Finite Group Databasebeta

← #14439254

Subgroups — #14439254

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic, complemented
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754581C211yesmaximal, characteristic
4C2×#91389C211yesmaximal, characteristic, complemented
5C2×#91315C211yesmaximal, characteristic, complemented
6C2×#91313C211yesmaximal, characteristic, complemented
7C5×Dic3×M16C211yesmaximal, characteristic, complemented
8#11748034C212yesmaximal, complemented
9#11748033C212yesmaximal, complemented
10#11748002C212yesmaximal, complemented
11#11747973C212yesmaximal, complemented
12#10610269—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91798—24no—
19C2×Dic60C2212yes—
20C2×#6706C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C3×#4055—24no—
24C2×C3×Dic20C2212yes—
25C2×C3×#677C2212yes—
26#91569—22no—
27C2×Dic3⋊Dic5—22no—
28#91458C2211yescharacteristic
29C4×#1202—22no—
30#91389—22no—
31#91389C2212yes—
32#91389C2212yes—
33#91389C2211yescharacteristic
34#91374C2211yescharacteristic
35#91364C2211yescharacteristic
36C2×#6662C2212yes—
37C2×#6662C2212yes—
38#91315—24no—
39C2×#6658C2212yes—
40#91313—24no—
41C2×#6657C2212yes—
42C5×#815C2212yes—
43C5×C8×Dic3C2212yes—
44#83972—51nomaximal, Hall
45C2×#4055—31no—
46C2×#4055—31no—
47C2×#4055—31no—
48C2×#4055D311yescharacteristic, complemented
49#65811—31no—
50C2×#4015—31no—
51C4×C5×M16—31no—
52#65004—32no—
53#65004—32no—
54#64988—32no—
55#64982—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×Dic30C2311yescharacteristic
68C22×C5×Dic3D412yes—
69C2×C3×C22⋊D5—21no—
70C22×C3×Dic5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—22no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83Dic60—24no—
84#6706—24no—
85C4×C5×Dic3D412yes—
86C4×C5×Dic3C2311yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C5×#208D414yescomplemented
89C2×C5×C3⋊C8C2312yes—
90C3×Dic20—24no—
91C3×#677—24no—
92Dic3⋊Dic5—22no—
93Dic3⋊Dic5—24no—
94Dic3⋊Dic5—24no—
95#6667—22no—
96#6665—22no—
97#6662—24no—
98#6662—24no—
99#6658—24no—
100#6657—24no—
101C2×C3×#137—51no—
102#5832—51no—
103C2×#951—51no—
104C2×#944—51no—
105C2×#942—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5175—52no—
110#5167—52no—
111Dic3×M16D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×Dic10—31no—
115C22×Dic10C2×D311yescharacteristic
116C2×C5×M16—31no—
117C2×C5×M16C2×D311yescharacteristic
118C2×C42×C5—31no—
119#4076—62no—
120C2×C4⋊Dic5—62no—
121#4055—24no—
122#4055—64no—
123#4055—64no—
124#4055—64no—
125C2×Dic20—32no—
126C2×Dic20—32no—
127C2×Dic20—32no—
128C2×Dic20C2×D312yes—
129C2×#677—32no—
130C2×#677—32no—
131C2×#677—32no—
132C2×#677C2×D312yes—
133#4021—31no—
134#4021—31no—
135#4020—31no—
136C4×D20—62no—
137#4015—32no—
138#4015—32no—
139#4015—31no—
140#4015—62no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3152—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—21no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—42no—
152C2×Dic15—21no—
153C2×Dic15—22no—
154C2×Dic15—42no—
155D60—21no—
156D60—21no—
157C4×D15—42no—
158Dic30—22no—
159Dic30—21no—
160Dic30—22no—
161Dic30—21no—
162Dic30—42no—
163C2×C5×Dic3—24no—
164C2×C5×Dic3C2×D412yes—
165C2×C5×Dic3C2×D412yes—
166C3×C22⋊D5—42no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—42no—
170C3×D20—21no—
171C3×D20—21no—
172C3×C4×D5—42no—
173C3×Dic10—22no—
174C3×Dic10—21no—
175C3×Dic10—22no—
176C3×Dic10—21no—
177C3×Dic10—42no—
178#1202—44no—
179C3×C5×C8C2×D414yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×Dic6—51no—
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16C2×D511yescharacteristic
189#951—104no—
190#947—51no—
191#944—52no—
192#944—52no—
193#944—51no—
194#944—102no—
195C2×#216—52no—
196C2×#216—52no—
197#942—104no—
198C2×#215—52no—
199#940—51no—
200#939—102no—
201#936—51no—
202C2×#214—52no—
203C4×#67—102no—
204C2×Dic3⋊C4—102no—
205C2×C4×Dic3C2×D511yescharacteristic
206C2×#208C2×D511yescharacteristic
207#909—104no—
208C2×Dic12—52no—
209C2×#204—52no—
210#815C2×D512yes—
211C8×Dic3C2×D512yes—
212C22×C4×C5—32no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—21no—
215C2×C22⋊D5—61no—
216C22×Dic5—21no—
217C22×Dic5—61no—
218#709—22no—
219#709—22no—
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×D20—62no—
224C2×D20C22×D311yescharacteristic
225C2×C4×D5—21no—
226C2×C4×D5—61no—
227C2×Dic10—22no—
228C2×Dic10—22no—
229C2×Dic10—21no—
230C2×Dic10—32no—
231C2×Dic10—31no—
232C2×Dic10—62no—
233C2×Dic10—62no—
234C2×Dic10—61no—
235C2×Dic10C22×D312yes—
236C2×Dic10C22×D311yescharacteristic
237C5×M16—34no—
238C5×M16#6714yescomplemented
239C2×C5×C8—32no—
240C2×C5×C8C22×D312yes—
241C42×C5—32no—
242C42×C5—31no—
243C42×C5—31no—
244#685—62no—
245#685—62no—
246C4⋊Dic5—64no—
247C4⋊Dic5—64no—
248C4⋊Dic5—62no—
249Dic20—24no—
250Dic20—64no—
251Dic20—64no—
252Dic20—64no—
253#677—24no—
254#677—64no—
255#677—64no—
256#677—64no—
257C2×#137—51no—
258C2×#137—151no—
259C2×#137—151no—
260C2×#137—151no—
261#532—151no—
262C2×C4⋊Q8—151no—
263#497—152no—
264#497—152no—
265#494—152no—
266#492—152no—
267C4×M16—31no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C3×C4×C5#12712yes—
276C3×C4×C5C22×D411yescharacteristic
277C3×C4×C5C22×D411yescharacteristic
278Dic15—42no—
279Dic15—41no—
280C3×Dic5—42no—
281C3×Dic5—41no—
282C5×Dic3—22no—
283C5×Dic3#13714yescomplemented
284C3×#41—102no—
285C3×#41—102no—
286C2×C3×Q8—52no—
287C2×C3×Q8—51no—
288C2×C3×Q8—101no—
289C2×C3×Q8—102no—
290C2×C3×Q8—102no—
291C2×C3×D4—51no—
292C2×C3×D4—101no—
293C22×C3×C4—101no—
294C22×C3×C4—101no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—101no—
297C2×#67—102no—
298C22×Dic3—101no—
299C22×Dic3D2012yes—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—52no—
305C2×Dic6—51no—
306C2×Dic6—102no—
307C2×Dic6—102no—
308C2×Dic6—101no—
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16D2014yescomplemented
312C2×C3×C8C22×D512yes—
313#217—102no—
314#216—104no—
315#216—104no—
316#215—104no—
317#214—104no—
318(C2×D3)⋊C4—102no—
319Dic3⋊C4—104no—
320Dic3⋊C4—104no—
321Dic3⋊C4—102no—
322C4×Dic3D2012yes—
323C4×Dic3C22×D511yescharacteristic
324C4×Dic3C22×D511yescharacteristic
325#208D2014yescomplemented
326C2×C3⋊C8C22×D512yes—
327Dic12—104no—
328#204—104no—
329C23×C5D3×D411yescharacteristic
330C22×D5—21no—
331C22×D5—61no—
332C2×C4×C5—32no—
333C2×C4×C5—32no—
334C2×C4×C5—64no—
335C2×C4×C5D3×D411yescharacteristic
336C2×C4×C5D3×D412yes—
337C2×C4×C5C2×#6712yes—
338C2×C4×C5C23×D311yescharacteristic
339C22⋊D5—42no—
340C22⋊D5—122no—
341C2×Dic5—22no—
342C2×Dic5—21no—
343C2×Dic5—42no—
344C2×Dic5—62no—
345C2×Dic5—61no—
346C2×Dic5—122no—
347D20—21no—
348D20—21no—
349D20—61no—
350D20—61no—
351D20—124no—
352C4×D5—42no—
353C4×D5—122no—
354Dic10—22no—
355Dic10—21no—
356Dic10—22no—
357Dic10—21no—
358Dic10—42no—
359Dic10—62no—
360Dic10—61no—
361Dic10—62no—
362Dic10—61no—
363Dic10—122no—
364C5×C8—34no—
365C5×C8C2×#6714yes—
366C2×#41—51no—
367C2×#41—151no—
368C22×Q8—51no—
369C22×Q8—151no—
370#137—104no—
371#137—304no—
372#137—304no—
373#137—304no—
374C2×Q16—52no—
375C2×Q16—152no—
376C2×Q16—152no—
377C2×Q16—152no—
378C2×SD16—52no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×M16—31no—
383C2×M16D3×D511yescharacteristic
384C4⋊Q8—152no—
385C4⋊Q8—152no—
386C4⋊Q8—151no—
387C4⋊Q8—302no—
388#127—151no—
389#124—151no—
390#124—151no—
391#121—302no—
392C4×D4—302no—
393C2×C4⋊C4—302no—
394C2×C42—31no—
395#97—32no—
396C4×C8—32no—
397C2×C3×C5—22no—
398C2×C3×C5C2×#12711yescharacteristic
399C2×C3×C5C2×#13712yes—
400D15—81no—
401C3×D5—81no—
402C23×C3—101no—
403C23×C3C2×D2011yescharacteristic
404C22×D3—101no—
405C3×Q8—102no—
406C3×Q8—101no—
407C3×Q8—102no—
408C3×Q8—101no—
409C3×Q8—202no—
410C3×D4—101no—
411C3×D4—101no—
412C3×D4—202no—
413C2×C3×C4—102no—
414C2×C3×C4—101no—
415C2×C3×C4—202no—
416C2×C3×C4—202no—
417C2×C3×C4C2×D2012yes—
418C2×C3×C4C2×D2011yescharacteristic
419C2×C3×C4C2×D2012yes—
420C2×C3×C4C23×D511yescharacteristic
421#67—202no—
422#67—204no—
423C2×Dic3—24no—
424C2×Dic3—102no—
425C2×Dic3—101no—
426C2×Dic3—202no—
427C2×Dic3C2×D2012yes—
428C2×Dic3C2×D2012yes—
429D12—101no—
430D12—101no—
431C4×D3—202no—
432Dic6—102no—
433Dic6—101no—
434Dic6—102no—
435Dic6—101no—
436Dic6—202no—
437C3×C8C2×D2014yes—
438C3⋊C8C2×D2014yes—
439C22×C5—22no—
440C22×C5#94012yes—
441C22×C5C2×D3×D411yescharacteristic
442C2×D5—42no—
443C2×D5—41no—
444C2×D5—122no—
445C2×D5—121no—
446C4×C5—34no—
447C4×C5—62no—
448C4×C5#94012yes—
449C4×C5C2×D3×D411yescharacteristic
450C4×C5C22×#6711yescharacteristic
451Dic5—42no—
452Dic5—41no—
453Dic5—122no—
454Dic5—121no—
455#41—102no—
456#41—102no—
457#41—302no—
458#41—302no—
459C2×Q8—51no—
460C2×Q8—52no—
461C2×Q8—101no—
462C2×Q8—102no—
463C2×Q8—102no—
464C2×Q8—151no—
465C2×Q8—152no—
466C2×Q8—301no—
467C2×Q8—302no—
468C2×Q8—302no—
469C2×D4—51no—
470C2×D4—101no—
471C2×D4—151no—
472C2×D4—302no—
473C2×D4—301no—
474C22×C4—32no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4C2×D3×D511yescharacteristic
480Q16—104no—
481Q16—304no—
482Q16—304no—
483Q16—304no—
484SD16—104no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488M16—34no—
489M16#120214yescomplemented
490C2×C8—32no—
491C2×C8C2×D3×D512yes—
492C4⋊C4—304no—
493C4⋊C4—304no—
494C4⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C42—32no—
498C42—31no—
499C42—31no—
500C3×C5#315211yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—201no—
503C22×C3—202no—
504C22×C3#402012yes—
505C22×C3C22×D2011yescharacteristic
506C2×D3—201no—
507C2×D3—202no—
508C3×C4—201no—
509C3×C4—202no—
510C3×C4#402012yes—
511C3×C4C22×D2011yescharacteristic
512C3×C4C22×D2011yescharacteristic
513Dic3—22no—
514Dic3—202no—
515Dic3—201no—
516Dic3#405514yescomplemented
517C2×C5—22no—
518C2×C5D3×#13712yes—
519C2×C5C2×#94011yescharacteristic
520D5—81no—
521D5—241no—
522C23—101no—
523C23—301no—
524C23D3×D2011yescharacteristic
525Q8—102no—
526Q8—101no—
527Q8—102no—
528Q8—101no—
529Q8—202no—
530Q8—302no—
531Q8—301no—
532Q8—302no—
533Q8—301no—
534Q8—602no—
535D4—101no—
536D4—101no—
537D4—202no—
538D4—301no—
539D4—301no—
540D4—604no—
541D4—602no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—64no—
545C2×C4—101no—
546C2×C4—102no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—301no—
550C2×C4—302no—
551C2×C4—602no—
552C2×C4—602no—
553C2×C4D3×D2011yescharacteristic
554C2×C4D3×D2012yes—
555C2×C4C2×#120212yes—
556C2×C4C22×D3×D511yescharacteristic
557C8—34no—
558C8C2×#120214yes—
559C2×C3—22no—
560C2×C3—401no—
561C2×C3C2×#402011yescharacteristic
562C2×C3C2×#405512yes—
563D3—401no—
564C5#8397211yescharacteristic, complemented, Sylow
565C22—22no—
566C22—202no—
567C22—201no—
568C22—602no—
569C22—601no—
570C22#9145812yes—
571C22C2×D3×D2011yescharacteristic
572C4—34no—
573C4—62no—
574C4—201no—
575C4—202no—
576C4—601no—
577C4—602no—
578C4#9145812yes—
579C4C2×D3×D2011yescharacteristic
580C4C22×#120211yescharacteristic
581C3#1061026911yescharacteristic, complemented, Sylow
582C2—22no—
583C2—401no—
584C2—1201no—
585C2D3×#405512yes—
586C2C2×#9145811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radical#11754581C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3152
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×#91798C2semidirect
2. C2×C3×#4055C2semidirect
4. C2×#91389C2semidirect
5. C2×#91315C2semidirect
6. C2×#91313C2semidirect
7. C5×Dic3×M16C2semidirect
8. #11748034C2semidirect
9. #11748033C2semidirect
10. #11748002C2semidirect
11. #11747973C2semidirect
48. C2×#4055D3semidirect
81. C3×C5×M16D4semidirect
88. C5×#208D4semidirect
111. Dic3×M16D5semidirect
238. C5×M16#67semidirect
283. C5×Dic3#137semidirect
311. C3×M16D20semidirect
325. #208D20semidirect
489. M16#1202semidirect
500. C3×C5#3152semidirect
516. Dic3#4055semidirect
564. C5#83972semidirect
581. C3#10610269semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C2×C3×#40552
#117545812
C2×#913892
C2×#913152
C2×#913132
C5×Dic3×M162
#117480342
#117480332
#117480022
#117479732
#106102693
#839725