Finite Group Databasebeta

← #12307811

Subgroups — #12307811

Order 1280.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2417C211yesmaximal, characteristic
2#10614527C211yesmaximal, characteristic, complemented
3#10614526C211yesmaximal, characteristic, complemented
4#10614516C211yesmaximal, characteristic, complemented
5#10614476C211yesmaximal, characteristic, complemented
6#10614118C211yesmaximal, characteristic
7#10614055C211yesmaximal, characteristic
8#10613903C211yesmaximal, characteristic, complemented
9C2×#65267C211yesmaximal, characteristic, complemented
10#10609630C211yesmaximal, characteristic, complemented
11#10609629C211yesmaximal, characteristic, complemented
12#10609615C211yesmaximal, characteristic, complemented
13#10609591C211yesmaximal, characteristic, complemented
14#10609123C211yesmaximal, characteristic, complemented
15#10609122C211yesmaximal, characteristic, complemented
16#10609116C211yesmaximal, characteristic, complemented
17#10609098C211yesmaximal, characteristic, complemented
18#10608316C211yesmaximal, characteristic, complemented
19#10608315C211yesmaximal, characteristic, complemented
20#10607876C211yesmaximal, characteristic, complemented
21#10607871C211yesmaximal, characteristic, complemented
22#10606601C211yesmaximal, characteristic
23#10606517C211yesmaximal, characteristic
24#10606474C211yesmaximal, characteristic
25#10606474C211yesmaximal, characteristic
26#10605729C211yesmaximal, characteristic, complemented
27#10605715C211yesmaximal, characteristic, complemented
28#10605712C211yesmaximal, characteristic, complemented
29#10605687C211yesmaximal, characteristic, complemented
30#10605658C211yesmaximal, characteristic, complemented
31#10605658C211yesmaximal, characteristic, complemented
32C2×C5×C22⋊Q8C2211yescharacteristic
33C2×C5×C22⋊Q8C2211yescharacteristic
34C2×C4×C5×D4C2211yescharacteristic
35C22×C5×C4⋊C4C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4036C2211yescharacteristic
39C2×#4036C2211yescharacteristic
40C2×#4025C2211yescharacteristic
41C5×#398C2211yescharacteristic
42C5×#398C2211yescharacteristic
43C5×#396C2211yescharacteristic
44C5×#396C2211yescharacteristic
45C5×#391C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#386C2211yescharacteristic
48C5×#386C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52#65519C2211yescharacteristic
53#65519C2211yescharacteristic
54#65518C2211yescharacteristic
55#65518C2211yescharacteristic
56#65509C2211yescharacteristic
57#65509C2211yescharacteristic
58#65509C2211yescharacteristic
59#65509C2211yescharacteristic
60#65501C2211yescharacteristic
61#65501C2211yescharacteristic
62#65501C2211yescharacteristic
63#65501C2211yescharacteristic
64#65500C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67#65499C2211yescharacteristic
68#65499C2211yescharacteristic
69C4×C22⋊Dic5C2211yescharacteristic
70C2×#3963C2211yescharacteristic
71C2×#3963C2211yescharacteristic
72C2×#3963C2211yescharacteristic
73C2×#3963C2211yescharacteristic
74#65275C2211yescharacteristic
75#65275C2211yescharacteristic
76#65275C2211yescharacteristic
77#65275C2211yescharacteristic
78#65274C2211yescharacteristic
79#65274C2211yescharacteristic
80#65274C2211yescharacteristic
81#65274C2211yescharacteristic
82#65273C2211yescharacteristic
83#65273C2211yescharacteristic
84#65273C2211yescharacteristic
85#65273C2211yescharacteristic
86#65273C2211yescharacteristic
87#65273C2211yescharacteristic
88#65273C2211yescharacteristic
89#65273C2211yescharacteristic
90#65271C2211yescharacteristic
91#65271C2211yescharacteristic
92#65270C2211yescharacteristic
93#65270C2211yescharacteristic
94#65270C2211yescharacteristic
95#65270C2211yescharacteristic
96#65270C2211yescharacteristic
97#65270C2211yescharacteristic
98#65270C2211yescharacteristic
99#65270C2211yescharacteristic
100#65269C2211yescharacteristic
101#65269C2211yescharacteristic
102#65267C2211yescharacteristic
103#65267C2211yescharacteristic
104#65267C2211yescharacteristic
105#65267C2211yescharacteristic
106#65267C2211yescharacteristic
107#65267C2211yescharacteristic
108#65267C2211yescharacteristic
109#65267C2211yescharacteristic
110#65266C2211yescharacteristic
111#65266C2211yescharacteristic
112#65262C2211yescharacteristic
113#65262C2211yescharacteristic
114#65261C2211yescharacteristic
115#65261C2211yescharacteristic
116#65261C2211yescharacteristic
117#65261C2211yescharacteristic
118#65261C2211yescharacteristic
119#65261C2211yescharacteristic
120#65242C2211yescharacteristic
121#65242C2211yescharacteristic
122#65242C2211yescharacteristic
123#65241C2211yescharacteristic
124#65241C2211yescharacteristic
125#65241C2211yescharacteristic
126#65241C2211yescharacteristic
127#65240C2211yescharacteristic
128#65240C2211yescharacteristic
129#65240C2211yescharacteristic
130#65240C2211yescharacteristic
131#65240C2211yescharacteristic
132#65239C2211yescharacteristic
133#65239C2211yescharacteristic
134#65239C2211yescharacteristic
135#65239C2211yescharacteristic
136#65237C2211yescharacteristic
137#65237C2211yescharacteristic
138#65237C2211yescharacteristic
139#65235C2211yescharacteristic
140#65235C2211yescharacteristic
141#65235C2211yescharacteristic
142#65235C2211yescharacteristic
143#65235C2211yescharacteristic
144#65235C2211yescharacteristic
145#65234C2211yescharacteristic
146#65234C2211yescharacteristic
147#65234C2211yescharacteristic
148#65233C2211yescharacteristic
149C22⋊C4×Dic5C2211yescharacteristic
150C22⋊C4×Dic5C2211yescharacteristic
151#65226C2211yescharacteristic
152#65225C2211yescharacteristic
153#65222C2211yescharacteristic
154#65222C2211yescharacteristic
155C5⋊#401C2211yescharacteristic
156C5⋊#401C2211yescharacteristic
157C5⋊#401C2211yescharacteristic
158#64950C2211yescharacteristic
159#64950C2211yescharacteristic
160#64949C2211yescharacteristic
161#64949C2211yescharacteristic
162#64949C2211yescharacteristic
163#64949C2211yescharacteristic
164#64949C2211yescharacteristic
165#64948C2211yescharacteristic
166#64948C2211yescharacteristic
167#64948C2211yescharacteristic
168#64947C2211yescharacteristic
169#64947C2211yescharacteristic
170#64947C2211yescharacteristic
171#64944C2211yescharacteristic
172#64944C2211yescharacteristic
173#64944C2211yescharacteristic
174#64943C2211yescharacteristic
175#64943C2211yescharacteristic
176#64942C2211yescharacteristic
177#64942C2211yescharacteristic
178#64942C2211yescharacteristic
179#64942C2211yescharacteristic
180#64942C2211yescharacteristic
181#64941C2211yescharacteristic
182#64940C2211yescharacteristic
183#64940C2211yescharacteristic
184#64940C2211yescharacteristic
185#64939C2211yescharacteristic
186#64939C2211yescharacteristic
187#36782—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×D4C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×C4×C5C2311yescharacteristic
193C23×C4×C5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C23×Dic5C2311yescharacteristic
198C5×C22⋊Q8—24no—
199C5×C22⋊Q8—42no—
200C4×C5×D4—24no—
201C2×C5×C4⋊C4—42no—
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×C4⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C5×C22⋊C4C2311yescharacteristic
221C2×C5×C22⋊C4C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
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
233C2×C22⋊Dic5C2311yescharacteristic
234C2×C22⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×#683—24no—
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×C4×Dic5—42no—
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281#4036—42no—
282#4036—42no—
283#4025—42no—
284C5×#95C2311yescharacteristic
285C5×#95C2311yescharacteristic
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292#3963C2311yescharacteristic
293#3963C2311yescharacteristic
294#3963C2311yescharacteristic
295#3963C2311yescharacteristic
296#3963C2311yescharacteristic
297#3963C2311yescharacteristic
298#3963C2311yescharacteristic
299#3963C2311yescharacteristic
300#3963C2311yescharacteristic
301#3963C2311yescharacteristic
302#3963C2311yescharacteristic
303#3963C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#2852—51no—
353#2851—51no—
354#2783—51no—
355#2783—51no—
356#2776—51no—
357#2776—51no—
358#2772—51no—
359#2769—51no—
360#2766—51no—
361#2766—51no—
362#2762—51no—
363#2762—51no—
364#2747—51no—
365#2744—51no—
366#2725—51no—
367#2719—51no—
368#2690—51no—
369#2689—51no—
370#2646—51no—
371#2643—51no—
372#2583—51no—
373#2579—51no—
374#2510—51no—
375#2510—51no—
376#2505—51no—
377#2505—51no—
378#2442—51no—
379#2417D511yescharacteristic
380#2329—51no—
381#2318—51no—
382C2×#387—51no—
383C24×C5C2411yescharacteristic
384C24×C5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C2×C5×D4—22no—
389C2×C5×D4—22no—
390C2×C5×D4—22no—
391C22×C4×C5—22no—
392C22×C4×C5—22no—
393C22×C4×C5—22no—
394C22×C4×C5—22no—
395C22×C4×C5—41no—
396C22×C4×C5—41no—
397C22×C4×C5—41no—
398C22×C4×C5—41no—
399C22×C4×C5—41no—
400C22×C4×C5—41no—
401C22×C4×C5—41no—
402C22×C4×C5#4114yes—
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
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C22×Dic5—22no—
417C22×Dic5—22no—
418C22×Dic5—22no—
419C22×Dic5—22no—
420C22×Dic5—41no—
421C22×Dic5—41no—
422C22×Dic5—41no—
423C22×Dic5—41no—
424C22×Dic5—41no—
425C22×Dic5—41no—
426C22×Dic5—41no—
427C22×Dic5—41no—
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C22×Dic5C2411yescharacteristic
443C22×Dic5C2411yescharacteristic
444C5×C4⋊C4—22no—
445C5×C4⋊C4—22no—
446C5×C4⋊C4—22no—
447C5×C4⋊C4—22no—
448C5×C4⋊C4—22no—
449C5×C4⋊C4—22no—
450C5×C4⋊C4—22no—
451C5×C4⋊C4—41no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C22⋊C4—22no—
457C5×C22⋊C4—22no—
458C5×C22⋊C4—22no—
459C5×C22⋊C4—22no—
460C5×C22⋊C4—22no—
461C5×C22⋊C4—41no—
462C5×C22⋊C4—41no—
463C5×C22⋊C4—41no—
464C42×C5—22no—
465C22⋊Dic5—22no—
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—
477C4⋊Dic5—22no—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
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—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—
511C4×Dic5—22no—
512C4×Dic5—22no—
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×#126—51no—
522C2×#125—51no—
523C2×#125—51no—
524C2×C22⋊Q8C2×D511yescharacteristic
525C2×C22⋊Q8C2×D511yescharacteristic
526C2×C4×D4C2×D511yescharacteristic
527C22×C4⋊C4—51no—
528C22×C4⋊C4C2×D511yescharacteristic
529C22×C42—51no—
530#401—51no—
531#401—51no—
532#401—51no—
533#400—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#398—51no—
557#398—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398C2×D511yescharacteristic
563#398C2×D511yescharacteristic
564#397—51no—
565#397—51no—
566#397—51no—
567#397—51no—
568#397—51no—
569#397—51no—
570#397—51no—
571#396—51no—
572#396—51no—
573#396—51no—
574#396C2×D511yescharacteristic
575#396C2×D511yescharacteristic
576#395—51no—
577#395—51no—
578#391—51no—
579#391—51no—
580#391C2×D511yescharacteristic
581#389—51no—
582#389—51no—
583#389—51no—
584#389—51no—
585#389—51no—
586#389—51no—
587#389—51no—
588#389—51no—
589#389—51no—
590#389—51no—
591#389—51no—
592#389—51no—
593#389C2×D511yescharacteristic
594#388—51no—
595#388—51no—
596#388—51no—
597#388—51no—
598#388—51no—
599#388—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#387—51no—
604#387—51no—
605#387—51no—
606#387—51no—
607#387—51no—
608#387—51no—
609#387—51no—
610#387—51no—
611#387—51no—
612#387—51no—
613#387—51no—
614#387—51no—
615#387—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#386—51no—
633#386—51no—
634#386—51no—
635#386—51no—
636#386C2×D511yescharacteristic
637#386C2×D511yescharacteristic
638#385—51no—
639#385—51no—
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#385—51no—
645#385—51no—
646#385—51no—
647#385—51no—
648#385—51no—
649#385—51no—
650#385—51no—
651#385—51no—
652#383—51no—
653#383—51no—
654#383—51no—
655#383—51no—
656#382—51no—
657#382—51no—
658#382—51no—
659#382—51no—
660#382—51no—
661#381—51no—
662#380—51no—
663#380—51no—
664#380—51no—
665#380—51no—
666#380C2×D511yescharacteristic
667#380C2×D511yescharacteristic
668#380C2×D511yescharacteristic
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C2×#95—51no—
673C2×#95—51no—
674C2×#95—51no—
675C2×#95—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5—21no—
683C23×C5—21no—
684C23×C5—21no—
685C23×C5—21no—
686C23×C5—21no—
687C23×C5C2×#4112yes—
688C23×C52−1+412yes—
689C23×C52−1+412yes—
690C23×C5C2511yescharacteristic
691C5×Q8—82no—
692C5×D4—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—44no—
730C2×C4×C5—44no—
731C2×C4×C5—82no—
732C2×C4×C5—82no—
733C2×C4×C5C2×#4112yes—
734C2×C4×C5C2×#4112yes—
735C2×C4×C5H(5,𝔽2)12yes—
736C2×Dic5—21no—
737C2×Dic5—21no—
738C2×Dic5—21no—
739C2×Dic5—21no—
740C2×Dic5—21no—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—44no—
785C2×Dic5—44no—
786C2×Dic5—44no—
787C2×Dic5—82no—
788C22×Q8C22×D511yescharacteristic
789C22×D4C22×D511yescharacteristic
790C23×C4—51no—
791C23×C4—51no—
792C23×C4—51no—
793C23×C4—51no—
794C23×C4C22×D511yescharacteristic
795C23×C4C22×D511yescharacteristic
796C23×C4C22×D511yescharacteristic
797C23×C4C22×D511yescharacteristic
798#126—202no—
799#125—202no—
800#125—202no—
801C22⋊Q8—24no—
802C22⋊Q8—42no—
803C4×D4—24no—
804C2×C4⋊C4—42no—
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⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—104no—
840C2×C4⋊C4C22×D511yescharacteristic
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
846C2×C4⋊C4C22×D511yescharacteristic
847C2×C4⋊C4C22×D511yescharacteristic
848C2×C4⋊C4C22×D511yescharacteristic
849C2×C4⋊C4C22×D511yescharacteristic
850C2×C4⋊C4C22×D511yescharacteristic
851C2×C4⋊C4C22×D511yescharacteristic
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⋊C4C22×D511yescharacteristic
865C2×C22⋊C4C22×D511yescharacteristic
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C22⋊C4C22×D511yescharacteristic
871C2×C22⋊C4C22×D511yescharacteristic
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×C42—202no—
883C2×C42C22×D511yescharacteristic
884#95—51no—
885#95—51no—
886#95—51no—
887#95—51no—
888#95—51no—
889#95—51no—
890#95—51no—
891#95—51no—
892#95—51no—
893#95—51no—
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952C22×C5—22no—
953C22×C5—22no—
954C22×C5—22no—
955C22×C5—22no—
956C22×C5—22no—
957C22×C5—22no—
958C22×C5—41no—
959C22×C5—41no—
960C22×C5—41no—
961C22×C5—41no—
962C22×C5—41no—
963C22×C5—41no—
964C22×C5—41no—
965C22×C5#54114yes—
966C22×C5C22×#4111yescharacteristic
967C22×C5C2×H(5,𝔽2)11yescharacteristic
968C22×C5C2×2−1+411yescharacteristic
969C22×C5C2×2−1+411yescharacteristic
970C22×C5#58511yescharacteristic
971C22×C5#58511yescharacteristic
972C22×C5#58511yescharacteristic
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—
985C4×C5—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—
1000Dic5—41no—
1001Dic5—41no—
1002C24C23×D511yescharacteristic
1003C24C23×D511yescharacteristic
1004C2×Q8—22no—
1005C2×Q8—41no—
1006C2×Q8—41no—
1007C2×D4—22no—
1008C2×D4—22no—
1009C2×D4—22no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—102no—
1038C22×C4—102no—
1039C22×C4—102no—
1040C22×C4—102no—
1041C22×C4—201no—
1042C22×C4—201no—
1043C22×C4—201no—
1044C22×C4—201no—
1045C22×C4—201no—
1046C22×C4—201no—
1047C22×C4—201no—
1048C22×C4—201no—
1049C22×C4#71114yes—
1050C22×C4C23×D511yescharacteristic
1051C22×C4C23×D511yescharacteristic
1052C22×C4C23×D511yescharacteristic
1053C22×C4C23×D511yescharacteristic
1054C22×C4C23×D511yescharacteristic
1055C22×C4C23×D511yescharacteristic
1056C22×C4C23×D511yescharacteristic
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C22×C4C23×D511yescharacteristic
1060C22×C4C23×D511yescharacteristic
1061C22×C4C23×D511yescharacteristic
1062C22×C4C23×D511yescharacteristic
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—22no—
1068C4⋊C4—22no—
1069C4⋊C4—22no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—102no—
1076C4⋊C4—102no—
1077C4⋊C4—102no—
1078C4⋊C4—102no—
1079C4⋊C4—102no—
1080C4⋊C4—102no—
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—
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—
1109C22⋊C4—22no—
1110C22⋊C4—22no—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—22no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—102no—
1118C22⋊C4—102no—
1119C22⋊C4—102no—
1120C22⋊C4—102no—
1121C22⋊C4—201no—
1122C22⋊C4—201no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C42—22no—
1130C42—102no—
1131C42—102no—
1132C42—201no—
1133C42—201no—
1134C42—201no—
1135C42—201no—
1136C42—201no—
1137C42—201no—
1138C42—201no—
1139C42—201no—
1140C2×C5—24no—
1141C2×C5—81no—
1142C2×C5C2×#54111yescharacteristic
1143C2×C5#349311yescharacteristic
1144C2×C5#350511yescharacteristic
1145C2×C5#353511yescharacteristic
1146C2×C5#354111yescharacteristic
1147C2×C5#355311yescharacteristic
1148C2×C5#356411yescharacteristic
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23C2×#71112yes—
1161C23#414712yes—
1162C23#415012yes—
1163C23C24×D511yescharacteristic
1164Q8—82no—
1165D4—44no—
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—44no—
1203C2×C4—44no—
1204C2×C4—82no—
1205C2×C4—82no—
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—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—204no—
1255C2×C4—204no—
1256C2×C4—204no—
1257C2×C4—402no—
1258C2×C4C2×#71112yes—
1259C2×C4C2×#71112yes—
1260C2×C4#414412yes—
1261C5#3678211yescharacteristic, complemented, Sylow
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22#6595914yes—
1276C22C22×#71111yescharacteristic
1277C22C2×#414411yescharacteristic
1278C22C2×#414711yescharacteristic
1279C22C2×#415011yescharacteristic
1280C22#6628311yescharacteristic
1281C22#6628511yescharacteristic
1282C22#6628711yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—201no—
1297C4—201no—
1298C4—201no—
1299C4—201no—
1300C4—201no—
1301C4—201no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C2—24no—
1313C2—81no—
1314C2#1061783811yescharacteristic
1315C2C2×#6595911yescharacteristic
1316C2#1061826711yescharacteristic
1317C2#1061854711yescharacteristic
1318C2#1061865511yescharacteristic
1319C2#1061875411yescharacteristic
1320C2#1061884211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2417C2
prime radicalC22×C5×D4C23
hypercenter#2417D5
hypocenterC5#36782
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2417

Complements

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

NH ≅ G/Ntype
2. #10614527C2semidirect
3. #10614526C2semidirect
4. #10614516C2semidirect
5. #10614476C2semidirect
8. #10613903C2semidirect
9. C2×#65267C2semidirect
10. #10609630C2semidirect
11. #10609629C2semidirect
12. #10609615C2semidirect
13. #10609591C2semidirect
14. #10609123C2semidirect
15. #10609122C2semidirect
16. #10609116C2semidirect
17. #10609098C2semidirect
18. #10608316C2semidirect
19. #10608315C2semidirect
20. #10607876C2semidirect
21. #10607871C2semidirect
26. #10605729C2semidirect
27. #10605715C2semidirect
28. #10605712C2semidirect
29. #10605687C2semidirect
30. #10605658C2semidirect
31. #10605658C2semidirect
1261. C5#36782semidirect

Maximal subgroups

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

subgroupindex
C5×#24172
#106145272
#106145262
#106145162
#106144762
#106141182
#106140552
#106139032
C2×#652672
#106096302
#106096292
#106096152
#106095912
#106091232
#106091222
#106091162
#106090982
#106083162
#106083152
#106078762
#106078712
#106066012
#106065172
#106064742
#106057292
#106057152
#106057122
#106056872
#106056582
#367825