Finite Group Databasebeta

← #14439179

Subgroups — #14439179

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 632 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#11754581C211yesmaximal, characteristic, complemented
4C2×#91458C211yesmaximal, characteristic, complemented
5C2×#91312C211yesmaximal, characteristic, complemented
6C2×#91301C211yesmaximal, characteristic, complemented
7C5×Dic3×M16C211yesmaximal, characteristic, complemented
8#11748009C212yesmaximal, complemented
9#11748007C212yesmaximal, complemented
10#11748005C212yesmaximal, complemented
11#11748002C212yesmaximal, complemented
12#10610261—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×#1202—22no—
18C2×C3×C5×M16C2211yescharacteristic
19#91797—24no—
20C2×D120C2212yescomplemented
21C2×#6706C2212yescomplemented
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C5×#208C2211yescharacteristic
24C3×#4054—24no—
25C2×C3×D40C2212yescomplemented
26C2×C3×#677C2212yescomplemented
27#91569—22no—
28#91458—22no—
29#91458C2212yes—
30#91458C2212yes—
31#91458C2211yescharacteristic, complemented
32C4×#1202—22no—
33#91389C2211yescharacteristic, complemented
34#91374C2211yescharacteristic, complemented
35#91364C2211yescharacteristic, complemented
36C2×#6658C2212yescomplemented
37#91312—24no—
38C2×#6657C2212yescomplemented
39#91301—24no—
40C2×#6653C2212yescomplemented
41C2×#6653C2212yescomplemented
42C5×#815C2212yescomplemented
43C5×C8×Dic3C2212yescomplemented
44#83937—51nomaximal, Hall
45C2×#4054—31no—
46C2×#4054—31no—
47C2×#4054—31no—
48C2×#4054D311yescharacteristic, complemented
49#65811—31no—
50C2×#4020—31no—
51C4×C5×M16—31no—
52#65001—32no—
53#65001—32no—
54#64984—32no—
55#64982—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×D60C2312yes—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3D412yes—
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20—22no—
74C2×C3×D20—22no—
75C2×C3×D20—21no—
76C2×C3×D20C2312yes—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—22no—
81C2×#1202—24no—
82C2×#1202—24no—
83C2×#1202—48no—
84C3×C5×M16D414yescomplemented
85C2×C3×C5×C8C2312yes—
86D120—24no—
87#6706—24no—
88C4×C5×Dic3D412yes—
89C4×C5×Dic3C2311yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C5×#208D414yescomplemented
92C2×C5×C3⋊C8C2312yes—
93C3×D40—24no—
94C3×#677—24no—
95Dic3⋊Dic5—22no—
96#6667—22no—
97#6665—22no—
98#6658—24no—
99#6657—24no—
100#6653—24no—
101#6653—24no—
102C2×C3×AGL(1,ℤ/8)—51no—
103#5832—51no—
104C2×#949—51no—
105C2×#940—51no—
106C2×#932—51no—
107C2×#908—51no—
108#5176—52no—
109#5175—52no—
110#5154—52no—
111#5151—52no—
112Dic3×M16D511yescharacteristic, complemented
113C2×#709—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C22×D20—62no—
117C22×D20C2×D311yescharacteristic
118C2×C5×M16—31no—
119C2×C5×M16C2×D311yescharacteristic
120C2×C42×C5—31no—
121#4076—62no—
122#4054—24no—
123#4054—64no—
124#4054—64no—
125#4054—64no—
126C2×D40—32no—
127C2×D40—32no—
128C2×D40—32no—
129C2×D40C2×D312yescomplemented
130C2×#677—32no—
131C2×#677—32no—
132C2×#677—32no—
133C2×#677C2×D312yescomplemented
134#4021—31no—
135#4021—31no—
136#4020—32no—
137#4020—32no—
138#4020—31no—
139#4020—62no—
140C4×D20—62no—
141#4015—31no—
142C5×#97—32no—
143C4×C5×C8—32no—
144#3151—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×D15—22no—
148C22×D15—44no—
149C22×D15—42no—
150C22×C3×D5—21no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—42no—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159C2×Dic15—21no—
160D60—22no—
161D60—22no—
162D60—21no—
163D60—21no—
164D60—42no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3C2×D412yes—
170C2×C5×Dic3C2×D412yes—
171C3×C22⋊D5—42no—
172C2×C3×Dic5—21no—
173C3×D20—22no—
174C3×D20—22no—
175C3×D20—21no—
176C3×D20—21no—
177C3×D20—42no—
178C3×C4×D5—42no—
179C3×Dic10—21no—
180C3×Dic10—21no—
181#1202—48no—
182#1202—44no—
183#1202—48no—
184C3×C5×C8C2×D414yescomplemented
185C5×C3⋊C8C2×D414yescomplemented
186C2×C3×#41—51no—
187C22×C3×D4—51no—
188C22×#67—102no—
189C2×#235—51no—
190C22×D12—51no—
191C3×AGL(1,ℤ/8)—104no—
192C2×C3×SD16—52no—
193C2×C3×D8—52no—
194C2×C3×M16C2×D511yescharacteristic
195#949—104no—
196#947—51no—
197#944—51no—
198C2×#215—52no—
199#940—51no—
200#940—52no—
201#940—52no—
202#940—102no—
203#939—102no—
204#936—51no—
205C2×#214—52no—
206#932—104no—
207C2×#213—52no—
208C2×#213—52no—
209C4×#67—102no—
210C2×C4×Dic3C2×D511yescharacteristic
211C2×#208C2×D511yescharacteristic
212#908—104no—
213C2×D24—52no—
214C2×#204—52no—
215#815C2×D512yescomplemented
216C8×Dic3C2×D512yescomplemented
217C23×D5—21no—
218C23×D5—61no—
219C22×C4×C5—32no—
220C22×C4×C5C22×D311yescharacteristic
221C2×C22⋊D5—21no—
222C2×C22⋊D5—61no—
223#709—22no—
224#709—22no—
225#709—62no—
226#709—62no—
227C2×D20—22no—
228C2×D20—22no—
229C2×D20—21no—
230C2×D20—32no—
231C2×D20—31no—
232C2×D20—62no—
233C2×D20—62no—
234C2×D20—64no—
235C2×D20—64no—
236C2×D20—62no—
237C2×D20—61no—
238C2×D20—128no—
239C2×D20C22×D312yes—
240C2×D20C22×D311yescharacteristic
241C2×C4×D5—21no—
242C2×C4×D5—61no—
243C2×Dic10—31no—
244C2×Dic10C22×D311yescharacteristic
245C5×M16—34no—
246C5×M16#6714yescomplemented
247C2×C5×C8—32no—
248C2×C5×C8C22×D312yes—
249C42×C5—32no—
250C42×C5—31no—
251C42×C5—31no—
252#685—62no—
253#685—62no—
254C4⋊Dic5—62no—
255D40—24no—
256D40—64no—
257D40—64no—
258D40—64no—
259#677—24no—
260#677—64no—
261#677—64no—
262#677—64no—
263C2×AGL(1,ℤ/8)—51no—
264C2×AGL(1,ℤ/8)—151no—
265C2×AGL(1,ℤ/8)—151no—
266C2×AGL(1,ℤ/8)—151no—
267#532—151no—
268C2×#127—151no—
269#496—152no—
270#496—152no—
271#493—152no—
272#492—152no—
273C4×M16—31no—
274C22×C3×C5—22no—
275C22×C3×C5#12712yes—
276C22×C3×C5C22×D411yescharacteristic
277C2×D15—41no—
278C2×D15—42no—
279C2×D15—44no—
280C2×D15—42no—
281C2×D15—84no—
282C2×C3×D5—41no—
283C2×C3×D5—42no—
284C2×C3×D5—44no—
285C2×C3×D5—42no—
286C2×C3×D5—84no—
287C3×C4×C5#12712yes—
288C3×C4×C5C22×D411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—41no—
291C3×Dic5—41no—
292C5×Dic3—22no—
293C5×Dic3AGL(1,ℤ/8)14yescomplemented
294C24×C3—101no—
295C23×D3—101no—
296C3×#41—102no—
297C3×#41—102no—
298C2×C3×Q8—51no—
299C2×C3×D4—51no—
300C2×C3×D4—52no—
301C2×C3×D4—101no—
302C2×C3×D4—102no—
303C2×C3×D4—102no—
304C2×C3×D4—101no—
305C22×C3×C4—101no—
306C22×C3×C4C22×D511yescharacteristic
307C2×#67—101no—
308C2×#67—102no—
309C2×#67—104no—
310C2×#67—104no—
311C2×#67—208no—
312C22×Dic3D2012yes—
313#235—102no—
314#235—102no—
315C2×D12—52no—
316C2×D12—51no—
317C2×D12—102no—
318C2×D12—102no—
319C2×D12—101no—
320C2×C4×D3—101no—
321C2×Dic6—51no—
322C3×SD16—104no—
323C3×D8—104no—
324C3×M16D2014yescomplemented
325C2×C3×C8C22×D512yes—
326#217—102no—
327#215—104no—
328#214—104no—
329#213—104no—
330#213—104no—
331(C2×D3)⋊C4—102no—
332Dic3⋊C4—102no—
333C4×Dic3D2012yes—
334C4×Dic3C22×D511yescharacteristic
335C4×Dic3C22×D511yescharacteristic
336#208D2014yescomplemented
337C2×C3⋊C8C22×D512yes—
338D24—104no—
339#204—104no—
340C23×C5D3×D411yescharacteristic
341C22×D5—21no—
342C22×D5—22no—
343C22×D5—44no—
344C22×D5—42no—
345C22×D5—61no—
346C22×D5—62no—
347C22×D5—124no—
348C22×D5—122no—
349C2×C4×C5—32no—
350C2×C4×C5—32no—
351C2×C4×C5—64no—
352C2×C4×C5D3×D411yescharacteristic
353C2×C4×C5D3×D412yes—
354C2×C4×C5C2×#6712yes—
355C2×C4×C5C23×D311yescharacteristic
356C22⋊D5—42no—
357C22⋊D5—122no—
358C2×Dic5—21no—
359C2×Dic5—61no—
360D20—22no—
361D20—21no—
362D20—22no—
363D20—21no—
364D20—42no—
365D20—62no—
366D20—61no—
367D20—62no—
368D20—61no—
369D20—124no—
370D20—128no—
371D20—128no—
372D20—122no—
373C4×D5—42no—
374C4×D5—122no—
375Dic10—21no—
376Dic10—21no—
377Dic10—61no—
378Dic10—61no—
379C5×C8—34no—
380C5×C8C2×#6714yescomplemented
381C2×#41—51no—
382C2×#41—151no—
383C22×D4—51no—
384C22×D4—151no—
385C22×D4—302no—
386AGL(1,ℤ/8)—104no—
387AGL(1,ℤ/8)—304no—
388AGL(1,ℤ/8)—304no—
389AGL(1,ℤ/8)—304no—
390C2×SD16—52no—
391C2×SD16—152no—
392C2×SD16—152no—
393C2×SD16—152no—
394C2×D8—52no—
395C2×D8—152no—
396C2×D8—152no—
397C2×D8—152no—
398C2×M16—31no—
399C2×M16D3×D511yescharacteristic
400C4⋊Q8—151no—
401#127—152no—
402#127—152no—
403#127—151no—
404#127—302no—
405#124—151no—
406#124—151no—
407#121—302no—
408C4×D4—302no—
409C2×C42—31no—
410#97—32no—
411C4×C8—32no—
412C2×C3×C5—22no—
413C2×C3×C5C2×#12711yescharacteristic
414C2×C3×C5C2×AGL(1,ℤ/8)12yes—
415D15—81no—
416D15—82no—
417C3×D5—81no—
418C3×D5—82no—
419C23×C3—101no—
420C23×C3—102no—
421C23×C3—204no—
422C23×C3—202no—
423C23×C3C2×D2011yescharacteristic
424C22×D3—101no—
425C22×D3—102no—
426C22×D3—204no—
427C22×D3—202no—
428C3×Q8—101no—
429C3×Q8—101no—
430C3×D4—101no—
431C3×D4—102no—
432C3×D4—101no—
433C3×D4—102no—
434C3×D4—202no—
435C3×D4—202no—
436C2×C3×C4—101no—
437C2×C3×C4—202no—
438C2×C3×C4C2×D2012yes—
439C2×C3×C4C2×D2011yescharacteristic
440C2×C3×C4C2×D2012yes—
441C2×C3×C4C23×D511yescharacteristic
442#67—208no—
443#67—202no—
444#67—204no—
445#67—208no—
446C2×Dic3—24no—
447C2×Dic3—101no—
448C2×Dic3C2×D2012yes—
449C2×Dic3C2×D2012yes—
450D12—102no—
451D12—101no—
452D12—101no—
453D12—102no—
454D12—202no—
455C4×D3—202no—
456Dic6—101no—
457Dic6—101no—
458C3×C8C2×D2014yescomplemented
459C3⋊C8C2×D2014yescomplemented
460C22×C5—22no—
461C22×C5#94012yes—
462C22×C5C2×D3×D411yescharacteristic
463C2×D5—44no—
464C2×D5—42no—
465C2×D5—41no—
466C2×D5—42no—
467C2×D5—84no—
468C2×D5—124no—
469C2×D5—122no—
470C2×D5—121no—
471C2×D5—122no—
472C2×D5—244no—
473C4×C5—34no—
474C4×C5—62no—
475C4×C5#94012yes—
476C4×C5C2×D3×D411yescharacteristic
477C4×C5C22×#6711yescharacteristic
478Dic5—41no—
479Dic5—121no—
480C24—101no—
481C24—301no—
482#41—102no—
483#41—102no—
484#41—302no—
485#41—302no—
486C2×Q8—51no—
487C2×Q8—151no—
488C2×D4—51no—
489C2×D4—52no—
490C2×D4—101no—
491C2×D4—102no—
492C2×D4—101no—
493C2×D4—102no—
494C2×D4—151no—
495C2×D4—152no—
496C2×D4—302no—
497C2×D4—304no—
498C2×D4—304no—
499C2×D4—301no—
500C2×D4—302no—
501C2×D4—301no—
502C2×D4—302no—
503C2×D4—608no—
504C22×C4—32no—
505C22×C4—101no—
506C22×C4—301no—
507C22×C4C2×D3×D511yescharacteristic
508SD16—104no—
509SD16—304no—
510SD16—304no—
511SD16—304no—
512D8—104no—
513D8—304no—
514D8—304no—
515D8—304no—
516M16—34no—
517M16#120214yescomplemented
518C2×C8—32no—
519C2×C8C2×D3×D512yes—
520C4⋊C4—302no—
521C22⋊C4—302no—
522C22⋊C4—302no—
523C42—32no—
524C42—31no—
525C42—31no—
526C3×C5#315111yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—201no—
529C22×C3—202no—
530C22×C3—204no—
531C22×C3—202no—
532C22×C3—404no—
533C22×C3#402012yes—
534C22×C3C22×D2011yescharacteristic
535C2×D3—201no—
536C2×D3—202no—
537C2×D3—204no—
538C2×D3—202no—
539C2×D3—404no—
540C3×C4—201no—
541C3×C4#402012yes—
542C3×C4C22×D2011yescharacteristic
543C3×C4C22×D2011yescharacteristic
544Dic3—22no—
545Dic3—201no—
546Dic3#405414yescomplemented
547C2×C5—22no—
548C2×C5D3×AGL(1,ℤ/8)12yes—
549C2×C5C2×#94011yescharacteristic
550D5—82no—
551D5—81no—
552D5—242no—
553D5—241no—
554C23—101no—
555C23—102no—
556C23—204no—
557C23—202no—
558C23—301no—
559C23—302no—
560C23—604no—
561C23—602no—
562C23D3×D2011yescharacteristic
563Q8—101no—
564Q8—101no—
565Q8—301no—
566Q8—301no—
567D4—101no—
568D4—102no—
569D4—101no—
570D4—102no—
571D4—202no—
572D4—202no—
573D4—301no—
574D4—302no—
575D4—301no—
576D4—302no—
577D4—608no—
578D4—604no—
579D4—608no—
580D4—602no—
581D4—602no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—64no—
585C2×C4—101no—
586C2×C4—202no—
587C2×C4—301no—
588C2×C4—602no—
589C2×C4D3×D2011yescharacteristic
590C2×C4D3×D2012yes—
591C2×C4C2×#120212yes—
592C2×C4C22×D3×D511yescharacteristic
593C8—34no—
594C8C2×#120214yescomplemented
595C2×C3—22no—
596C2×C3—402no—
597C2×C3—401no—
598C2×C3C2×#402011yescharacteristic
599C2×C3C2×#405412yes—
600D3—402no—
601D3—401no—
602C5#8393711yescharacteristic, complemented, Sylow
603C22—22no—
604C22—204no—
605C22—202no—
606C22—201no—
607C22—202no—
608C22—404no—
609C22—604no—
610C22—602no—
611C22—601no—
612C22—602no—
613C22—1204no—
614C22#9145812yes—
615C22C2×D3×D2011yescharacteristic
616C4—34no—
617C4—62no—
618C4—201no—
619C4—601no—
620C4#9145812yes—
621C4C2×D3×D2011yescharacteristic
622C4C22×#120211yescharacteristic
623C3#1061026111yescharacteristic, complemented, Sylow
624C2—22no—
625C2—402no—
626C2—401no—
627C2—1202no—
628C2—1201no—
629C2D3×#405412yes—
630C2C2×#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#3151
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. #11754581C2semidirect
4. C2×#91458C2semidirect
5. C2×#91312C2semidirect
6. C2×#91301C2semidirect
7. C5×Dic3×M16C2semidirect
8. #11748009C2semidirect
9. #11748007C2semidirect
10. #11748005C2semidirect
11. #11748002C2semidirect
20. C2×D120C22semidirect
21. C2×#6706C22semidirect
25. C2×C3×D40C22semidirect
26. C2×C3×#677C22semidirect
31. #91458C22semidirect
33. #91389C22semidirect
34. #91374C22semidirect
35. #91364C22semidirect
36. C2×#6658C22semidirect
38. C2×#6657C22semidirect
40. C2×#6653C22semidirect
41. C2×#6653C22semidirect
42. C5×#815C22semidirect
43. C5×C8×Dic3C22semidirect
48. C2×#4054D3semidirect
84. C3×C5×M16D4semidirect
91. C5×#208D4semidirect
112. Dic3×M16D5semidirect
129. C2×D40C2×D3semidirect
133. C2×#677C2×D3semidirect
184. C3×C5×C8C2×D4semidirect
185. C5×C3⋊C8C2×D4semidirect
215. #815C2×D5semidirect
216. C8×Dic3C2×D5semidirect
246. C5×M16#67semidirect
293. C5×Dic3AGL(1,ℤ/8)semidirect
324. C3×M16D20semidirect
336. #208D20semidirect
380. C5×C8C2×#67semidirect
458. C3×C8C2×D20semidirect
459. C3⋊C8C2×D20semidirect
517. M16#1202semidirect
526. C3×C5#3151semidirect
546. Dic3#4054semidirect
594. C8C2×#1202semidirect
602. C5#83937semidirect
623. C3#10610261semidirect

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
#117545812
C2×#914582
C2×#913122
C2×#913012
C5×Dic3×M162
#117480092
#117480072
#117480052
#117480022
#106102613
#839375