Finite Group Databasebeta

← #14439548

Subgroups — #14439548

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2#11756589C211yesmaximal, characteristic, complemented
3C2×#91839C211yesmaximal, characteristic, complemented
4#11756564C211yesmaximal, characteristic, complemented
5C22×#6715C211yesmaximal, characteristic, complemented
6C2×#91797C211yesmaximal, characteristic, complemented
7#11751277C212yesmaximal, complemented
8#11751269C212yesmaximal, complemented
9#11751255C212yesmaximal, complemented
10#11751252C212yesmaximal, complemented
11#11751223C211yesmaximal, characteristic, complemented
12#10615671—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C2×#6817C2211yescharacteristic
16C22×D60C2211yescharacteristic
17C3×C5×AGL(1,ℤ/8)—24no—
18C2×C3×C5×SD16C2212yescomplemented
19C2×C3×C5×D8C2212yescomplemented
20C2×C3×C5×M16C2211yescharacteristic
21#91842—22no—
22#91839—24no—
23#91836C2212yescomplemented
24C2×#6718C2211yescharacteristic, complemented
25C2×#6717C2211yescharacteristic, complemented
26#91829C2212yescomplemented
27#91829C2212yescomplemented
28#91827—22no—
29#91826—22no—
30#91825C2212yescomplemented
31C2×#6716C2211yescharacteristic, complemented
32C2×#6715—24no—
33C2×#6715C2212yes—
34C2×#6715C2212yes—
35C2×#6715C2211yescharacteristic, complemented
36#91819—22no—
37#91815C2211yescharacteristic
38C22×C3⋊#168C2211yescharacteristic
39#91797—24no—
40C2×D120C2212yescomplemented
41C2×#6706C2212yescomplemented
42#91099C2212yescomplemented
43C8×Dic15C2212yescomplemented
44#83940—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)D311yescharacteristic, complemented
46#66164—31no—
47C2×#4096—31no—
48#66139—31no—
49C22×#686—31no—
50C2×#4054—31no—
51#65465—32no—
52#65457—32no—
53#65443—32no—
54#65440—32no—
55#65411—31no—
56C24×C3×C5—21no—
57C23×D15—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4—22no—
63C2×C3×C5×D4—22no—
64C2×C3×C5×D4—21no—
65C2×C3×C5×D4C2312yes—
66C2×C3×C5×D4C2311yescharacteristic
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5C2311yescharacteristic
69C2×#1220—21no—
70C2×#1220—24no—
71C2×#1220—24no—
72#6817—22no—
73#6817—22no—
74C2×D60—22no—
75C2×D60—22no—
76C2×D60—21no—
77C2×D60C2312yes—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C3×C5×SD16—24no—
82C3×C5×D8—24no—
83C3×C5×M16D414yescomplemented
84C2×C3×C5×C8C2312yes—
85#6719—24no—
86#6719D412yes—
87#6718—22no—
88#6717—22no—
89#6716—22no—
90#6715—24no—
91#6715—24no—
92#6715—22no—
93#6714—24no—
94C4⋊Dic15D412yes—
95C4×Dic15C2312yes—
96C2×C3⋊#168D414yescomplemented
97C2×C3⋊#168C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99D120—24no—
100#6706—24no—
101C2×C3×AGL(1,ℤ/8)D511yescharacteristic, complemented
102#5830—51no—
103C2×#950—51no—
104#5805—51no—
105C22×#213—51no—
106C2×#908—51no—
107#5176—52no—
108#5168—52no—
109#5154—52no—
110#5151—52no—
111#5122—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C22×D20—31no—
116C5×AGL(1,ℤ/8)—24no—
117C2×C5×SD16C2×D312yescomplemented
118C2×C5×D8C2×D312yescomplemented
119C2×C5×M16C2×D311yescharacteristic
120#4099—62no—
121#4096—64no—
122#4093—32no—
123C2×#689—31no—
124C2×#688—31no—
125#4086—32no—
126#4086—32no—
127#4084—62no—
128#4083—62no—
129#4082—32no—
130C2×#687—31no—
131C2×#686—32no—
132C2×#686—32no—
133C2×#686—31no—
134C2×#686—64no—
135#4076—62no—
136#4072—31no—
137C22×#168—31no—
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—21no—
146C23×C3×C5—42no—
147C23×C3×C5—82no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—22no—
150C22×D15—21no—
151C22×D15—42no—
152C22×D15—82no—
153C3×C5×Q8—21no—
154C3×C5×Q8—21no—
155C3×C5×D4—22no—
156C3×C5×D4—21no—
157C3×C5×D4—21no—
158C3×C5×D4—22no—
159C3×C5×D4—42no—
160C3×C5×D4—42no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—42no—
163C2×C3×C4×C5C2×D411yescharacteristic
164C2×C3×C4×C5C2×D412yes—
165C2×C3×C4×C5C2×D412yes—
166C2×C3×C4×C5C2411yescharacteristic
167#1220—42no—
168#1220—84no—
169#1220—84no—
170C2×Dic15—21no—
171C2×Dic15C2×D414yes—
172D60—22no—
173D60—21no—
174D60—22no—
175D60—21no—
176D60—42no—
177C4×D15—42no—
178Dic30—21no—
179Dic30—21no—
180C3×C5×C8C2×D414yes—
181C3⋊#168C2×D412yes—
182C3⋊#168C2×D412yes—
183C2×C3×#41C2×D511yescharacteristic
184C22×C3×D4C2×D511yescharacteristic
185C2×#235—51no—
186C22×D12—51no—
187C3×AGL(1,ℤ/8)—24no—
188C2×C3×SD16C2×D512yescomplemented
189C2×C3×D8C2×D512yescomplemented
190C2×C3×M16C2×D511yescharacteristic
191#953—102no—
192#950—104no—
193#947—52no—
194C2×#216—51no—
195C2×#215—51no—
196#940—52no—
197#940—52no—
198#938—102no—
199#937—102no—
200#936—52no—
201C2×#214—51no—
202C2×#213—51no—
203C2×#213—52no—
204C2×#213—52no—
205C2×#213—104no—
206#930—102no—
207#926—51no—
208C22×C3⋊C8—51no—
209#908—104no—
210C2×D24—52no—
211C2×#204—52no—
212#815—52no—
213C8×Dic3—52no—
214C24×C5—21no—
215C23×D5—61no—
216C5×#41—22no—
217C5×#41—22no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—22no—
221C2×C5×D4—21no—
222C2×C5×D4—22no—
223C2×C5×D4C22×D311yescharacteristic
224C2×C5×D4C22×D312yes—
225C22×C4×C5—21no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—64no—
228C2×C22⋊D5—64no—
229C2×C22⋊D5—61no—
230#709—62no—
231#709—62no—
232C2×D20—32no—
233C2×D20—31no—
234C2×D20—62no—
235C2×D20—62no—
236C2×D20—61no—
237C2×C4×D5—61no—
238C2×Dic10—31no—
239C5×SD16—24no—
240C5×D8—24no—
241C5×M16#6714yescomplemented
242C2×C5×C8C22×D312yes—
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—62no—
246#688—62no—
247#687—62no—
248#686—62no—
249#686—64no—
250#686—64no—
251#685—64no—
252C4⋊Dic5—32no—
253C4×Dic5—32no—
254C2×#168—34no—
255C2×#168—31no—
256C2×#168—31no—
257D40—64no—
258#677—64no—
259C2×AGL(1,ℤ/8)—151no—
260C2×AGL(1,ℤ/8)D1511yescharacteristic, complemented
261C2×#135—151no—
262C22×D8—151no—
263#535—151no—
264#535—151no—
265#496—152no—
266#496—152no—
267#495—152no—
268#493—152no—
269#405—151no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5—44no—
275C22×C3×C5—84no—
276C22×C3×C5#12712yes—
277C22×C3×C5C22×D411yescharacteristic
278C2×D15—41no—
279C2×D15—42no—
280C2×D15—42no—
281C2×D15—44no—
282C2×D15—84no—
283C3×C4×C5—41no—
284C3×C4×C5#12712yes—
285C3×C4×C5C22×D411yescharacteristic
286C3×C4×C5C22×D411yescharacteristic
287Dic15—24no—
288Dic15—41no—
289C24×C3—21no—
290C23×D3—101no—
291C3×#41—22no—
292C3×#41—22no—
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—22no—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4C22×D512yes—
299C2×C3×D4C22×D511yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—104no—
303C2×#67—104no—
304C2×#67—101no—
305#235—102no—
306#235—102no—
307C2×D12—52no—
308C2×D12—51no—
309C2×D12—102no—
310C2×D12—102no—
311C2×D12—101no—
312C2×C4×D3—101no—
313C2×Dic6—51no—
314C3×SD16—24no—
315C3×D8—24no—
316C3×M16C22⋊D514yescomplemented
317C2×C3×C8C22×D512yes—
318#217—52no—
319#217—104no—
320#216—102no—
321#215—102no—
322#214—102no—
323#213—104no—
324#213—104no—
325#213—102no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3—52no—
328C4×Dic3—52no—
329C2×C3⋊C8—54no—
330C2×C3⋊C8—51no—
331C2×C3⋊C8—51no—
332D24—104no—
333#204—104no—
334C23×C5—22no—
335C23×C5—21no—
336C23×C5—42no—
337C23×C5—82no—
338C23×C5D3×D411yescharacteristic
339C22×D5—62no—
340C22×D5—61no—
341C22×D5—122no—
342C22×D5—242no—
343C5×Q8—21no—
344C5×Q8—21no—
345C5×D4—22no—
346C5×D4—21no—
347C5×D4—21no—
348C5×D4—22no—
349C5×D4—42no—
350C5×D4—42no—
351C2×C4×C5—21no—
352C2×C4×C5—42no—
353C2×C4×C5D3×D411yescharacteristic
354C2×C4×C5D3×D412yes—
355C2×C4×C5C2×#6712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—122no—
358C22⋊D5—244no—
359C22⋊D5—244no—
360C2×Dic5—34no—
361C2×Dic5—61no—
362D20—62no—
363D20—61no—
364D20—62no—
365D20—61no—
366D20—122no—
367C4×D5—122no—
368Dic10—61no—
369Dic10—61no—
370C5×C8C2×#6714yes—
371#168—32no—
372#168—32no—
373C2×#41—151no—
374C2×#41C2×D1511yescharacteristic
375C22×D4—151no—
376C22×D4C2×D1511yescharacteristic
377AGL(1,ℤ/8)—24no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—151no—
382C2×SD16—151no—
383C2×SD16—152no—
384C2×SD16C2×D1512yescomplemented
385C2×D8—152no—
386C2×D8—152no—
387C2×D8—151no—
388C2×D8—152no—
389C2×D8—304no—
390C2×D8C2×D1512yescomplemented
391C2×M16C2×D1511yescharacteristic
392C22×C8—151no—
393#127—152no—
394#127—152no—
395#124—152no—
396#124—152no—
397#121—302no—
398#121—302no—
399#120—302no—
400#120—302no—
401#117—151no—
402#97—152no—
403C4×C8—152no—
404C2×C3×C5—22no—
405C2×C3×C5—81no—
406C2×C3×C5—82no—
407C2×C3×C5C2×#12711yescharacteristic
408C2×C3×C5#57612yes—
409D15—81no—
410D15—82no—
411C23×C3—22no—
412C23×C3—21no—
413C23×C3—42no—
414C23×C3—82no—
415C23×C3D4×D511yescharacteristic
416C22×D3—102no—
417C22×D3—101no—
418C22×D3—202no—
419C22×D3—402no—
420C3×Q8—21no—
421C3×Q8—21no—
422C3×D4—22no—
423C3×D4—21no—
424C3×D4—21no—
425C3×D4—22no—
426C3×D4—42no—
427C3×D4—42no—
428C2×C3×C4—21no—
429C2×C3×C4—42no—
430C2×C3×C4D4×D512yes—
431C2×C3×C4D4×D511yescharacteristic
432C2×C3×C4C2×C22⋊D512yes—
433C2×C3×C4C23×D511yescharacteristic
434#67—202no—
435#67—404no—
436#67—404no—
437C2×Dic3—54no—
438C2×Dic3—101no—
439D12—102no—
440D12—101no—
441D12—102no—
442D12—101no—
443D12—202no—
444C4×D3—202no—
445Dic6—101no—
446Dic6—101no—
447C3×C8C2×C22⋊D514yes—
448C3⋊C8—52no—
449C3⋊C8—52no—
450C22×C5—22no—
451C22×C5—42no—
452C22×C5—44no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—84no—
456C22×C5#94012yes—
457C22×C5C2×D3×D411yescharacteristic
458C2×D5—122no—
459C2×D5—124no—
460C2×D5—121no—
461C2×D5—122no—
462C2×D5—244no—
463C4×C5—41no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C22×#6711yescharacteristic
467Dic5—64no—
468Dic5—121no—
469C24—21no—
470C24—301no—
471#41—22no—
472#41—22no—
473#41—302no—
474#41—302no—
475C2×Q8—151no—
476C2×Q8C22×D1511yescharacteristic
477C2×D4—21no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—152no—
482C2×D4—151no—
483C2×D4—304no—
484C2×D4—304no—
485C2×D4—301no—
486C2×D4—302no—
487C2×D4—301no—
488C2×D4—302no—
489C2×D4C22×D1512yes—
490C2×D4C22×D1511yescharacteristic
491C22×C4—21no—
492C22×C4—301no—
493C22×C4C22×D1511yescharacteristic
494Q16—302no—
495SD16—24no—
496SD16—302no—
497SD16—302no—
498SD16—304no—
499D8—24no—
500D8—304no—
501D8—304no—
502D8—302no—
503D8—304no—
504M16#122014yescomplemented
505C2×C8—154no—
506C2×C8—151no—
507C2×C8—151no—
508C2×C8C22×D1512yes—
509C4⋊C4—152no—
510C22⋊C4—152no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—152no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—41no—
519C22×C3—42no—
520C22×C3—84no—
521C22×C3#408612yes—
522C22×C3C2×D4×D511yescharacteristic
523C2×D3—202no—
524C2×D3—204no—
525C2×D3—201no—
526C2×D3—202no—
527C2×D3—404no—
528C3×C4—41no—
529C3×C4#408612yes—
530C3×C4C2×D4×D511yescharacteristic
531C3×C4C22×C22⋊D511yescharacteristic
532Dic3—104no—
533Dic3—201no—
534C2×C5—22no—
535C2×C5—82no—
536C2×C5—81no—
537C2×C5#577412yes—
538C2×C5C2×#94011yescharacteristic
539D5—242no—
540D5—241no—
541C23—22no—
542C23—21no—
543C23—42no—
544C23—82no—
545C23—302no—
546C23—301no—
547C23—602no—
548C23—1202no—
549C23D4×D1511yescharacteristic
550Q8—21no—
551Q8—21no—
552Q8—301no—
553Q8—301no—
554D4—22no—
555D4—21no—
556D4—21no—
557D4—22no—
558D4—42no—
559D4—42no—
560D4—302no—
561D4—301no—
562D4—301no—
563D4—302no—
564D4—602no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—154no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D4×D1511yescharacteristic
574C2×C4D4×D1512yes—
575C2×C4C2×#122012yes—
576C2×C4C23×D1511yescharacteristic
577C8—152no—
578C8—152no—
579C8C2×#122014yes—
580C2×C3—22no—
581C2×C3—82no—
582C2×C3—81no—
583C2×C3#6610812yes—
584C2×C3C2×#408611yescharacteristic
585D3—402no—
586D3—401no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—41no—
590C22—42no—
591C22—42no—
592C22—44no—
593C22—84no—
594C22—601no—
595C22—602no—
596C22—602no—
597C22—604no—
598C22—1204no—
599C22#9182912yes—
600C22C2×D4×D1511yescharacteristic
601C4—41no—
602C4—304no—
603C4—601no—
604C4#9182912yes—
605C4C2×D4×D1511yescharacteristic
606C4C22×#122011yescharacteristic
607C3#1061567111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—82no—
610C2—81no—
611C2—1202no—
612C2—1201no—
613C2#1175653312yes—
614C2C2×#9182911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×AGL(1,ℤ/8)C2
socleC22×C3×C5C22×D4
hypercenterC2×AGL(1,ℤ/8)D15
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×AGL(1,ℤ/8)C2semidirect
2. #11756589C2semidirect
3. C2×#91839C2semidirect
4. #11756564C2semidirect
5. C22×#6715C2semidirect
6. C2×#91797C2semidirect
7. #11751277C2semidirect
8. #11751269C2semidirect
9. #11751255C2semidirect
10. #11751252C2semidirect
11. #11751223C2semidirect
18. C2×C3×C5×SD16C22semidirect
19. C2×C3×C5×D8C22semidirect
23. #91836C22semidirect
24. C2×#6718C22semidirect
25. C2×#6717C22semidirect
26. #91829C22semidirect
27. #91829C22semidirect
30. #91825C22semidirect
31. C2×#6716C22semidirect
35. C2×#6715C22semidirect
40. C2×D120C22semidirect
41. C2×#6706C22semidirect
42. #91099C22semidirect
43. C8×Dic15C22semidirect
45. C2×C5×AGL(1,ℤ/8)D3semidirect
83. C3×C5×M16D4semidirect
96. C2×C3⋊#168D4semidirect
101. C2×C3×AGL(1,ℤ/8)D5semidirect
117. C2×C5×SD16C2×D3semidirect
118. C2×C5×D8C2×D3semidirect
188. C2×C3×SD16C2×D5semidirect
189. C2×C3×D8C2×D5semidirect
241. C5×M16#67semidirect
260. C2×AGL(1,ℤ/8)D15semidirect
316. C3×M16C22⋊D5semidirect
384. C2×SD16C2×D15semidirect
390. C2×D8C2×D15semidirect
504. M16#1220semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10615671semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×AGL(1,ℤ/8)2
#117565892
C2×#918392
#117565642
C22×#67152
C2×#917972
#117512772
#117512692
#117512552
#117512522
#117512232
#106156713
#839405