Finite Group Databasebeta

← #12313872

Subgroups — #12313872

Order 1280.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2855C211yesmaximal, characteristic, complemented
2#10614512C211yesmaximal, characteristic, complemented
3#10614502C211yesmaximal, characteristic
4#10613810C211yesmaximal, characteristic
5C2×#65222C211yesmaximal, characteristic, complemented
6#10608388C211yesmaximal, characteristic, complemented
7#10608327C211yesmaximal, characteristic, complemented
8#10608311C211yesmaximal, characteristic, complemented
9#10608307C211yesmaximal, characteristic, complemented
10#10608005C211yesmaximal, characteristic, complemented
11#10607884C211yesmaximal, characteristic, complemented
12#10607881C211yesmaximal, characteristic, complemented
13#10607867C211yesmaximal, characteristic, complemented
14#10607151C211yesmaximal, characteristic, complemented
15#10607133C211yesmaximal, characteristic, complemented
16#10607000C211yesmaximal, characteristic, complemented
17#10606942C211yesmaximal, characteristic, complemented
18#10606940C211yesmaximal, characteristic, complemented
19#10606935C211yesmaximal, characteristic, complemented
20#10606928C211yesmaximal, characteristic, complemented
21#10606925C211yesmaximal, characteristic, complemented
22#10606351C211yesmaximal, characteristic
23#10606233C211yesmaximal, characteristic, complemented
24#10606118C211yesmaximal, characteristic, complemented
25#10606114C211yesmaximal, characteristic
26#10605810C211yesmaximal, characteristic, complemented
27#10605808C211yesmaximal, characteristic, complemented
28#10605807C211yesmaximal, characteristic
29#10605806C211yesmaximal, characteristic
30#10605674C211yesmaximal, characteristic
31#10605648C211yesmaximal, characteristic, complemented
32C2×C5×C22⋊Q8C2211yescharacteristic
33C22×C42×C5C2211yescharacteristic
34C2×#4075C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C2×#4032C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4024C2211yescharacteristic
40C2×#4024C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#387C2211yescharacteristic
46C5×#387C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C5×#385C2211yescharacteristic
50C5×#385C2211yescharacteristic
51C5×#381C2211yescharacteristic
52C5×#381C2211yescharacteristic
53C5×#380C2211yescharacteristic
54#65520C2211yescharacteristic
55#65519C2211yescharacteristic
56#65519C2211yescharacteristic
57#65518C2211yescharacteristic
58#65502C2211yescharacteristic
59#65502C2211yescharacteristic
60#65500C2211yescharacteristic
61#65499C2211yescharacteristic
62#65499C2211yescharacteristic
63C2×#3963C2211yescharacteristic
64C2×#3963C2211yescharacteristic
65C2×#3963C2211yescharacteristic
66C2×#3963C2211yescharacteristic
67#65282C2211yescharacteristic
68#65281C2211yescharacteristic
69#65281C2211yescharacteristic
70#65281C2211yescharacteristic
71#65279C2211yescharacteristic
72#65279C2211yescharacteristic
73#65279C2211yescharacteristic
74#65278C2211yescharacteristic
75#65276C2211yescharacteristic
76#65275C2211yescharacteristic
77#65275C2211yescharacteristic
78#65275C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65272C2211yescharacteristic
82#65271C2211yescharacteristic
83#65270C2211yescharacteristic
84#65270C2211yescharacteristic
85#65269C2211yescharacteristic
86#65269C2211yescharacteristic
87#65269C2211yescharacteristic
88#65268C2211yescharacteristic
89#65268C2211yescharacteristic
90#65268C2211yescharacteristic
91#65268C2211yescharacteristic
92#65267C2211yescharacteristic
93#65267C2211yescharacteristic
94#65267C2211yescharacteristic
95#65266C2211yescharacteristic
96#65266C2211yescharacteristic
97#65263C2211yescharacteristic
98#65263C2211yescharacteristic
99#65262C2211yescharacteristic
100#65261C2211yescharacteristic
101#65261C2211yescharacteristic
102#65261C2211yescharacteristic
103#65247C2211yescharacteristic
104#65247C2211yescharacteristic
105#65239C2211yescharacteristic
106#65235C2211yescharacteristic
107#65232C2211yescharacteristic
108#65232C2211yescharacteristic
109#65232C2211yescharacteristic
110#65231C2211yescharacteristic
111#65231C2211yescharacteristic
112C22⋊C4×Dic5C2211yescharacteristic
113C22⋊C4×Dic5C2211yescharacteristic
114C22⋊C4×Dic5C2211yescharacteristic
115#65229C2211yescharacteristic
116#65229C2211yescharacteristic
117#65229C2211yescharacteristic
118#65229C2211yescharacteristic
119#65222C2211yescharacteristic
120#65222C2211yescharacteristic
121#65222C2211yescharacteristic
122#65222C2211yescharacteristic
123#65222C2211yescharacteristic
124#65222C2211yescharacteristic
125#65222C2211yescharacteristic
126#65222C2211yescharacteristic
127#65222C2211yescharacteristic
128#65222C2211yescharacteristic
129#65222C2211yescharacteristic
130#65222C2211yescharacteristic
131#64964C2211yescharacteristic
132#64964C2211yescharacteristic
133#64964C2211yescharacteristic
134#64964C2211yescharacteristic
135#64964C2211yescharacteristic
136#64962C2211yescharacteristic
137#64962C2211yescharacteristic
138#64959C2211yescharacteristic
139#64959C2211yescharacteristic
140#64958C2211yescharacteristic
141#64957C2211yescharacteristic
142#64956C2211yescharacteristic
143#64956C2211yescharacteristic
144#64953C2211yescharacteristic
145C5⋊#401C2211yescharacteristic
146C5⋊#401C2211yescharacteristic
147#64949C2211yescharacteristic
148#64949C2211yescharacteristic
149#64949C2211yescharacteristic
150#64949C2211yescharacteristic
151#64949C2211yescharacteristic
152#64949C2211yescharacteristic
153#64949C2211yescharacteristic
154#64948C2211yescharacteristic
155#64947C2211yescharacteristic
156#64947C2211yescharacteristic
157#64947C2211yescharacteristic
158#64947C2211yescharacteristic
159#64947C2211yescharacteristic
160#64947C2211yescharacteristic
161#64947C2211yescharacteristic
162#64946C2211yescharacteristic
163#64946C2211yescharacteristic
164#64946C2211yescharacteristic
165#64946C2211yescharacteristic
166#64944C2211yescharacteristic
167#64944C2211yescharacteristic
168#64943C2211yescharacteristic
169#64942C2211yescharacteristic
170#64942C2211yescharacteristic
171#64941C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64940C2211yescharacteristic
176#64940C2211yescharacteristic
177#64940C2211yescharacteristic
178#64939C2211yescharacteristic
179#64939C2211yescharacteristic
180#64939C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36999—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C22×C22⋊D5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C5×C22⋊Q8—42no—
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C42×C5—42no—
215C2×C42×C5C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222#4075—42no—
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×#683—24no—
243C2×#683—42no—
244C2×#683C2311yescharacteristic
245C2×#683C2311yescharacteristic
246C2×#683C2311yescharacteristic
247C2×#683C2311yescharacteristic
248C2×#683C2311yescharacteristic
249C2×#683C2311yescharacteristic
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×C4×Dic5C2311yescharacteristic
270C2×C4×Dic5C2311yescharacteristic
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276#4032—42no—
277#4027—24no—
278#4024—24no—
279#4024—42no—
280C5×#95C2311yescharacteristic
281C5×#95C2311yescharacteristic
282C5×#95C2311yescharacteristic
283C5×#95C2311yescharacteristic
284C5×#95C2311yescharacteristic
285C5×#95C2311yescharacteristic
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294#3963C2311yescharacteristic
295#3963C2311yescharacteristic
296#3963C2311yescharacteristic
297#3963C2311yescharacteristic
298#3963C2311yescharacteristic
299#3963C2311yescharacteristic
300#3963C2311yescharacteristic
301#3963C2311yescharacteristic
302#3963C2311yescharacteristic
303#3963C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#2855D511yescharacteristic, complemented
353#2853—51no—
354#2799—51no—
355#2798—51no—
356#2774—51no—
357#2773—51no—
358#2767—51no—
359#2767—51no—
360#2766—51no—
361#2762—51no—
362#2759—51no—
363#2758—51no—
364#2755—51no—
365#2754—51no—
366#2747—51no—
367#2745—51no—
368#2742—51no—
369#2738—51no—
370#2627—51no—
371#2623—51no—
372#2564—51no—
373#2549—51no—
374#2503—51no—
375#2493—51no—
376#2493—51no—
377#2488—51no—
378#2488—51no—
379#2486—51no—
380#2329—51no—
381#2318—51no—
382C2×#387—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C22×C4×C5—22no—
389C22×C4×C5—22no—
390C22×C4×C5—22no—
391C22×C4×C5—22no—
392C22×C4×C5—22no—
393C22×C4×C5—22no—
394C22×C4×C5—41no—
395C22×C4×C5—41no—
396C22×C4×C5—41no—
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C2×C22⋊D5—22no—
412C2×C22⋊D5—22no—
413C2×C22⋊D5—22no—
414C22×Dic5—22no—
415C22×Dic5—22no—
416C22×Dic5—22no—
417C22×Dic5—22no—
418C22×Dic5—22no—
419C22×Dic5—41no—
420C22×Dic5—41no—
421C22×Dic5—41no—
422C22×Dic5—41no—
423C22×Dic5—41no—
424C22×Dic5—41no—
425C22×Dic5#4114yes—
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C2×C4×D5—22no—
442C2×C4×D5—41no—
443C2×C4×D5—41no—
444C2×Dic10—22no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C2×Dic10—41no—
449C2×Dic10—41no—
450C5×C4⋊C4—22no—
451C5×C4⋊C4—41no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C22⋊C4—22no—
460C5×C22⋊C4—22no—
461C5×C22⋊C4—22no—
462C5×C22⋊C4—22no—
463C42×C5—41no—
464C42×C5—41no—
465C42×C5—41no—
466C42×C5—41no—
467C22⋊Dic5—22no—
468C22⋊Dic5—22no—
469C22⋊Dic5—22no—
470#685—22no—
471#685—22no—
472#685—41no—
473#685—41no—
474#685—41no—
475#685—41no—
476#685—41no—
477#685—41no—
478#685—41no—
479#685—41no—
480#685—41no—
481#685—41no—
482#685—41no—
483C4⋊Dic5—22no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489#683—22no—
490#683—22no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—22no—
495#683—22no—
496#683—22no—
497#683—41no—
498#683—41no—
499#683—41no—
500#683—41no—
501#683—41no—
502#683—41no—
503#683—41no—
504#683—41no—
505#683—41no—
506#683—41no—
507#683—41no—
508#683—41no—
509#683—41no—
510#683—41no—
511#683—41no—
512#683—41no—
513#683—41no—
514C4×Dic5—22no—
515C4×Dic5—41no—
516C4×Dic5—41no—
517C4×Dic5—41no—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C2×#123—51no—
522C2×#123—51no—
523C2×C22⋊Q8—51no—
524C2×C22⋊Q8—51no—
525C2×C22⋊Q8C2×D511yescharacteristic
526C2×C4×D4—51no—
527C22×C4⋊C4—51no—
528C22×C4⋊C4—51no—
529C22×C42C2×D511yescharacteristic
530#401—51no—
531#401—51no—
532#400—51no—
533#400—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#400—51no—
551#399—51no—
552#399—51no—
553#399—51no—
554#398—51no—
555#398—51no—
556#398—51no—
557#398—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398—51no—
563#398—51no—
564#397—51no—
565#397—51no—
566#397—51no—
567#397—51no—
568#397—51no—
569#397—51no—
570#395—51no—
571#395—51no—
572#395—51no—
573#395—51no—
574#395—51no—
575#393—51no—
576#393—51no—
577#393—51no—
578#391—51no—
579#391—51no—
580#391—51no—
581#391—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#391—51no—
586#391C2×D511yescharacteristic
587#391C2×D511yescharacteristic
588#389—51no—
589#389—51no—
590#389—51no—
591#389—51no—
592#389—51no—
593#389—51no—
594#389C2×D511yescharacteristic
595#389C2×D511yescharacteristic
596#388—51no—
597#388—51no—
598#388—51no—
599#388—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#388—51no—
604#388—51no—
605#388—51no—
606#387—51no—
607#387—51no—
608#387—51no—
609#387—51no—
610#387—51no—
611#387—51no—
612#387—51no—
613#387—51no—
614#387—51no—
615#387—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387C2×D511yescharacteristic
633#387C2×D511yescharacteristic
634#387C2×D511yescharacteristic
635#387C2×D511yescharacteristic
636#386—51no—
637#386—51no—
638#386—51no—
639#386—51no—
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#385—51no—
645#385—51no—
646#385C2×D511yescharacteristic
647#385C2×D511yescharacteristic
648#383—51no—
649#383—51no—
650#383—51no—
651#382—51no—
652#382—51no—
653#382—51no—
654#382—51no—
655#382—51no—
656#381—51no—
657#381—51no—
658#381—51no—
659#381—51no—
660#381—51no—
661#381C2×D511yescharacteristic
662#381C2×D511yescharacteristic
663#380—51no—
664#380—51no—
665#380—51no—
666#380—51no—
667#380—51no—
668#380C2×D511yescharacteristic
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C2×#95—51no—
673C2×#95—51no—
674C2×#95—51no—
675C2×#95—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5C2×#4112yes—
681C23×C5H(5,𝔽2)12yes—
682C23×C52−1+412yes—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5—21no—
691C5×Q8—82no—
692C2×C4×C5—21no—
693C2×C4×C5—21no—
694C2×C4×C5—21no—
695C2×C4×C5—21no—
696C2×C4×C5—21no—
697C2×C4×C5—21no—
698C2×C4×C5—21no—
699C2×C4×C5—21no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—44no—
734C2×C4×C5—44no—
735C2×C4×C5—44no—
736C2×C4×C52−1+412yes—
737C22⋊D5—44no—
738C2×Dic5—21no—
739C2×Dic5—21no—
740C2×Dic5—21no—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—44no—
782C2×Dic5—44no—
783C2×Dic5—82no—
784C2×Dic5—82no—
785C2×Dic5C2×#4112yes—
786C2×Dic5C2×#4112yes—
787C4×D5—82no—
788Dic10—82no—
789Dic10—82no—
790C22×Q8—51no—
791C22×Q8—51no—
792C22×Q8C22×D511yescharacteristic
793C22×D4—51no—
794C23×C4—51no—
795C23×C4—51no—
796C23×C4—51no—
797C23×C4—51no—
798C23×C4—51no—
799C23×C4C22×D511yescharacteristic
800C23×C4C22×D511yescharacteristic
801C23×C4C22×D511yescharacteristic
802#123—202no—
803#123—202no—
804C22⋊Q8—42no—
805C22⋊Q8—104no—
806C22⋊Q8—202no—
807C4×D4—104no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—51no—
810C2×C4⋊C4—51no—
811C2×C4⋊C4—51no—
812C2×C4⋊C4—51no—
813C2×C4⋊C4—51no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—104no—
840C2×C4⋊C4—202no—
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
846C2×C4⋊C4C22×D511yescharacteristic
847C2×C4⋊C4C22×D511yescharacteristic
848C2×C4⋊C4C22×D511yescharacteristic
849C2×C4⋊C4C22×D511yescharacteristic
850C2×C22⋊C4—51no—
851C2×C22⋊C4—51no—
852C2×C22⋊C4—51no—
853C2×C22⋊C4—51no—
854C2×C22⋊C4—51no—
855C2×C22⋊C4—51no—
856C2×C22⋊C4—51no—
857C2×C22⋊C4—51no—
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C42—42no—
871C2×C42—51no—
872C2×C42—51no—
873C2×C42—51no—
874C2×C42—51no—
875C2×C42—51no—
876C2×C42—51no—
877C2×C42—51no—
878C2×C42C22×D511yescharacteristic
879C2×C42C22×D511yescharacteristic
880C2×C42C22×D511yescharacteristic
881C2×C42C22×D511yescharacteristic
882#95—51no—
883#95—51no—
884#95—51no—
885#95—51no—
886#95—51no—
887#95—51no—
888#95—51no—
889#95—51no—
890#95—51no—
891#95—51no—
892#95—51no—
893#95—51no—
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95C22×D511yescharacteristic
941#95C22×D511yescharacteristic
942#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954C22×C5—22no—
955C22×C5—22no—
956C22×C5—22no—
957C22×C5—22no—
958C22×C5—22no—
959C22×C5—22no—
960C22×C5#54214yes—
961C22×C5C22×#4111yescharacteristic
962C22×C5C2×H(5,𝔽2)11yescharacteristic
963C22×C5C2×2−1+411yescharacteristic
964C22×C5C2×2−1+411yescharacteristic
965C22×C5#58511yescharacteristic
966C22×C5#58511yescharacteristic
967C22×C5#58511yescharacteristic
968C2×D5—41no—
969C2×D5—41no—
970C2×D5—41no—
971C2×D5—41no—
972C2×D5—41no—
973C2×D5—41no—
974C2×D5—41no—
975C4×C5—22no—
976C4×C5—41no—
977C4×C5—41no—
978C4×C5—41no—
979C4×C5—41no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985C4×C5—41no—
986C4×C5—41no—
987C4×C5—41no—
988C4×C5—41no—
989Dic5—22no—
990Dic5—22no—
991Dic5—41no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000Dic5—41no—
1001Dic5—41no—
1002Dic5—41no—
1003Dic5—41no—
1004C24—51no—
1005C24C23×D511yescharacteristic
1006C2×Q8—22no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—102no—
1010C2×Q8—201no—
1011C2×Q8—201no—
1012C2×Q8—201no—
1013C2×Q8—201no—
1014C2×Q8—201no—
1015C2×D4—102no—
1016C2×D4—102no—
1017C2×D4—102no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—54no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—51no—
1039C22×C4—51no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—102no—
1044C22×C4—102no—
1045C22×C4—102no—
1046C22×C4—102no—
1047C22×C4—102no—
1048C22×C4—102no—
1049C22×C4—201no—
1050C22×C4—201no—
1051C22×C4—201no—
1052C22×C4—201no—
1053C22×C4—201no—
1054C22×C4—201no—
1055C22×C4—201no—
1056C22×C4—201no—
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C22×C4C23×D511yescharacteristic
1060C22×C4C23×D511yescharacteristic
1061C22×C4C23×D511yescharacteristic
1062C22×C4C23×D511yescharacteristic
1063C22×C4C23×D511yescharacteristic
1064C22×C4C23×D511yescharacteristic
1065C22×C4C23×D511yescharacteristic
1066C22×C4C23×D511yescharacteristic
1067C22×C4C23×D511yescharacteristic
1068C22×C4C23×D511yescharacteristic
1069C22×C4C23×D511yescharacteristic
1070C22×C4C23×D511yescharacteristic
1071C4⋊C4—22no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—102no—
1081C4⋊C4—102no—
1082C4⋊C4—102no—
1083C4⋊C4—102no—
1084C4⋊C4—102no—
1085C4⋊C4—102no—
1086C4⋊C4—102no—
1087C4⋊C4—102no—
1088C4⋊C4—102no—
1089C4⋊C4—201no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—102no—
1116C22⋊C4—102no—
1117C22⋊C4—102no—
1118C22⋊C4—102no—
1119C22⋊C4—102no—
1120C22⋊C4—201no—
1121C22⋊C4—201no—
1122C22⋊C4—201no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C22⋊C4—201no—
1130C22⋊C4—201no—
1131C42—41no—
1132C42—41no—
1133C42—41no—
1134C42—41no—
1135C42—102no—
1136C42—201no—
1137C42—201no—
1138C42—201no—
1139C42—201no—
1140C42—201no—
1141C42—201no—
1142C2×C5—24no—
1143C2×C5C2×#54211yescharacteristic
1144C2×C5#349111yescharacteristic
1145C2×C5#350711yescharacteristic
1146C2×C5#353311yescharacteristic
1147C2×C5#353511yescharacteristic
1148C2×C5#356311yescharacteristic
1149C2×C5#356411yescharacteristic
1150D5—81no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23—101no—
1160C23—101no—
1161C23—101no—
1162C23#414412yes—
1163C23#414712yes—
1164C23D5×#4112yes—
1165C23C24×D511yescharacteristic
1166Q8—82no—
1167Q8—402no—
1168Q8—402no—
1169D4—204no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—44no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—52no—
1215C2×C4—52no—
1216C2×C4—101no—
1217C2×C4—101no—
1218C2×C4—101no—
1219C2×C4—101no—
1220C2×C4—101no—
1221C2×C4—101no—
1222C2×C4—101no—
1223C2×C4—101no—
1224C2×C4—101no—
1225C2×C4—101no—
1226C2×C4—101no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—204no—
1260C2×C4—204no—
1261C2×C4—402no—
1262C2×C4—402no—
1263C2×C4—402no—
1264C2×C4#415012yes—
1265C5#3699911yescharacteristic, complemented, Sylow
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—201no—
1273C22—201no—
1274C22—201no—
1275C22—201no—
1276C22—201no—
1277C22—201no—
1278C22—201no—
1279C22#6597414yes—
1280C22C2×#414411yescharacteristic
1281C22C2×#414711yescharacteristic
1282C22C2×D5×#4111yescharacteristic
1283C22C2×#415011yescharacteristic
1284C22#6628311yescharacteristic
1285C22#6628311yescharacteristic
1286C22#6628311yescharacteristic
1287C4—22no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—102no—
1302C4—102no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C4—201no—
1313C4—201no—
1314C4—201no—
1315C4—201no—
1316C2—24no—
1317C2—401no—
1318C2C2×#6597411yescharacteristic
1319C2#1061790411yescharacteristic
1320C2#1061795011yescharacteristic
1321C2#1061802311yescharacteristic
1322C2#1061805611yescharacteristic
1323C2#1061817211yescharacteristic
1324C2#1061819311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2855C2
prime radicalC22×C22⋊D5C23
hypercenter#2855D5
hypocenterC5#36999
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2855

Complements

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

NH ≅ G/Ntype
1. C5×#2855C2semidirect
2. #10614512C2semidirect
5. C2×#65222C2semidirect
6. #10608388C2semidirect
7. #10608327C2semidirect
8. #10608311C2semidirect
9. #10608307C2semidirect
10. #10608005C2semidirect
11. #10607884C2semidirect
12. #10607881C2semidirect
13. #10607867C2semidirect
14. #10607151C2semidirect
15. #10607133C2semidirect
16. #10607000C2semidirect
17. #10606942C2semidirect
18. #10606940C2semidirect
19. #10606935C2semidirect
20. #10606928C2semidirect
21. #10606925C2semidirect
23. #10606233C2semidirect
24. #10606118C2semidirect
26. #10605810C2semidirect
27. #10605808C2semidirect
31. #10605648C2semidirect
352. #2855D5semidirect
1265. C5#36999semidirect

Maximal subgroups

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

subgroupindex
C5×#28552
#106145122
#106145022
#106138102
C2×#652222
#106083882
#106083272
#106083112
#106083072
#106080052
#106078842
#106078812
#106078672
#106071512
#106071332
#106070002
#106069422
#106069402
#106069352
#106069282
#106069252
#106063512
#106062332
#106061182
#106061142
#106058102
#106058082
#106058072
#106058062
#106056742
#106056482
#369995