Finite Group Databasebeta

← #14439611

Subgroups — #14439611

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×#91797C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3#11754609C211yesmaximal, characteristic, complemented
4#11754602C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic, complemented
6C22×#6653C211yesmaximal, characteristic, complemented
7C5×#5122C211yesmaximal, characteristic, complemented
8#11748009C212yesmaximal, complemented
9#11748007C212yesmaximal, complemented
10#11748005C212yesmaximal, complemented
11#11747969C212yesmaximal, complemented
12#10610296—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91797—24no—
19C2×D120C2212yescomplemented
20C2×#6706C2212yescomplemented
21C5×#926C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4054—24no—
24C2×C3×D40C2212yescomplemented
25C2×C3×#677C2212yescomplemented
26#91572—22no—
27#91564—22no—
28#91465—22no—
29#91458C2212yescomplemented
30#91458C2212yescomplemented
31#91450—22no—
32#91374C2212yescomplemented
33#91364C2212yescomplemented
34C2×#6662C2211yescharacteristic, complemented
35C2×#6658C2211yescharacteristic, complemented
36#91311—24no—
37C2×#6657C2211yescharacteristic, complemented
38C2×#6653—24no—
39C2×#6653C2212yes—
40C2×#6653C2212yes—
41C2×#6653C2211yescharacteristic, complemented
42C5×#815C2212yescomplemented
43C5×C8×Dic3C2212yescomplemented
44#83940—51nomaximal, Hall
45C2×#4054—31no—
46C2×#4054D311yescharacteristic, complemented
47C2×#4050—31no—
48C22×D40—31no—
49#65859—31no—
50#65859—31no—
51C5×#405—31no—
52#65001—32no—
53#65001—32no—
54#64985—32no—
55#64984—32no—
56C23×D15—21no—
57C23×C3×D5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60#6817—22no—
61#6817—22no—
62C2×D60—22no—
63C2×D60—22no—
64C2×D60—21no—
65C2×D60C2311yescharacteristic
66C2×D60C2312yes—
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20—22no—
73C2×C3×D20—22no—
74C2×C3×D20—21no—
75C2×C3×D20C2311yescharacteristic
76C2×C3×D20C2312yes—
77C2×C3×C4×D5—21no—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1202—24no—
80C2×#1202—24no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83D120—24no—
84#6706—24no—
85C5×#217D412yes—
86C5×C4⋊Dic3D412yes—
87C4×C5×Dic3C2312yes—
88C2×C5×C3⋊C8D414yescomplemented
89C2×C5×C3⋊C8C2311yescharacteristic
90C2×C5×C3⋊C8C2311yescharacteristic
91C3×D40—24no—
92C3×#677—24no—
93#6667—24no—
94#6665—24no—
95#6662—22no—
96#6658—22no—
97#6657—22no—
98#6653—24no—
99#6653—24no—
100#6653—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
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#5122D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×D20—31no—
115C22×D20C2×D311yescharacteristic
116C2×C5×M16C2×D311yescharacteristic
117C22×C5×C8—31no—
118C5×#117—31no—
119#4054—24no—
120#4054—64no—
121C2×Dic20—31no—
122#4050—64no—
123C2×D40—32no—
124C2×D40—32no—
125C2×D40—31no—
126C2×D40—32no—
127C2×D40—64no—
128C2×D40C2×D312yescomplemented
129C2×#677—31no—
130C2×#677—31no—
131C2×#677—32no—
132C2×#677C2×D312yescomplemented
133#4041—62no—
134#4041—62no—
135#4028—62no—
136#4028—62no—
137#4021—32no—
138#4021—32no—
139#4020—32no—
140#4020—32no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3155—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—22no—
146C22×D15—21no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C3×D5—22no—
150C22×C3×D5—21no—
151C22×C3×D5—42no—
152C22×C3×D5—82no—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157#1220—42no—
158C2×Dic15—21no—
159D60—21no—
160D60—22no—
161D60—21no—
162D60—22no—
163D60—42no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C2×C5×Dic3C2×D414yes—
168C3×C22⋊D5—42no—
169C2×C3×Dic5—21no—
170C3×D20—21no—
171C3×D20—22no—
172C3×D20—21no—
173C3×D20—22no—
174C3×D20—42no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178#1202—84no—
179#1202—84no—
180C3×C5×C8C2×D414yes—
181C5×C3⋊C8C2×D412yes—
182C5×C3⋊C8C2×D412yes—
183C2×C3×#41—51no—
184C22×C3×D4—51no—
185C2×#235—51no—
186C22×D12—51no—
187C3×AGL(1,ℤ/8)—104no—
188C2×C3×SD16—52no—
189C2×C3×D8—52no—
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#926C2×D511yescharacteristic
208C22×C3⋊C8C2×D511yescharacteristic
209#908—104no—
210C2×D24—52no—
211C2×#204—52no—
212#815C2×D512yescomplemented
213C8×Dic3C2×D512yescomplemented
214C23×D5—21no—
215C23×D5—61no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—21no—
218C2×C22⋊D5—61no—
219#709—22no—
220#709—22no—
221#709—62no—
222#709—62no—
223C2×D20—22no—
224C2×D20—22no—
225C2×D20—21no—
226C2×D20—32no—
227C2×D20—31no—
228C2×D20—62no—
229C2×D20—62no—
230C2×D20—61no—
231C2×D20—64no—
232C2×D20—64no—
233C2×D20C22×D312yes—
234C2×D20C22×D311yescharacteristic
235C2×C4×D5—21no—
236C2×C4×D5—61no—
237C2×Dic10—31no—
238C2×Dic10C22×D311yescharacteristic
239C5×M16#6714yescomplemented
240C2×C5×C8—34no—
241C2×C5×C8—31no—
242C2×C5×C8—31no—
243C2×C5×C8C22×D312yes—
244C5×C4⋊C4—32no—
245C5×C22⋊C4—32no—
246C42×C5—32no—
247#685—64no—
248#685—64no—
249Dic20—62no—
250D40—24no—
251D40—64no—
252D40—64no—
253D40—62no—
254D40—64no—
255#677—24no—
256#677—62no—
257#677—62no—
258#677—64no—
259C2×AGL(1,ℤ/8)—51no—
260C2×AGL(1,ℤ/8)—151no—
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—31no—
270C22×C3×C5—22no—
271C22×C3×C5#12712yes—
272C22×C3×C5C22×D411yescharacteristic
273C2×D15—41no—
274C2×D15—42no—
275C2×D15—42no—
276C2×D15—44no—
277C2×D15—84no—
278C2×C3×D5—41no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—44no—
282C2×C3×D5—84no—
283C3×C4×C5#12712yes—
284C3×C4×C5C22×D411yescharacteristic
285C3×C4×C5C22×D411yescharacteristic
286Dic15—41no—
287C3×Dic5—41no—
288C5×Dic3—24no—
289C24×C3—101no—
290C23×D3—101no—
291C3×#41—102no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—52no—
295C2×C3×D4—51no—
296C2×C3×D4—101no—
297C2×C3×D4—102no—
298C2×C3×D4—102no—
299C2×C3×D4—101no—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—101no—
303C2×#67—104no—
304C2×#67—104no—
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—104no—
315C3×D8—104no—
316C3×M16D2014yescomplemented
317C2×C3×C8C22×D512yes—
318#217—104no—
319#217D2012yes—
320#216—102no—
321#215—102no—
322#214—102no—
323#213—104no—
324#213—104no—
325#213—102no—
326(C2×D3)⋊C4—104no—
327C4⋊Dic3D2012yes—
328C4×Dic3C22×D512yes—
329C2×C3⋊C8D2014yescomplemented
330C2×C3⋊C8C22×D511yescharacteristic
331C2×C3⋊C8C22×D511yescharacteristic
332D24—104no—
333#204—104no—
334C23×C5D3×D411yescharacteristic
335C22×D5—22no—
336C22×D5—21no—
337C22×D5—42no—
338C22×D5—62no—
339C22×D5—61no—
340C22×D5—82no—
341C22×D5—122no—
342C22×D5—242no—
343C2×C4×C5—34no—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—42no—
349C22⋊D5—122no—
350C2×Dic5—21no—
351C2×Dic5—61no—
352D20—21no—
353D20—22no—
354D20—22no—
355D20—21no—
356D20—42no—
357D20—61no—
358D20—62no—
359D20—62no—
360D20—61no—
361D20—122no—
362D20—244no—
363D20—244no—
364C4×D5—42no—
365C4×D5—122no—
366Dic10—21no—
367Dic10—21no—
368Dic10—61no—
369Dic10—61no—
370C5×C8—32no—
371C5×C8—32no—
372C5×C8C2×#6714yes—
373C2×#41—51no—
374C2×#41—151no—
375C22×D4—51no—
376C22×D4—151no—
377AGL(1,ℤ/8)—104no—
378AGL(1,ℤ/8)—304no—
379#135—304no—
380C2×Q16—151no—
381C2×SD16—52no—
382C2×SD16—151no—
383C2×SD16—151no—
384C2×SD16—152no—
385C2×D8—52no—
386C2×D8—152no—
387C2×D8—152no—
388C2×D8—151no—
389C2×D8—152no—
390C2×D8—304no—
391C2×M16D3×D511yescharacteristic
392C22×C8—31no—
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—31no—
402#97—32no—
403C4×C8—32no—
404C2×C3×C5—22no—
405C2×C3×C5C2×#12711yescharacteristic
406C2×C3×C5#57612yes—
407D15—81no—
408D15—82no—
409C3×D5—81no—
410C3×D5—82no—
411C23×C3—102no—
412C23×C3—101no—
413C23×C3—202no—
414C23×C3—402no—
415C23×C3C2×D2011yescharacteristic
416C22×D3—102no—
417C22×D3—101no—
418C22×D3—202no—
419C22×D3—402no—
420C3×Q8—101no—
421C3×Q8—101no—
422C3×D4—102no—
423C3×D4—101no—
424C3×D4—101no—
425C3×D4—102no—
426C3×D4—202no—
427C3×D4—202no—
428C2×C3×C4—101no—
429C2×C3×C4—202no—
430C2×C3×C4C2×D2012yes—
431C2×C3×C4C2×D2011yescharacteristic
432C2×C3×C4C2×D2012yes—
433C2×C3×C4C23×D511yescharacteristic
434#67—202no—
435#67—404no—
436#67—404no—
437C2×Dic3—101no—
438C2×Dic3C2×D2014yes—
439D12—102no—
440D12—101no—
441D12—102no—
442D12—101no—
443D12—202no—
444C4×D3—202no—
445Dic6—101no—
446Dic6—101no—
447C3×C8C2×D2014yes—
448C3⋊C8C2×D2012yes—
449C3⋊C8C2×D2012yes—
450C22×C5—22no—
451C22×C5#94012yes—
452C22×C5C2×D3×D411yescharacteristic
453C2×D5—42no—
454C2×D5—44no—
455C2×D5—41no—
456C2×D5—42no—
457C2×D5—84no—
458C2×D5—122no—
459C2×D5—124no—
460C2×D5—121no—
461C2×D5—122no—
462C2×D5—244no—
463C4×C5—64no—
464C4×C5#94012yes—
465C4×C5C2×D3×D411yescharacteristic
466C4×C5C22×#6711yescharacteristic
467Dic5—41no—
468Dic5—121no—
469C24—101no—
470C24—301no—
471#41—102no—
472#41—102no—
473#41—302no—
474#41—302no—
475C2×Q8—51no—
476C2×Q8—151no—
477C2×D4—52no—
478C2×D4—51no—
479C2×D4—101no—
480C2×D4—102no—
481C2×D4—101no—
482C2×D4—102no—
483C2×D4—152no—
484C2×D4—151no—
485C2×D4—304no—
486C2×D4—304no—
487C2×D4—301no—
488C2×D4—302no—
489C2×D4—301no—
490C2×D4—302no—
491C22×C4—101no—
492C22×C4—301no—
493C22×C4C2×D3×D511yescharacteristic
494Q16—302no—
495SD16—104no—
496SD16—302no—
497SD16—302no—
498SD16—304no—
499D8—104no—
500D8—304no—
501D8—304no—
502D8—302no—
503D8—304no—
504M16#120214yescomplemented
505C2×C8—34no—
506C2×C8—31no—
507C2×C8—31no—
508C2×C8C2×D3×D512yes—
509C4⋊C4—32no—
510C22⋊C4—32no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—32no—
514C3×C5#315511yescharacteristic, complemented, Hall
515C22×C3—22no—
516C22×C3—201no—
517C22×C3—202no—
518C22×C3—202no—
519C22×C3—204no—
520C22×C3—404no—
521C22×C3#402012yes—
522C22×C3C22×D2011yescharacteristic
523C2×D3—201no—
524C2×D3—202no—
525C2×D3—202no—
526C2×D3—204no—
527C2×D3—404no—
528C3×C4—201no—
529C3×C4#402012yes—
530C3×C4C22×D2011yescharacteristic
531C3×C4C22×D2011yescharacteristic
532Dic3—24no—
533Dic3—201no—
534C2×C5—22no—
535C2×C5#577412yes—
536C2×C5C2×#94011yescharacteristic
537D5—82no—
538D5—81no—
539D5—242no—
540D5—241no—
541C23—102no—
542C23—101no—
543C23—202no—
544C23—302no—
545C23—301no—
546C23—402no—
547C23—602no—
548C23—1202no—
549C23D3×D2011yescharacteristic
550Q8—101no—
551Q8—101no—
552Q8—301no—
553Q8—301no—
554D4—102no—
555D4—101no—
556D4—101no—
557D4—102no—
558D4—202no—
559D4—202no—
560D4—302no—
561D4—301no—
562D4—301no—
563D4—302no—
564D4—602no—
565D4—602no—
566D4—1204no—
567D4—1204no—
568C2×C4—34no—
569C2×C4—101no—
570C2×C4—202no—
571C2×C4—301no—
572C2×C4—602no—
573C2×C4D3×D2011yescharacteristic
574C2×C4D3×D2012yes—
575C2×C4C2×#120212yes—
576C2×C4C22×D3×D511yescharacteristic
577C8—32no—
578C8—32no—
579C8C2×#120214yes—
580C2×C3—22no—
581C2×C3—402no—
582C2×C3—401no—
583C2×C3C2×#402011yescharacteristic
584C2×C3#6608612yes—
585D3—402no—
586D3—401no—
587C5#8394011yescharacteristic, complemented, Sylow
588C22—22no—
589C22—202no—
590C22—204no—
591C22—201no—
592C22—202no—
593C22—404no—
594C22—602no—
595C22—604no—
596C22—601no—
597C22—602no—
598C22—1204no—
599C22#9145812yes—
600C22C2×D3×D2011yescharacteristic
601C4—64no—
602C4—201no—
603C4—601no—
604C4#9145812yes—
605C4C2×D3×D2011yescharacteristic
606C4C22×#120211yescharacteristic
607C3#1061029611yescharacteristic, complemented, Sylow
608C2—22no—
609C2—402no—
610C2—401no—
611C2—1202no—
612C2—1201no—
613C2#1175403112yes—
614C2C2×#9145811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3155
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91797C2semidirect
2. C2×C3×#4054C2semidirect
3. #11754609C2semidirect
4. #11754602C2semidirect
5. C2×#91311C2semidirect
6. C22×#6653C2semidirect
7. C5×#5122C2semidirect
8. #11748009C2semidirect
9. #11748007C2semidirect
10. #11748005C2semidirect
11. #11747969C2semidirect
19. C2×D120C22semidirect
20. C2×#6706C22semidirect
24. C2×C3×D40C22semidirect
25. C2×C3×#677C22semidirect
29. #91458C22semidirect
30. #91458C22semidirect
32. #91374C22semidirect
33. #91364C22semidirect
34. C2×#6662C22semidirect
35. C2×#6658C22semidirect
37. C2×#6657C22semidirect
41. C2×#6653C22semidirect
42. C5×#815C22semidirect
43. C5×C8×Dic3C22semidirect
46. C2×#4054D3semidirect
81. C3×C5×M16D4semidirect
88. C2×C5×C3⋊C8D4semidirect
111. #5122D5semidirect
128. C2×D40C2×D3semidirect
132. C2×#677C2×D3semidirect
212. #815C2×D5semidirect
213. C8×Dic3C2×D5semidirect
239. C5×M16#67semidirect
316. C3×M16D20semidirect
329. C2×C3⋊C8D20semidirect
504. M16#1202semidirect
514. C3×C5#3155semidirect
587. C5#83940semidirect
607. C3#10610296semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
C2×C3×#40542
#117546092
#117546022
C2×#913112
C22×#66532
C5×#51222
#117480092
#117480072
#117480052
#117479692
#106102963
#839405