Finite Group Databasebeta

← #12305801

Subgroups — #12305801

Order 1280.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2399C211yesmaximal, characteristic, complemented
2#10614223C211yesmaximal, characteristic
3#10614222C211yesmaximal, characteristic, complemented
4C4×#4092C211yesmaximal, characteristic, complemented
5#10614198C211yesmaximal, characteristic, complemented
6#10609744C211yesmaximal, characteristic, complemented
7#10609741C211yesmaximal, characteristic
8#10609740C211yesmaximal, characteristic
9#10609736C211yesmaximal, characteristic
10#10609672C211yesmaximal, characteristic, complemented
11#10609670C211yesmaximal, characteristic, complemented
12#10609662C211yesmaximal, characteristic, complemented
13#10609660C211yesmaximal, characteristic, complemented
14#10609011C211yesmaximal, characteristic, complemented
15#10609010C211yesmaximal, characteristic, complemented
16#10609009C211yesmaximal, characteristic, complemented
17#10609005C211yesmaximal, characteristic
18#10608976C211yesmaximal, characteristic, complemented
19#10608975C211yesmaximal, characteristic, complemented
20#10608974C211yesmaximal, characteristic, complemented
21#10608972C211yesmaximal, characteristic, complemented
22#10605510C211yesmaximal, characteristic, complemented
23#10605510C211yesmaximal, characteristic, complemented
24#10605509C211yesmaximal, characteristic, complemented
25#10605508C211yesmaximal, characteristic
26C4×#4042C211yesmaximal, characteristic, complemented
27C4×#4040C211yesmaximal, characteristic
28#10605401C211yesmaximal, characteristic, complemented
29#10605401C211yesmaximal, characteristic, complemented
30#10605151C211yesmaximal, characteristic, complemented
31#10605151C211yesmaximal, characteristic, complemented
32C2×C4×C5×Q8C2211yescharacteristic
33C2×C4×C5×Q8C2211yescharacteristic
34C2×#4092C2211yescharacteristic
35C2×#4042C2211yescharacteristic
36C2×#4040C2211yescharacteristic
37C2×C4×D20C2211yescharacteristic
38C2×#4018C2211yescharacteristic
39C2×C42×D5C2211yescharacteristic
40C2×C4×Dic10C2211yescharacteristic
41C5×#398C2211yescharacteristic
42C5×#398C2211yescharacteristic
43C5×#398C2211yescharacteristic
44C5×#398C2211yescharacteristic
45C5×#395C2211yescharacteristic
46C5×#395C2211yescharacteristic
47C5×#395C2211yescharacteristic
48C5×#395C2211yescharacteristic
49C4×C5×C4⋊C4C2211yescharacteristic
50C4×C5×C4⋊C4C2211yescharacteristic
51C4×C5×C4⋊C4C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#376C2211yescharacteristic
54#65520C2211yescharacteristic
55#65520C2211yescharacteristic
56#65520C2211yescharacteristic
57#65519C2211yescharacteristic
58#65518C2211yescharacteristic
59#65518C2211yescharacteristic
60#65518C2211yescharacteristic
61#65283C2211yescharacteristic
62#65283C2211yescharacteristic
63#65283C2211yescharacteristic
64#65283C2211yescharacteristic
65#65283C2211yescharacteristic
66#65282C2211yescharacteristic
67#65282C2211yescharacteristic
68#65282C2211yescharacteristic
69#65282C2211yescharacteristic
70#65282C2211yescharacteristic
71#65281C2211yescharacteristic
72#65281C2211yescharacteristic
73#65281C2211yescharacteristic
74#65280C2211yescharacteristic
75#65280C2211yescharacteristic
76#65280C2211yescharacteristic
77#65279C2211yescharacteristic
78#65278C2211yescharacteristic
79#65278C2211yescharacteristic
80#65278C2211yescharacteristic
81#65278C2211yescharacteristic
82#65276C2211yescharacteristic
83#65275C2211yescharacteristic
84#65275C2211yescharacteristic
85#65275C2211yescharacteristic
86#65275C2211yescharacteristic
87#65273C2211yescharacteristic
88#65273C2211yescharacteristic
89#65273C2211yescharacteristic
90#65273C2211yescharacteristic
91#65273C2211yescharacteristic
92#65272C2211yescharacteristic
93#65272C2211yescharacteristic
94#65272C2211yescharacteristic
95#65272C2211yescharacteristic
96#65271C2211yescharacteristic
97#65271C2211yescharacteristic
98#65271C2211yescharacteristic
99#65271C2211yescharacteristic
100#65271C2211yescharacteristic
101#65270C2211yescharacteristic
102#65270C2211yescharacteristic
103#65269C2211yescharacteristic
104#65269C2211yescharacteristic
105#65269C2211yescharacteristic
106#65269C2211yescharacteristic
107#65269C2211yescharacteristic
108#65268C2211yescharacteristic
109#65268C2211yescharacteristic
110#65268C2211yescharacteristic
111#65267C2211yescharacteristic
112#65267C2211yescharacteristic
113#65262C2211yescharacteristic
114#65261C2211yescharacteristic
115C4×#685C2211yescharacteristic
116C4×#685C2211yescharacteristic
117C4×#685C2211yescharacteristic
118C4×#685C2211yescharacteristic
119C4×#685C2211yescharacteristic
120C4×#685C2211yescharacteristic
121C4×#685C2211yescharacteristic
122C4×#685C2211yescharacteristic
123C4×#685C2211yescharacteristic
124C4×#685C2211yescharacteristic
125C4×C4⋊Dic5C2211yescharacteristic
126C4×C4⋊Dic5C2211yescharacteristic
127#65221C2211yescharacteristic
128#65221C2211yescharacteristic
129C4×#683C2211yescharacteristic
130C4×#683C2211yescharacteristic
131C4×#683C2211yescharacteristic
132C4×#683C2211yescharacteristic
133C4×#683C2211yescharacteristic
134C4×#683C2211yescharacteristic
135C4×#683C2211yescharacteristic
136C4×#683C2211yescharacteristic
137C4×#683C2211yescharacteristic
138C4×#683C2211yescharacteristic
139#64965C2211yescharacteristic
140#64965C2211yescharacteristic
141#64965C2211yescharacteristic
142#64964C2211yescharacteristic
143#64964C2211yescharacteristic
144#64964C2211yescharacteristic
145#64964C2211yescharacteristic
146#64964C2211yescharacteristic
147#64964C2211yescharacteristic
148#64964C2211yescharacteristic
149#64964C2211yescharacteristic
150#64964C2211yescharacteristic
151#64964C2211yescharacteristic
152#64963C2211yescharacteristic
153#64963C2211yescharacteristic
154#64962C2211yescharacteristic
155#64961C2211yescharacteristic
156#64958C2211yescharacteristic
157#64957C2211yescharacteristic
158#64956C2211yescharacteristic
159#64954C2211yescharacteristic
160#64953C2211yescharacteristic
161C5⋊#401C2211yescharacteristic
162C5⋊#401C2211yescharacteristic
163C5⋊#401C2211yescharacteristic
164C5⋊#401C2211yescharacteristic
165#64949C2211yescharacteristic
166#64949C2211yescharacteristic
167#64949C2211yescharacteristic
168#64948C2211yescharacteristic
169#64948C2211yescharacteristic
170#64947C2211yescharacteristic
171#64947C2211yescharacteristic
172#64947C2211yescharacteristic
173#64947C2211yescharacteristic
174#64947C2211yescharacteristic
175#64947C2211yescharacteristic
176#64947C2211yescharacteristic
177#64947C2211yescharacteristic
178#64947C2211yescharacteristic
179#64947C2211yescharacteristic
180#64947C2211yescharacteristic
181#64946C2211yescharacteristic
182#64946C2211yescharacteristic
183#64946C2211yescharacteristic
184#64944C2211yescharacteristic
185#64941C2211yescharacteristic
186#64935C2211yescharacteristic
187#36679—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×D20C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C4×C5×Q8—42no—
197C4×C5×Q8—42no—
198C2×C5×C4⋊C4C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C42×C5C2311yescharacteristic
213C2×C42×C5C2311yescharacteristic
214C2×C42×C5C2311yescharacteristic
215C2×C42×C5C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219#4092—24no—
220C2×#685C2311yescharacteristic
221C2×#685C2311yescharacteristic
222C2×#685C2311yescharacteristic
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×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
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×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282#4042—24no—
283#4040—24no—
284C4×D20—42no—
285#4018—42no—
286C42×D5—42no—
287C4×Dic10—42no—
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
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#2841—51no—
353#2839—51no—
354#2839—51no—
355#2838—51no—
356#2838—51no—
357#2835—51no—
358#2834—51no—
359#2833—51no—
360#2833—51no—
361#2831—51no—
362#2831—51no—
363#2827—51no—
364#2827—51no—
365#2817—51no—
366#2814—51no—
367#2814—51no—
368#2402—51no—
369#2402—51no—
370#2401—51no—
371#2401—51no—
372#2401—51no—
373#2401—51no—
374#2399—51no—
375#2399D511yescharacteristic, complemented
376#2398—51no—
377#2396—51no—
378#2396—51no—
379#2395—51no—
380C4×C22⋊Q8—51no—
381C4×C22⋊Q8—51no—
382C4×#123—51no—
383C23×D5C2411yescharacteristic
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
405C22×C4×C5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C2×D20—22no—
421C2×D20—41no—
422C2×D20—41no—
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—22no—
427C2×C4×D5—22no—
428C2×C4×D5—22no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×C4×D5—41no—
433C2×C4×D5—41no—
434C2×C4×D5#4114yes—
435C2×Dic10—22no—
436C2×Dic10—41no—
437C2×Dic10—41no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—22no—
440C5×C4⋊C4—41no—
441C5×C4⋊C4—41no—
442C5×C4⋊C4—41no—
443C5×C4⋊C4—41no—
444C5×C4⋊C4—41no—
445C5×C4⋊C4—41no—
446C5×C4⋊C4—41no—
447C5×C4⋊C4—41no—
448C5×C4⋊C4—41no—
449C5×C4⋊C4—41no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C42×C5—22no—
453C42×C5—22no—
454C42×C5—22no—
455C42×C5—22no—
456C42×C5—22no—
457C42×C5—22no—
458C42×C5—22no—
459#685—22no—
460#685—22no—
461#685—22no—
462#685—22no—
463#685—22no—
464#685—22no—
465#685—22no—
466#685—41no—
467#685—41no—
468#685—41no—
469#685—41no—
470#685—41no—
471#685—41no—
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—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—22no—
515C4×Dic5—22no—
516C4×Dic5—22no—
517C4×Dic5—22no—
518C4×Dic5—22no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C2×#123—51no—
522C2×C22⋊Q8—51no—
523C2×C22⋊Q8—51no—
524C2×C4×Q8—51no—
525C2×C4×Q8C2×D511yescharacteristic
526C2×C4×Q8C2×D511yescharacteristic
527C2×C4×D4—51no—
528C2×#117—51no—
529C22×C42—51no—
530#401—51no—
531#401—51no—
532#401—51no—
533#401—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#400—51no—
552#400—51no—
553#400—51no—
554#400—51no—
555#400—51no—
556#400—51no—
557#400—51no—
558#400—51no—
559#399—51no—
560#399—51no—
561#399—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398—51no—
567#398—51no—
568#398—51no—
569#398—51no—
570#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#398—51no—
579#398C2×D511yescharacteristic
580#398C2×D511yescharacteristic
581#398C2×D511yescharacteristic
582#398C2×D511yescharacteristic
583#397—51no—
584#397—51no—
585#397—51no—
586#397—51no—
587#397—51no—
588#397—51no—
589#397—51no—
590#397—51no—
591#397—51no—
592#397—51no—
593#397—51no—
594#397—51no—
595#397—51no—
596#397—51no—
597#397—51no—
598#397—51no—
599#397—51no—
600#396—51no—
601#396—51no—
602#396—51no—
603#396—51no—
604#396—51no—
605#396—51no—
606#396—51no—
607#396—51no—
608#395—51no—
609#395—51no—
610#395—51no—
611#395—51no—
612#395—51no—
613#395—51no—
614#395C2×D511yescharacteristic
615#395C2×D511yescharacteristic
616#395C2×D511yescharacteristic
617#395C2×D511yescharacteristic
618#394—51no—
619#394—51no—
620#394—51no—
621#394—51no—
622#393—51no—
623#393—51no—
624#393—51no—
625#393—51no—
626#391—51no—
627#391—51no—
628#389—51no—
629#389—51no—
630#388—51no—
631#388—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#386—51no—
639#385—51no—
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#381—51no—
645#380—51no—
646#380—51no—
647C4×C4⋊C4—51no—
648C4×C4⋊C4—51no—
649C4×C4⋊C4—51no—
650C4×C4⋊C4—51no—
651C4×C4⋊C4—51no—
652C4×C4⋊C4—51no—
653C4×C4⋊C4—51no—
654C4×C4⋊C4—51no—
655C4×C4⋊C4—51no—
656C4×C4⋊C4—51no—
657C4×C4⋊C4—51no—
658C4×C4⋊C4—51no—
659C4×C4⋊C4C2×D511yescharacteristic
660C4×C4⋊C4C2×D511yescharacteristic
661C4×C4⋊C4C2×D511yescharacteristic
662C4×C4⋊C4C2×D511yescharacteristic
663C4×C22⋊C4—51no—
664C4×C22⋊C4—51no—
665C4×C22⋊C4—51no—
666C4×C22⋊C4—51no—
667C4×C22⋊C4—51no—
668C4×C22⋊C4—51no—
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C4×C22⋊C4—51no—
673#376—51no—
674#376—51no—
675#376C2×D511yescharacteristic
676C23×C5C2511yescharacteristic
677C22×D5—21no—
678C22×D5—21no—
679C22×D5—21no—
680C22×D5—21no—
681C22×D5—21no—
682C22×D5—21no—
683C22×D5—21no—
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5C2×#4112yes—
691C5×Q8—44no—
692C5×Q8—44no—
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—
735C2×C4×C5H(5,𝔽2)12yes—
736C2×C4×C52−1+412yes—
737C2×C4×C52−1+412yes—
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×Dic5C2×#4112yes—
780D20—44no—
781C4×D5—44no—
782C4×D5—44no—
783C4×D5—44no—
784C4×D5—44no—
785Dic10—44no—
786C22×Q8—51no—
787C22×Q8C22×D511yescharacteristic
788C22×Q8C22×D511yescharacteristic
789C22×D4—51no—
790C23×C4—51no—
791C23×C4—51no—
792C23×C4—51no—
793C23×C4—51no—
794#123—104no—
795C22⋊Q8—104no—
796C22⋊Q8—104no—
797C4×Q8—42no—
798C4×Q8—42no—
799C4×Q8—202no—
800C4×D4—202no—
801#117—202no—
802C2×C4⋊C4—51no—
803C2×C4⋊C4—51no—
804C2×C4⋊C4—51no—
805C2×C4⋊C4—51no—
806C2×C4⋊C4—51no—
807C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
833C2×C4⋊C4C22×D511yescharacteristic
834C2×C4⋊C4C22×D511yescharacteristic
835C2×C4⋊C4C22×D511yescharacteristic
836C2×C4⋊C4C22×D511yescharacteristic
837C2×C4⋊C4C22×D511yescharacteristic
838C2×C4⋊C4C22×D511yescharacteristic
839C2×C4⋊C4C22×D511yescharacteristic
840C2×C4⋊C4C22×D511yescharacteristic
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
846C2×C22⋊C4—51no—
847C2×C22⋊C4—51no—
848C2×C22⋊C4—51no—
849C2×C22⋊C4—51no—
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⋊C4—51no—
867C2×C22⋊C4—51no—
868C2×C22⋊C4—51no—
869C2×C22⋊C4—51no—
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
882C2×C42C22×D511yescharacteristic
883C2×C42C22×D511yescharacteristic
884C2×C42C22×D511yescharacteristic
885C2×C42C22×D511yescharacteristic
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#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
950C22×C5C22×#4111yescharacteristic
951C22×C5C2×H(5,𝔽2)11yescharacteristic
952C22×C5C2×2−1+411yescharacteristic
953C22×C5C2×2−1+411yescharacteristic
954C22×C5#58511yescharacteristic
955C22×C5#58511yescharacteristic
956C22×C5#58511yescharacteristic
957C2×D5—22no—
958C2×D5—22no—
959C2×D5—22no—
960C2×D5—41no—
961C2×D5—41no—
962C2×D5—41no—
963C2×D5—41no—
964C2×D5—41no—
965C2×D5—41no—
966C2×D5—41no—
967C2×D5—41no—
968C2×D5—41no—
969C2×D5—41no—
970C2×D5—41no—
971C4×C5—22no—
972C4×C5—41no—
973C4×C5—41no—
974C4×C5—41no—
975C4×C5—41no—
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#56314yes—
986Dic5—22no—
987Dic5—41no—
988Dic5—41no—
989Dic5—41no—
990Dic5—41no—
991Dic5—41no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000C24—51no—
1001C24—51no—
1002C2×Q8—22no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—41no—
1006C2×Q8—41no—
1007C2×Q8—41no—
1008C2×Q8—102no—
1009C2×Q8—201no—
1010C2×Q8—201no—
1011C2×D4—102no—
1012C2×D4—201no—
1013C2×D4—201no—
1014C22×C4—51no—
1015C22×C4—54no—
1016C22×C4—51no—
1017C22×C4—51no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—51no—
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—102no—
1030C22×C4—102no—
1031C22×C4—102no—
1032C22×C4—102no—
1033C22×C4—102no—
1034C22×C4—102no—
1035C22×C4—201no—
1036C22×C4—201no—
1037C22×C4—201no—
1038C22×C4—201no—
1039C22×C4—201no—
1040C22×C4C23×D511yescharacteristic
1041C22×C4C23×D511yescharacteristic
1042C22×C4C23×D511yescharacteristic
1043C22×C4C23×D511yescharacteristic
1044C22×C4C23×D511yescharacteristic
1045C22×C4C23×D511yescharacteristic
1046C22×C4C23×D511yescharacteristic
1047C22×C4C23×D511yescharacteristic
1048C22×C4C23×D511yescharacteristic
1049C22×C4C23×D511yescharacteristic
1050C22×C4C23×D511yescharacteristic
1051C22×C4C23×D511yescharacteristic
1052C22×C4C23×D511yescharacteristic
1053C22×C4C23×D511yescharacteristic
1054C22×C4C23×D511yescharacteristic
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—102no—
1070C4⋊C4—102no—
1071C4⋊C4—102no—
1072C4⋊C4—102no—
1073C4⋊C4—102no—
1074C4⋊C4—102no—
1075C4⋊C4—201no—
1076C4⋊C4—201no—
1077C4⋊C4—201no—
1078C4⋊C4—201no—
1079C4⋊C4—201no—
1080C4⋊C4—201no—
1081C4⋊C4—201no—
1082C4⋊C4—201no—
1083C4⋊C4—201no—
1084C4⋊C4—201no—
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—
1099C22⋊C4—102no—
1100C22⋊C4—102no—
1101C22⋊C4—102no—
1102C22⋊C4—102no—
1103C22⋊C4—102no—
1104C22⋊C4—102no—
1105C22⋊C4—102no—
1106C22⋊C4—201no—
1107C22⋊C4—201no—
1108C22⋊C4—201no—
1109C22⋊C4—201no—
1110C22⋊C4—201no—
1111C22⋊C4—201no—
1112C22⋊C4—201no—
1113C22⋊C4—201no—
1114C22⋊C4—201no—
1115C22⋊C4—201no—
1116C22⋊C4—201no—
1117C22⋊C4—201no—
1118C22⋊C4—201no—
1119C22⋊C4—201no—
1120C22⋊C4—201no—
1121C22⋊C4—201no—
1122C22⋊C4—201no—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—22no—
1127C42—22no—
1128C42—22no—
1129C42—22no—
1130C42—102no—
1131C42—102no—
1132C42—102no—
1133C42—102no—
1134C42—102no—
1135C42—102no—
1136C42—201no—
1137C42—201no—
1138C2×C5#345911yescharacteristic
1139C2×C5#346111yescharacteristic
1140C2×C5#346111yescharacteristic
1141C2×C5C2×#56311yescharacteristic
1142C2×C5#352911yescharacteristic
1143C2×C5#353111yescharacteristic
1144C2×C5#353111yescharacteristic
1145D5—42no—
1146D5—81no—
1147C23—52no—
1148C23—101no—
1149C23—101no—
1150C23—101no—
1151C23—101no—
1152C23—101no—
1153C23—101no—
1154C23—101no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23—101no—
1160C23—101no—
1161C23C24×D511yescharacteristic
1162Q8—44no—
1163Q8—44no—
1164Q8—204no—
1165D4—204no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
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—52no—
1208C2×C4—101no—
1209C2×C4—101no—
1210C2×C4—101no—
1211C2×C4—101no—
1212C2×C4—101no—
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—204no—
1250C2×C4—204no—
1251C2×C4—204no—
1252C2×C4—204no—
1253C2×C4#414412yes—
1254C2×C4#414712yes—
1255C2×C4#414712yes—
1256C2×C4D5×#4112yes—
1257C5#3667911yescharacteristic, complemented, Sylow
1258C22—102no—
1259C22—102no—
1260C22—102no—
1261C22—201no—
1262C22—201no—
1263C22—201no—
1264C22—201no—
1265C22—201no—
1266C22—201no—
1267C22—201no—
1268C22—201no—
1269C22—201no—
1270C22—201no—
1271C22—201no—
1272C22C2×#414411yescharacteristic
1273C22C2×#414711yescharacteristic
1274C22C2×#414711yescharacteristic
1275C22C2×D5×#4111yescharacteristic
1276C22#6628311yescharacteristic
1277C22#6628311yescharacteristic
1278C22#6628311yescharacteristic
1279C4—22no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—102no—
1294C4—201no—
1295C4—201no—
1296C4—201no—
1297C4—201no—
1298C4—201no—
1299C4—201no—
1300C4—201no—
1301C4—201no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4#6606914yes—
1308C2—202no—
1309C2—401no—
1310C2#1061793711yescharacteristic
1311C2#1061794911yescharacteristic
1312C2C2×#6606911yescharacteristic
1313C2#1061817611yescharacteristic
1314C2#1061817611yescharacteristic
1315C2#1061818711yescharacteristic
1316C2#1061818711yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutator, socle, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC5×#2399C2
prime radicalC22×D20C23
hypercenter#2399D5
hypocenterC5#36679
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #2399

Complements

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

NH ≅ G/Ntype
1. C5×#2399C2semidirect
3. #10614222C2semidirect
4. C4×#4092C2semidirect
5. #10614198C2semidirect
6. #10609744C2semidirect
10. #10609672C2semidirect
11. #10609670C2semidirect
12. #10609662C2semidirect
13. #10609660C2semidirect
14. #10609011C2semidirect
15. #10609010C2semidirect
16. #10609009C2semidirect
18. #10608976C2semidirect
19. #10608975C2semidirect
20. #10608974C2semidirect
21. #10608972C2semidirect
22. #10605510C2semidirect
23. #10605510C2semidirect
24. #10605509C2semidirect
26. C4×#4042C2semidirect
28. #10605401C2semidirect
29. #10605401C2semidirect
30. #10605151C2semidirect
31. #10605151C2semidirect
375. #2399D5semidirect
1257. C5#36679semidirect

Maximal subgroups

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

subgroupindex
C5×#23992
#106142232
#106142222
C4×#40922
#106141982
#106097442
#106097412
#106097402
#106097362
#106096722
#106096702
#106096622
#106096602
#106090112
#106090102
#106090092
#106090052
#106089762
#106089752
#106089742
#106089722
#106055102
#106055092
#106055082
C4×#40422
C4×#40402
#106054012
#106051512
#366795