Finite Group Databasebeta

← #14483221

Subgroups — #14483221

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C212yesmaximal, complemented
2C4×#6821C211yesmaximal, characteristic, complemented
3C5×#5577C211yesmaximal, characteristic, complemented
4C3×Q8×D20C211yesmaximal, characteristic, complemented
5#11755244C212yesmaximal, complemented
6#11753887C216yesmaximal, complemented
7#11753886C216yesmaximal, complemented
8#11752737C213yesmaximal, complemented
9C4×#6777C213yesmaximal, complemented
10#11752561C213yesmaximal, complemented
11#11752559C213yesmaximal, complemented
12#10618667—31nomaximal, Hall
13C2×#6821C2211yescharacteristic
14C2×C5×#239C2212yescomplemented
15C2×C3×Q8×D5C2212yescomplemented
16D5×#239—216no—
17C2×#6777C2213yes—
18C2×D5×D12C2216yescomplemented
19C2×C4×D3×D5C2216yescomplemented
20C2×#6769C2216yescomplemented
21C2×#6768C2216yescomplemented
22C3×C4×C5×Q8C2211yescharacteristic, complemented
23Q8×Dic15C2211yescharacteristic, complemented
24#91782C2213yescomplemented
25#91781C2213yescomplemented
26C4×D60C2213yescomplemented
27C42×D15C2213yescomplemented
28C5×#895C2216yescomplemented
29C5×#874C2213yescomplemented
30C4×C5×D12C2213yescomplemented
31C3×#4043C2216yescomplemented
32C3×C4×D20C2213yes—
33C3×#4015C2213yescomplemented
34#91475C22112yescomplemented
35#91473C2216yescomplemented
36#91466C2216yescomplemented
37#91466C2216yescomplemented
38#91449C2216yescomplemented
39#91442C2216yescomplemented
40C4×#1201C2216yescomplemented
41#91438C22112yescomplemented
42#91437C2213yescomplemented
43#91435C2213yescomplemented
44#91435C2216yescomplemented
45#91434C2211yescharacteristic
46#91370C2216yescomplemented
47#91369C2216yescomplemented
48D4×#239—51nomaximal, Hall
49C2×D5×#41—32no—
50C5×#550—31no—
51#66165—32no—
52#66051—33no—
53#66050—33no—
54#65946—36no—
55#65940—36no—
56Q8×D20D311yescharacteristic, complemented
57C4×#713—31no—
58#65885—33no—
59C4×D4×D5—33no—
60C22×D3×D5C2316yes—
61C2×C3×C5×Q8C2311yescharacteristic
62#6821D418yescomplemented
63C2×D60C2313yes—
64C2×C4×D15C2313yes—
65C2×C4×D15C2313yes—
66C2×C4×D15C2313yes—
67C5×#239—28no—
68C2×C5×D12C2313yes—
69C2×C5×D12C2316yes—
70C2×C5×D12C2316yes—
71C2×C4×C5×D3C2316yes—
72C3×Q8×D5—28no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5C2316yes—
75C2×C3×Dic10C2316yes—
76C2×#1203C23112yes—
77C2×#1201C2316yes—
78C2×#1200C2316yes—
79C2×D3×Dic5C2316yes—
80C2×D5×Dic3C2312yes—
81#6777—212no—
82D5×D12—224no—
83C4×D3×D5—224no—
84#6769—224no—
85#6768—224no—
86C3×C5×C4⋊C4C2313yes—
87C3×C42×C5C2313yes—
88#6714C2316yes—
89C4⋊Dic15C2313yes—
90C4×Dic15C2311yescharacteristic
91C4×Dic15C2313yes—
92C4×Dic15C2313yes—
93C5×(C2×D3)⋊C4C2316yes—
94C5×C4⋊Dic3C2311yescharacteristic
95C3×#685C2316yes—
96C3×C4⋊Dic5C2313yes—
97C3×C4⋊Dic5C2316yes—
98#6669C2316yes—
99(C2×D3)⋊Dic5C23112yes—
100(C2×D3)⋊Dic5C2316yes—
101#6665C2312yes—
102C22×#239—52no—
103C3×D4×Q8—51no—
104#5817—52no—
105#5726—53no—
106#5725—53no—
107#5630—56no—
108#5627—56no—
109#5577D511yescharacteristic, complemented
110C4×#239—51no—
111D4×D12—53no—
112C4×D3×D4—53no—
113C2×C5×#41—32no—
114D5×#41—616no—
115C2×#713—31no—
116C2×Q8×D5C2×D312yescomplemented
117C2×#711—36no—
118C2×D4×D5—33no—
119C2×D4×D5—36no—
120C2×#709—36no—
121C22×C4×D5—36no—
122C5×#127—33no—
123C5×#121—36no—
124C4×C5×Q8C2×D311yescharacteristic, complemented
125C4×C5×D4—33no—
126Q8×Dic5—31no—
127#4084—36no—
128#4084—36no—
129#4084—36no—
130#4083—312no—
131#4082—36no—
132D4×Dic5—33no—
133D4×Dic5—36no—
134C4×C22⋊D5—36no—
135#4070—36no—
136#4043C2×D316yescomplemented
137#4039—31no—
138#4039—33no—
139#4038—33no—
140D5×C4⋊C4—33no—
141#4029—312no—
142#4027—36no—
143D5×C22⋊C4—36no—
144C4×D20—33no—
145C4×D20C2×D313yes—
146C42×D5—33no—
147#4015C2×D313yescomplemented
148D4×#41—151noSylow
149C22×D15C2413yes—
150C22×C5×D3C2416yes—
151C22×C3×D5C2412yes—
152C2×D3×D5—212no—
153C2×D3×D5—212no—
154C2×D3×D5—46no—
155C3×C5×Q8C2×D414yescomplemented
156C2×C3×C4×C5C2413yes—
157C2×C3×C4×C5C2413yes—
158C2×C3×C4×C5C2411yescharacteristic
159C2×Dic15C2411yescharacteristic
160C2×Dic15C2413yes—
161C2×Dic15C2411yescharacteristic
162D60C2×D4112yescomplemented
163C4×D15—26no—
164C4×D15—43no—
165C4×D15C2×D4112yescomplemented
166C2×C5×Dic3C2412yes—
167C5×D12—212no—
168C5×D12—26no—
169C5×D12—46no—
170C4×C5×D3—212no—
171C2×C3×Dic5C2416yes—
172C3×D20#4114yescomplemented
173C3×C4×D5—212no—
174C3×Dic10—212no—
175#1203—224no—
176#1201—212no—
177#1200—212no—
178D3×Dic5—212no—
179D5×Dic3—24no—
180C22×C3×Q8—52no—
181C2×#239—51no—
182C2×#239—56no—
183C2×#239—56no—
184C2×#239—1016no—
185C2×#239C2×D512yescomplemented
186C2×D3×D4—53no—
187C22×D12—56no—
188C22×C4×D3—56no—
189C3×C4⋊Q8—53no—
190C3×C22⋊Q8—56no—
191C3×C4×Q8C2×D511yescharacteristic, complemented
192C3×C4×D4—53no—
193#947—56no—
194#946—56no—
195Q8×Dic3—51no—
196D4×Dic3—51no—
197#930—56no—
198C4×#67—56no—
199#895—56no—
200#895—56no—
201#895C2×D516yescomplemented
202#894—512no—
203#893—53no—
204#893—56no—
205#893—53no—
206#892—53no—
207D3×C4⋊C4—53no—
208#882—512no—
209#67⋊C4—56no—
210D3×C22⋊C4—56no—
211#874C2×D513yescomplemented
212C4×D12—53no—
213C4×D12C2×D513yescomplemented
214C42×D3—53no—
215C23×D5—36no—
216C5×#41—68no—
217C2×C5×Q8C22×D311yescharacteristic
218C2×C5×D4—33no—
219C2×C5×D4—36no—
220C2×C5×D4—36no—
221C22×C4×C5—36no—
222C2×C22⋊D5—36no—
223C2×C22⋊D5—312no—
224C22×Dic5—36no—
225#713—38no—
226Q8×D5—28no—
227#711—624no—
228D4×D5—624no—
229D4×D5—612no—
230#709—624no—
231C2×D20—33no—
232C2×D20C22×D311yescharacteristic
233C2×C4×D5—33no—
234C2×C4×D5—32no—
235C2×C4×D5—33no—
236C2×C4×D5—36no—
237C2×C4×D5—33no—
238C2×C4×D5—624no—
239C2×C4×D5C22×D316yes—
240C2×Dic10C22×D316yes—
241C5×C4⋊C4—31no—
242C5×C4⋊C4C22×D313yes—
243C5×C22⋊C4—36no—
244C42×C5C22×D313yes—
245C22⋊Dic5—36no—
246C22⋊Dic5—312no—
247#685—32no—
248#685—36no—
249#685C22×D316yes—
250C4⋊Dic5—33no—
251C4⋊Dic5C22×D313yes—
252C4⋊Dic5C22×D316yes—
253#683—36no—
254C4×Dic5—31no—
255C4×Dic5—33no—
256C4×Dic5—33no—
257C22×#41—152no—
258#550—31no—
259D4×Q8—51no—
260#548—152no—
261#547—153no—
262#546—156no—
263D42—153no—
264#532—153no—
265#525—156no—
266C4×#41—151no—
267C2×C4×D4—153no—
268C22×C3×C5C2511yescharacteristic
269C2×D15—23no—
270C2×D15—23no—
271C2×D15C22×D416yes—
272C2×C5×D3—26no—
273C2×C5×D3—26no—
274C2×C5×D3—26no—
275C2×C3×D5—22no—
276C2×C3×D5—22no—
277C2×C3×D5C2×#4114yescomplemented
278D3×D5—424no—
279C3×C4×C5—23no—
280C3×C4×C5C22×D416yes—
281C3×C4×C5C2×#4112yescomplemented
282Dic15—23no—
283Dic15—21no—
284Dic15C22×D412yes—
285C3×Dic5—26no—
286C5×Dic3—22no—
287C23×D3—56no—
288C2×C3×Q8—56no—
289C2×C3×Q8—108no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—51no—
292C22×C3×C4—56no—
293C2×#67—56no—
294C22×Dic3—52no—
295#239—28no—
296#239—58no—
297#239—1024no—
298#239—1024no—
299D3×D4—1012no—
300C2×D12—53no—
301C2×D12—512no—
302C2×D12—1024no—
303C2×D12C22×D513yes—
304C2×D12C22×D516yes—
305C2×D12C22×D516yes—
306C2×C4×D3—53no—
307C2×C4×D3—56no—
308C2×C4×D3—53no—
309C2×C4×D3—56no—
310C2×C4×D3—53no—
311C2×C4×D3—1024no—
312C2×C4×D3C22×D516yes—
313C3×C4⋊C4—53no—
314C3×C4⋊C4—56no—
315C3×C4⋊C4C22×D513yes—
316C3×C22⋊C4—56no—
317C3×C42C22×D513yes—
318#217—52no—
319(C2×D3)⋊C4—56no—
320(C2×D3)⋊C4—512no—
321(C2×D3)⋊C4—56no—
322(C2×D3)⋊C4C22×D516yes—
323C4⋊Dic3—53no—
324C4⋊Dic3C22×D511yescharacteristic
325Dic3⋊C4—56no—
326C4×Dic3—51no—
327C4×Dic3—53no—
328C4×Dic3—53no—
329C23×C5—36no—
330C22×D5—33no—
331C22×D5—612no—
332C22×D5—612no—
333C22×D5—126no—
334C22×D5C23×D312yes—
335C5×Q8D3×D414yescomplemented
336C5×D4—612no—
337C5×D4—66no—
338C5×D4—126no—
339C2×C4×C5—32no—
340C2×C4×C5—612no—
341C2×C4×C5C23×D313yes—
342C2×C4×C5C23×D313yes—
343C2×C4×C5C23×D311yescharacteristic
344C22⋊D5—624no—
345C22⋊D5—612no—
346C2×Dic5—31no—
347C2×Dic5—31no—
348C2×Dic5—33no—
349C2×Dic5—612no—
350C2×Dic5C23×D316yes—
351D20—312no—
352D20#23914yescomplemented
353C4×D5—212no—
354C4×D5—312no—
355C4×D5—612no—
356C4×D5—64no—
357C4×D5—66no—
358C4×D5—123no—
359Dic10—212no—
360C2×#41—32no—
361C2×#41—156no—
362C2×#41—156no—
363C2×#41—151no—
364C2×#41—3016no—
365C22×Q8—52no—
366C22×D4—156no—
367C22×D4—153no—
368C23×C4—156no—
369C4⋊Q8—53no—
370#127—33no—
371#124—156no—
372#123—1512no—
373C22⋊Q8—56no—
374C22⋊Q8—156no—
375#121—36no—
376#121—156no—
377#121—156no—
378#121—156no—
379#120—1512no—
380C4×Q8—151no—
381C4×Q8D3×D511yescharacteristic, complemented
382C4×D4—33no—
383C4×D4—53no—
384C4×D4—156no—
385C4×D4—151no—
386C4×D4—153no—
387C4×D4—156no—
388C4×D4—156no—
389C4×D4—153no—
390C4×D4—153no—
391#117—153no—
392C2×C4⋊C4—153no—
393C2×C22⋊C4—156no—
394C2×C42—153no—
395C2×C3×C5C23×D411yescharacteristic
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5#58511yescharacteristic
398D15—26no—
399C3×D5—24no—
400C5×D3—46no—
401C23×C3—52no—
402C22×D3—53no—
403C22×D3—1012no—
404C22×D3—1012no—
405C22×D3—206no—
406C22×D3C23×D516yes—
407C3×Q8—1012no—
408C3×Q8D4×D514yescomplemented
409C3×D4—54no—
410C2×C3×C4—56no—
411C2×C3×C4—1012no—
412C2×C3×C4C23×D513yes—
413C2×C3×C4C23×D513yes—
414C2×C3×C4C23×D511yescharacteristic
415#67—1012no—
416C2×Dic3—51no—
417C2×Dic3—51no—
418C2×Dic3—53no—
419C2×Dic3—104no—
420C2×Dic3C23×D512yes—
421D12—212no—
422D12—26no—
423D12—46no—
424D12—512no—
425D12—1024no—
426C4×D3—212no—
427C4×D3—512no—
428C4×D3—1012no—
429C4×D3—1012no—
430C4×D3—106no—
431C4×D3—203no—
432C22×C5—66no—
433C22×C5—66no—
434C22×C5—66no—
435C22×C5C24×D311yescharacteristic
436C2×D5—22no—
437C2×D5—22no—
438C2×D5—36no—
439C2×D5—63no—
440C2×D5—63no—
441C2×D5—1224no—
442C2×D5C2×#23914yescomplemented
443C4×C5—23no—
444C4×C5—62no—
445C4×C5C2×D3×D416yes—
446C4×C5C2×#23912yescomplemented
447Dic5—26no—
448Dic5—32no—
449Dic5—63no—
450Dic5—61no—
451C24—156no—
452#41—68no—
453#41—158no—
454#41—3024no—
455#41—3024no—
456C2×Q8—56no—
457C2×Q8—108no—
458C2×Q8C2×D3×D511yescharacteristic
459C2×D4—33no—
460C2×D4—36no—
461C2×D4—36no—
462C2×D4—51no—
463C2×D4—1512no—
464C2×D4—156no—
465C2×D4—153no—
466C2×D4—3024no—
467C2×D4—3012no—
468C22×C4—36no—
469C22×C4—56no—
470C22×C4—156no—
471C22×C4—152no—
472C22×C4—156no—
473C22×C4—153no—
474C22×C4—153no—
475C22×C4—153no—
476C22×C4—3024no—
477C4⋊C4—31no—
478C4⋊C4—53no—
479C4⋊C4—56no—
480C4⋊C4—156no—
481C4⋊C4—153no—
482C4⋊C4C2×D3×D513yes—
483C22⋊C4—36no—
484C22⋊C4—56no—
485C22⋊C4—152no—
486C22⋊C4—156no—
487C22⋊C4—1512no—
488C22⋊C4—156no—
489C42—151no—
490C42—153no—
491C42—153no—
492C42C2×D3×D513yes—
493C3×C5D4×#4111yescharacteristic, complemented, Hall
494C22×C3—54no—
495C22×C3—102no—
496C22×C3—102no—
497C22×C3C24×D511yescharacteristic
498C2×D3—26no—
499C2×D3—26no—
500C2×D3—26no—
501C2×D3—56no—
502C2×D3—103no—
503C2×D3—103no—
504C2×D3—2024no—
505C3×C4—23no—
506C3×C4—106no—
507C3×C4C2×D4×D516yes—
508C3×C4D5×#4112yescomplemented
509Dic3—22no—
510Dic3—52no—
511Dic3—103no—
512Dic3—101no—
513C2×C5—126no—
514C2×C5C22×D3×D411yescharacteristic
515C2×C5C22×#23911yescharacteristic
516C2×C5#596811yescharacteristic
517D5—24no—
518D5—66no—
519C23—36no—
520C23—52no—
521C23—153no—
522C23—3012no—
523C23—3012no—
524C23—606no—
525Q8—1012no—
526Q8#677714yescomplemented
527D4—54no—
528D4—612no—
529D4—66no—
530D4—126no—
531D4—1512no—
532D4—3024no—
533D4—3012no—
534C2×C4—32no—
535C2×C4—56no—
536C2×C4—612no—
537C2×C4—1012no—
538C2×C4—151no—
539C2×C4—1512no—
540C2×C4—151no—
541C2×C4—153no—
542C2×C4—3012no—
543C2×C4—304no—
544C2×C4—3012no—
545C2×C4—306no—
546C2×C4—603no—
547C2×C4C22×D3×D513yes—
548C2×C4C22×D3×D513yes—
549C2×C4C22×D3×D511yescharacteristic
550C2×C3—104no—
551C2×C3C22×D4×D511yescharacteristic
552C2×C3C2×D5×#4111yescharacteristic
553C2×C3#6628511yescharacteristic
554D3—46no—
555D3—106no—
556C5D4×#23911yescharacteristic, complemented, Sylow
557C22—54no—
558C22—66no—
559C22—66no—
560C22—66no—
561C22—102no—
562C22—102no—
563C22—156no—
564C22—303no—
565C22—303no—
566C22—6024no—
567C22C23×D3×D511yescharacteristic
568C4—23no—
569C4—62no—
570C4—106no—
571C4—152no—
572C4—301no—
573C4—303no—
574C4C2×#677716yes—
575C4D5×#23912yescomplemented
576C3#1061866711yescharacteristic, complemented, Sylow
577C2—104no—
578C2—126no—
579C2—306no—
580C2C22×#677711yescharacteristic
581C2C2×D5×#23911yescharacteristic
582C2#1175706411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5D4×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D5×#239C2semidirect
2. C4×#6821C2semidirect
3. C5×#5577C2semidirect
4. C3×Q8×D20C2semidirect
5. #11755244C2semidirect
6. #11753887C2semidirect
7. #11753886C2semidirect
8. #11752737C2semidirect
9. C4×#6777C2semidirect
10. #11752561C2semidirect
11. #11752559C2semidirect
14. C2×C5×#239C22semidirect
15. C2×C3×Q8×D5C22semidirect
18. C2×D5×D12C22semidirect
19. C2×C4×D3×D5C22semidirect
20. C2×#6769C22semidirect
21. C2×#6768C22semidirect
22. C3×C4×C5×Q8C22semidirect
23. Q8×Dic15C22semidirect
24. #91782C22semidirect
25. #91781C22semidirect
26. C4×D60C22semidirect
27. C42×D15C22semidirect
28. C5×#895C22semidirect
29. C5×#874C22semidirect
30. C4×C5×D12C22semidirect
31. C3×#4043C22semidirect
33. C3×#4015C22semidirect
34. #91475C22semidirect
35. #91473C22semidirect
36. #91466C22semidirect
37. #91466C22semidirect
38. #91449C22semidirect
39. #91442C22semidirect
40. C4×#1201C22semidirect
41. #91438C22semidirect
42. #91437C22semidirect
43. #91435C22semidirect
44. #91435C22semidirect
46. #91370C22semidirect
47. #91369C22semidirect
56. Q8×D20D3semidirect
62. #6821D4semidirect
109. #5577D5semidirect
116. C2×Q8×D5C2×D3semidirect
124. C4×C5×Q8C2×D3semidirect
136. #4043C2×D3semidirect
147. #4015C2×D3semidirect
155. C3×C5×Q8C2×D4semidirect
162. D60C2×D4semidirect
165. C4×D15C2×D4semidirect
172. C3×D20#41semidirect
185. C2×#239C2×D5semidirect
191. C3×C4×Q8C2×D5semidirect
201. #895C2×D5semidirect
211. #874C2×D5semidirect
213. C4×D12C2×D5semidirect
277. C2×C3×D5C2×#41semidirect
281. C3×C4×C5C2×#41semidirect
335. C5×Q8D3×D4semidirect
352. D20#239semidirect
381. C4×Q8D3×D5semidirect
408. C3×Q8D4×D5semidirect
442. C2×D5C2×#239semidirect
446. C4×C5C2×#239semidirect
493. C3×C5D4×#41semidirect
508. C3×C4D5×#41semidirect
526. Q8#6777semidirect
556. C5D4×#239semidirect
575. C4D5×#239semidirect
576. C3#10618667semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2392
C4×#68212
C5×#55772
C3×Q8×D202
#117552442
#117538872
#117538862
#117527372
C4×#67772
#117525612
#117525592
#106186673
D4×#2395