Finite Group Databasebeta

← #12307503

Subgroups — #12307503

Order 1280.

1494 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×#2857C211yesmaximal, characteristic, complemented
2#10614979C211yesmaximal, characteristic, complemented
3#10614978C211yesmaximal, characteristic, complemented
4#10614554C211yesmaximal, characteristic
5#10614554C211yesmaximal, characteristic
6#10614477C211yesmaximal, characteristic, complemented
7#10614477C211yesmaximal, characteristic, complemented
8#10613806C211yesmaximal, characteristic, complemented
9#10613796C211yesmaximal, characteristic
10#10608325C211yesmaximal, characteristic, complemented
11#10608323C211yesmaximal, characteristic, complemented
12#10608313C211yesmaximal, characteristic, complemented
13#10608309C211yesmaximal, characteristic, complemented
14#10607822C211yesmaximal, characteristic, complemented
15#10607820C211yesmaximal, characteristic, complemented
16#10607819C211yesmaximal, characteristic, complemented
17#10607817C211yesmaximal, characteristic, complemented
18#10607789C211yesmaximal, characteristic, complemented
19#10607785C211yesmaximal, characteristic, complemented
20#10607757C211yesmaximal, characteristic, complemented
21#10607755C211yesmaximal, characteristic, complemented
22#10606082C211yesmaximal, characteristic, complemented
23#10606080C211yesmaximal, characteristic, complemented
24#10605726C211yesmaximal, characteristic, complemented
25#10605723C211yesmaximal, characteristic
26#10605721C211yesmaximal, characteristic
27#10605720C211yesmaximal, characteristic, complemented
28#10605715C211yesmaximal, characteristic, complemented
29#10605708C211yesmaximal, characteristic
30#10605696C211yesmaximal, characteristic
31#10605691C211yesmaximal, characteristic, complemented
32C2×C5×C4⋊Q8C2211yescharacteristic
33C2×C5×C22⋊Q8C2211yescharacteristic
34C2×C5×C22⋊Q8C2211yescharacteristic
35C22×C42×C5C2211yescharacteristic
36C2×C4×C22⋊D5C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C2×#4044C2211yescharacteristic
39C2×#4035C2211yescharacteristic
40C2×#4018C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#384C2211yescharacteristic
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52#65520C2211yescharacteristic
53#65520C2211yescharacteristic
54#65519C2211yescharacteristic
55#65519C2211yescharacteristic
56#65519C2211yescharacteristic
57#65519C2211yescharacteristic
58#65518C2211yescharacteristic
59#65518C2211yescharacteristic
60#65502C2211yescharacteristic
61#65502C2211yescharacteristic
62#65501C2211yescharacteristic
63#65500C2211yescharacteristic
64#65500C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67#65499C2211yescharacteristic
68#65499C2211yescharacteristic
69C4×C22⋊Dic5C2211yescharacteristic
70#65283C2211yescharacteristic
71#65283C2211yescharacteristic
72#65283C2211yescharacteristic
73#65282C2211yescharacteristic
74#65282C2211yescharacteristic
75#65282C2211yescharacteristic
76#65279C2211yescharacteristic
77#65279C2211yescharacteristic
78#65279C2211yescharacteristic
79#65278C2211yescharacteristic
80#65278C2211yescharacteristic
81#65278C2211yescharacteristic
82#65278C2211yescharacteristic
83#65275C2211yescharacteristic
84#65275C2211yescharacteristic
85#65275C2211yescharacteristic
86#65273C2211yescharacteristic
87#65273C2211yescharacteristic
88#65273C2211yescharacteristic
89#65272C2211yescharacteristic
90#65272C2211yescharacteristic
91#65272C2211yescharacteristic
92#65271C2211yescharacteristic
93#65271C2211yescharacteristic
94#65270C2211yescharacteristic
95#65270C2211yescharacteristic
96#65270C2211yescharacteristic
97#65270C2211yescharacteristic
98#65270C2211yescharacteristic
99#65270C2211yescharacteristic
100#65270C2211yescharacteristic
101#65270C2211yescharacteristic
102#65270C2211yescharacteristic
103#65270C2211yescharacteristic
104#65269C2211yescharacteristic
105#65269C2211yescharacteristic
106#65269C2211yescharacteristic
107#65267C2211yescharacteristic
108#65267C2211yescharacteristic
109#65267C2211yescharacteristic
110#65267C2211yescharacteristic
111#65267C2211yescharacteristic
112#65267C2211yescharacteristic
113#65267C2211yescharacteristic
114#65267C2211yescharacteristic
115#65267C2211yescharacteristic
116#65267C2211yescharacteristic
117C4⋊C4×Dic5C2211yescharacteristic
118C4⋊C4×Dic5C2211yescharacteristic
119C4⋊C4×Dic5C2211yescharacteristic
120C4⋊C4×Dic5C2211yescharacteristic
121#65261C2211yescharacteristic
122#65261C2211yescharacteristic
123#65261C2211yescharacteristic
124#65248C2211yescharacteristic
125#65248C2211yescharacteristic
126#65248C2211yescharacteristic
127#65248C2211yescharacteristic
128#65241C2211yescharacteristic
129#65241C2211yescharacteristic
130#65241C2211yescharacteristic
131#65241C2211yescharacteristic
132#65240C2211yescharacteristic
133#65240C2211yescharacteristic
134#65240C2211yescharacteristic
135#65240C2211yescharacteristic
136#65240C2211yescharacteristic
137#65240C2211yescharacteristic
138#65240C2211yescharacteristic
139#65240C2211yescharacteristic
140#65229C2211yescharacteristic
141#65229C2211yescharacteristic
142C4×#685C2211yescharacteristic
143#65222C2211yescharacteristic
144#65222C2211yescharacteristic
145#65222C2211yescharacteristic
146#65222C2211yescharacteristic
147#65222C2211yescharacteristic
148#65222C2211yescharacteristic
149#65221C2211yescharacteristic
150C4×#683C2211yescharacteristic
151#65218C2211yescharacteristic
152#65218C2211yescharacteristic
153#65217C2211yescharacteristic
154#65217C2211yescharacteristic
155#64966C2211yescharacteristic
156#64964C2211yescharacteristic
157#64963C2211yescharacteristic
158#64962C2211yescharacteristic
159#64959C2211yescharacteristic
160#64959C2211yescharacteristic
161#64959C2211yescharacteristic
162#64958C2211yescharacteristic
163C5⋊#401C2211yescharacteristic
164#64950C2211yescharacteristic
165#64950C2211yescharacteristic
166#64949C2211yescharacteristic
167#64949C2211yescharacteristic
168#64949C2211yescharacteristic
169#64948C2211yescharacteristic
170#64948C2211yescharacteristic
171#64947C2211yescharacteristic
172#64947C2211yescharacteristic
173#64946C2211yescharacteristic
174#64945C2211yescharacteristic
175#64944C2211yescharacteristic
176#64944C2211yescharacteristic
177#64943C2211yescharacteristic
178#64942C2211yescharacteristic
179#64942C2211yescharacteristic
180#64942C2211yescharacteristic
181#64941C2211yescharacteristic
182#64940C2211yescharacteristic
183#64939C2211yescharacteristic
184#64936C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36772—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×C4×C5C2311yescharacteristic
193C22×C22⋊D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C5×C4⋊Q8—42no—
197C5×C22⋊Q8—24no—
198C5×C22⋊Q8—24no—
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×C5×C4⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C42×C5—42no—
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C4×C22⋊D5—24no—
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×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
254#4070—42no—
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
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285#4044—42no—
286#4035—42no—
287#4018—42no—
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
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#2857D511yescharacteristic, complemented
353#2855—51no—
354#2799—51no—
355#2798—51no—
356#2793—51no—
357#2791—51no—
358#2787—51no—
359#2781—51no—
360#2779—51no—
361#2770—51no—
362#2759—51no—
363#2755—51no—
364#2747—51no—
365#2741—51no—
366#2716—51no—
367#2713—51no—
368#2702—51no—
369#2690—51no—
370#2638—51no—
371#2638—51no—
372#2590—51no—
373#2589—51no—
374#2588—51no—
375#2587—51no—
376#2533—51no—
377#2528—51no—
378#2478—51no—
379#2475—51no—
380#2332—51no—
381#2332—51no—
382#2290—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—22no—
387C2×C5×Q8—41no—
388C2×C5×Q8—41no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
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×C5—41no—
398C22×C4×C5—41no—
399C22×C4×C5#4114yes—
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
411C22×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C2×C22⋊D5—22no—
415C2×C22⋊D5—41no—
416C2×C22⋊D5—41no—
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C2×C4×D5—22no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×Dic10—22no—
436C2×Dic10—41no—
437C2×Dic10—41no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—22no—
440C5×C4⋊C4—22no—
441C5×C4⋊C4—22no—
442C5×C4⋊C4—22no—
443C5×C4⋊C4—22no—
444C5×C4⋊C4—22no—
445C5×C4⋊C4—22no—
446C5×C4⋊C4—41no—
447C5×C4⋊C4—41no—
448C5×C4⋊C4—41no—
449C5×C4⋊C4—41no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C5×C22⋊C4—22no—
453C5×C22⋊C4—22no—
454C5×C22⋊C4—22no—
455C5×C22⋊C4—22no—
456C42×C5—22no—
457C42×C5—22no—
458C42×C5—41no—
459C42×C5—41no—
460C22⋊Dic5—22no—
461C22⋊Dic5—41no—
462C22⋊Dic5—41no—
463C22⋊Dic5—41no—
464C22⋊Dic5—41no—
465C22⋊Dic5—41no—
466C22⋊Dic5—41no—
467#685—22no—
468#685—22no—
469#685—22no—
470#685—22no—
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—
480C4⋊Dic5—22no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489C4⋊Dic5—41no—
490C4⋊Dic5—41no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—22no—
495#683—22no—
496#683—22no—
497#683—22no—
498#683—22no—
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—
510C4×Dic5—22no—
511C4×Dic5—41no—
512C4×Dic5—41no—
513C4×Dic5—41no—
514C4×Dic5—41no—
515C4×Dic5—41no—
516C4×Dic5—41no—
517C4×Dic5—41no—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C2×C4⋊Q8C2×D511yescharacteristic
522C2×#126—51no—
523C2×#125—51no—
524C2×C22⋊Q8—51no—
525C2×C22⋊Q8C2×D511yescharacteristic
526C2×C22⋊Q8C2×D511yescharacteristic
527C2×C4×D4—51no—
528C2×#117—51no—
529C22×C42C2×D511yescharacteristic
530#401—51no—
531#400—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#399—51no—
544#398—51no—
545#398—51no—
546#398—51no—
547#398—51no—
548#398—51no—
549#398—51no—
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#397—51no—
557#397—51no—
558#397—51no—
559#397—51no—
560#397—51no—
561#397—51no—
562#397—51no—
563#397—51no—
564#397—51no—
565#396—51no—
566#396—51no—
567#396—51no—
568#395—51no—
569#395—51no—
570#395—51no—
571#394—51no—
572#394—51no—
573#394—51no—
574#394—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#389C2×D511yescharacteristic
597#389C2×D511yescharacteristic
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#388—51no—
607#388—51no—
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388—51no—
613#388—51no—
614#388—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#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#386—51no—
649#386—51no—
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385—51no—
657#385—51no—
658#384C2×D511yescharacteristic
659#383—51no—
660#382—51no—
661#381—51no—
662#381—51no—
663#380—51no—
664#380C2×D511yescharacteristic
665#380C2×D511yescharacteristic
666#380C2×D511yescharacteristic
667#380C2×D511yescharacteristic
668C4×C4⋊C4—51no—
669C4×C4⋊C4—51no—
670C4×C4⋊C4—51no—
671C4×C4⋊C4—51no—
672C4×C4⋊C4—51no—
673C4×C22⋊C4—51no—
674C4×C22⋊C4—51no—
675#376—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5C2×#4112yes—
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—
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—44no—
731C2×C4×C5—44no—
732C2×C4×C5—44no—
733C2×C4×C5C2×#4112yes—
734C2×C4×C5C2×#4112yes—
735C2×C4×C5H(5,𝔽2)12yes—
736C2×C4×C52−1+412yes—
737C2×C4×C52−1+412yes—
738C22⋊D5—44no—
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—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C4×D5—44no—
785Dic10—82no—
786C22×Q8—51no—
787C22×Q8C22×D511yescharacteristic
788C22×Q8C22×D511yescharacteristic
789C22×D4—51no—
790C23×C4—51no—
791C23×C4C22×D511yescharacteristic
792C23×C4C22×D511yescharacteristic
793C23×C4C22×D511yescharacteristic
794C4⋊Q8—42no—
795#126—202no—
796#125—202no—
797C22⋊Q8—24no—
798C22⋊Q8—24no—
799C22⋊Q8—202no—
800C4×D4—104no—
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⋊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×C42—51no—
879C2×C42—51no—
880C2×C42—51no—
881C2×C42—51no—
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#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
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×C5—22no—
951C22×C5—22no—
952C22×C5—22no—
953C22×C5—41no—
954C22×C5—41no—
955C22×C5—41no—
956C22×C5—41no—
957C22×C5C22×#4111yescharacteristic
958C22×C5C2×H(5,𝔽2)11yescharacteristic
959C22×C5C2×2−1+411yescharacteristic
960C22×C5C2×2−1+411yescharacteristic
961C22×C5#58511yescharacteristic
962C22×C5#58511yescharacteristic
963C22×C5#58511yescharacteristic
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—22no—
973C4×C5—22no—
974C4×C5—22no—
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—
985Dic5—41no—
986Dic5—41no—
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—
1001C24C23×D511yescharacteristic
1002C2×Q8—22no—
1003C2×Q8—22no—
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—22no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
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—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—102no—
1038C22×C4—201no—
1039C22×C4—201no—
1040C22×C4#71114yes—
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—22no—
1058C4⋊C4—22no—
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
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—102no—
1076C4⋊C4—102no—
1077C4⋊C4—102no—
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—22no—
1100C22⋊C4—22no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—102no—
1104C22⋊C4—102no—
1105C22⋊C4—102no—
1106C22⋊C4—102no—
1107C22⋊C4—102no—
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—41no—
1126C42—41no—
1127C42—102no—
1128C42—201no—
1129C42—201no—
1130C42—201no—
1131C42—201no—
1132C42—201no—
1133C42—201no—
1134C42—201no—
1135C42—201no—
1136C42—201no—
1137C42—201no—
1138C2×C5—42no—
1139C2×C5#345511yescharacteristic
1140C2×C5#350511yescharacteristic
1141C2×C5#350911yescharacteristic
1142C2×C5#353511yescharacteristic
1143C2×C5#354111yescharacteristic
1144C2×C5#355711yescharacteristic
1145C2×C5#356511yescharacteristic
1146D5—81no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—101no—
1154C23—101no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23—101no—
1160C23C2×#71112yes—
1161C23C24×D511yescharacteristic
1162Q8—82no—
1163Q8—82no—
1164Q8—402no—
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—44no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—101no—
1207C2×C4—101no—
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—101no—
1250C2×C4—101no—
1251C2×C4—204no—
1252C2×C4C2×#71112yes—
1253C2×C4C2×#71112yes—
1254C2×C4#414412yes—
1255C2×C4#414712yes—
1256C2×C4#414712yes—
1257C5#3677211yescharacteristic, complemented, Sylow
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—201no—
1266C22—201no—
1267C22—201no—
1268C22—201no—
1269C22—201no—
1270C22—201no—
1271C22—201no—
1272C22C22×#71111yescharacteristic
1273C22C2×#414411yescharacteristic
1274C22C2×#414711yescharacteristic
1275C22C2×#414711yescharacteristic
1276C22#6628311yescharacteristic
1277C22#6628311yescharacteristic
1278C22#6628311yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—201no—
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—201no—
1308C2—42no—
1309C2—401no—
1310C2#1061783811yescharacteristic
1311C2#1061789011yescharacteristic
1312C2#1061789211yescharacteristic
1313C2#1061810511yescharacteristic
1314C2#1061813711yescharacteristic
1315C2#1061819111yescharacteristic
1316C2#1061819411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2857C2
prime radicalC22×C22⋊D5C23
hypercenter#2857D5
hypocenterC5#36772
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C5×#2857C2semidirect
2. #10614979C2semidirect
3. #10614978C2semidirect
6. #10614477C2semidirect
7. #10614477C2semidirect
8. #10613806C2semidirect
10. #10608325C2semidirect
11. #10608323C2semidirect
12. #10608313C2semidirect
13. #10608309C2semidirect
14. #10607822C2semidirect
15. #10607820C2semidirect
16. #10607819C2semidirect
17. #10607817C2semidirect
18. #10607789C2semidirect
19. #10607785C2semidirect
20. #10607757C2semidirect
21. #10607755C2semidirect
22. #10606082C2semidirect
23. #10606080C2semidirect
24. #10605726C2semidirect
27. #10605720C2semidirect
28. #10605715C2semidirect
31. #10605691C2semidirect
352. #2857D5semidirect
1257. C5#36772semidirect

Maximal subgroups

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

subgroupindex
C5×#28572
#106149792
#106149782
#106145542
#106144772
#106138062
#106137962
#106083252
#106083232
#106083132
#106083092
#106078222
#106078202
#106078192
#106078172
#106077892
#106077852
#106077572
#106077552
#106060822
#106060802
#106057262
#106057232
#106057212
#106057202
#106057152
#106057082
#106056962
#106056912
#367725