Finite Group Databasebeta

← #13007913

Subgroups — #13007913

Order 1280.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×Q8×#41C211yesmaximal, characteristic, complemented
2#10618944C211yesmaximal, characteristic, complemented
3#10618943C211yesmaximal, characteristic, complemented
4#10618927C212yesmaximal, complemented
5#10618925C211yesmaximal, characteristic, complemented
6#10618924C211yesmaximal, characteristic, complemented
7#10618923C212yesmaximal, complemented
8#10618836C216yesmaximal, complemented
9#10618834C213yesmaximal, complemented
10#10618831C213yesmaximal, complemented
11#10618830C216yesmaximal, complemented
12#10618652C213yesmaximal, complemented
13#10618649C213yesmaximal, complemented
14#10618177C213yesmaximal, complemented
15#10618177C216yesmaximal, complemented
16#10618174C216yesmaximal, complemented
17#10618158C213yesmaximal, complemented
18#41×D20C211yesmaximal, characteristic, complemented
19#41×D20C212yesmaximal, complemented
20#10617735C212yesmaximal, complemented
21C4×D5×#41C211yesmaximal, characteristic, complemented
22C2×#65914C213yesmaximal, complemented
23#10617703C213yesmaximal, complemented
24C2×D5×#41C2211yescharacteristic
25C2×D5×#41C2212yes—
26C5×Q82C2211yescharacteristic, complemented
27C5×#557C2212yescomplemented
28C5×#557C2211yescharacteristic, complemented
29C5×#554C2216yescomplemented
30C5×#554C2213yescomplemented
31C5×D4×Q8C2213yescomplemented
32C5×#533C2213yescomplemented
33C5×#533C2216yescomplemented
34C4×C5×#41C2211yescharacteristic
35C4×C5×#41C2212yes—
36C2×C4×C5×Q8C2213yescomplemented
37#41×Dic5C2211yescharacteristic
38#66151C2216yescomplemented
39C2×#4093C2213yescomplemented
40C2×#4092C2213yescomplemented
41#66068C2216yescomplemented
42#66068C2213yescomplemented
43#66067C2216yescomplemented
44#66067C2216yescomplemented
45#66067C2216yescomplemented
46#66067C2216yescomplemented
47#66066C2213yescomplemented
48#66066C2216yescomplemented
49#66064C2216yescomplemented
50#66064C2213yescomplemented
51#66062C2213yescomplemented
52#66062C2213yescomplemented
53#66060C2213yescomplemented
54#66060C2216yescomplemented
55#66059C2213yescomplemented
56#66059C2213yescomplemented
57#66032C2216yescomplemented
58#66032C2216yescomplemented
59#66031C2216yescomplemented
60#66031C2216yescomplemented
61#66029C2216yescomplemented
62#66029C2216yescomplemented
63#66029C2216yescomplemented
64#66028C2216yescomplemented
65#66028C2216yescomplemented
66#66028C2216yescomplemented
67#66025C2216yescomplemented
68#66025C2216yescomplemented
69#65979C22112yescomplemented
70#65979C22112yescomplemented
71#65978C22112yescomplemented
72#65978C22112yescomplemented
73#65976C2216yescomplemented
74#65976C22112yescomplemented
75#65971C22112yescomplemented
76#65971C22112yescomplemented
77#65971C22112yescomplemented
78#65964C2216yescomplemented
79#65964C22112yescomplemented
80#65961C2216yescomplemented
81#65961C2216yescomplemented
82#65958C2216yescomplemented
83#65958C2216yescomplemented
84#65919C2213yescomplemented
85#65919C2216yescomplemented
86#65918C2213yescomplemented
87#65918C2216yescomplemented
88#65914C2213yes—
89#65914C2211yescharacteristic
90#65914C2213yescomplemented
91#65914C2213yescomplemented
92#65914C2216yescomplemented
93#65914C2213yescomplemented
94#65914C2213yescomplemented
95#65914C2216yescomplemented
96#65914C2216yescomplemented
97#65914C2216yescomplemented
98#65914C22112yescomplemented
99#65914C22112yescomplemented
100#65914C2213yescomplemented
101#65914C2216yescomplemented
102#65914C2213yescomplemented
103#65911C2212yescomplemented
104#65911C2211yescharacteristic, complemented
105#65911C2213yescomplemented
106#65910C2212yescomplemented
107#65910C2212yescomplemented
108#65910C2212yescomplemented
109Q8×D20C2212yescomplemented
110Q8×D20C2211yescharacteristic, complemented
111#65908C2212yescomplemented
112#65908C2212yescomplemented
113C4×#713C2211yescharacteristic, complemented
114C4×#713C2216yescomplemented
115C4×#713C2216yescomplemented
116C4×#713C2211yescharacteristic, complemented
117#65906C2212yescomplemented
118#65906C2212yescomplemented
119C4×Q8×D5C2211yescharacteristic, complemented
120C4×Q8×D5C2211yescharacteristic, complemented
121#65904C2213yescomplemented
122#65889C2213yescomplemented
123#65889C2216yescomplemented
124#65888C2216yescomplemented
125#65888C2216yescomplemented
126#65888C2216yescomplemented
127D4×D20C2213yescomplemented
128D4×D20C2216yescomplemented
129#65880C2216yescomplemented
130#65880C2216yescomplemented
131#65879C2216yescomplemented
132#65879C2216yescomplemented
133C4×D4×D5C2213yescomplemented
134C4×D4×D5C2213yescomplemented
135C4×#711C2213yescomplemented
136C4×#711C2213yescomplemented
137#65858C2216yescomplemented
138#65858C2216yescomplemented
139#65858C2216yescomplemented
140#65856C2216yescomplemented
141#65856C2213yescomplemented
142D5×#117C2213yescomplemented
143D5×#117C2216yescomplemented
144#65848C22112yescomplemented
145#65848C2216yescomplemented
146C2×#4044C2216yescomplemented
147C2×#4041C2213yes—
148C2×#4040C2216yescomplemented
149C2×#4036C2213yescomplemented
150#65811C2213yescomplemented
151#65811C2216yescomplemented
152C4×#709C2213yescomplemented
153C4×#709C2216yescomplemented
154C2×C4×D20C2213yescomplemented
155C2×C4×D20C2216yescomplemented
156C2×#4018C2216yescomplemented
157C2×C42×D5C2213yescomplemented
158#62816—51nomaximal, Sylow
159C2×C5×#41C2311yescharacteristic
160C22×C5×Q8C2313yes—
161D5×#41—28no—
162D5×#41—216no—
163C2×#713C2311yescharacteristic
164C2×#713C2312yes—
165C2×#713C2316yes—
166C2×#713C2316yes—
167C2×Q8×D5C2311yescharacteristic
168C2×Q8×D5C2312yes—
169C2×#711C2313yes—
170C2×#711C2316yes—
171C2×D4×D5C2313yes—
172C2×D4×D5C2316yes—
173C2×#709C2313yes—
174C2×#709C2316yes—
175C22×D20C2316yes—
176C22×D20C2313yes—
177C22×C4×D5C2313yes—
178C22×C4×D5C2316yes—
179C22×C4×D5C2313yes—
180C22×C4×D5C2313yes—
181C5×C4⋊Q8C2313yes—
182C5×C4⋊Q8C2313yes—
183C5×C4⋊Q8C2316yes—
184C5×C4⋊Q8C2316yes—
185C5×#125C2316yes—
186C5×#125C2316yes—
187C5×#125C2316yes—
188C5×C22⋊Q8C2316yes—
189C5×C22⋊Q8C23112yes—
190C5×C22⋊Q8C2316yes—
191C5×C22⋊Q8C23112yes—
192C4×C5×Q8C2313yes—
193C4×C5×Q8C2311yescharacteristic
194C4×C5×Q8C2311yescharacteristic
195C4×C5×Q8C2312yes—
196C4×C5×Q8C2312yes—
197C4×C5×Q8C2313yes—
198C4×C5×Q8C2316yes—
199C4×C5×Q8C2311yescharacteristic
200C4×C5×Q8C2316yes—
201C4×C5×Q8C2313yes—
202C4×C5×Q8C2316yes—
203C4×C5×D4C2313yes—
204C4×C5×D4C2313yes—
205C4×C5×D4C2316yes—
206C4×C5×D4C2316yes—
207C5×#117C2313yes—
208C5×#117C2316yes—
209C2×C5×C4⋊C4C2313yes—
210C2×C5×C4⋊C4C2316yes—
211C2×C42×C5C2313yes—
212C2×C42×C5C2316yes—
213#4093C2313yes—
214#4093C2316yes—
215#4093C2313yes—
216#4093C23112yes—
217#4093C2316yes—
218#4093C23112yes—
219#4093C2316yes—
220#4093C2311yescharacteristic
221#4093C2313yes—
222#4092C2313yes—
223#4092C23112yes—
224#4092C2313yes—
225#4092C2316yes—
226#4092C2316yes—
227#4092C23112yes—
228#4092C2316yes—
229#4092C2311yescharacteristic
230#4092C2313yes—
231Q8×Dic5C2316yes—
232Q8×Dic5C2316yes—
233Q8×Dic5C2311yescharacteristic
234Q8×Dic5C2311yescharacteristic
235D4×Dic5C2313yes—
236D4×Dic5C2313yes—
237#4076C23112yes—
238#4076C2316yes—
239#4076C2316yes—
240#4076C23112yes—
241C4×C22⋊D5C2316yes—
242C4×C22⋊D5C23112yes—
243C4×C22⋊D5C2316yes—
244C4×C22⋊D5C23112yes—
245C2×#685C2316yes—
246C2×#685C2316yes—
247C2×#685C2316yes—
248C2×#685C2316yes—
249C2×#685C2316yes—
250#4072C2313yes—
251C2×C4⋊Dic5C2316yes—
252C2×C4⋊Dic5C2313yes—
253C2×#683C2316yes—
254C2×#683C2316yes—
255C2×C4×Dic5C2313yes—
256C2×C4×Dic5C2313yes—
257C2×C4×Dic5C2313yes—
258#4044C2316yes—
259#4044C23112yes—
260#4044C23112yes—
261#4044C2316yes—
262#4044C23112yes—
263#4044C23112yes—
264#4044C2312yes—
265#4044C2316yes—
266#4044C2316yes—
267#4044C2316yes—
268#4044C2316yes—
269#4044C2316yes—
270#4044C23112yes—
271#4043C2316yes—
272#4043C2316yes—
273#4043C2316yes—
274#4043C2316yes—
275#4043C2316yes—
276#4043C2316yes—
277#4041C2313yes—
278#4041C2316yes—
279#4041C2316yes—
280#4041C2316yes—
281#4041C2316yes—
282#4041C2316yes—
283#4041C2316yes—
284#4041C2316yes—
285#4041C2313yes—
286#4041C23112yes—
287#4041C2311yescharacteristic
288#4041C2313yes—
289#4041C2316yes—
290#4041C2316yes—
291#4041C23112yes—
292#4040C2316yes—
293#4040C23112yes—
294#4040C23112yes—
295#4040C2316yes—
296#4040C23112yes—
297#4040C23112yes—
298#4040C2312yes—
299#4040C2316yes—
300#4040C2316yes—
301#4040C2316yes—
302#4040C2316yes—
303#4040C2316yes—
304#4040C23112yes—
305#4039C2316yes—
306#4039C2316yes—
307#4039C2316yes—
308#4039C2316yes—
309#4039C23112yes—
310#4039C2313yes—
311#4039C2313yes—
312#4039C23112yes—
313#4038C2316yes—
314#4038C2316yes—
315#4038C2313yes—
316#4038C2316yes—
317#4038C2316yes—
318#4038C2313yes—
319#4038C23112yes—
320#4038C23112yes—
321D5×C4⋊C4C2313yes—
322D5×C4⋊C4C2316yes—
323D5×C4⋊C4C2316yes—
324D5×C4⋊C4C2313yes—
325#4036C2313yes—
326#4036C2316yes—
327#4036C2313yes—
328#4036C23112yes—
329#4036C2311yescharacteristic
330#4036C2313yes—
331#4036C2316yes—
332#4036C2316yes—
333#4036C23112yes—
334#4033C2316yes—
335#4033C2316yes—
336#4033C2313yes—
337#4033C2313yes—
338#4032C23112yes—
339#4032C23112yes—
340#4032C23112yes—
341#4028C23112yes—
342#4028C23112yes—
343#4028C23112yes—
344#4027C2316yes—
345#4027C2316yes—
346#4027C23112yes—
347#4027C23112yes—
348D5×C22⋊C4C2316yes—
349D5×C22⋊C4C23112yes—
350#4023C2316yes—
351#4023C23112yes—
352#4021C2316yes—
353#4021C2316yes—
354#4021C2316yes—
355#4020C2313yes—
356#4020C2316yes—
357C4×D20C2316yes—
358C4×D20C2313yes—
359C4×D20C2313yes—
360C4×D20C2316yes—
361C4×D20C2312yes—
362C4×D20C2311yescharacteristic
363C4×D20C2313yes—
364C4×D20C2316yes—
365C4×D20C2313yes—
366C4×D20C2316yes—
367C4×D20C2316yes—
368C4×D20C2316yes—
369C4×D20C2316yes—
370C4×D20C2316yes—
371C4×D20C2316yes—
372C4×D20C2316yes—
373C4×D20C2313yes—
374C4×D20C2316yes—
375C4×D20C2316yes—
376C4×D20C23112yes—
377#4018C2312yes—
378#4018C2316yes—
379#4018C2316yes—
380#4018C2316yes—
381#4018C2316yes—
382#4018C2316yes—
383#4018C2316yes—
384#4018C2316yes—
385#4018C2316yes—
386C42×D5C2313yes—
387C42×D5C2313yes—
388C42×D5C2311yescharacteristic
389C42×D5C2313yes—
390C42×D5C2313yes—
391C42×D5C2313yes—
392C42×D5C2313yes—
393C42×D5C2313yes—
394C42×D5C23112yes—
395#4015C2313yes—
396#4015C2316yes—
397C4×Dic10C2313yes—
398C4×Dic10C2316yes—
399C4×Dic10C2313yes—
400C4×Dic10C2316yes—
401#3524—52no—
402#3523—51no—
403#3522—51no—
404#3521—56no—
405#3520—53no—
406#3519—53no—
407#3518—51no—
408#3517—51no—
409#3516—52no—
410#3515—53no—
411#3514—53no—
412#3513—56no—
413#3480—53no—
414Q8×#41D511yescharacteristic, complemented
415#3475—56no—
416#3475—53no—
417D4×#41—51no—
418D4×#41—52no—
419#3455—56no—
420#3444—53no—
421C2×#529—53no—
422#3428—52no—
423C2×C4×#41—51no—
424C23×D5C2413yes—
425C23×D5C2416yes—
426C5×#41#4118yescomplemented
427C2×C5×Q8—46no—
428C2×C5×Q8C2411yescharacteristic
429C2×C5×Q8C2413yes—
430C2×C5×Q8C2416yes—
431C2×C5×Q8C2416yes—
432C2×C5×Q8C2411yescharacteristic
433C2×C5×D4C2413yes—
434C22×C4×C5C2413yes—
435C22×C4×C5C2413yes—
436C22×C4×C5C2416yes—
437C22×C4×C5C2416yes—
438C22×C4×C5C2413yes—
439C2×C22⋊D5C2416yes—
440C2×C22⋊D5C24112yes—
441C22×Dic5C2413yes—
442C22×Dic5C2416yes—
443C22×Dic5C2413yes—
444C22×Dic5C2413yes—
445#713—24no—
446#713—28no—
447#713—412no—
448#713—412no—
449Q8×D5—24no—
450Q8×D5—28no—
451#711—212no—
452#711—224no—
453D4×D5—212no—
454D4×D5—224no—
455#709—212no—
456#709—224no—
457C2×D20—46no—
458C2×D20—412no—
459C2×D20C2412yes—
460C2×D20C2411yescharacteristic
461C2×D20C2413yes—
462C2×D20C2416yes—
463C2×D20C2413yes—
464C2×D20C2416yes—
465C2×D20C2416yes—
466C2×D20C2416yes—
467C2×D20C2416yes—
468C2×D20C2416yes—
469C2×D20C24112yes—
470C2×C4×D5—212no—
471C2×C4×D5—224no—
472C2×C4×D5—46no—
473C2×C4×D5—46no—
474C2×C4×D5C2411yescharacteristic
475C2×C4×D5C2411yescharacteristic
476C2×C4×D5C2411yescharacteristic
477C2×C4×D5C2412yes—
478C2×C4×D5C2413yes—
479C2×C4×D5C2416yes—
480C2×C4×D5C2413yes—
481C2×C4×D5C2416yes—
482C2×C4×D5C2413yes—
483C2×C4×D5C2416yes—
484C2×C4×D5C2413yes—
485C2×C4×D5C2413yes—
486C2×C4×D5C2413yes—
487C2×C4×D5C2413yes—
488C2×C4×D5C2413yes—
489C2×C4×D5C2413yes—
490C2×C4×D5C24112yes—
491C2×C4×D5C24112yes—
492C2×Dic10C2413yes—
493C2×Dic10C2416yes—
494C5×C4⋊C4C2411yescharacteristic
495C5×C4⋊C4C2412yes—
496C5×C4⋊C4C2416yes—
497C5×C4⋊C4C2416yes—
498C5×C4⋊C4C2416yes—
499C5×C4⋊C4C2413yes—
500C5×C4⋊C4C2416yes—
501C5×C4⋊C4C2413yes—
502C5×C4⋊C4C2413yes—
503C5×C4⋊C4C2416yes—
504C5×C4⋊C4C2416yes—
505C5×C4⋊C4C24112yes—
506C5×C4⋊C4C2416yes—
507C5×C22⋊C4C2416yes—
508C5×C22⋊C4C24112yes—
509C42×C5C2411yescharacteristic
510C42×C5C2412yes—
511C42×C5C2413yes—
512C42×C5C2416yes—
513C42×C5C2416yes—
514C42×C5C2413yes—
515C42×C5C2413yes—
516C42×C5C2416yes—
517C22⋊Dic5C2416yes—
518#685C2412yes—
519#685C2412yes—
520#685C2416yes—
521#685C2416yes—
522#685C2416yes—
523#685C2416yes—
524#685C2416yes—
525#685C2416yes—
526#685C2416yes—
527#685C2416yes—
528#685C2412yes—
529#685C2412yes—
530#685C2412yes—
531#685C2416yes—
532#685C2416yes—
533#685C2416yes—
534#685C2416yes—
535#685C2416yes—
536#685C2416yes—
537#685C2416yes—
538#685C2416yes—
539#685C2416yes—
540#685C24112yes—
541#685C24112yes—
542#685C24112yes—
543C4⋊Dic5C2413yes—
544C4⋊Dic5C2413yes—
545C4⋊Dic5C2416yes—
546C4⋊Dic5C2413yes—
547C4⋊Dic5C2416yes—
548C4⋊Dic5C24112yes—
549C4⋊Dic5C2412yes—
550C4⋊Dic5C2411yescharacteristic
551C4⋊Dic5C2416yes—
552C4⋊Dic5C2416yes—
553C4⋊Dic5C2416yes—
554#683C2416yes—
555#683C2416yes—
556#683C2416yes—
557#683C2416yes—
558#683C2412yes—
559#683C2412yes—
560#683C2416yes—
561#683C2416yes—
562#683C2416yes—
563#683C2416yes—
564C4×Dic5C2413yes—
565C4×Dic5C2413yes—
566C4×Dic5C24112yes—
567C4×Dic5C24112yes—
568C4×Dic5C2413yes—
569C4×Dic5C2411yescharacteristic
570C4×Dic5C2411yescharacteristic
571C4×Dic5C2411yescharacteristic
572C4×Dic5C2413yes—
573C4×Dic5C2413yes—
574C4×Dic5C2413yes—
575C4×Dic5C2413yes—
576C4×Dic5C2413yes—
577C4×Dic5C2413yes—
578C22×#41—51no—
579C22×#41—52no—
580#559—56no—
581#559—53no—
582Q82C2×D511yescharacteristic, complemented
583#557—53no—
584#557C2×D512yescomplemented
585#557C2×D511yescharacteristic, complemented
586#556—53no—
587#556—56no—
588#556—56no—
589#556—53no—
590#555—56no—
591#555—53no—
592#554—53no—
593#554—56no—
594#554C2×D516yescomplemented
595#554C2×D513yescomplemented
596#553—56no—
597#553—56no—
598#553—56no—
599#553—512no—
600#553—56no—
601#552—56no—
602#552—56no—
603#552—56no—
604#552—56no—
605#552—512no—
606#551—512no—
607#551—512no—
608#551—512no—
609#550—51no—
610#550—52no—
611#550—53no—
612D4×Q8—52no—
613D4×Q8—51no—
614D4×Q8C2×D513yescomplemented
615#548—56no—
616#548—52no—
617#548—52no—
618#548—52no—
619#547—56no—
620#547—53no—
621#547—53no—
622#547—56no—
623#546—512no—
624#546—56no—
625#546—56no—
626#546—56no—
627#546—56no—
628D42—56no—
629D42—53no—
630#542—56no—
631#542—56no—
632#542—56no—
633#542—56no—
634#541—56no—
635#541—56no—
636#540—56no—
637#540—56no—
638#539—512no—
639#539—512no—
640#538—512no—
641#538—512no—
642#533—53no—
643#533—53no—
644#533C2×D513yescomplemented
645#533C2×D516yescomplemented
646#532—53no—
647#532—53no—
648#532—53no—
649#532—56no—
650#529—56no—
651#529—56no—
652#529—56no—
653#529—56no—
654#529—51no—
655#529—53no—
656#529—53no—
657#529—56no—
658#529—56no—
659#529—53no—
660#529—53no—
661#529—56no—
662#529—53no—
663#529—53no—
664#529—53no—
665#529—56no—
666#529—56no—
667#529—512no—
668#529—512no—
669C2×#126—56no—
670C2×#125—53no—
671C2×#124—53no—
672#525—56no—
673#525—56no—
674#525—56no—
675#525—56no—
676#525—56no—
677C2×#123—56no—
678C2×C22⋊Q8—53no—
679C2×#121—53no—
680#520—52no—
681#520—52no—
682#520—56no—
683#520—56no—
684#519—52no—
685#519—52no—
686#518—56no—
687#518—56no—
688C4×#41—51no—
689C4×#41—51no—
690C4×#41—51no—
691C4×#41—56no—
692C4×#41—56no—
693C4×#41—53no—
694C4×#41—53no—
695C4×#41—53no—
696C4×#41—56no—
697C4×#41—53no—
698C4×#41—56no—
699C4×#41C2×D511yescharacteristic
700C4×#41C2×D512yes—
701C2×C4×Q8—51no—
702C2×C4×Q8—51no—
703C2×C4×Q8C2×D513yescomplemented
704C2×C4×D4—53no—
705C2×C4×D4—53no—
706C2×C4×D4—56no—
707C2×C4×D4—53no—
708C2×#117—53no—
709C2×#117—56no—
710C2×#117—56no—
711C22×C42—53no—
712C23×C5C2513yes—
713C22×D5—26no—
714C22×D5—212no—
715C22×D5—26no—
716C22×D5—43no—
717C22×D5—46no—
718C22×D5—46no—
719C22×D5C2512yes—
720C22×D5C2513yes—
721C22×D5C2516yes—
722C22×D5C2511yescharacteristic
723C5×Q8—26no—
724C5×Q8—22no—
725C5×Q8—46no—
726C5×Q8—46no—
727C5×Q8C2×#4114yes—
728C5×D4C2×#41112yes—
729C2×C4×C5—26no—
730C2×C4×C5—43no—
731C2×C4×C5—46no—
732C2×C4×C5—46no—
733C2×C4×C5C2×#41112yes—
734C2×C4×C5C2511yescharacteristic
735C2×C4×C5C2513yes—
736C2×C4×C5C2516yes—
737C2×C4×C5C2513yes—
738C2×C4×C5C2516yes—
739C2×C4×C5C2512yes—
740C2×C4×C5C2512yes—
741C2×C4×C5C2513yes—
742C2×C4×C5C2511yescharacteristic
743C2×C4×C5C2511yescharacteristic
744C22⋊D5—212no—
745C22⋊D5—224no—
746C2×Dic5—26no—
747C2×Dic5—212no—
748C2×Dic5—43no—
749C2×Dic5—43no—
750C2×Dic5C2511yescharacteristic
751C2×Dic5C2511yescharacteristic
752C2×Dic5C2513yes—
753C2×Dic5C2513yes—
754C2×Dic5C2511yescharacteristic
755C2×Dic5C2513yes—
756C2×Dic5C2516yes—
757C2×Dic5C2512yes—
758D20—24no—
759D20—212no—
760D20—26no—
761D20—212no—
762D20—22no—
763D20—26no—
764D20—46no—
765D20—46no—
766D20—46no—
767D20—46no—
768D20—412no—
769C4×D5—22no—
770C4×D5—26no—
771C4×D5—22no—
772C4×D5—24no—
773C4×D5—26no—
774C4×D5—212no—
775C4×D5—26no—
776C4×D5—212no—
777C4×D5—26no—
778C4×D5—212no—
779C4×D5—22no—
780C4×D5—26no—
781C4×D5—43no—
782C4×D5—43no—
783C4×D5—43no—
784C4×D5—43no—
785C4×D5—412no—
786C4×D5—412no—
787Dic10—26no—
788Dic10—212no—
789C2×#41—51no—
790C2×#41—52no—
791C2×#41—56no—
792C2×#41—56no—
793C2×#41—53no—
794C2×#41—56no—
795C2×#41—53no—
796C2×#41—56no—
797C2×#41—108no—
798C2×#41—1016no—
799C2×#41C22×D511yescharacteristic
800C22×Q8—51no—
801C22×Q8—52no—
802C22×Q8C22×D513yes—
803C22×D4—53no—
804C22×D4—56no—
805C22×D4—56no—
806C22×D4—53no—
807C23×C4—56no—
808C23×C4—53no—
809C23×C4—53no—
810C23×C4—53no—
811C4⋊Q8—53no—
812C4⋊Q8—56no—
813C4⋊Q8C22×D513yes—
814C4⋊Q8C22×D513yes—
815C4⋊Q8C22×D516yes—
816C4⋊Q8C22×D516yes—
817#127—53no—
818#127—56no—
819#126—52no—
820#126—56no—
821#126—56no—
822#126—56no—
823#126—56no—
824#126—56no—
825#126—56no—
826#126—56no—
827#126—512no—
828#126—512no—
829#126—512no—
830#126—512no—
831#126—512no—
832#125—51no—
833#125—53no—
834#125—56no—
835#125—56no—
836#125—53no—
837#125—53no—
838#125—56no—
839#125—512no—
840#125—512no—
841#125C22×D516yes—
842#125C22×D516yes—
843#125C22×D516yes—
844#124—51no—
845#124—53no—
846#124—56no—
847#124—53no—
848#124—53no—
849#124—56no—
850#124—56no—
851#124—512no—
852#124—512no—
853#124—56no—
854#124—56no—
855#124—56no—
856#123—52no—
857#123—56no—
858#123—56no—
859#123—56no—
860#123—56no—
861#123—56no—
862#123—56no—
863#123—56no—
864#123—512no—
865#123—512no—
866#123—512no—
867#123—512no—
868#123—512no—
869#123—512no—
870#123—512no—
871#123—512no—
872C22⋊Q8—51no—
873C22⋊Q8—53no—
874C22⋊Q8—56no—
875C22⋊Q8—53no—
876C22⋊Q8—53no—
877C22⋊Q8—56no—
878C22⋊Q8—56no—
879C22⋊Q8—512no—
880C22⋊Q8—512no—
881C22⋊Q8—56no—
882C22⋊Q8—56no—
883C22⋊Q8—56no—
884C22⋊Q8—56no—
885C22⋊Q8—56no—
886C22⋊Q8—56no—
887C22⋊Q8C22×D516yes—
888C22⋊Q8C22×D516yes—
889C22⋊Q8C22×D5112yes—
890C22⋊Q8C22×D5112yes—
891#121—56no—
892#121—56no—
893#121—512no—
894#121—512no—
895#121—51no—
896#121—53no—
897#121—56no—
898#121—56no—
899#121—53no—
900#121—53no—
901#121—56no—
902#121—56no—
903#121—56no—
904#121—56no—
905#121—56no—
906#121—56no—
907#121—56no—
908#121—512no—
909#121—512no—
910#120—512no—
911#120—512no—
912#120—512no—
913C4×Q8—51no—
914C4×Q8—51no—
915C4×Q8—56no—
916C4×Q8—56no—
917C4×Q8—53no—
918C4×Q8—53no—
919C4×Q8—56no—
920C4×Q8—56no—
921C4×Q8—53no—
922C4×Q8—53no—
923C4×Q8—56no—
924C4×Q8—56no—
925C4×Q8C22×D511yescharacteristic
926C4×Q8C22×D511yescharacteristic
927C4×Q8C22×D511yescharacteristic
928C4×Q8C22×D513yes—
929C4×Q8C22×D516yes—
930C4×Q8C22×D513yes—
931C4×Q8C22×D513yes—
932C4×Q8C22×D516yes—
933C4×Q8C22×D516yes—
934C4×Q8C22×D512yes—
935C4×Q8C22×D512yes—
936C4×D4—53no—
937C4×D4—53no—
938C4×D4—56no—
939C4×D4—56no—
940C4×D4—512no—
941C4×D4—512no—
942C4×D4—53no—
943C4×D4—53no—
944C4×D4—56no—
945C4×D4—56no—
946C4×D4—512no—
947C4×D4—512no—
948C4×D4—56no—
949C4×D4—56no—
950C4×D4—56no—
951C4×D4—56no—
952C4×D4—512no—
953C4×D4—512no—
954C4×D4—51no—
955C4×D4—52no—
956C4×D4—56no—
957C4×D4—53no—
958C4×D4—53no—
959C4×D4—53no—
960C4×D4—56no—
961C4×D4—56no—
962C4×D4—56no—
963C4×D4—56no—
964C4×D4—53no—
965C4×D4—56no—
966C4×D4—56no—
967C4×D4—56no—
968C4×D4—53no—
969C4×D4—56no—
970C4×D4—56no—
971C4×D4—56no—
972C4×D4—56no—
973C4×D4—512no—
974C4×D4C22×D513yes—
975C4×D4C22×D513yes—
976C4×D4C22×D516yes—
977C4×D4C22×D516yes—
978#117—53no—
979#117—53no—
980#117—53no—
981#117—56no—
982#117—56no—
983#117—56no—
984#117—56no—
985#117—512no—
986#117—512no—
987#117—56no—
988#117—512no—
989#117—56no—
990#117—52no—
991#117—56no—
992#117—56no—
993#117—56no—
994#117—56no—
995#117—56no—
996#117—56no—
997#117—56no—
998#117C22×D513yes—
999#117C22×D516yes—
1000C2×C4⋊C4—56no—
1001C2×C4⋊C4—56no—
1002C2×C4⋊C4—53no—
1003C2×C4⋊C4—56no—
1004C2×C4⋊C4—53no—
1005C2×C4⋊C4—53no—
1006C2×C4⋊C4—56no—
1007C2×C4⋊C4—56no—
1008C2×C4⋊C4C22×D513yes—
1009C2×C4⋊C4C22×D516yes—
1010C2×C22⋊C4—56no—
1011C2×C22⋊C4—56no—
1012C2×C22⋊C4—56no—
1013C2×C22⋊C4—56no—
1014C2×C22⋊C4—56no—
1015C2×C22⋊C4—56no—
1016C2×C22⋊C4—512no—
1017C2×C42—53no—
1018C2×C42—53no—
1019C2×C42—53no—
1020C2×C42—53no—
1021C2×C42—512no—
1022C2×C42—53no—
1023C2×C42—53no—
1024C2×C42—53no—
1025C2×C42—53no—
1026C2×C42—53no—
1027C2×C42—53no—
1028C2×C42—51no—
1029C2×C42C22×D516yes—
1030C2×C42C22×D513yes—
1031C22×C5—23no—
1032C22×C5—23no—
1033C22×C5C22×#4116yes—
1034C22×C5C2611yescharacteristic
1035C2×D5—21no—
1036C2×D5—21no—
1037C2×D5—22no—
1038C2×D5—23no—
1039C2×D5—26no—
1040C2×D5—23no—
1041C2×D5—26no—
1042C2×D5—26no—
1043C2×D5—23no—
1044C2×D5—22no—
1045C2×D5—22no—
1046C2×D5—412no—
1047C2×D5—812no—
1048C2×D5#58512yes—
1049C4×C5—21no—
1050C4×C5—23no—
1051C4×C5—26no—
1052C4×C5—23no—
1053C4×C5—26no—
1054C4×C5—22no—
1055C4×C5—22no—
1056C4×C5C22×#4116yes—
1057C4×C5C22×#4112yes—
1058C4×C5#58512yes—
1059Dic5—23no—
1060Dic5—26no—
1061Dic5—21no—
1062Dic5—22no—
1063Dic5—23no—
1064Dic5—23no—
1065Dic5—21no—
1066Dic5—21no—
1067C24—53no—
1068C24—56no—
1069#41—104no—
1070#41—108no—
1071#41—1012no—
1072#41—1024no—
1073#41—1012no—
1074#41—1024no—
1075#41—2012no—
1076#41—2012no—
1077#41#71318yescomplemented
1078C2×Q8—46no—
1079C2×Q8—53no—
1080C2×Q8—56no—
1081C2×Q8—104no—
1082C2×Q8—108no—
1083C2×Q8C23×D513yes—
1084C2×Q8C23×D511yescharacteristic
1085C2×Q8C23×D516yes—
1086C2×Q8C23×D516yes—
1087C2×Q8C23×D511yescharacteristic
1088C2×D4—56no—
1089C2×D4—512no—
1090C2×D4—56no—
1091C2×D4—52no—
1092C2×D4—51no—
1093C2×D4—53no—
1094C2×D4—56no—
1095C2×D4—53no—
1096C2×D4—56no—
1097C2×D4—56no—
1098C2×D4—512no—
1099C2×D4—56no—
1100C2×D4—56no—
1101C2×D4—1012no—
1102C2×D4—1024no—
1103C2×D4—206no—
1104C2×D4—2012no—
1105C2×D4C23×D513yes—
1106C22×C4—53no—
1107C22×C4—56no—
1108C22×C4—53no—
1109C22×C4—53no—
1110C22×C4—51no—
1111C22×C4—51no—
1112C22×C4—53no—
1113C22×C4—53no—
1114C22×C4—53no—
1115C22×C4—53no—
1116C22×C4—56no—
1117C22×C4—56no—
1118C22×C4—51no—
1119C22×C4—56no—
1120C22×C4—53no—
1121C22×C4—52no—
1122C22×C4—53no—
1123C22×C4—53no—
1124C22×C4—53no—
1125C22×C4—53no—
1126C22×C4—512no—
1127C22×C4—512no—
1128C22×C4—1012no—
1129C22×C4—1024no—
1130C22×C4—206no—
1131C22×C4—206no—
1132C22×C4C23×D513yes—
1133C22×C4C23×D513yes—
1134C22×C4C23×D516yes—
1135C22×C4C23×D516yes—
1136C22×C4C23×D513yes—
1137C4⋊C4—53no—
1138C4⋊C4—53no—
1139C4⋊C4—52no—
1140C4⋊C4—56no—
1141C4⋊C4—56no—
1142C4⋊C4—52no—
1143C4⋊C4—51no—
1144C4⋊C4—52no—
1145C4⋊C4—53no—
1146C4⋊C4—56no—
1147C4⋊C4—56no—
1148C4⋊C4—56no—
1149C4⋊C4—56no—
1150C4⋊C4—56no—
1151C4⋊C4—56no—
1152C4⋊C4—56no—
1153C4⋊C4—56no—
1154C4⋊C4—56no—
1155C4⋊C4—56no—
1156C4⋊C4—56no—
1157C4⋊C4—512no—
1158C4⋊C4C23×D513yes—
1159C4⋊C4C23×D513yes—
1160C4⋊C4C23×D516yes—
1161C4⋊C4C23×D516yes—
1162C4⋊C4C23×D511yescharacteristic
1163C4⋊C4C23×D512yes—
1164C4⋊C4C23×D513yes—
1165C4⋊C4C23×D516yes—
1166C4⋊C4C23×D516yes—
1167C4⋊C4C23×D516yes—
1168C4⋊C4C23×D516yes—
1169C4⋊C4C23×D516yes—
1170C4⋊C4C23×D5112yes—
1171C22⋊C4—56no—
1172C22⋊C4—52no—
1173C22⋊C4—56no—
1174C22⋊C4—56no—
1175C22⋊C4—52no—
1176C22⋊C4—52no—
1177C22⋊C4—52no—
1178C22⋊C4—52no—
1179C22⋊C4—56no—
1180C22⋊C4—56no—
1181C22⋊C4—56no—
1182C22⋊C4—56no—
1183C22⋊C4—56no—
1184C22⋊C4—56no—
1185C22⋊C4—56no—
1186C22⋊C4—56no—
1187C22⋊C4—56no—
1188C22⋊C4—56no—
1189C22⋊C4—56no—
1190C22⋊C4—56no—
1191C22⋊C4—56no—
1192C22⋊C4—56no—
1193C22⋊C4—56no—
1194C22⋊C4—512no—
1195C22⋊C4—512no—
1196C22⋊C4—512no—
1197C22⋊C4C23×D516yes—
1198C22⋊C4C23×D5112yes—
1199C42—51no—
1200C42—51no—
1201C42—53no—
1202C42—53no—
1203C42—53no—
1204C42—53no—
1205C42—53no—
1206C42—53no—
1207C42—53no—
1208C42—53no—
1209C42—512no—
1210C42—512no—
1211C42—51no—
1212C42—53no—
1213C42C23×D513yes—
1214C42C23×D513yes—
1215C42C23×D516yes—
1216C42C23×D516yes—
1217C42C23×D511yescharacteristic
1218C42C23×D513yes—
1219C42C23×D516yes—
1220C42C23×D512yes—
1221C2×C5—26no—
1222C2×C5C23×#4111yescharacteristic
1223C2×C5C2×#58511yescharacteristic
1224C2×C5C2×#58511yescharacteristic
1225D5—22no—
1226D5—43no—
1227D5—46no—
1228D5—42no—
1229C23—51no—
1230C23—52no—
1231C23—53no—
1232C23—56no—
1233C23—106no—
1234C23—106no—
1235C23—1012no—
1236C23—203no—
1237C23—206no—
1238C23—206no—
1239C23C24×D513yes—
1240Q8—22no—
1241Q8—26no—
1242Q8—46no—
1243Q8—46no—
1244Q8—106no—
1245Q8—1012no—
1246Q8C2×#71314yes—
1247D4—104no—
1248D4—1012no—
1249D4—1012no—
1250D4—1024no—
1251D4—106no—
1252D4—1012no—
1253D4—102no—
1254D4—106no—
1255D4—206no—
1256D4—206no—
1257D4—206no—
1258D4—2012no—
1259D4—206no—
1260D4C2×#713112yes—
1261C2×C4—26no—
1262C2×C4—43no—
1263C2×C4—46no—
1264C2×C4—46no—
1265C2×C4—51no—
1266C2×C4—51no—
1267C2×C4—53no—
1268C2×C4—51no—
1269C2×C4—53no—
1270C2×C4—53no—
1271C2×C4—56no—
1272C2×C4—52no—
1273C2×C4—102no—
1274C2×C4—106no—
1275C2×C4—106no—
1276C2×C4—1012no—
1277C2×C4—102no—
1278C2×C4—104no—
1279C2×C4—106no—
1280C2×C4—1012no—
1281C2×C4—106no—
1282C2×C4—1012no—
1283C2×C4—106no—
1284C2×C4—1012no—
1285C2×C4—102no—
1286C2×C4—106no—
1287C2×C4—203no—
1288C2×C4—203no—
1289C2×C4—203no—
1290C2×C4—203no—
1291C2×C4—2012no—
1292C2×C4—2012no—
1293C2×C4—203no—
1294C2×C4—203no—
1295C2×C4C2×#713112yes—
1296C2×C4C24×D511yescharacteristic
1297C2×C4C24×D513yes—
1298C2×C4C24×D516yes—
1299C2×C4C24×D513yes—
1300C2×C4C24×D516yes—
1301C2×C4C24×D512yes—
1302C2×C4C24×D512yes—
1303C2×C4C24×D513yes—
1304C2×C4C24×D511yescharacteristic
1305C2×C4C24×D511yescharacteristic
1306C5#6281611yescharacteristic, complemented, Sylow
1307C22—23no—
1308C22—23no—
1309C22—52no—
1310C22—101no—
1311C22—101no—
1312C22—102no—
1313C22—103no—
1314C22—106no—
1315C22—103no—
1316C22—106no—
1317C22—102no—
1318C22—106no—
1319C22—103no—
1320C22—102no—
1321C22—2012no—
1322C22—4012no—
1323C22C22×#71316yes—
1324C22C25×D511yescharacteristic
1325C4—23no—
1326C4—22no—
1327C4—26no—
1328C4—21no—
1329C4—22no—
1330C4—23no—
1331C4—26no—
1332C4—101no—
1333C4—102no—
1334C4—103no—
1335C4—106no—
1336C4—101no—
1337C4—103no—
1338C4—101no—
1339C4—103no—
1340C4C22×#71312yes—
1341C4C22×#71316yes—
1342C4#6628312yes—
1343C2—26no—
1344C2—102no—
1345C2—203no—
1346C2—202no—
1347C2—206no—
1348C2C23×#71311yescharacteristic
1349C2C2×#6628311yescharacteristic
1350C2D5×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC5×Q8×#41C2
hypercenterQ8×#41D5
hypocenterC5#62816
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C5×Q8×#41C2semidirect
2. #10618944C2semidirect
3. #10618943C2semidirect
4. #10618927C2semidirect
5. #10618925C2semidirect
6. #10618924C2semidirect
7. #10618923C2semidirect
8. #10618836C2semidirect
9. #10618834C2semidirect
10. #10618831C2semidirect
11. #10618830C2semidirect
12. #10618652C2semidirect
13. #10618649C2semidirect
14. #10618177C2semidirect
15. #10618177C2semidirect
16. #10618174C2semidirect
17. #10618158C2semidirect
18. #41×D20C2semidirect
19. #41×D20C2semidirect
20. #10617735C2semidirect
21. C4×D5×#41C2semidirect
22. C2×#65914C2semidirect
23. #10617703C2semidirect
26. C5×Q82C22semidirect
27. C5×#557C22semidirect
28. C5×#557C22semidirect
29. C5×#554C22semidirect
30. C5×#554C22semidirect
31. C5×D4×Q8C22semidirect
32. C5×#533C22semidirect
33. C5×#533C22semidirect
36. C2×C4×C5×Q8C22semidirect
38. #66151C22semidirect
39. C2×#4093C22semidirect
40. C2×#4092C22semidirect
41. #66068C22semidirect
42. #66068C22semidirect
43. #66067C22semidirect
44. #66067C22semidirect
45. #66067C22semidirect
46. #66067C22semidirect
47. #66066C22semidirect
48. #66066C22semidirect
49. #66064C22semidirect
50. #66064C22semidirect
51. #66062C22semidirect
52. #66062C22semidirect
53. #66060C22semidirect
54. #66060C22semidirect
55. #66059C22semidirect
56. #66059C22semidirect
57. #66032C22semidirect
58. #66032C22semidirect
59. #66031C22semidirect
60. #66031C22semidirect
61. #66029C22semidirect
62. #66029C22semidirect
63. #66029C22semidirect
64. #66028C22semidirect
65. #66028C22semidirect
66. #66028C22semidirect
67. #66025C22semidirect
68. #66025C22semidirect
69. #65979C22semidirect
70. #65979C22semidirect
71. #65978C22semidirect
72. #65978C22semidirect
73. #65976C22semidirect
74. #65976C22semidirect
75. #65971C22semidirect
76. #65971C22semidirect
77. #65971C22semidirect
78. #65964C22semidirect
79. #65964C22semidirect
80. #65961C22semidirect
81. #65961C22semidirect
82. #65958C22semidirect
83. #65958C22semidirect
84. #65919C22semidirect
85. #65919C22semidirect
86. #65918C22semidirect
87. #65918C22semidirect
90. #65914C22semidirect
91. #65914C22semidirect
92. #65914C22semidirect
93. #65914C22semidirect
94. #65914C22semidirect
95. #65914C22semidirect
96. #65914C22semidirect
97. #65914C22semidirect
98. #65914C22semidirect
99. #65914C22semidirect
100. #65914C22semidirect
101. #65914C22semidirect
102. #65914C22semidirect
103. #65911C22semidirect
104. #65911C22semidirect
105. #65911C22semidirect
106. #65910C22semidirect
107. #65910C22semidirect
108. #65910C22semidirect
109. Q8×D20C22semidirect
110. Q8×D20C22semidirect
111. #65908C22semidirect
112. #65908C22semidirect
113. C4×#713C22semidirect
114. C4×#713C22semidirect
115. C4×#713C22semidirect
116. C4×#713C22semidirect
117. #65906C22semidirect
118. #65906C22semidirect
119. C4×Q8×D5C22semidirect
120. C4×Q8×D5C22semidirect
121. #65904C22semidirect
122. #65889C22semidirect
123. #65889C22semidirect
124. #65888C22semidirect
125. #65888C22semidirect
126. #65888C22semidirect
127. D4×D20C22semidirect
128. D4×D20C22semidirect
129. #65880C22semidirect
130. #65880C22semidirect
131. #65879C22semidirect
132. #65879C22semidirect
133. C4×D4×D5C22semidirect
134. C4×D4×D5C22semidirect
135. C4×#711C22semidirect
136. C4×#711C22semidirect
137. #65858C22semidirect
138. #65858C22semidirect
139. #65858C22semidirect
140. #65856C22semidirect
141. #65856C22semidirect
142. D5×#117C22semidirect
143. D5×#117C22semidirect
144. #65848C22semidirect
145. #65848C22semidirect
146. C2×#4044C22semidirect
148. C2×#4040C22semidirect
149. C2×#4036C22semidirect
150. #65811C22semidirect
151. #65811C22semidirect
152. C4×#709C22semidirect
153. C4×#709C22semidirect
154. C2×C4×D20C22semidirect
155. C2×C4×D20C22semidirect
156. C2×#4018C22semidirect
157. C2×C42×D5C22semidirect
414. Q8×#41D5semidirect
426. C5×#41#41semidirect
582. Q82C2×D5semidirect
584. #557C2×D5semidirect
585. #557C2×D5semidirect
594. #554C2×D5semidirect
595. #554C2×D5semidirect
614. D4×Q8C2×D5semidirect
644. #533C2×D5semidirect
645. #533C2×D5semidirect
703. C2×C4×Q8C2×D5semidirect
1077. #41#713semidirect
1306. C5#62816semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×#412
#106189442
#106189432
#106189272
#106189252
#106189242
#106189232
#106188362
#106188342
#106188312
#106188302
#106186522
#106186492
#106181772
#106181742
#106181582
#41×D202
#106177352
C4×D5×#412
C2×#659142
#106177032
#628165