Finite Group Databasebeta

← #14439607

Subgroups — #14439607

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
1#11756589C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3C2×C3×#4096C211yesmaximal, characteristic, complemented
4#11754604C211yesmaximal, characteristic, complemented
5C22×#6654C211yesmaximal, characteristic, complemented
6C2×#91301C211yesmaximal, characteristic, complemented
7#11749343C212yesmaximal, complemented
8#11749321C212yesmaximal, complemented
9#11749095C212yesmaximal, complemented
10#11749077C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615671—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C22×C5×D12C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91836C2212yescomplemented
18#91829C2212yescomplemented
19#91826—22no—
20#91819—22no—
21#91815C2211yescharacteristic
22C5×#949—24no—
23C2×C5×#215C2212yescomplemented
24C2×C5×#213C2212yescomplemented
25C2×C5×#208C2211yescharacteristic
26C3×#4096—24no—
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic, complemented
29C2×C3×#687C2211yescharacteristic, complemented
30C2×C3×#686C2211yescharacteristic, complemented
31C22×C3×#168C2211yescharacteristic
32#91568—22no—
33#91463C2212yescomplemented
34#91449—22no—
35#91370C2212yescomplemented
36C2×#6658C2212yescomplemented
37C2×#6654—24no—
38C2×#6654C2212yes—
39C2×#6654C2212yes—
40#91301—24no—
41C2×#6653C2212yescomplemented
42#90954C2212yescomplemented
43#90951C2212yescomplemented
44#83906—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66164—31no—
47C2×#4096D311yescharacteristic, complemented
48#66139—31no—
49C22×#686—31no—
50C2×#4054—31no—
51#65465—32no—
52#65457—32no—
53#65443—32no—
54#65440—32no—
55#65411—31no—
56C23×D15—21no—
57C23×C5×D3—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×#1220—24no—
66C2×D60—22no—
67C2×D60—22no—
68C2×D60—21no—
69C2×D60C2312yes—
70C2×C5×D12—22no—
71C2×C5×D12—22no—
72C2×C5×D12—21no—
73C2×C5×D12C2312yes—
74C2×C3×C22⋊D5—21no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1201—24no—
81#6719D412yes—
82#6714—24no—
83C4⋊Dic15D412yes—
84C4×Dic15C2312yes—
85C5×#215—24no—
86C5×#213—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×#689—22no—
90C3×#688—22no—
91C3×#687—22no—
92C3×#686—22no—
93C2×C3×#168D414yescomplemented
94C2×C3×#168C2311yescharacteristic
95C2×C3×#168C2311yescharacteristic
96(C2×D3)⋊Dic5—24no—
97#6658—24no—
98#6654—24no—
99#6654—24no—
100#6653—24no—
101C2×C3×#135—51no—
102#5830—51no—
103#5830—51no—
104C2×#949—51no—
105C2×#949D511yescharacteristic, complemented
106C22×D24—51no—
107#5191—52no—
108#5176—52no—
109#5176—52no—
110#5151—52no—
111#5101—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×D4—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120#4099—62no—
121#4096—24no—
122#4093—32no—
123C2×#689C2×D311yescharacteristic, complemented
124C2×#688C2×D311yescharacteristic, complemented
125#4086—32no—
126#4086—32no—
127#4084—62no—
128#4083—62no—
129#4082—32no—
130C2×#687C2×D311yescharacteristic, complemented
131C2×#686—32no—
132C2×#686—32no—
133C2×#686—64no—
134C2×#686C2×D311yescharacteristic, complemented
135#4076—62no—
136#4072—31no—
137C22×#168C2×D311yescharacteristic
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3155—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C5×D3—22no—
150C22×C5×D3—42no—
151C22×C5×D3—82no—
152C22×C3×D5—21no—
153C3×C5×Q8—21no—
154C3×C5×Q8—21no—
155C3×C5×D4—21no—
156C3×C5×D4—21no—
157C3×C5×D4—42no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—42no—
160C2×C3×C4×C5C2×D411yescharacteristic
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2411yescharacteristic
164#1220—84no—
165C2×Dic15C2×D414yes—
166D60—22no—
167D60—22no—
168D60—42no—
169C5×D12—22no—
170C5×D12—22no—
171C5×D12—42no—
172C3×C22⋊D5—42no—
173C2×C3×Dic5—21no—
174C3×D20—21no—
175C3×D20—21no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179#1201—84no—
180C3×#168C2×D412yes—
181C3×#168C2×D412yes—
182C5×C3⋊C8C2×D414yes—
183C2×C3×#41—51no—
184C2×C3×#41C2×D511yescharacteristic
185C22×D12—51no—
186C22×D12C2×D511yescharacteristic
187C3×#135—104no—
188C2×C3×Q16—51no—
189C2×C3×SD16—51no—
190C2×C3×SD16—51no—
191C2×C3×D8—51no—
192C22×C3×C8—51no—
193#949—24no—
194#949—104no—
195#947—52no—
196#947—52no—
197C2×#215—52no—
198C2×#215C2×D512yescomplemented
199#940—52no—
200#940—52no—
201#937—102no—
202#937—102no—
203C2×#213—52no—
204C2×#213C2×D512yescomplemented
205#930—102no—
206#930—102no—
207#926—51no—
208C2×#208C2×D511yescharacteristic
209C2×D24—52no—
210C2×D24—52no—
211C2×D24—104no—
212#815—52no—
213C8×Dic3—52no—
214C24×C5—61no—
215C23×D5—61no—
216C5×#41—22no—
217C5×#41—22no—
218C2×C5×Q8C22×D311yescharacteristic
219C2×C5×D4—21no—
220C2×C5×D4—32no—
221C2×C5×D4—62no—
222C2×C5×D4—61no—
223C2×C5×D4—62no—
224C2×C5×D4C22×D311yescharacteristic
225C22×C4×C5—21no—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—21no—
228C2×C22⋊D5—64no—
229C2×C22⋊D5—64no—
230#709—22no—
231#709—22no—
232C2×D20—32no—
233C2×D20—62no—
234C2×D20—62no—
235C2×D20—61no—
236C2×D20C22×D311yescharacteristic
237C2×C4×D5—21no—
238C2×Dic10C22×D311yescharacteristic
239C5×SD16—64no—
240C5×D8—64no—
241C5×M16—34no—
242C2×C5×C8—32no—
243C22⋊Dic5—32no—
244C22⋊Dic5—64no—
245#689—22no—
246#688—22no—
247#687—22no—
248#686—22no—
249#686—64no—
250#686—64no—
251#685—64no—
252C4⋊Dic5—32no—
253C4×Dic5—32no—
254C2×#168#6714yescomplemented
255C2×#168C22×D311yescharacteristic
256C2×#168C22×D311yescharacteristic
257D40—64no—
258#677—64no—
259C2×AGL(1,ℤ/8)—31no—
260C2×AGL(1,ℤ/8)—151no—
261C2×#135—51no—
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#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—42no—
276C2×D15—44no—
277C2×D15—84no—
278C2×C5×D3—42no—
279C2×C5×D3—44no—
280C2×C5×D3—84no—
281C2×C3×D5—41no—
282C2×C3×D5—42no—
283C3×C4×C5—41no—
284C3×C4×C5#12712yes—
285C3×C4×C5C22×D411yescharacteristic
286C3×C4×C5C22×D411yescharacteristic
287Dic15—24no—
288C3×Dic5—41no—
289C23×D3—21no—
290C23×D3—101no—
291C3×#41—22no—
292C3×#41—22no—
293C3×#41—102no—
294C3×#41—102no—
295C2×C3×Q8—51no—
296C2×C3×Q8C22×D511yescharacteristic
297C2×C3×D4—21no—
298C2×C3×D4—51no—
299C2×C3×D4—101no—
300C2×C3×D4C22×D511yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—101no—
303C22×C3×C4C22×D511yescharacteristic
304C2×#67—104no—
305C2×#67—104no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12—21no—
309C2×D12—52no—
310C2×D12—102no—
311C2×D12—102no—
312C2×D12—101no—
313C2×D12C22×D512yes—
314C3×Q16—102no—
315C3×SD16—102no—
316C3×SD16—102no—
317C3×D8—102no—
318C2×C3×C8—54no—
319C2×C3×C8—51no—
320C2×C3×C8—51no—
321#217—52no—
322#215—24no—
323#215—104no—
324#213—24no—
325#213—104no—
326(C2×D3)⋊C4—104no—
327(C2×D3)⋊C4—104no—
328C4⋊Dic3—52no—
329C4×Dic3—52no—
330#208C22⋊D514yescomplemented
331C2×C3⋊C8C22×D512yes—
332D24—104no—
333D24—104no—
334C23×C5—21no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—242no—
338C23×C5D3×D411yescharacteristic
339C22×D5—21no—
340C22×D5—62no—
341C22×D5—122no—
342C22×D5—242no—
343C5×Q8—21no—
344C5×Q8—21no—
345C5×D4—21no—
346C5×D4—21no—
347C5×D4—42no—
348C5×D4—62no—
349C5×D4—62no—
350C5×D4—122no—
351C2×C4×C5—21no—
352C2×C4×C5—42no—
353C2×C4×C5D3×D412yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5C2×#6712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—42no—
358C22⋊D5—244no—
359C22⋊D5—244no—
360C2×Dic5—21no—
361C2×Dic5—34no—
362D20—21no—
363D20—21no—
364D20—62no—
365D20—62no—
366D20—122no—
367C4×D5—42no—
368Dic10—21no—
369Dic10—21no—
370C5×C8—34no—
371#168C2×#6712yes—
372#168C2×#6712yes—
373C2×#41—51no—
374C2×#41D3×D511yescharacteristic
375C22×D4—31no—
376C22×D4—151no—
377AGL(1,ℤ/8)—64no—
378AGL(1,ℤ/8)—304no—
379#135—104no—
380C2×Q16—51no—
381C2×SD16—32no—
382C2×SD16—51no—
383C2×SD16—51no—
384C2×SD16—152no—
385C2×D8—32no—
386C2×D8—51no—
387C2×D8—152no—
388C2×D8—152no—
389C2×D8—152no—
390C2×D8—304no—
391C2×M16—31no—
392C22×C8—51no—
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×C5C2×#12711yescharacteristic
407C2×C3×C5#57612yes—
408D15—82no—
409C3×D5—81no—
410C5×D3—82no—
411C23×C3—21no—
412C23×C3—101no—
413C23×C3D4×D511yescharacteristic
414C22×D3—22no—
415C22×D3—42no—
416C22×D3—82no—
417C22×D3—102no—
418C22×D3—202no—
419C22×D3—402no—
420C3×Q8—21no—
421C3×Q8—21no—
422C3×Q8—101no—
423C3×Q8—101no—
424C3×D4—21no—
425C3×D4—21no—
426C3×D4—42no—
427C3×D4—101no—
428C3×D4—101no—
429C3×D4—202no—
430C2×C3×C4—21no—
431C2×C3×C4—42no—
432C2×C3×C4—101no—
433C2×C3×C4—202no—
434C2×C3×C4D4×D512yes—
435C2×C3×C4D4×D511yescharacteristic
436C2×C3×C4C2×C22⋊D512yes—
437C2×C3×C4C23×D511yescharacteristic
438#67—404no—
439#67—404no—
440C2×Dic3—54no—
441D12—22no—
442D12—22no—
443D12—42no—
444D12—102no—
445D12—102no—
446D12—202no—
447C3×C8—52no—
448C3×C8—52no—
449C3⋊C8C2×C22⋊D514yes—
450C22×C5—22no—
451C22×C5—42no—
452C22×C5—41no—
453C22×C5—124no—
454C22×C5—122no—
455C22×C5—244no—
456C22×C5#94012yes—
457C22×C5C2×D3×D411yescharacteristic
458C2×D5—42no—
459C2×D5—41no—
460C2×D5—124no—
461C2×D5—122no—
462C2×D5—244no—
463C4×C5—41no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C22×#6711yescharacteristic
467Dic5—41no—
468Dic5—64no—
469C24—61no—
470C24—301no—
471#41—22no—
472#41—22no—
473#41—102no—
474#41—102no—
475C2×Q8—51no—
476C2×Q8C2×D3×D511yescharacteristic
477C2×D4—21no—
478C2×D4—32no—
479C2×D4—51no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—61no—
483C2×D4—101no—
484C2×D4—152no—
485C2×D4—304no—
486C2×D4—304no—
487C2×D4—302no—
488C2×D4—302no—
489C2×D4—301no—
490C2×D4C2×D3×D511yescharacteristic
491C22×C4—21no—
492C22×C4—101no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—102no—
495SD16—64no—
496SD16—102no—
497SD16—102no—
498SD16—304no—
499D8—64no—
500D8—102no—
501D8—304no—
502D8—304no—
503D8—304no—
504M16—34no—
505C2×C8—32no—
506C2×C8—54no—
507C2×C8—51no—
508C2×C8—51no—
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—41no—
518C22×C3—202no—
519C22×C3—201no—
520C22×C3#408612yes—
521C22×C3C2×D4×D511yescharacteristic
522C2×D3—44no—
523C2×D3—42no—
524C2×D3—84no—
525C2×D3—204no—
526C2×D3—202no—
527C2×D3—404no—
528C3×C4—41no—
529C3×C4—201no—
530C3×C4#408612yes—
531C3×C4C2×D4×D511yescharacteristic
532C3×C4C22×C22⋊D511yescharacteristic
533Dic3—104no—
534C2×C5—22no—
535C2×C5—81no—
536C2×C5—242no—
537C2×C5#576912yes—
538C2×C5C2×#94011yescharacteristic
539D5—81no—
540D5—242no—
541C23—21no—
542C23—62no—
543C23—101no—
544C23—122no—
545C23—242no—
546C23—302no—
547C23—602no—
548C23—1202no—
549C23#679011yescharacteristic
550Q8—21no—
551Q8—21no—
552Q8—101no—
553Q8—101no—
554D4—21no—
555D4—21no—
556D4—42no—
557D4—62no—
558D4—62no—
559D4—101no—
560D4—101no—
561D4—122no—
562D4—202no—
563D4—302no—
564D4—302no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—21no—
569C2×C4—42no—
570C2×C4—101no—
571C2×C4—154no—
572C2×C4—202no—
573C2×C4D5×#6712yes—
574C2×C4D3×C22⋊D512yes—
575C2×C4#679011yescharacteristic
576C2×C4C22×D3×D511yescharacteristic
577C8—34no—
578C8—52no—
579C8—52no—
580C2×C3—22no—
581C2×C3—81no—
582C2×C3—401no—
583C2×C3#6610812yes—
584C2×C3C2×#408611yescharacteristic
585D3—82no—
586D3—402no—
587C5#8390611yescharacteristic, complemented, Sylow
588C22—22no—
589C22—42no—
590C22—41no—
591C22—124no—
592C22—122no—
593C22—202no—
594C22—201no—
595C22—244no—
596C22—604no—
597C22—602no—
598C22—1204no—
599C22#9156712yes—
600C22C2×#679011yescharacteristic
601C4—41no—
602C4—201no—
603C4—304no—
604C4#9156712yes—
605C4C2×D5×#6711yescharacteristic
606C4C2×D3×C22⋊D511yescharacteristic
607C3#1061567111yescharacteristic, complemented, Sylow
608C2—22no—
609C2—81no—
610C2—242no—
611C2—401no—
612C2—1202no—
613C2#1175533212yes—
614C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756589C2semidirect
2. C2×C5×#949C2semidirect
3. C2×C3×#4096C2semidirect
4. #11754604C2semidirect
5. C22×#6654C2semidirect
6. C2×#91301C2semidirect
7. #11749343C2semidirect
8. #11749321C2semidirect
9. #11749095C2semidirect
10. #11749077C2semidirect
11. #11748324C2semidirect
17. #91836C22semidirect
18. #91829C22semidirect
23. C2×C5×#215C22semidirect
24. C2×C5×#213C22semidirect
27. C2×C3×#689C22semidirect
28. C2×C3×#688C22semidirect
29. C2×C3×#687C22semidirect
30. C2×C3×#686C22semidirect
33. #91463C22semidirect
35. #91370C22semidirect
36. C2×#6658C22semidirect
41. C2×#6653C22semidirect
42. #90954C22semidirect
43. #90951C22semidirect
47. C2×#4096D3semidirect
87. C5×#208D4semidirect
93. C2×C3×#168D4semidirect
105. C2×#949D5semidirect
123. C2×#689C2×D3semidirect
124. C2×#688C2×D3semidirect
130. C2×#687C2×D3semidirect
134. C2×#686C2×D3semidirect
198. C2×#215C2×D5semidirect
204. C2×#213C2×D5semidirect
254. C2×#168#67semidirect
330. #208C22⋊D5semidirect
514. C3×C5#3155semidirect
587. C5#83906semidirect
607. C3#10615671semidirect

Maximal subgroups

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

subgroupindex
#117565892
C2×C5×#9492
C2×C3×#40962
#117546042
C22×#66542
C2×#913012
#117493432
#117493212
#117490952
#117490772
#117483242
#106156713
#839065