Finite Group Databasebeta

← #12307840

Subgroups — #12307840

Order 1280.

1540 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2335C211yesmaximal, characteristic, complemented
2#10614633C211yesmaximal, characteristic
3#10614574C211yesmaximal, characteristic, complemented
4#10608137C211yesmaximal, characteristic
5#10608114C211yesmaximal, characteristic, complemented
6#10607896C211yesmaximal, characteristic, complemented
7#10607849C211yesmaximal, characteristic, complemented
8#10607690C211yesmaximal, characteristic, complemented
9#10607671C211yesmaximal, characteristic, complemented
10#10607522C211yesmaximal, characteristic, complemented
11#10607481C211yesmaximal, characteristic, complemented
12#10607459C211yesmaximal, characteristic, complemented
13#10607455C211yesmaximal, characteristic, complemented
14#10607419C211yesmaximal, characteristic, complemented
15#10607393C211yesmaximal, characteristic, complemented
16#10607176C211yesmaximal, characteristic, complemented
17#10607136C211yesmaximal, characteristic, complemented
18#10606960C211yesmaximal, characteristic, complemented
19#10606874C211yesmaximal, characteristic, complemented
20#10606565C211yesmaximal, characteristic, complemented
21#10606536C211yesmaximal, characteristic
22#10606295C211yesmaximal, characteristic, complemented
23#10606288C211yesmaximal, characteristic, complemented
24#10605680C211yesmaximal, characteristic, complemented
25#10605631C211yesmaximal, characteristic, complemented
26#10605542C211yesmaximal, characteristic, complemented
27#10605440C211yesmaximal, characteristic, complemented
28#10605293C211yesmaximal, characteristic, complemented
29#10605275C211yesmaximal, characteristic, complemented
30#10605263C211yesmaximal, characteristic, complemented
31#10605176C211yesmaximal, characteristic, complemented
32C2×C5×#123C2211yescharacteristic
33C2×#4081C2211yescharacteristic
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4072C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C2×#4036C2211yescharacteristic
38C2×#4035C2211yescharacteristic
39C2×#4029C2211yescharacteristic
40C2×C42×D5C2211yescharacteristic
41C5×#390C2211yescharacteristic
42C5×#389C2211yescharacteristic
43C5×#388C2211yescharacteristic
44C5×#388C2211yescharacteristic
45C5×#388C2211yescharacteristic
46C5×#388C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C5×#386C2211yescharacteristic
50C5×#385C2211yescharacteristic
51C5×#380C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C22⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4C2211yescharacteristic
55#65512C2211yescharacteristic
56#65511C2211yescharacteristic
57#65509C2211yescharacteristic
58#65502C2211yescharacteristic
59#65501C2211yescharacteristic
60#65500C2211yescharacteristic
61#65499C2211yescharacteristic
62C4×C22⋊Dic5C2211yescharacteristic
63#65283C2211yescharacteristic
64#65283C2211yescharacteristic
65#65283C2211yescharacteristic
66#65279C2211yescharacteristic
67#65278C2211yescharacteristic
68#65278C2211yescharacteristic
69#65278C2211yescharacteristic
70#65275C2211yescharacteristic
71#65274C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65273C2211yescharacteristic
75#65273C2211yescharacteristic
76#65272C2211yescharacteristic
77#65272C2211yescharacteristic
78#65271C2211yescharacteristic
79#65271C2211yescharacteristic
80#65270C2211yescharacteristic
81#65269C2211yescharacteristic
82#65269C2211yescharacteristic
83#65267C2211yescharacteristic
84#65265C2211yescharacteristic
85#65262C2211yescharacteristic
86#65261C2211yescharacteristic
87#65261C2211yescharacteristic
88#65261C2211yescharacteristic
89#65250C2211yescharacteristic
90#65248C2211yescharacteristic
91#65247C2211yescharacteristic
92#65247C2211yescharacteristic
93#65246C2211yescharacteristic
94#65245C2211yescharacteristic
95#65245C2211yescharacteristic
96#65245C2211yescharacteristic
97#65245C2211yescharacteristic
98#65241C2211yescharacteristic
99#65241C2211yescharacteristic
100#65241C2211yescharacteristic
101#65241C2211yescharacteristic
102#65241C2211yescharacteristic
103#65240C2211yescharacteristic
104#65239C2211yescharacteristic
105#65239C2211yescharacteristic
106#65238C2211yescharacteristic
107#65238C2211yescharacteristic
108#65238C2211yescharacteristic
109#65237C2211yescharacteristic
110#65237C2211yescharacteristic
111#65237C2211yescharacteristic
112#65237C2211yescharacteristic
113#65237C2211yescharacteristic
114#65237C2211yescharacteristic
115#65235C2211yescharacteristic
116#65234C2211yescharacteristic
117#65234C2211yescharacteristic
118#65234C2211yescharacteristic
119#65234C2211yescharacteristic
120#65234C2211yescharacteristic
121#65233C2211yescharacteristic
122#65233C2211yescharacteristic
123#65232C2211yescharacteristic
124#65232C2211yescharacteristic
125#65232C2211yescharacteristic
126#65231C2211yescharacteristic
127#65231C2211yescharacteristic
128#65229C2211yescharacteristic
129#65229C2211yescharacteristic
130#65229C2211yescharacteristic
131C4×#685C2211yescharacteristic
132#65226C2211yescharacteristic
133#65225C2211yescharacteristic
134#65222C2211yescharacteristic
135#65222C2211yescharacteristic
136#65222C2211yescharacteristic
137#65222C2211yescharacteristic
138#65222C2211yescharacteristic
139#65222C2211yescharacteristic
140#65222C2211yescharacteristic
141#65222C2211yescharacteristic
142#65222C2211yescharacteristic
143#65221C2211yescharacteristic
144C4×#683C2211yescharacteristic
145#65217C2211yescharacteristic
146#65217C2211yescharacteristic
147#64965C2211yescharacteristic
148#64964C2211yescharacteristic
149#64957C2211yescharacteristic
150#64957C2211yescharacteristic
151#64957C2211yescharacteristic
152#64957C2211yescharacteristic
153#64957C2211yescharacteristic
154#64956C2211yescharacteristic
155#64956C2211yescharacteristic
156#64953C2211yescharacteristic
157C5⋊#401C2211yescharacteristic
158C5⋊#401C2211yescharacteristic
159#64949C2211yescharacteristic
160#64949C2211yescharacteristic
161#64949C2211yescharacteristic
162#64949C2211yescharacteristic
163#64948C2211yescharacteristic
164#64948C2211yescharacteristic
165#64947C2211yescharacteristic
166#64947C2211yescharacteristic
167#64947C2211yescharacteristic
168#64947C2211yescharacteristic
169#64946C2211yescharacteristic
170#64946C2211yescharacteristic
171#64944C2211yescharacteristic
172#64944C2211yescharacteristic
173#64944C2211yescharacteristic
174#64944C2211yescharacteristic
175#64944C2211yescharacteristic
176#64943C2211yescharacteristic
177#64942C2211yescharacteristic
178#64942C2211yescharacteristic
179#64942C2211yescharacteristic
180#64941C2211yescharacteristic
181#64941C2211yescharacteristic
182#64941C2211yescharacteristic
183#64941C2211yescharacteristic
184#64939C2211yescharacteristic
185#64936C2211yescharacteristic
186#64936C2211yescharacteristic
187#36783—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C22×C22⋊D5C2311yescharacteristic
192C22×C22⋊D5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C5×#123—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×C22⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233#4081—42no—
234C4×C22⋊D5—24no—
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×#685C2311yescharacteristic
245#4072—42no—
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
254C2×C4⋊Dic5C2311yescharacteristic
255C2×C4⋊Dic5C2311yescharacteristic
256C2×#683—24no—
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×#683C2311yescharacteristic
275C2×#683C2311yescharacteristic
276C2×#683C2311yescharacteristic
277C2×#683C2311yescharacteristic
278C2×#683C2311yescharacteristic
279C2×#683C2311yescharacteristic
280C2×#683C2311yescharacteristic
281C2×#683C2311yescharacteristic
282C2×#683C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290#4036—42no—
291#4035—42no—
292#4029—42no—
293C42×D5—42no—
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
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#2853—51no—
353#2851—51no—
354#2793—51no—
355#2790—51no—
356#2780—51no—
357#2776—51no—
358#2765—51no—
359#2765—51no—
360#2749—51no—
361#2746—51no—
362#2744—51no—
363#2743—51no—
364#2743—51no—
365#2739—51no—
366#2719—51no—
367#2707—51no—
368#2694—51no—
369#2693—51no—
370#2655—51no—
371#2654—51no—
372#2602—51no—
373#2587—51no—
374#2579—51no—
375#2576—51no—
376#2533—51no—
377#2530—51no—
378#2441—51no—
379#2413—51no—
380#2335D511yescharacteristic, complemented
381#2313—51no—
382#2290—51no—
383C24×C5C2411yescharacteristic
384C24×C5C2411yescharacteristic
385C23×D5C2411yescharacteristic
386C2×C5×D4—22no—
387C2×C5×D4—41no—
388C2×C5×D4—41no—
389C22×C4×C5—41no—
390C22×C4×C5—41no—
391C22×C4×C5—41no—
392C22×C4×C5—41no—
393C22×C4×C5—41no—
394C22×C4×C5#4114yes—
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×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C2×C22⋊D5—22no—
409C2×C22⋊D5—22no—
410C2×C22⋊D5—22no—
411C2×C22⋊D5—41no—
412C2×C22⋊D5—41no—
413C2×C22⋊D5—41no—
414C22×Dic5—22no—
415C22×Dic5—22no—
416C22×Dic5—41no—
417C22×Dic5—41no—
418C22×Dic5—41no—
419C22×Dic5—41no—
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C2×C4×D5—22no—
436C2×C4×D5—22no—
437C2×C4×D5—22no—
438C2×C4×D5—41no—
439C2×C4×D5—41no—
440C2×C4×D5—41no—
441C2×C4×D5—41no—
442C2×C4×D5—41no—
443C2×C4×D5—41no—
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×C22⋊C4—22no—
452C5×C22⋊C4—22no—
453C5×C22⋊C4—22no—
454C5×C22⋊C4—41no—
455C5×C22⋊C4—41no—
456C5×C22⋊C4—41no—
457C5×C22⋊C4—41no—
458C5×C22⋊C4—41no—
459C5×C22⋊C4—41no—
460C5×C22⋊C4—41no—
461C42×C5—41no—
462C42×C5—41no—
463C42×C5—41no—
464C42×C5—41no—
465C42×C5—41no—
466C22⋊Dic5—22no—
467C22⋊Dic5—22no—
468C22⋊Dic5—22no—
469C22⋊Dic5—41no—
470C22⋊Dic5—41no—
471C22⋊Dic5—41no—
472C22⋊Dic5—41no—
473C22⋊Dic5—41no—
474C22⋊Dic5—41no—
475C22⋊Dic5—41no—
476C22⋊Dic5—41no—
477C22⋊Dic5—41no—
478#685—22no—
479#685—22no—
480#685—22no—
481#685—41no—
482#685—41no—
483#685—41no—
484#685—41no—
485#685—41no—
486#685—41no—
487#685—41no—
488C4⋊Dic5—22no—
489C4⋊Dic5—22no—
490C4⋊Dic5—41no—
491C4⋊Dic5—41no—
492C4⋊Dic5—41no—
493C4⋊Dic5—41no—
494C4⋊Dic5—41no—
495C4⋊Dic5—41no—
496C4⋊Dic5—41no—
497C4⋊Dic5—41no—
498#683—22no—
499#683—22no—
500#683—22no—
501#683—22no—
502#683—22no—
503#683—22no—
504#683—22no—
505#683—41no—
506#683—41no—
507#683—41no—
508#683—41no—
509#683—41no—
510#683—41no—
511#683—41no—
512#683—41no—
513#683—41no—
514#683—41no—
515#683—41no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524C4×Dic5—22no—
525C4×Dic5—22no—
526C4×Dic5—22no—
527C4×Dic5—41no—
528C4×Dic5—41no—
529C4×Dic5—41no—
530C4×Dic5—41no—
531C2×#125—51no—
532C2×#125—51no—
533C2×#123—51no—
534C2×#123—51no—
535C2×#123C2×D511yescharacteristic
536C2×C4×D4—51no—
537C2×#117—51no—
538C22×C4⋊C4—51no—
539C22×C42—51no—
540#401—51no—
541#401—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#399—51no—
556#399—51no—
557#399—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398—51no—
567#398—51no—
568#397—51no—
569#397—51no—
570#397—51no—
571#397—51no—
572#397—51no—
573#397—51no—
574#396—51no—
575#396—51no—
576#396—51no—
577#396—51no—
578#396—51no—
579#396—51no—
580#396—51no—
581#396—51no—
582#396—51no—
583#396—51no—
584#394—51no—
585#394—51no—
586#394—51no—
587#392—51no—
588#390—51no—
589#390C2×D511yescharacteristic
590#389—51no—
591#389—51no—
592#389—51no—
593#389—51no—
594#389—51no—
595#389—51no—
596#389—51no—
597#389—51no—
598#389—51no—
599#389C2×D511yescharacteristic
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#388C2×D511yescharacteristic
613#388C2×D511yescharacteristic
614#388C2×D511yescharacteristic
615#388C2×D511yescharacteristic
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#387C2×D511yescharacteristic
641#387C2×D511yescharacteristic
642#386—51no—
643#386—51no—
644#386—51no—
645#386—51no—
646#386—51no—
647#386—51no—
648#386—51no—
649#386—51no—
650#386C2×D511yescharacteristic
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385—51no—
657#385—51no—
658#385—51no—
659#385—51no—
660#385—51no—
661#385—51no—
662#385—51no—
663#385C2×D511yescharacteristic
664#384—51no—
665#383—51no—
666#382—51no—
667#382—51no—
668#381—51no—
669#381—51no—
670#381—51no—
671#381—51no—
672#381—51no—
673#380—51no—
674#380—51no—
675#380—51no—
676#380—51no—
677#380—51no—
678#380C2×D511yescharacteristic
679C4×C4⋊C4—51no—
680C4×C4⋊C4C2×D511yescharacteristic
681C4×C22⋊C4—51no—
682C4×C22⋊C4—51no—
683C4×C22⋊C4C2×D511yescharacteristic
684C4×C22⋊C4C2×D511yescharacteristic
685#376—51no—
686C23×C5—21no—
687C23×C5—21no—
688C23×C5—21no—
689C23×C5—21no—
690C23×C5—21no—
691C23×C5—21no—
692C23×C5—21no—
693C23×C5—21no—
694C23×C5—21no—
695C23×C5—21no—
696C23×C5—21no—
697C23×C5—21no—
698C23×C5—21no—
699C23×C5C2×#4112yes—
700C23×C5C2511yescharacteristic
701C22×D5—21no—
702C22×D5—21no—
703C22×D5—21no—
704C22×D5—21no—
705C22×D5—21no—
706C22×D5—21no—
707C22×D52−1+412yes—
708C5×D4—82no—
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×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—44no—
747C2×C4×C5—82no—
748C2×C4×C5C2×#4112yes—
749C2×C4×C5C2×#4112yes—
750C22⋊D5—44no—
751C22⋊D5—82no—
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—
784C2×Dic5—21no—
785C2×Dic5—21no—
786C2×Dic5—21no—
787C2×Dic5—21no—
788C2×Dic5—21no—
789C2×Dic5—21no—
790C2×Dic5—21no—
791C2×Dic5—21no—
792C2×Dic5—21no—
793C2×Dic5—21no—
794C2×Dic5—21no—
795C2×Dic5—21no—
796C2×Dic5—44no—
797C2×Dic5—82no—
798C2×Dic5H(5,𝔽2)12yes—
799C4×D5—44no—
800C4×D5—44no—
801C4×D5—44no—
802C22×D4—51no—
803C22×D4—51no—
804C22×D4C22×D511yescharacteristic
805C23×C4—51no—
806C23×C4—51no—
807C23×C4—51no—
808C23×C4—51no—
809C23×C4—51no—
810C23×C4C22×D511yescharacteristic
811C23×C4C22×D511yescharacteristic
812#125—202no—
813#125—202no—
814#123—24no—
815#123—202no—
816#123—202no—
817C4×D4—104no—
818#117—202no—
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—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—51no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—51no—
852C2×C4⋊C4—51no—
853C2×C4⋊C4—51no—
854C2×C4⋊C4—51no—
855C2×C4⋊C4—104no—
856C2×C4⋊C4C22×D511yescharacteristic
857C2×C4⋊C4C22×D511yescharacteristic
858C2×C4⋊C4C22×D511yescharacteristic
859C2×C4⋊C4C22×D511yescharacteristic
860C2×C4⋊C4C22×D511yescharacteristic
861C2×C4⋊C4C22×D511yescharacteristic
862C2×C4⋊C4C22×D511yescharacteristic
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×C22⋊C4—51no—
871C2×C22⋊C4—51no—
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—51no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4C22×D511yescharacteristic
886C2×C22⋊C4C22×D511yescharacteristic
887C2×C22⋊C4C22×D511yescharacteristic
888C2×C22⋊C4C22×D511yescharacteristic
889C2×C22⋊C4C22×D511yescharacteristic
890C2×C22⋊C4C22×D511yescharacteristic
891C2×C22⋊C4C22×D511yescharacteristic
892C2×C22⋊C4C22×D511yescharacteristic
893C2×C22⋊C4C22×D511yescharacteristic
894C2×C22⋊C4C22×D511yescharacteristic
895C2×C42—51no—
896C2×C42—51no—
897C2×C42—51no—
898C2×C42—51no—
899C2×C42—51no—
900C2×C42—51no—
901C2×C42—51no—
902C2×C42—202no—
903C2×C42C22×D511yescharacteristic
904C2×C42C22×D511yescharacteristic
905C2×C42C22×D511yescharacteristic
906C2×C42C22×D511yescharacteristic
907C2×C42C22×D511yescharacteristic
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#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
948#95—51no—
949#95—51no—
950#95—51no—
951#95—51no—
952#95—51no—
953#95—51no—
954#95—51no—
955#95—51no—
956#95C22×D511yescharacteristic
957#95C22×D511yescharacteristic
958#95C22×D511yescharacteristic
959#95C22×D511yescharacteristic
960#95C22×D511yescharacteristic
961#95C22×D511yescharacteristic
962#95C22×D511yescharacteristic
963#95C22×D511yescharacteristic
964#95C22×D511yescharacteristic
965#95C22×D511yescharacteristic
966C22×C5—22no—
967C22×C5—22no—
968C22×C5—22no—
969C22×C5—41no—
970C22×C5—41no—
971C22×C5—41no—
972C22×C5—41no—
973C22×C5—41no—
974C22×C5—41no—
975C22×C5—41no—
976C22×C5—41no—
977C22×C5—41no—
978C22×C5—41no—
979C22×C5—41no—
980C22×C5C22×#4111yescharacteristic
981C22×C5C2×H(5,𝔽2)11yescharacteristic
982C22×C5C2×2−1+411yescharacteristic
983C22×C5#58511yescharacteristic
984C22×C5#58511yescharacteristic
985C22×C5#58511yescharacteristic
986C22×C5#58511yescharacteristic
987C2×D5—22no—
988C2×D5—22no—
989C2×D5—22no—
990C2×D5—41no—
991C2×D5—41no—
992C2×D5—41no—
993C2×D5—41no—
994C4×C5—22no—
995C4×C5—22no—
996C4×C5—41no—
997C4×C5—41no—
998C4×C5—41no—
999C4×C5—41no—
1000C4×C5—41no—
1001C4×C5—41no—
1002C4×C5—41no—
1003C4×C5—41no—
1004C4×C5—41no—
1005C4×C5—41no—
1006C4×C5—41no—
1007Dic5—22no—
1008Dic5—41no—
1009Dic5—41no—
1010Dic5—41no—
1011Dic5—41no—
1012Dic5—41no—
1013Dic5—41no—
1014Dic5—41no—
1015Dic5—41no—
1016Dic5—41no—
1017Dic5—41no—
1018Dic5—41no—
1019Dic5—41no—
1020Dic5—41no—
1021Dic5—41no—
1022C24—51no—
1023C24C23×D511yescharacteristic
1024C24C23×D511yescharacteristic
1025C2×D4—22no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—102no—
1029C2×D4—102no—
1030C2×D4—102no—
1031C2×D4—201no—
1032C2×D4—201no—
1033C2×D4—201no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4—51no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—51no—
1044C22×C4—51no—
1045C22×C4—51no—
1046C22×C4—51no—
1047C22×C4—51no—
1048C22×C4—51no—
1049C22×C4—51no—
1050C22×C4—51no—
1051C22×C4—51no—
1052C22×C4—51no—
1053C22×C4—51no—
1054C22×C4—102no—
1055C22×C4—102no—
1056C22×C4—102no—
1057C22×C4—102no—
1058C22×C4—102no—
1059C22×C4—201no—
1060C22×C4—201no—
1061C22×C4—201no—
1062C22×C4—201no—
1063C22×C4—201no—
1064C22×C4—201no—
1065C22×C4—201no—
1066C22×C4—201no—
1067C22×C4—201no—
1068C22×C4—201no—
1069C22×C4#70914yes—
1070C22×C4C23×D511yescharacteristic
1071C22×C4C23×D511yescharacteristic
1072C22×C4C23×D511yescharacteristic
1073C22×C4C23×D511yescharacteristic
1074C22×C4C23×D511yescharacteristic
1075C22×C4C23×D511yescharacteristic
1076C22×C4C23×D511yescharacteristic
1077C22×C4C23×D511yescharacteristic
1078C22×C4C23×D511yescharacteristic
1079C22×C4C23×D511yescharacteristic
1080C22×C4C23×D511yescharacteristic
1081C22×C4C23×D511yescharacteristic
1082C22×C4C23×D511yescharacteristic
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—102no—
1091C4⋊C4—102no—
1092C4⋊C4—102no—
1093C4⋊C4—102no—
1094C4⋊C4—102no—
1095C4⋊C4—102no—
1096C4⋊C4—102no—
1097C4⋊C4—102no—
1098C4⋊C4—102no—
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—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
1119C4⋊C4—201no—
1120C4⋊C4—201no—
1121C4⋊C4—201no—
1122C4⋊C4—201no—
1123C4⋊C4—201no—
1124C4⋊C4—201no—
1125C4⋊C4—201no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—102no—
1137C22⋊C4—102no—
1138C22⋊C4—102no—
1139C22⋊C4—102no—
1140C22⋊C4—102no—
1141C22⋊C4—102no—
1142C22⋊C4—201no—
1143C22⋊C4—201no—
1144C22⋊C4—201no—
1145C22⋊C4—201no—
1146C22⋊C4—201no—
1147C22⋊C4—201no—
1148C22⋊C4—201no—
1149C22⋊C4—201no—
1150C22⋊C4—201no—
1151C22⋊C4—201no—
1152C22⋊C4—201no—
1153C22⋊C4—201no—
1154C22⋊C4—201no—
1155C22⋊C4—201no—
1156C22⋊C4—201no—
1157C22⋊C4—201no—
1158C42—41no—
1159C42—41no—
1160C42—41no—
1161C42—41no—
1162C42—41no—
1163C42—102no—
1164C42—102no—
1165C42—102no—
1166C42—201no—
1167C42—201no—
1168C42—201no—
1169C42—201no—
1170C2×C5—42no—
1171C2×C5—81no—
1172C2×C5#345511yescharacteristic
1173C2×C5#349511yescharacteristic
1174C2×C5#350511yescharacteristic
1175C2×C5#353511yescharacteristic
1176C2×C5#353911yescharacteristic
1177C2×C5#355311yescharacteristic
1178C2×C5#356611yescharacteristic
1179D5—42no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—52no—
1194C23—101no—
1195C23—101no—
1196C23—101no—
1197C23—101no—
1198C23—101no—
1199C23—101no—
1200C23C2×#70912yes—
1201C23C24×D511yescharacteristic
1202D4—82no—
1203D4—204no—
1204D4—402no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—44no—
1243C2×C4—52no—
1244C2×C4—82no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—101no—
1263C2×C4—101no—
1264C2×C4—101no—
1265C2×C4—101no—
1266C2×C4—101no—
1267C2×C4—101no—
1268C2×C4—101no—
1269C2×C4—101no—
1270C2×C4—101no—
1271C2×C4—101no—
1272C2×C4—101no—
1273C2×C4—101no—
1274C2×C4—101no—
1275C2×C4—101no—
1276C2×C4—101no—
1277C2×C4—101no—
1278C2×C4—101no—
1279C2×C4—101no—
1280C2×C4—101no—
1281C2×C4—101no—
1282C2×C4—101no—
1283C2×C4—101no—
1284C2×C4—101no—
1285C2×C4—101no—
1286C2×C4—101no—
1287C2×C4—101no—
1288C2×C4—101no—
1289C2×C4—204no—
1290C2×C4—204no—
1291C2×C4—204no—
1292C2×C4—204no—
1293C2×C4—402no—
1294C2×C4C2×#70912yes—
1295C2×C4C2×#70912yes—
1296C5#3678311yescharacteristic, complemented, Sylow
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—102no—
1312C22—102no—
1313C22—102no—
1314C22—201no—
1315C22—201no—
1316C22—201no—
1317C22—201no—
1318C22C22×#70911yescharacteristic
1319C22#6628311yescharacteristic
1320C22#6628311yescharacteristic
1321C22D5×H(5,𝔽2)11yescharacteristic
1322C22#6628511yescharacteristic
1323C22#6628511yescharacteristic
1324C22D5×2−1+411yescharacteristic
1325C4—22no—
1326C4—22no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—102no—
1339C4—201no—
1340C4—201no—
1341C4—201no—
1342C4—201no—
1343C4—201no—
1344C4—201no—
1345C4—201no—
1346C4—201no—
1347C4—201no—
1348C4—201no—
1349C4—201no—
1350C4—201no—
1351C4—201no—
1352C4—201no—
1353C2—42no—
1354C2—81no—
1355C2—202no—
1356C2#1061773811yescharacteristic
1357C2#1061776211yescharacteristic
1358C2#1061780511yescharacteristic
1359C2#1061831211yescharacteristic
1360C2#1061836411yescharacteristic
1361C2#1061837411yescharacteristic
1362C2#1061846111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2335C2
prime radical#65512C22
hypercenter#2335D5
hypocenterC5#36783
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2335

Complements

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

NH ≅ G/Ntype
1. C5×#2335C2semidirect
3. #10614574C2semidirect
5. #10608114C2semidirect
6. #10607896C2semidirect
7. #10607849C2semidirect
8. #10607690C2semidirect
9. #10607671C2semidirect
10. #10607522C2semidirect
11. #10607481C2semidirect
12. #10607459C2semidirect
13. #10607455C2semidirect
14. #10607419C2semidirect
15. #10607393C2semidirect
16. #10607176C2semidirect
17. #10607136C2semidirect
18. #10606960C2semidirect
19. #10606874C2semidirect
20. #10606565C2semidirect
22. #10606295C2semidirect
23. #10606288C2semidirect
24. #10605680C2semidirect
25. #10605631C2semidirect
26. #10605542C2semidirect
27. #10605440C2semidirect
28. #10605293C2semidirect
29. #10605275C2semidirect
30. #10605263C2semidirect
31. #10605176C2semidirect
380. #2335D5semidirect
1296. C5#36783semidirect

Maximal subgroups

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

subgroupindex
C5×#23352
#106146332
#106145742
#106081372
#106081142
#106078962
#106078492
#106076902
#106076712
#106075222
#106074812
#106074592
#106074552
#106074192
#106073932
#106071762
#106071362
#106069602
#106068742
#106065652
#106065362
#106062952
#106062882
#106056802
#106056312
#106055422
#106054402
#106052932
#106052752
#106052632
#106051762
#367835