Finite Group Databasebeta

← #14439486

Subgroups — #14439486

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic, complemented
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754609C211yesmaximal, characteristic, complemented
4#11754278C211yesmaximal, characteristic, complemented
5C22×#6658C211yesmaximal, characteristic, complemented
6C2×#91311C211yesmaximal, characteristic, complemented
7C5×#5122C211yesmaximal, characteristic, complemented
8#11748034C212yesmaximal, complemented
9#11748007C212yesmaximal, complemented
10#11748002C212yesmaximal, complemented
11#11747974C212yesmaximal, complemented
12#10610295—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91797—24no—
19C2×D120C2212yes—
20C2×#6706C2212yes—
21C5×#926C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4055—24no—
24C2×C3×Dic20C2212yescomplemented
25C2×C3×#677C2212yescomplemented
26#91572—22no—
27#91546—22no—
28#91458C2212yes—
29#91450—22no—
30#91390—22no—
31#91389C2212yescomplemented
32#91374C2212yes—
33#91374C2212yescomplemented
34C2×#6662C2211yescharacteristic, complemented
35C2×#6658—24no—
36C2×#6658C2212yes—
37C2×#6658C2212yes—
38C2×#6658C2211yescharacteristic, complemented
39#91311—24no—
40C2×#6657C2211yescharacteristic, complemented
41C2×#6653C2211yescharacteristic, complemented
42C5×#815C2212yescomplemented
43C5×C8×Dic3C2212yescomplemented
44#83974—51nomaximal, Hall
45C2×#4055D311yescharacteristic, complemented
46C2×#4054—31no—
47C2×#4050—31no—
48C22×#677—31no—
49#65860—31no—
50#65859—31no—
51C5×#405—31no—
52#65004—32no—
53#65001—32no—
54#64985—32no—
55#64982—32no—
56C23×D15—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60—22no—
62C2×D60—22no—
63C2×D60—21no—
64C2×D60C2312yes—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C2×C3×C22⋊D5—21no—
69C22×C3×Dic5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2312yes—
78C2×C3×Dic10C2311yescharacteristic
79C2×#1202—24no—
80C3×C5×M16D414yescomplemented
81C2×C3×C5×C8C2312yes—
82D120—24no—
83#6706—24no—
84C5×#217D412yes—
85C5×C4⋊Dic3D412yes—
86C4×C5×Dic3C2312yes—
87C2×C5×C3⋊C8D414yescomplemented
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2311yescharacteristic
90C3×Dic20—24no—
91C3×#677—24no—
92Dic3⋊Dic5—24no—
93#6667—24no—
94#6667—24no—
95#6662—22no—
96#6658—22no—
97#6658—24no—
98#6658—24no—
99#6657—22no—
100#6653—22no—
101C2×C3×#137—51no—
102#5830—51no—
103C2×#950—51no—
104#5816—51no—
105C22×#215—51no—
106C2×#908—51no—
107#5191—52no—
108#5190—52no—
109#5176—52no—
110#5175—52no—
111#5122D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×D20—31no—
115C22×Dic10C2×D311yescharacteristic
116C2×C5×M16C2×D311yescharacteristic
117C22×C5×C8—31no—
118C5×#117—31no—
119#4055—24no—
120#4054—64no—
121C2×Dic20—31no—
122C2×Dic20C2×D312yescomplemented
123#4050—64no—
124C2×D40—31no—
125C2×D40—32no—
126C2×#677—31no—
127C2×#677—32no—
128C2×#677—32no—
129C2×#677—31no—
130C2×#677—32no—
131C2×#677—64no—
132C2×#677C2×D312yescomplemented
133#4043—62no—
134#4041—62no—
135#4032—62no—
136#4028—62no—
137#4021—32no—
138#4021—32no—
139#4020—32no—
140#4015—32no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×D15—22no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C3×D5—21no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—42no—
155C2×Dic15—21no—
156D60—22no—
157D60—21no—
158D60—22no—
159D60—21no—
160D60—42no—
161C4×D15—42no—
162Dic30—21no—
163Dic30—21no—
164C2×C5×Dic3C2×D414yes—
165C3×C22⋊D5—42no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—42no—
169C3×D20—21no—
170C3×D20—21no—
171C3×C4×D5—42no—
172C3×Dic10—22no—
173C3×Dic10—21no—
174C3×Dic10—22no—
175C3×Dic10—21no—
176C3×Dic10—42no—
177#1202—84no—
178C3×C5×C8C2×D414yes—
179C5×C3⋊C8C2×D412yes—
180C5×C3⋊C8C2×D412yes—
181C2×C3×#41—51no—
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×D12—51no—
185C3×#137—104no—
186C2×C3×Q16—52no—
187C2×C3×SD16—52no—
188C2×C3×M16C2×D511yescharacteristic
189#950—104no—
190#947—52no—
191#947—52no—
192#946—102no—
193#944—52no—
194C2×#216—51no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#215—51no—
198C2×#215—104no—
199#940—52no—
200#937—102no—
201C2×#214—51no—
202C2×#213—51no—
203#930—102no—
204#929—102no—
205#926C2×D511yescharacteristic
206C22×C3⋊C8C2×D511yescharacteristic
207#908—104no—
208C2×D24—52no—
209C2×#204—52no—
210#815C2×D512yescomplemented
211C8×Dic3C2×D512yescomplemented
212C23×D5—61no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—21no—
215C2×C22⋊D5—61no—
216C22×Dic5—21no—
217#709—22no—
218#709—22no—
219#709—62no—
220#709—62no—
221C2×D20—32no—
222C2×D20—31no—
223C2×D20—62no—
224C2×D20—62no—
225C2×D20—61no—
226C2×D20—64no—
227C2×D20C22×D311yescharacteristic
228C2×C4×D5—21no—
229C2×C4×D5—61no—
230C2×Dic10—22no—
231C2×Dic10—22no—
232C2×Dic10—21no—
233C2×Dic10—31no—
234C2×Dic10C22×D312yes—
235C2×Dic10C22×D311yescharacteristic
236C5×M16#6714yescomplemented
237C2×C5×C8—34no—
238C2×C5×C8—31no—
239C2×C5×C8—31no—
240C2×C5×C8C22×D312yes—
241C5×C4⋊C4—32no—
242C5×C22⋊C4—32no—
243C42×C5—32no—
244#685—64no—
245#685—64no—
246C4⋊Dic5—64no—
247Dic20—24no—
248Dic20—62no—
249D40—62no—
250D40—64no—
251#677—24no—
252#677—64no—
253#677—64no—
254#677—62no—
255#677—62no—
256#677—64no—
257C2×#137—51no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—151no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—31no—
268C22×C3×C5—22no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C2×D15—44no—
274C2×D15—42no—
275C2×D15—84no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—41no—
282C3×Dic5—42no—
283C3×Dic5—41no—
284C5×Dic3—24no—
285C23×D3—101no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—52no—
289C2×C3×Q8—51no—
290C2×C3×Q8—101no—
291C2×C3×Q8—102no—
292C2×C3×Q8—102no—
293C2×C3×D4—51no—
294C2×C3×D4—101no—
295C22×C3×C4—101no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—101no—
299C2×#67—104no—
300#235—102no—
301#235—102no—
302C2×D12—52no—
303C2×D12—51no—
304C2×D12—102no—
305C2×D12—102no—
306C2×D12—101no—
307C2×C4×D3—101no—
308C2×Dic6—51no—
309C3×Q16—104no—
310C3×SD16—104no—
311C3×M16D2014yescomplemented
312C2×C3×C8C22×D512yes—
313#217D2012yes—
314#216—102no—
315#215—104no—
316#215—104no—
317#215—102no—
318#214—102no—
319#213—102no—
320(C2×D3)⋊C4—104no—
321(C2×D3)⋊C4—104no—
322C4⋊Dic3D2012yes—
323Dic3⋊C4—104no—
324C4×Dic3C22×D512yes—
325C2×C3⋊C8D2014yescomplemented
326C2×C3⋊C8C22×D511yescharacteristic
327C2×C3⋊C8C22×D511yescharacteristic
328D24—104no—
329#204—104no—
330C23×C5D3×D411yescharacteristic
331C22×D5—21no—
332C22×D5—61no—
333C22×D5—62no—
334C22×D5—122no—
335C22×D5—242no—
336C2×C4×C5—34no—
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5D3×D412yes—
339C2×C4×C5C2×#6712yes—
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—42no—
342C22⋊D5—122no—
343C2×Dic5—22no—
344C2×Dic5—21no—
345C2×Dic5—42no—
346C2×Dic5—61no—
347D20—21no—
348D20—21no—
349D20—62no—
350D20—61no—
351D20—62no—
352D20—61no—
353D20—122no—
354D20—244no—
355C4×D5—42no—
356C4×D5—122no—
357Dic10—22no—
358Dic10—21no—
359Dic10—22no—
360Dic10—21no—
361Dic10—42no—
362Dic10—61no—
363Dic10—61no—
364C5×C8—32no—
365C5×C8—32no—
366C5×C8C2×#6714yes—
367C2×#41—51no—
368C2×#41—151no—
369C22×Q8—51no—
370C22×D4—151no—
371#137—104no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—52no—
375C2×Q16—151no—
376C2×SD16—52no—
377C2×SD16—151no—
378C2×SD16—152no—
379C2×SD16—152no—
380C2×SD16—151no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16D3×D511yescharacteristic
386C22×C8—31no—
387C4⋊Q8—152no—
388#127—152no—
389#124—152no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—302no—
394#120—302no—
395#117—31no—
396#97—32no—
397C4×C8—32no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401D15—81no—
402D15—82no—
403C3×D5—81no—
404C23×C3—101no—
405C23×C3C2×D2011yescharacteristic
406C22×D3—101no—
407C22×D3—102no—
408C22×D3—202no—
409C22×D3—402no—
410C3×Q8—102no—
411C3×Q8—101no—
412C3×Q8—102no—
413C3×Q8—101no—
414C3×Q8—202no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—202no—
418C2×C3×C4—102no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4—202no—
422C2×C3×C4C2×D2012yes—
423C2×C3×C4C2×D2011yescharacteristic
424C2×C3×C4C2×D2012yes—
425C2×C3×C4C23×D511yescharacteristic
426#67—202no—
427#67—404no—
428C2×Dic3—101no—
429C2×Dic3C2×D2014yes—
430D12—102no—
431D12—101no—
432D12—101no—
433D12—102no—
434D12—202no—
435C4×D3—202no—
436Dic6—101no—
437Dic6—101no—
438C3×C8C2×D2014yes—
439C3⋊C8C2×D2012yes—
440C3⋊C8C2×D2012yes—
441C22×C5—22no—
442C22×C5#94012yes—
443C22×C5C2×D3×D411yescharacteristic
444C2×D5—42no—
445C2×D5—41no—
446C2×D5—124no—
447C2×D5—122no—
448C2×D5—121no—
449C2×D5—122no—
450C2×D5—244no—
451C4×C5—64no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C22×#6711yescharacteristic
455Dic5—42no—
456Dic5—41no—
457Dic5—121no—
458C24—301no—
459#41—102no—
460#41—102no—
461#41—302no—
462#41—302no—
463C2×Q8—51no—
464C2×Q8—52no—
465C2×Q8—101no—
466C2×Q8—102no—
467C2×Q8—102no—
468C2×Q8—151no—
469C2×D4—51no—
470C2×D4—101no—
471C2×D4—151no—
472C2×D4—152no—
473C2×D4—304no—
474C2×D4—301no—
475C2×D4—302no—
476C2×D4—301no—
477C2×D4—302no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—104no—
483Q16—302no—
484SD16—104no—
485SD16—302no—
486SD16—304no—
487SD16—304no—
488SD16—302no—
489SD16—304no—
490D8—302no—
491D8—304no—
492M16#120214yescomplemented
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8C2×D3×D512yes—
497C4⋊C4—32no—
498C4⋊C4—304no—
499C22⋊C4—32no—
500C22⋊C4—304no—
501C22⋊C4—304no—
502C42—32no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—201no—
506C22×C3—202no—
507C22×C3#402012yes—
508C22×C3C22×D2011yescharacteristic
509C2×D3—201no—
510C2×D3—202no—
511C2×D3—204no—
512C2×D3—202no—
513C2×D3—404no—
514C3×C4—201no—
515C3×C4—202no—
516C3×C4#402012yes—
517C3×C4C22×D2011yescharacteristic
518C3×C4C22×D2011yescharacteristic
519Dic3—24no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5#577812yes—
523C2×C5C2×#94011yescharacteristic
524D5—81no—
525D5—242no—
526D5—241no—
527C23—101no—
528C23—301no—
529C23—302no—
530C23—602no—
531C23—1202no—
532C23D3×D2011yescharacteristic
533Q8—102no—
534Q8—101no—
535Q8—102no—
536Q8—101no—
537Q8—202no—
538Q8—301no—
539Q8—301no—
540D4—101no—
541D4—101no—
542D4—202no—
543D4—301no—
544D4—302no—
545D4—301no—
546D4—302no—
547D4—602no—
548D4—602no—
549D4—1204no—
550C2×C4—34no—
551C2×C4—101no—
552C2×C4—102no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—301no—
556C2×C4—602no—
557C2×C4D3×D2011yescharacteristic
558C2×C4D3×D2012yes—
559C2×C4C2×#120212yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—32no—
562C8—32no—
563C8C2×#120214yes—
564C2×C3—22no—
565C2×C3—401no—
566C2×C3C2×#402011yescharacteristic
567C2×C3#6608512yes—
568D3—402no—
569D3—401no—
570C5#8397411yescharacteristic, complemented, Sylow
571C22—22no—
572C22—202no—
573C22—201no—
574C22—604no—
575C22—602no—
576C22—601no—
577C22—602no—
578C22—1204no—
579C22#9145812yes—
580C22C2×D3×D2011yescharacteristic
581C4—64no—
582C4—201no—
583C4—202no—
584C4—601no—
585C4#9145812yes—
586C4C2×D3×D2011yescharacteristic
587C4C22×#120211yescharacteristic
588C3#1061029511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—401no—
591C2—1202no—
592C2—1201no—
593C2#1175403212yes—
594C2C2×#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#3154
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×#4055C2semidirect
3. #11754609C2semidirect
4. #11754278C2semidirect
5. C22×#6658C2semidirect
6. C2×#91311C2semidirect
7. C5×#5122C2semidirect
8. #11748034C2semidirect
9. #11748007C2semidirect
10. #11748002C2semidirect
11. #11747974C2semidirect
24. C2×C3×Dic20C22semidirect
25. C2×C3×#677C22semidirect
31. #91389C22semidirect
33. #91374C22semidirect
34. C2×#6662C22semidirect
38. C2×#6658C22semidirect
40. C2×#6657C22semidirect
41. C2×#6653C22semidirect
42. C5×#815C22semidirect
43. C5×C8×Dic3C22semidirect
45. C2×#4055D3semidirect
80. C3×C5×M16D4semidirect
87. C2×C5×C3⋊C8D4semidirect
111. #5122D5semidirect
122. C2×Dic20C2×D3semidirect
132. C2×#677C2×D3semidirect
210. #815C2×D5semidirect
211. C8×Dic3C2×D5semidirect
236. C5×M16#67semidirect
311. C3×M16D20semidirect
325. C2×C3⋊C8D20semidirect
492. M16#1202semidirect
503. C3×C5#3154semidirect
570. C5#83974semidirect
588. C3#10610295semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
C2×C3×#40552
#117546092
#117542782
C22×#66582
C2×#913112
C5×#51222
#117480342
#117480072
#117480022
#117479742
#106102953
#839745