Finite Group Databasebeta

← #14439467

Subgroups — #14439467

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
1#11756285C211yesmaximal, characteristic, complemented
2C3×#65859C211yesmaximal, characteristic, complemented
3C2×#91313C211yesmaximal, characteristic, complemented
4C2×#91312C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic, complemented
6C22×#6657C211yesmaximal, characteristic, complemented
7C5×#4997C211yesmaximal, characteristic, complemented
8#11747074C212yesmaximal, complemented
9#11747073C212yesmaximal, complemented
10#11747072C212yesmaximal, complemented
11#11747071C212yesmaximal, complemented
12#10610295—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C3×C5×#117C2211yescharacteristic
18#91786—22no—
19#91775—22no—
20#91764C2212yescomplemented
21#91758C2212yescomplemented
22C2×C5×#208C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4041—22no—
25C3×#4028—22no—
26C3×#4021C2212yes—
27C3×#4020C2212yes—
28C2×#6662C2212yescomplemented
29C2×#6662C2211yescharacteristic, complemented
30C2×#6658C2211yescharacteristic, complemented
31#91313—24no—
32#91312—24no—
33#91311—24no—
34C2×#6657—24no—
35C2×#6657C2212yes—
36C2×#6657C2212yes—
37C2×#6657C2212yes—
38C2×#6657C2212yescomplemented
39C2×#6657C2211yescharacteristic, complemented
40C2×#6653C2212yes—
41C2×#6653C2211yescharacteristic, complemented
42C5×#803C2212yescomplemented
43C4×C5×C3⋊C8C2212yescomplemented
44#83381—51nomaximal, Hall
45C2×#4055—31no—
46C2×#4054—31no—
47C2×#4050—31no—
48C22×#677—31no—
49#65860—31no—
50#65859D311yescharacteristic, complemented
51C5×#405—31no—
52#65004—32no—
53#65001—32no—
54#64985—32no—
55#64982—32no—
56C23×C3×D5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C22×Dic15—21no—
60#6817—22no—
61#6817—22no—
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×Dic30—22no—
65C2×Dic30—22no—
66C2×Dic30—21no—
67C2×Dic30C2311yescharacteristic
68C2×Dic30C2312yes—
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×D20—24no—
76C2×C3×D20C2312yes—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C3×C5×C4⋊C4D412yes—
81C3×C5×C22⋊C4D412yes—
82C3×C42×C5C2312yes—
83#6714—24no—
84C4⋊Dic15—24no—
85C5×#208D414yescomplemented
86C2×C5×C3⋊C8D414yescomplemented
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2311yescharacteristic
89C2×C5×C3⋊C8C2312yes—
90C3×#685—24no—
91#6662—22no—
92#6662—24no—
93#6658—22no—
94#6657—24no—
95#6657—24no—
96#6657—24no—
97#6657—22no—
98#6657—24no—
99#6653—24no—
100#6653—22no—
101C3×#535—51no—
102C2×#951—51no—
103C2×#950—51no—
104C22×#214—51no—
105C2×#932—51no—
106#5526—51no—
107#5076—52no—
108#5074—52no—
109#5060—52no—
110#5059—52no—
111#4997D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×D20C2×D311yescharacteristic
115C22×Dic10—31no—
116C2×C5×M16—31no—
117C22×C5×C8—31no—
118C5×#117C2×D311yescharacteristic
119#4055—64no—
120#4054—64no—
121C2×Dic20—31no—
122C2×Dic20—32no—
123#4050—64no—
124C2×D40—31no—
125C2×D40—32no—
126C2×#677—32no—
127C2×#677—32no—
128C2×#677—31no—
129C2×#677—32no—
130C2×#677—32no—
131C2×#677—31no—
132C2×#677—64no—
133#4043—62no—
134#4041—22no—
135#4032—62no—
136#4028—22no—
137#4021—32no—
138#4021C2×D312yes—
139#4020C2×D312yes—
140#4015—32no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—22no—
147C22×C3×D5—21no—
148C22×C3×D5—42no—
149C22×C3×D5—82no—
150C2×C3×C4×C5C2×D414yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220—42no—
156C2×Dic15—21no—
157C2×Dic15—22no—
158C2×Dic15—42no—
159D60—21no—
160D60—21no—
161C4×D15—42no—
162Dic30—22no—
163Dic30—21no—
164Dic30—22no—
165Dic30—21no—
166Dic30—42no—
167C3×C22⋊D5—42no—
168C2×C3×Dic5—21no—
169C3×D20—22no—
170C3×D20—21no—
171C3×D20—22no—
172C3×D20—21no—
173C3×D20—42no—
174C3×D20—84no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C5×C3⋊C8C2×D412yes—
179C5×C3⋊C8C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×D4—51no—
183C2×#235—51no—
184C22×Dic6—51no—
185C3×#127—52no—
186C3×#124—52no—
187C3×#121—102no—
188C3×#120—102no—
189C3×#117C2×D511yescharacteristic
190#951—104no—
191#950—104no—
192C2×#216—51no—
193C2×#216—52no—
194C2×#215—51no—
195C2×#214—52no—
196C2×#214—52no—
197C2×#214—52no—
198C2×#214—51no—
199C2×#214—52no—
200C2×#214—104no—
201#932—104no—
202C2×#213—52no—
203C2×#213—51no—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8C2×D511yescharacteristic
206#897—102no—
207#886—102no—
208#875—52no—
209#869—52no—
210#803C2×D512yescomplemented
211C4×C3⋊C8C2×D512yescomplemented
212C23×D5—21no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—21no—
215C2×C22⋊D5—61no—
216C22×Dic5—61no—
217#709—22no—
218#709—22no—
219#709—62no—
220#709—62no—
221C2×D20—22no—
222C2×D20—22no—
223C2×D20—21no—
224C2×D20—24no—
225C2×D20—31no—
226C2×D20C22×D312yes—
227C2×D20C22×D311yescharacteristic
228C2×C4×D5—21no—
229C2×C4×D5—61no—
230C2×Dic10—32no—
231C2×Dic10—31no—
232C2×Dic10—62no—
233C2×Dic10—62no—
234C2×Dic10—61no—
235C2×Dic10C22×D311yescharacteristic
236C5×M16—34no—
237C2×C5×C8—34no—
238C2×C5×C8—31no—
239C2×C5×C8—31no—
240C2×C5×C8—32no—
241C5×C4⋊C4#6712yes—
242C5×C22⋊C4#6712yes—
243C42×C5C22×D312yes—
244#685—24no—
245#685—64no—
246C4⋊Dic5—64no—
247Dic20—62no—
248Dic20—64no—
249D40—62no—
250D40—64no—
251#677—62no—
252#677—64no—
253#677—64no—
254#677—62no—
255#677—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—51no—
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×C3×D5—41no—
274C2×C3×D5—42no—
275C2×C3×D5—42no—
276C2×C3×D5—44no—
277C2×C3×D5—84no—
278C3×C4×C5—24no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—42no—
283Dic15—41no—
284C3×Dic5—41no—
285C24×C3—101no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×D4—52no—
290C2×C3×D4—51no—
291C2×C3×D4—101no—
292C2×C3×D4—102no—
293C2×C3×D4—102no—
294C2×C3×D4—101no—
295C2×C3×D4—104no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—101no—
299C22×Dic3—101no—
300#235—102no—
301#235—102no—
302C2×D12—51no—
303C2×C4×D3—101no—
304C2×Dic6—51no—
305C2×Dic6—52no—
306C2×Dic6—102no—
307C2×Dic6—102no—
308C2×Dic6—101no—
309C3×C4⋊C4D2012yes—
310C3×C22⋊C4—104no—
311C3×C22⋊C4D2012yes—
312C3×C42C22×D512yes—
313#216—102no—
314#216—104no—
315#215—102no—
316#214—104no—
317#214—104no—
318#214—104no—
319#214—102no—
320#214—104no—
321#213—104no—
322#213—102no—
323(C2×D3)⋊C4—104no—
324C4⋊Dic3—104no—
325#208D2014yescomplemented
326C2×C3⋊C8D2014yescomplemented
327C2×C3⋊C8C22×D511yescharacteristic
328C2×C3⋊C8C22×D512yes—
329C2×C3⋊C8C22×D511yescharacteristic
330C23×C5C2×#6711yescharacteristic
331C22×D5—22no—
332C22×D5—21no—
333C22×D5—42no—
334C22×D5—61no—
335C22×D5—82no—
336C2×C4×C5D3×D412yes—
337C2×C4×C5D3×D412yes—
338C2×C4×C5C2×#6714yes—
339C2×C4×C5C2×#6711yescharacteristic
340C2×C4×C5C23×D311yescharacteristic
341C22⋊D5—42no—
342C22⋊D5—122no—
343C2×Dic5—21no—
344C2×Dic5—61no—
345C2×Dic5—62no—
346C2×Dic5—122no—
347D20—22no—
348D20—21no—
349D20—22no—
350D20—21no—
351D20—42no—
352D20—61no—
353D20—61no—
354D20—84no—
355C4×D5—42no—
356C4×D5—122no—
357Dic10—21no—
358Dic10—21no—
359Dic10—62no—
360Dic10—61no—
361Dic10—62no—
362Dic10—61no—
363Dic10—122no—
364C5×C8—32no—
365C5×C8—32no—
366C5×C8—34no—
367C2×#41—51no—
368C2×#41—151no—
369C22×Q8—151no—
370C22×D4—51no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—151no—
375C2×Q16—152no—
376C2×SD16—152no—
377C2×SD16—152no—
378C2×SD16—151no—
379C2×SD16—152no—
380C2×SD16—152no—
381C2×SD16—151no—
382C2×SD16—304no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16—31no—
386C22×C8—31no—
387C4⋊Q8—152no—
388#127—52no—
389#124—52no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—102no—
394#120—102no—
395#117D3×D511yescharacteristic
396#97—32no—
397C4×C8—32no—
398C2×C3×C5—22no—
399C2×C3×C5C2×#12711yescharacteristic
400C2×C3×C5#57712yes—
401D15—81no—
402C3×D5—81no—
403C3×D5—82no—
404C23×C3—102no—
405C23×C3—101no—
406C23×C3—202no—
407C23×C3—402no—
408C23×C3C2×D2011yescharacteristic
409C22×D3—101no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×D4—102no—
413C3×D4—101no—
414C3×D4—102no—
415C3×D4—101no—
416C3×D4—202no—
417C3×D4—202no—
418C3×D4—404no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4C2×D2012yes—
422C2×C3×C4C2×D2012yes—
423C2×C3×C4C2×D2014yes—
424C2×C3×C4C2×D2011yescharacteristic
425C2×C3×C4C23×D511yescharacteristic
426#67—202no—
427C2×Dic3—101no—
428C2×Dic3—102no—
429C2×Dic3—202no—
430D12—101no—
431D12—101no—
432C4×D3—202no—
433Dic6—102no—
434Dic6—101no—
435Dic6—102no—
436Dic6—101no—
437Dic6—202no—
438C3⋊C8C2×D2012yes—
439C3⋊C8C2×D2012yes—
440C3⋊C8C2×D2014yes—
441C22×C5—22no—
442C22×C5#94012yes—
443C22×C5C22×#6711yescharacteristic
444C2×D5—41no—
445C2×D5—42no—
446C2×D5—42no—
447C2×D5—44no—
448C2×D5—84no—
449C2×D5—121no—
450C2×D5—122no—
451C4×C5—24no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C2×D3×D411yescharacteristic
455Dic5—41no—
456Dic5—122no—
457Dic5—121no—
458C24—101no—
459#41—102no—
460#41—102no—
461#41—302no—
462#41—302no—
463C2×Q8—51no—
464C2×Q8—152no—
465C2×Q8—151no—
466C2×Q8—301no—
467C2×Q8—302no—
468C2×Q8—302no—
469C2×D4—52no—
470C2×D4—51no—
471C2×D4—101no—
472C2×D4—102no—
473C2×D4—102no—
474C2×D4—101no—
475C2×D4—104no—
476C2×D4—151no—
477C2×D4—301no—
478C22×C4—101no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—302no—
483Q16—304no—
484SD16—304no—
485SD16—304no—
486SD16—302no—
487SD16—304no—
488SD16—304no—
489SD16—302no—
490D8—302no—
491D8—304no—
492M16—34no—
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—32no—
496C2×C8—31no—
497C4⋊C4—304no—
498C4⋊C4#120212yes—
499C22⋊C4—104no—
500C22⋊C4—304no—
501C22⋊C4#120212yes—
502C42C2×D3×D512yes—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—201no—
506C22×C3—202no—
507C22×C3—202no—
508C22×C3—204no—
509C22×C3—404no—
510C22×C3#402012yes—
511C22×C3C22×D2011yescharacteristic
512C2×D3—201no—
513C2×D3—202no—
514C3×C4—24no—
515C3×C4—201no—
516C3×C4#402012yes—
517C3×C4C22×D2011yescharacteristic
518C3×C4C22×D2011yescharacteristic
519Dic3—202no—
520Dic3—201no—
521C2×C5—22no—
522C2×C5C2×#94011yescharacteristic
523C2×C5#583612yes—
524D5—82no—
525D5—81no—
526D5—241no—
527C23—102no—
528C23—101no—
529C23—202no—
530C23—301no—
531C23—402no—
532C23C2×#120211yescharacteristic
533Q8—101no—
534Q8—101no—
535Q8—302no—
536Q8—301no—
537Q8—302no—
538Q8—301no—
539Q8—602no—
540D4—102no—
541D4—101no—
542D4—102no—
543D4—101no—
544D4—202no—
545D4—202no—
546D4—301no—
547D4—301no—
548D4—404no—
549D4—602no—
550C2×C4—101no—
551C2×C4—202no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4—602no—
556C2×C4D3×D2012yes—
557C2×C4D3×D2012yes—
558C2×C4C2×#120214yes—
559C2×C4C2×#120211yescharacteristic
560C2×C4C22×D3×D511yescharacteristic
561C8—32no—
562C8—32no—
563C8—34no—
564C2×C3—22no—
565C2×C3—402no—
566C2×C3—401no—
567C2×C3C2×#402011yescharacteristic
568C2×C3#6608512yes—
569D3—401no—
570C5#8338111yescharacteristic, complemented, Sylow
571C22—22no—
572C22—202no—
573C22—204no—
574C22—201no—
575C22—202no—
576C22—404no—
577C22—602no—
578C22—601no—
579C22#9145812yes—
580C22C22×#120211yescharacteristic
581C4—24no—
582C4—201no—
583C4—601no—
584C4—602no—
585C4#9145812yes—
586C4C2×D3×D2011yescharacteristic
587C4C2×D3×D2011yescharacteristic
588C3#1061029511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—402no—
591C2—401no—
592C2—1201no—
593C2C2×#9145811yescharacteristic
594C2#1175530912yes—
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756285C2semidirect
2. C3×#65859C2semidirect
3. C2×#91313C2semidirect
4. C2×#91312C2semidirect
5. C2×#91311C2semidirect
6. C22×#6657C2semidirect
7. C5×#4997C2semidirect
8. #11747074C2semidirect
9. #11747073C2semidirect
10. #11747072C2semidirect
11. #11747071C2semidirect
20. #91764C22semidirect
21. #91758C22semidirect
28. C2×#6662C22semidirect
29. C2×#6662C22semidirect
30. C2×#6658C22semidirect
38. C2×#6657C22semidirect
39. C2×#6657C22semidirect
41. C2×#6653C22semidirect
42. C5×#803C22semidirect
43. C4×C5×C3⋊C8C22semidirect
50. #65859D3semidirect
85. C5×#208D4semidirect
86. C2×C5×C3⋊C8D4semidirect
111. #4997D5semidirect
210. #803C2×D5semidirect
211. C4×C3⋊C8C2×D5semidirect
325. #208D20semidirect
326. C2×C3⋊C8D20semidirect
503. C3×C5#3154semidirect
570. C5#83381semidirect
588. C3#10610295semidirect

Maximal subgroups

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

subgroupindex
#117562852
C3×#658592
C2×#913132
C2×#913122
C2×#913112
C22×#66572
C5×#49972
#117470742
#117470732
#117470722
#117470712
#106102953
#833815