Dic15C2×D412yes—
179C3×Dic5—21no—
180C3×Dic5—21no—
181C5×Dic3—21no—
182C5×Dic3—21no—
183C5×Dic3C2×D412yes—
184C23×D3—51no—
185C2×C3×D4—51no—
186C22×C3×C4—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C22×Dic3—51no—
192C22×Dic3—51no—
193#237—104no—
194C2×D12—51no—
195C2×D12—51no—
196C2×C4×D3—51no—
197C2×C4×D3—51no—
198C2×C4×D3—51no—
199C2×C4×D3—51no—
200C2×C4×D3—104no—
201C2×C4×D3C2×D511yescharacteristic
202C2×Dic6C2×D511yescharacteristic, complemented
203C3×C4⋊C4—51no—
204C3×C4⋊C4C2×D511yescharacteristic, complemented
205C3×C22⋊C4—51no—
206C3×C22⋊C4—51no—
207C3×C22⋊C4—51no—
208#217—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4—51no—
213(C2×D3)⋊C4C2×D511yescharacteristic
214(C2×D3)⋊C4C2×D511yescharacteristic
215Dic3⋊C4—51no—
216Dic3⋊C4—51no—
217Dic3⋊C4C2×D511yescharacteristic, complemented
218Dic3⋊C4C2×D511yescharacteristic, complemented
219C4×Dic3—51no—
220C4×Dic3—51no—
221C23×C5—31no—
222C22×D5—31no—
223C22×D5—31no—
224C22×D5—62no—
225C22×D5—62no—
226C22×D5—62no—
227C22×D5C22×D311yescharacteristic
228C22×D5C22×D311yescharacteristic
229C5×Q8—62no—
230C2×C4×C5—31no—
231C2×C4×C5—31no—
232C2×C4×C5—31no—
233C2×C4×C5—62no—
234C2×C4×C5C22×D311yescharacteristic
235C2×C4×C5C22×D311yescharacteristic
236C2×C4×C5C22×D311yescharacteristic
237C22⋊D5—62no—
238C22⋊D5—62no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—62no—
242C2×Dic5C22×D311yescharacteristic
243C2×Dic5C22×D311yescharacteristic
244D20—22no—
245D20—62no—
246D20—62no—
247D20—62no—
248D20—62no—
249C4×D5—22no—
250C4×D5—34no—
251C4×D5—62no—
252C4×D5—62no—
253C4×D5—62no—
254C4×D5—62no—
255C2×#41—151no—
256C23×C4—151no—
257#123—51no—
258#123—151no—
259C22⋊Q8—31no—
260C22⋊Q8—151no—
261#121—151no—
262#121—151no—
263#120—151no—
264#120—151no—
265C4×D4—151no—
266C4×D4—151no—
267C4×D4—151no—
268C4×D4—151no—
269#117—151no—
270C2×C3×C5C22×D411yescharacteristic
271C2×C3×C5C2×#4111yescharacteristic
272C2×C3×C5C2×#4111yescharacteristic
273D15—22no—
274D15—41no—
275C3×D5—22no—
276C3×D5—41no—
277C5×D3—22no—
278C23×C3—51no—
279C23×C3—51no—
280C22×D3—51no—
281C22×D3—51no—
282C22×D3—102no—
283C22×D3—102no—
284C22×D3—102no—
285C22×D3C22×D511yescharacteristic
286C3×D4—102no—
287C2×C3×C4—51no—
288C2×C3×C4—51no—
289C2×C3×C4—102no—
290C2×C3×C4C22×D511yescharacteristic
291C2×C3×C4C22×D511yescharacteristic
292C2×C3×C4C22×D511yescharacteristic
293#67—102no—
294#67—102no—
295#67—102no—
296#67—102no—
297C2×Dic3—51no—
298C2×Dic3—54no—
299C2×Dic3—51no—
300C2×Dic3—102no—
301C2×Dic3C22×D511yescharacteristic
302C2×Dic3C22×D511yescharacteristic
303C2×Dic3C22×D511yescharacteristic
304D12—102no—
305D12—102no—
306C4×D3—22no—
307C4×D3—102no—
308C4×D3—102no—
309C4×D3—102no—
310C4×D3—102no—
311Dic6—22no—
312C22×C5—32no—
313C22×C5—61no—
314C22×C5—61no—
315C22×C5C23×D311yescharacteristic
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—32no—
322C2×D5—68no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C2×D5—61no—
328C2×D5D3×D412yes—
329C4×C5—21no—
330C4×C5—21no—
331C4×C5—21no—
332C4×C5—32no—
333C4×C5—61no—
334C4×C5—61no—
335Dic5—21no—
336Dic5—21no—
337Dic5—32no—
338Dic5—61no—
339C24—151no—
340#41—304no—
341C2×Q8—31no—
342C2×D4—51no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C2×D4—151no—
349C22×C4—31no—
350C22×C4—51no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—151no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—304no—
358C4⋊C4—31no—
359C4⋊C4—31no—
360C4⋊C4—51no—
361C4⋊C4—151no—
362C4⋊C4—151no—
363C4⋊C4D3×D511yescharacteristic, complemented
364C22⋊C4—31no—
365C22⋊C4—31no—
366C22⋊C4—51no—
367C22⋊C4—51no—
368C22⋊C4—51no—
369C22⋊C4—151no—
370C22⋊C4—151no—
371C22⋊C4—151no—
372C22⋊C4—151no—
373C22⋊C4—151no—
374C42—151no—
375C42—151no—
376C3×C5#52511yescharacteristic, complemented, Hall
377C22×C3—52no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3—101no—
381C22×C3—101no—
382C22×C3—101no—
383C22×C3C23×D511yescharacteristic
384C2×D3—21no—
385C2×D3—21no—
386C2×D3—52no—
387C2×D3—108no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—101no—
391C2×D3—101no—
392C2×D3—101no—
393C2×D3#71312yescomplemented
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—101no—
398C3×C4—101no—
399Dic3—21no—
400Dic3—21no—
401Dic3—52no—
402Dic3—101no—
403Dic3D4×D512yes—
404C2×C5—62no—
405C2×C5C2×D3×D411yescharacteristic
406C2×C5D3×#4111yescharacteristic
407C2×C5D3×#4111yescharacteristic
408D5—22no—
409D5—41no—
410D5—62no—
411D5—121no—
412C23—31no—
413C23—51no—
414C23—51no—
415C23—151no—
416C23—151no—
417C23—302no—
418C23—302no—
419C23—302no—
420Q8—62no—
421D4—102no—
422D4—302no—
423D4—302no—
424D4—302no—
425D4—302no—
426D4—302no—
427D4—302no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—62no—
434C2×C4—102no—
435C2×C4—154no—
436C2×C4—151no—
437C2×C4—151no—
438C2×C4—302no—
439C2×C4—302no—
440C2×C4—302no—
441C2×C4—302no—
442C2×C4—302no—
443C2×C4C2×D3×D511yescharacteristic
444C2×C4C2×D3×D511yescharacteristic
445C2×C4C2×D3×D511yescharacteristic
446C2×C3—102no—
447C2×C3—201no—
448C2×C3C2×D4×D511yescharacteristic
449C2×C3C2×#71311yescharacteristic
450C2×C3D5×#4111yescharacteristic
451D3—22no—
452D3—102no—
453D3—201no—
454C5#565611yescharacteristic, complemented, Sylow
455C22—32no—
456C22—52no—
457C22—61no—
458C22—61no—
459C22—101no—
460C22—101no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—152no—
465C22—308no—
466C22—301no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22—301no—
471C22C22×D3×D511yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—32no—
476C4—61no—
477C4—61no—
478C4—101no—
479C4—101no—
480C4—152no—
481C4—301no—
482C3#6596111yescharacteristic, complemented, Sylow
483C2—62no—
484C2—102no—
485C2—201no—
486C2—302no—
487C2—601no—
488C2#9201611yescharacteristic
489C2D3×D4×D511yescharacteristic
490C2D3×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×D5C2semidirect
2. C2×#6766C2semidirect
3. #91782C2semidirect
4. C5×#896C2semidirect
5. C3×#4040C2semidirect
6. #91476C2semidirect
7. #91474C2semidirect
8. #91459C2semidirect
9. #91454C2semidirect
10. #91442C2semidirect
11. #91424C2semidirect
12. #91406C2semidirect
13. #91396C2semidirect
14. #91394C2semidirect
15. #91348C2semidirect
20. C2×C4×D15C22semidirect
22. C2×C5×Dic6C22semidirect
28. C2×#1202C22semidirect
33. C2×D5×Dic3C22semidirect
36. C3×C5×C4⋊C4C22semidirect
38. #6714C22semidirect
39. C4×Dic15C22semidirect
42. C5×Dic3⋊C4C22semidirect
43. C5×Dic3⋊C4C22semidirect
45. C3×#685C22semidirect
46. C3×#685C22semidirect
47. C3×#683C22semidirect
48. Dic3⋊Dic5C22semidirect
49. #6669C22semidirect
51. #6667C22semidirect
53. Dic3×Dic5C22semidirect
62. #4040D3semidirect
103. D5×Dic3D4semidirect
110. #896D5semidirect
140. C5×C4⋊C4C2×D3semidirect
149. #685C2×D3semidirect
150. #685C2×D3semidirect
153. #683C2×D3semidirect
163. C2×D15#41semidirect
166. C2×C5×D3#41semidirect
202. C2×Dic6C2×D5semidirect
204. C3×C4⋊C4C2×D5semidirect
217. Dic3⋊C4C2×D5semidirect
218. Dic3⋊C4C2×D5semidirect
363. C4⋊C4D3×D5semidirect
376. C3×C5#525semidirect
393. C2×D3#713semidirect
454. C5#5656semidirect
482. C3#65961semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×D52
C2×#67662
#917822
C5×#8962
C3×#40402
#914762
#914742
#914592
#914542
#914422
#914242
#914062
#913962
#913942
#913482
#659613
#56565