Finite Group Databasebeta

← #14439468

Subgroups — #14439468

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#11756284C211yesmaximal, characteristic, complemented
2C3×#65860C211yesmaximal, characteristic, complemented
3C2×#91315C211yesmaximal, characteristic, complemented
4C22×#6658C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic, complemented
6C2×#91301C211yesmaximal, characteristic, complemented
7C5×#4997C211yesmaximal, characteristic, complemented
8#11747076C212yesmaximal, complemented
9#11747075C212yesmaximal, complemented
10#11747072C212yesmaximal, complemented
11#11747036C212yesmaximal, complemented
12#10610295—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C3×C5×#117C2211yescharacteristic
18#91784—22no—
19#91771—22no—
20#91764C2212yes—
21#91763C2212yes—
22C2×C5×#208C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4043—22no—
25C3×#4032—22no—
26C3×#4021C2212yescomplemented
27C3×#4015C2212yescomplemented
28C2×#6662C2212yescomplemented
29C2×#6662C2211yescharacteristic, complemented
30#91315—24no—
31C2×#6658—24no—
32C2×#6658C2212yes—
33C2×#6658C2212yes—
34C2×#6658C2212yes—
35C2×#6658C2211yescharacteristic, complemented
36C2×#6658C2212yescomplemented
37#91311—24no—
38C2×#6657C2211yescharacteristic, complemented
39#91301—24no—
40C2×#6653C2212yes—
41C2×#6653C2211yescharacteristic, complemented
42C5×#803C2212yescomplemented
43C4×C5×C3⋊C8C2212yescomplemented
44#83402—51nomaximal, Hall
45C2×#4055—31no—
46C2×#4054—31no—
47C2×#4050—31no—
48C22×#677—31no—
49#65860D311yescharacteristic, complemented
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×D60—24no—
65C2×D60C2311yescharacteristic
66C2×D60C2312yes—
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
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
80C3×C5×C4⋊C4D412yes—
81C3×C5×C22⋊C4D412yes—
82C3×C42×C5C2312yes—
83#6714—24no—
84C5×#208D414yescomplemented
85C2×C5×C3⋊C8D414yescomplemented
86C2×C5×C3⋊C8C2311yescharacteristic
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2312yes—
89C3×#685—24no—
90C3×C4⋊Dic5—24no—
91#6662—22no—
92#6662—24no—
93#6658—24no—
94#6658—22no—
95#6658—24no—
96#6658—24no—
97#6658—24no—
98#6657—22no—
99#6653—24no—
100#6653—22no—
101C3×#536—51no—
102C2×#950—51no—
103C2×#949—51no—
104C2×#942—51no—
105C22×#215—51no—
106#5525—51no—
107#5086—52no—
108#5085—52no—
109#5059—52no—
110#5058—52no—
111#4997D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×D20—31no—
115C22×Dic10C2×D311yescharacteristic
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—31no—
127C2×#677—32no—
128C2×#677—32no—
129C2×#677—31no—
130C2×#677—32no—
131C2×#677—32no—
132C2×#677—64no—
133#4043—22no—
134#4041—62no—
135#4032—22no—
136#4028—62no—
137#4021—32no—
138#4021C2×D312yescomplemented
139#4020—32no—
140#4015C2×D312yescomplemented
141C5×#97—32no—
142C4×C5×C8—32no—
143#3154—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—22no—
146C22×D15—21no—
147C22×D15—42no—
148C22×D15—82no—
149C22×C3×D5—21no—
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—
157D60—22no—
158D60—21no—
159D60—22no—
160D60—21no—
161D60—42no—
162D60—84no—
163C4×D15—42no—
164Dic30—21no—
165Dic30—21no—
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—
178C5×C3⋊C8C2×D412yes—
179C5×C3⋊C8C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×Q8—51no—
183C2×#235—51no—
184C22×D12—51no—
185C3×C4⋊Q8—52no—
186C3×#124—52no—
187C3×#123—102no—
188C3×C22⋊Q8—102no—
189C3×#117C2×D511yescharacteristic
190#950—104no—
191#949—104no—
192C2×#216—52no—
193C2×#216—51no—
194#942—104no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#215—52no—
198C2×#215—52no—
199C2×#215—51no—
200C2×#215—104no—
201C2×#214—51no—
202C2×#213—52no—
203C2×#213—51no—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8C2×D511yescharacteristic
206#895—102no—
207#882—102no—
208#875—52no—
209#874—52no—
210#803C2×D512yescomplemented
211C4×C3⋊C8C2×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—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—24no—
247Dic20—62no—
248Dic20—64no—
249D40—62no—
250D40—64no—
251#677—64no—
252#677—64no—
253#677—62no—
254#677—64no—
255#677—64no—
256#677—62no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—151no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—51no—
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—42no—
274C2×D15—44no—
275C2×D15—84no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5—24no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—42no—
284C3×Dic5—41no—
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—
299#235—102no—
300#235—102no—
301C2×D12—51no—
302C2×D12—52no—
303C2×D12—102no—
304C2×D12—102no—
305C2×D12—101no—
306C2×D12—104no—
307C2×C4×D3—101no—
308C2×Dic6—51no—
309C3×C4⋊C4—104no—
310C3×C4⋊C4D2012yes—
311C3×C22⋊C4—104no—
312C3×C22⋊C4D2012yes—
313C3×C42C22×D512yes—
314#216—104no—
315#216—102no—
316#215—104no—
317#215—104no—
318#215—104no—
319#215—104no—
320#215—102no—
321#214—102no—
322#213—104no—
323#213—102no—
324(C2×D3)⋊C4—104no—
325#208D2014yescomplemented
326C2×C3⋊C8D2014yescomplemented
327C2×C3⋊C8C22×D511yescharacteristic
328C2×C3⋊C8C22×D512yes—
329C2×C3⋊C8C22×D511yescharacteristic
330C23×C5C2×#6711yescharacteristic
331C22×D5—21no—
332C22×D5—62no—
333C22×D5—61no—
334C22×D5—122no—
335C22×D5—242no—
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—22no—
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×C8—34no—
367C2×#41—51no—
368C2×#41—151no—
369C22×Q8—51no—
370C22×D4—151no—
371#137—304no—
372AGL(1,ℤ/8)—304no—
373#135—304no—
374C2×Q16—151no—
375C2×Q16—152no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×SD16—152no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—151no—
384C2×D8—152no—
385C2×M16—31no—
386C22×C8—31no—
387C4⋊Q8—52no—
388#127—152no—
389#124—52no—
390#124—152no—
391#123—102no—
392C22⋊Q8—102no—
393#121—302no—
394#120—302no—
395#117D3×D511yescharacteristic
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—102no—
407C22×D3—101no—
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×D2012yes—
424C2×C3×C4C2×D2014yes—
425C2×C3×C4C2×D2011yescharacteristic
426C2×C3×C4C23×D511yescharacteristic
427#67—202no—
428C2×Dic3—101no—
429D12—102no—
430D12—101no—
431D12—102no—
432D12—101no—
433D12—202no—
434D12—404no—
435C4×D3—202no—
436Dic6—101no—
437Dic6—101no—
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—121no—
447C2×D5—122no—
448C2×D5—122no—
449C2×D5—124no—
450C2×D5—244no—
451C4×C5—24no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C2×D3×D411yescharacteristic
455Dic5—42no—
456Dic5—41no—
457Dic5—121no—
458C24—301no—
459#41—102no—
460#41—102no—
461#41—302no—
462#41—302no—
463C2×Q8—52no—
464C2×Q8—51no—
465C2×Q8—101no—
466C2×Q8—102no—
467C2×Q8—102no—
468C2×Q8—151no—
469C2×D4—51no—
470C2×D4—101no—
471C2×D4—152no—
472C2×D4—151no—
473C2×D4—301no—
474C2×D4—302no—
475C2×D4—302no—
476C2×D4—301no—
477C2×D4—304no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—302no—
483Q16—304no—
484SD16—302no—
485SD16—304no—
486SD16—304no—
487SD16—302no—
488SD16—304no—
489SD16—304no—
490D8—302no—
491D8—304no—
492M16—34no—
493C2×C8—34no—
494C2×C8—31no—
495C2×C8—32no—
496C2×C8—31no—
497C4⋊C4—104no—
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#402012yes—
508C22×C3C22×D2011yescharacteristic
509C2×D3—201no—
510C2×D3—202no—
511C2×D3—202no—
512C2×D3—204no—
513C2×D3—404no—
514C3×C4—24no—
515C3×C4—201no—
516C3×C4—202no—
517C3×C4#402012yes—
518C3×C4C22×D2011yescharacteristic
519C3×C4C22×D2011yescharacteristic
520Dic3—201no—
521C2×C5—22no—
522C2×C5C2×#94011yescharacteristic
523C2×C5#583712yes—
524D5—81no—
525D5—242no—
526D5—241no—
527C23—101no—
528C23—302no—
529C23—301no—
530C23—602no—
531C23—1202no—
532C23C2×#120211yescharacteristic
533Q8—102no—
534Q8—101no—
535Q8—102no—
536Q8—101no—
537Q8—202no—
538Q8—301no—
539Q8—301no—
540D4—101no—
541D4—101no—
542D4—202no—
543D4—302no—
544D4—301no—
545D4—302no—
546D4—301no—
547D4—602no—
548D4—602no—
549D4—1204no—
550C2×C4—102no—
551C2×C4—101no—
552C2×C4—202no—
553C2×C4—202no—
554C2×C4—301no—
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—401no—
566C2×C3C2×#402011yescharacteristic
567C2×C3#6608512yes—
568D3—402no—
569D3—401no—
570C5#8340211yescharacteristic, complemented, Sylow
571C22—22no—
572C22—202no—
573C22—201no—
574C22—602no—
575C22—604no—
576C22—601no—
577C22—602no—
578C22—1204no—
579C22#9145812yes—
580C22C22×#120211yescharacteristic
581C4—24no—
582C4—201no—
583C4—202no—
584C4—601no—
585C4#9145812yes—
586C4C2×D3×D2011yescharacteristic
587C4C2×D3×D2011yescharacteristic
588C3#1061029511yescharacteristic, complemented, Sylow
589C2—22no—
590C2—401no—
591C2—1202no—
592C2—1201no—
593C2C2×#9145811yescharacteristic
594C2#1175531012yes—
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. #11756284C2semidirect
2. C3×#65860C2semidirect
3. C2×#91315C2semidirect
4. C22×#6658C2semidirect
5. C2×#91311C2semidirect
6. C2×#91301C2semidirect
7. C5×#4997C2semidirect
8. #11747076C2semidirect
9. #11747075C2semidirect
10. #11747072C2semidirect
11. #11747036C2semidirect
26. C3×#4021C22semidirect
27. C3×#4015C22semidirect
28. C2×#6662C22semidirect
29. C2×#6662C22semidirect
35. C2×#6658C22semidirect
36. C2×#6658C22semidirect
38. C2×#6657C22semidirect
41. C2×#6653C22semidirect
42. C5×#803C22semidirect
43. C4×C5×C3⋊C8C22semidirect
49. #65860D3semidirect
84. C5×#208D4semidirect
85. C2×C5×C3⋊C8D4semidirect
111. #4997D5semidirect
138. #4021C2×D3semidirect
140. #4015C2×D3semidirect
210. #803C2×D5semidirect
211. C4×C3⋊C8C2×D5semidirect
325. #208D20semidirect
326. C2×C3⋊C8D20semidirect
503. C3×C5#3154semidirect
570. C5#83402semidirect
588. C3#10610295semidirect

Maximal subgroups

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

subgroupindex
#117562842
C3×#658602
C2×#913152
C22×#66582
C2×#913112
C2×#913012
C5×#49972
#117470762
#117470752
#117470722
#117470362
#106102953
#834025