Finite Group Databasebeta

← #12313855

Subgroups — #12313855

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×#2759C211yesmaximal, characteristic, complemented
2#10610161C211yesmaximal, characteristic, complemented
3#10610152C211yesmaximal, characteristic, complemented
4#10609417C211yesmaximal, characteristic
5#10609336C211yesmaximal, characteristic, complemented
6#10609332C211yesmaximal, characteristic, complemented
7#10609216C211yesmaximal, characteristic
8#10608988C211yesmaximal, characteristic, complemented
9#10608962C211yesmaximal, characteristic, complemented
10#10608600C211yesmaximal, characteristic
11#10608598C211yesmaximal, characteristic
12#10608581C211yesmaximal, characteristic, complemented
13#10608567C211yesmaximal, characteristic, complemented
14#10608368C211yesmaximal, characteristic, complemented
15#10608343C211yesmaximal, characteristic, complemented
16#10608325C211yesmaximal, characteristic, complemented
17#10608315C211yesmaximal, characteristic, complemented
18#10608309C211yesmaximal, characteristic, complemented
19#10608251C211yesmaximal, characteristic, complemented
20#10607690C211yesmaximal, characteristic
21#10607598C211yesmaximal, characteristic
22#10607491C211yesmaximal, characteristic, complemented
23#10607461C211yesmaximal, characteristic, complemented
24#10607446C211yesmaximal, characteristic, complemented
25#10607188C211yesmaximal, characteristic
26#10607179C211yesmaximal, characteristic, complemented
27D5×#387C211yesmaximal, characteristic, complemented
28#10606940C211yesmaximal, characteristic, complemented
29#10606940C211yesmaximal, characteristic, complemented
30#10606031C211yesmaximal, characteristic, complemented
31#10606011C211yesmaximal, characteristic, complemented
32C2×#4092C2211yescharacteristic
33C2×#4092C2211yescharacteristic
34C2×#4042C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4029C2211yescharacteristic
38C2×#4029C2211yescharacteristic
39C2×#4027C2211yescharacteristic
40C2×C42×D5C2211yescharacteristic
41C5×#401C2211yescharacteristic
42C5×#397C2211yescharacteristic
43C5×#397C2211yescharacteristic
44C5×#395C2211yescharacteristic
45C5×#393C2211yescharacteristic
46C5×#393C2211yescharacteristic
47C5×#391C2211yescharacteristic
48C5×#391C2211yescharacteristic
49C5×#391C2211yescharacteristic
50C5×#388C2211yescharacteristic
51C5×#388C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#387C2211yescharacteristic
54C5×#387C2211yescharacteristic
55C5×#383C2211yescharacteristic
56#65519C2211yescharacteristic
57#65519C2211yescharacteristic
58#65519C2211yescharacteristic
59#65518C2211yescharacteristic
60#65518C2211yescharacteristic
61#65518C2211yescharacteristic
62#65278C2211yescharacteristic
63#65278C2211yescharacteristic
64#65275C2211yescharacteristic
65#65275C2211yescharacteristic
66#65270C2211yescharacteristic
67#65270C2211yescharacteristic
68#65269C2211yescharacteristic
69#65269C2211yescharacteristic
70#65269C2211yescharacteristic
71#65269C2211yescharacteristic
72#65269C2211yescharacteristic
73#65267C2211yescharacteristic
74#65267C2211yescharacteristic
75#65266C2211yescharacteristic
76#65266C2211yescharacteristic
77#65261C2211yescharacteristic
78#65261C2211yescharacteristic
79#65245C2211yescharacteristic
80#65245C2211yescharacteristic
81#65245C2211yescharacteristic
82#65245C2211yescharacteristic
83#65242C2211yescharacteristic
84#65242C2211yescharacteristic
85#65241C2211yescharacteristic
86#65241C2211yescharacteristic
87#65240C2211yescharacteristic
88#65240C2211yescharacteristic
89#65240C2211yescharacteristic
90#65238C2211yescharacteristic
91#65238C2211yescharacteristic
92#65238C2211yescharacteristic
93#65236C2211yescharacteristic
94#65235C2211yescharacteristic
95#65235C2211yescharacteristic
96#65234C2211yescharacteristic
97#65234C2211yescharacteristic
98#65233C2211yescharacteristic
99#65233C2211yescharacteristic
100#65232C2211yescharacteristic
101#65231C2211yescharacteristic
102#65231C2211yescharacteristic
103#65231C2211yescharacteristic
104C4×#685C2211yescharacteristic
105C4×#685C2211yescharacteristic
106#65225C2211yescharacteristic
107#65222C2211yescharacteristic
108#65222C2211yescharacteristic
109#65222C2211yescharacteristic
110#65222C2211yescharacteristic
111#65222C2211yescharacteristic
112#65222C2211yescharacteristic
113#65218C2211yescharacteristic
114#65217C2211yescharacteristic
115#64957C2211yescharacteristic
116#64957C2211yescharacteristic
117#64957C2211yescharacteristic
118#64957C2211yescharacteristic
119#64956C2211yescharacteristic
120#64956C2211yescharacteristic
121#64956C2211yescharacteristic
122#64955C2211yescharacteristic
123#64953C2211yescharacteristic
124#64953C2211yescharacteristic
125#64953C2211yescharacteristic
126#64953C2211yescharacteristic
127#64953C2211yescharacteristic
128#64953C2211yescharacteristic
129D5×#95C2211yescharacteristic
130D5×#95C2211yescharacteristic
131D5×#95C2211yescharacteristic
132D5×#95C2211yescharacteristic
133C5⋊#401C2211yescharacteristic
134#64950C2211yescharacteristic
135#64950C2211yescharacteristic
136#64949C2211yescharacteristic
137#64949C2211yescharacteristic
138#64949C2211yescharacteristic
139#64949C2211yescharacteristic
140#64949C2211yescharacteristic
141#64949C2211yescharacteristic
142#64948C2211yescharacteristic
143#64948C2211yescharacteristic
144#64948C2211yescharacteristic
145#64948C2211yescharacteristic
146#64947C2211yescharacteristic
147#64947C2211yescharacteristic
148#64947C2211yescharacteristic
149#64947C2211yescharacteristic
150#64947C2211yescharacteristic
151#64947C2211yescharacteristic
152#64947C2211yescharacteristic
153#64946C2211yescharacteristic
154#64946C2211yescharacteristic
155#64946C2211yescharacteristic
156#64945C2211yescharacteristic
157#64944C2211yescharacteristic
158#64944C2211yescharacteristic
159#64944C2211yescharacteristic
160#64943C2211yescharacteristic
161#64943C2211yescharacteristic
162#64943C2211yescharacteristic
163#64943C2211yescharacteristic
164#64942C2211yescharacteristic
165#64942C2211yescharacteristic
166#64942C2211yescharacteristic
167#64942C2211yescharacteristic
168#64942C2211yescharacteristic
169#64941C2211yescharacteristic
170#64941C2211yescharacteristic
171#64941C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64940C2211yescharacteristic
176#64940C2211yescharacteristic
177#64939C2211yescharacteristic
178#64939C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64936C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36999—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×C4×D5C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C22⋊C4C2311yescharacteristic
206C2×C5×C22⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C42×C5C2311yescharacteristic
213C2×C42×C5C2311yescharacteristic
214C2×C42×C5C2311yescharacteristic
215C2×C22⋊Dic5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221#4092—24no—
222#4092—42no—
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×C4⋊Dic5C2311yescharacteristic
231C2×C4⋊Dic5C2311yescharacteristic
232C2×C4⋊Dic5C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×#683C2311yescharacteristic
241C2×#683C2311yescharacteristic
242C2×#683C2311yescharacteristic
243C2×#683C2311yescharacteristic
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×C4×Dic5C2311yescharacteristic
266C2×C4×Dic5C2311yescharacteristic
267C2×C4×Dic5C2311yescharacteristic
268C2×C4×Dic5C2311yescharacteristic
269C2×C4×Dic5C2311yescharacteristic
270C2×C4×Dic5C2311yescharacteristic
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273#4042—42no—
274D5×C4⋊C4—24no—
275D5×C4⋊C4—42no—
276#4029—42no—
277#4029—42no—
278#4027—24no—
279C42×D5—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
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
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#2855—51no—
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#2759D511yescharacteristic, complemented
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—
388C2×C5×Q8—41no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C2×C22⋊D5—22no—
406C2×C22⋊D5—22no—
407C2×C22⋊D5—22no—
408C22×Dic5—22no—
409C22×Dic5—41no—
410C22×Dic5—41no—
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C2×C4×D5—22no—
427C2×C4×D5—22no—
428C2×C4×D5—22no—
429C2×C4×D5—22no—
430C2×C4×D5—22no—
431C2×C4×D5—22no—
432C2×C4×D5—22no—
433C2×C4×D5—22no—
434C2×C4×D5—22no—
435C2×C4×D5—22no—
436C2×C4×D5—22no—
437C2×C4×D5—41no—
438C2×C4×D5—41no—
439C2×C4×D5—41no—
440C2×C4×D5—41no—
441C2×C4×D5—41no—
442C2×C4×D5—41no—
443C2×C4×D5—41no—
444C2×C4×D5—41no—
445C2×C4×D5—41no—
446C2×C4×D5#4114yes—
447C2×Dic10—22no—
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×C22⋊C4—22no—
456C5×C22⋊C4—41no—
457C5×C22⋊C4—41no—
458C5×C22⋊C4—41no—
459C5×C22⋊C4—41no—
460C5×C22⋊C4—41no—
461C5×C22⋊C4—41no—
462C42×C5—41no—
463C42×C5—41no—
464C42×C5—41no—
465C22⋊Dic5—22no—
466C22⋊Dic5—41no—
467C22⋊Dic5—41no—
468C22⋊Dic5—41no—
469C22⋊Dic5—41no—
470C22⋊Dic5—41no—
471#685—22no—
472#685—22no—
473#685—22no—
474#685—22no—
475#685—22no—
476#685—22no—
477#685—22no—
478C4⋊Dic5—22no—
479C4⋊Dic5—22no—
480C4⋊Dic5—22no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488#683—22no—
489#683—22no—
490#683—22no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—41no—
495#683—41no—
496#683—41no—
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—
513C4×Dic5—22no—
514C4×Dic5—41no—
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⋊Q8—51no—
526C2×C4×D4—51no—
527C22×C4⋊C4—51no—
528C22×C4⋊C4—51no—
529C22×C42—51no—
530#401—51no—
531#401C2×D511yescharacteristic
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#397C2×D511yescharacteristic
569#397C2×D511yescharacteristic
570#395—51no—
571#395—51no—
572#395—51no—
573#395—51no—
574#395C2×D511yescharacteristic
575#393—51no—
576#393C2×D511yescharacteristic
577#393C2×D511yescharacteristic
578#391—51no—
579#391—51no—
580#391—51no—
581#391—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#391C2×D511yescharacteristic
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#389—51no—
595#389—51no—
596#388—51no—
597#388—51no—
598#388—51no—
599#388—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#388C2×D511yescharacteristic
604#388C2×D511yescharacteristic
605#388C2×D511yescharacteristic
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#387—51no—
633#387—51no—
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#385—51no—
647#385—51no—
648#383—51no—
649#383—51no—
650#383C2×D511yescharacteristic
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#381—51no—
662#381—51no—
663#380—51no—
664#380—51no—
665#380—51no—
666#380—51no—
667#380—51no—
668#380—51no—
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×C5—21no—
681C23×C5—21no—
682C23×C5—21no—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5C2×#4112yes—
689C22×D5H(5,𝔽2)12yes—
690C22×D52−1+412yes—
691C5×Q8—82no—
692C5×Q8—82no—
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—21no—
734C2×C4×C5C2×#4112yes—
735C22⋊D5—44no—
736C2×Dic5—21no—
737C2×Dic5—21no—
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—82no—
780C2×Dic5C2×#4112yes—
781C2×Dic52−1+412yes—
782C4×D5—44no—
783C4×D5—44no—
784C4×D5—44no—
785C4×D5—44no—
786C4×D5—44no—
787C4×D5—82no—
788C4×D5—82no—
789Dic10—82no—
790C22×Q8—51no—
791C22×Q8C22×D511yescharacteristic
792C22×Q8C22×D511yescharacteristic
793C22×D4—51no—
794C23×C4—51no—
795C23×C4—51no—
796C23×C4—51no—
797C23×C4—51no—
798C23×C4—51no—
799C23×C4—51no—
800C23×C4—51no—
801C23×C4—51no—
802#123—202no—
803#123—202no—
804C22⋊Q8—104no—
805C22⋊Q8—202no—
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—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—104no—
844C2×C4⋊C4—202no—
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⋊C4C22×D511yescharacteristic
864C2×C22⋊C4C22×D511yescharacteristic
865C2×C22⋊C4C22×D511yescharacteristic
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C42—51no—
871C2×C42—51no—
872C2×C42—51no—
873C2×C42—51no—
874C2×C42—51no—
875C2×C42—51no—
876C2×C42—51no—
877C2×C42—51no—
878C2×C42—202no—
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#95C22×D511yescharacteristic
937#95C22×D511yescharacteristic
938#95C22×D511yescharacteristic
939#95C22×D511yescharacteristic
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—41no—
955C22×C5—41no—
956C22×C5—41no—
957C22×C5—41no—
958C22×C5—41no—
959C22×C5—41no—
960C22×C5—41no—
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—22no—
969C2×D5—22no—
970C2×D5—22no—
971C2×D5—22no—
972C2×D5—22no—
973C2×D5—22no—
974C2×D5#54214yes—
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—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—102no—
1013C2×Q8—201no—
1014C2×Q8—201no—
1015C2×D4—102no—
1016C2×D4—102no—
1017C2×D4—102no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—54no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—102no—
1035C22×C4—102no—
1036C22×C4—102no—
1037C22×C4—102no—
1038C22×C4—102no—
1039C22×C4—102no—
1040C22×C4—102no—
1041C22×C4—102no—
1042C22×C4—102no—
1043C22×C4—102no—
1044C22×C4—102no—
1045C22×C4—102no—
1046C22×C4—201no—
1047C22×C4—201no—
1048C22×C4—201no—
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—102no—
1077C4⋊C4—102no—
1078C4⋊C4—102no—
1079C4⋊C4—102no—
1080C4⋊C4—102no—
1081C4⋊C4—102no—
1082C4⋊C4—102no—
1083C4⋊C4—102no—
1084C4⋊C4—102no—
1085C4⋊C4—201no—
1086C4⋊C4—201no—
1087C4⋊C4—201no—
1088C4⋊C4—201no—
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—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—102no—
1119C22⋊C4—102no—
1120C22⋊C4—102no—
1121C22⋊C4—102no—
1122C22⋊C4—102no—
1123C22⋊C4—102no—
1124C22⋊C4—102no—
1125C22⋊C4—102no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C22⋊C4—201no—
1130C22⋊C4—201no—
1131C42—41no—
1132C42—41no—
1133C42—41no—
1134C42—102no—
1135C42—201no—
1136C42—201no—
1137C42—201no—
1138C42—201no—
1139C42—201no—
1140C42—201no—
1141C42—201no—
1142C2×C5—81no—
1143C2×C5C2×#54211yescharacteristic
1144C2×C5#349111yescharacteristic
1145C2×C5#350711yescharacteristic
1146C2×C5#353311yescharacteristic
1147C2×C5#353511yescharacteristic
1148C2×C5#356311yescharacteristic
1149C2×C5#356411yescharacteristic
1150D5—24no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—52no—
1159C23—52no—
1160C23—52no—
1161C23—101no—
1162C23—101no—
1163C23—101no—
1164C23—101no—
1165C23C24×D511yescharacteristic
1166Q8—82no—
1167Q8—82no—
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—52no—
1212C2×C4—52no—
1213C2×C4—101no—
1214C2×C4—101no—
1215C2×C4—101no—
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—204no—
1257C2×C4—204no—
1258C2×C4—204no—
1259C2×C4—204no—
1260C2×C4—204no—
1261C2×C4—402no—
1262C2×C4—402no—
1263C2×C4—402no—
1264C2×C4D5×#4112yes—
1265C5#3699911yescharacteristic, complemented, Sylow
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—54no—
1274C22—102no—
1275C22—102no—
1276C22—102no—
1277C22—102no—
1278C22—102no—
1279C22—102no—
1280C22C2×D5×#4111yescharacteristic
1281C22#6628311yescharacteristic
1282C22#6628311yescharacteristic
1283C22D5×H(5,𝔽2)11yescharacteristic
1284C22#6628511yescharacteristic
1285C22D5×2−1+411yescharacteristic
1286C22D5×2−1+411yescharacteristic
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—81no—
1317C2—104no—
1318C2#1061832011yescharacteristic
1319C2D5×#54211yescharacteristic
1320C2#1061846111yescharacteristic
1321C2#1061871711yescharacteristic
1322C2#1061890811yescharacteristic
1323C2#1061891411yescharacteristic
1324C2#1061903711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2759C2
prime radicalC22×C22⋊D5C23
hypercenter#2759D5
hypocenterC5#36999
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2759

Complements

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

NH ≅ G/Ntype
1. C5×#2759C2semidirect
2. #10610161C2semidirect
3. #10610152C2semidirect
5. #10609336C2semidirect
6. #10609332C2semidirect
8. #10608988C2semidirect
9. #10608962C2semidirect
12. #10608581C2semidirect
13. #10608567C2semidirect
14. #10608368C2semidirect
15. #10608343C2semidirect
16. #10608325C2semidirect
17. #10608315C2semidirect
18. #10608309C2semidirect
19. #10608251C2semidirect
22. #10607491C2semidirect
23. #10607461C2semidirect
24. #10607446C2semidirect
26. #10607179C2semidirect
27. D5×#387C2semidirect
28. #10606940C2semidirect
29. #10606940C2semidirect
30. #10606031C2semidirect
31. #10606011C2semidirect
362. #2759D5semidirect
1265. C5#36999semidirect

Maximal subgroups

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

subgroupindex
C5×#27592
#106101612
#106101522
#106094172
#106093362
#106093322
#106092162
#106089882
#106089622
#106086002
#106085982
#106085812
#106085672
#106083682
#106083432
#106083252
#106083152
#106083092
#106082512
#106076902
#106075982
#106074912
#106074612
#106074462
#106071882
#106071792
D5×#3872
#106069402
#106060312
#106060112
#369995