Finite Group Databasebeta

← #12308308

Subgroups — #12308308

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×#2721C211yesmaximal, characteristic, complemented
2#10614851C211yesmaximal, characteristic
3#10614830C211yesmaximal, characteristic, complemented
4#10614780C211yesmaximal, characteristic, complemented
5#10614763C211yesmaximal, characteristic, complemented
6#10609839C211yesmaximal, characteristic
7#10609810C211yesmaximal, characteristic, complemented
8#10609801C211yesmaximal, characteristic, complemented
9#10609760C211yesmaximal, characteristic
10#10609696C211yesmaximal, characteristic, complemented
11#10609687C211yesmaximal, characteristic, complemented
12#10609630C211yesmaximal, characteristic, complemented
13#10609614C211yesmaximal, characteristic, complemented
14#10609419C211yesmaximal, characteristic
15#10609334C211yesmaximal, characteristic, complemented
16#10609107C211yesmaximal, characteristic, complemented
17#10609035C211yesmaximal, characteristic
18#10608016C211yesmaximal, characteristic, complemented
19#10607876C211yesmaximal, characteristic, complemented
20#10607602C211yesmaximal, characteristic
21#10607530C211yesmaximal, characteristic, complemented
22#10607447C211yesmaximal, characteristic, complemented
23#10607188C211yesmaximal, characteristic
24#10607093C211yesmaximal, characteristic, complemented
25#10607031C211yesmaximal, characteristic, complemented
26D5×#387C211yesmaximal, characteristic, complemented
27#10606995C211yesmaximal, characteristic, complemented
28#10606977C211yesmaximal, characteristic, complemented
29#10606923C211yesmaximal, characteristic, complemented
30#10606083C211yesmaximal, characteristic, complemented
31#10606060C211yesmaximal, characteristic, complemented
32C2×C5×#126C2211yescharacteristic
33C2×C5×#125C2211yescharacteristic
34C2×#4043C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4036C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4025C2211yescharacteristic
40C2×C42×D5C2211yescharacteristic
41C5×#399C2211yescharacteristic
42C5×#399C2211yescharacteristic
43C5×#398C2211yescharacteristic
44C5×#398C2211yescharacteristic
45C5×#397C2211yescharacteristic
46C5×#396C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#388C2211yescharacteristic
49C5×#388C2211yescharacteristic
50C5×#387C2211yescharacteristic
51C5×#387C2211yescharacteristic
52C5×#387C2211yescharacteristic
53C5×#384C2211yescharacteristic
54#65278C2211yescharacteristic
55#65278C2211yescharacteristic
56#65278C2211yescharacteristic
57#65278C2211yescharacteristic
58#65278C2211yescharacteristic
59#65278C2211yescharacteristic
60#65278C2211yescharacteristic
61#65278C2211yescharacteristic
62#65278C2211yescharacteristic
63#65276C2211yescharacteristic
64#65276C2211yescharacteristic
65#65276C2211yescharacteristic
66#65275C2211yescharacteristic
67#65275C2211yescharacteristic
68#65275C2211yescharacteristic
69#65273C2211yescharacteristic
70#65273C2211yescharacteristic
71#65273C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65273C2211yescharacteristic
75#65273C2211yescharacteristic
76#65272C2211yescharacteristic
77#65272C2211yescharacteristic
78#65272C2211yescharacteristic
79#65271C2211yescharacteristic
80#65271C2211yescharacteristic
81#65271C2211yescharacteristic
82#65271C2211yescharacteristic
83#65271C2211yescharacteristic
84#65270C2211yescharacteristic
85#65270C2211yescharacteristic
86#65270C2211yescharacteristic
87#65270C2211yescharacteristic
88#65270C2211yescharacteristic
89#65270C2211yescharacteristic
90#65270C2211yescharacteristic
91#65270C2211yescharacteristic
92#65269C2211yescharacteristic
93#65269C2211yescharacteristic
94#65267C2211yescharacteristic
95#65267C2211yescharacteristic
96#65267C2211yescharacteristic
97#65267C2211yescharacteristic
98#65267C2211yescharacteristic
99#65267C2211yescharacteristic
100#65266C2211yescharacteristic
101#65266C2211yescharacteristic
102#65266C2211yescharacteristic
103#65265C2211yescharacteristic
104#65263C2211yescharacteristic
105#65262C2211yescharacteristic
106#65261C2211yescharacteristic
107#65261C2211yescharacteristic
108#65261C2211yescharacteristic
109#65261C2211yescharacteristic
110#65245C2211yescharacteristic
111#65245C2211yescharacteristic
112#65245C2211yescharacteristic
113#65245C2211yescharacteristic
114#65245C2211yescharacteristic
115#65245C2211yescharacteristic
116#65242C2211yescharacteristic
117#65241C2211yescharacteristic
118#65241C2211yescharacteristic
119#65241C2211yescharacteristic
120#65241C2211yescharacteristic
121#65240C2211yescharacteristic
122#65240C2211yescharacteristic
123#65239C2211yescharacteristic
124#65239C2211yescharacteristic
125#65238C2211yescharacteristic
126#65237C2211yescharacteristic
127#65236C2211yescharacteristic
128#65233C2211yescharacteristic
129#65233C2211yescharacteristic
130#65233C2211yescharacteristic
131#65233C2211yescharacteristic
132#65232C2211yescharacteristic
133#65231C2211yescharacteristic
134#65231C2211yescharacteristic
135#65231C2211yescharacteristic
136C4×#685C2211yescharacteristic
137C4×#685C2211yescharacteristic
138#65226C2211yescharacteristic
139#65222C2211yescharacteristic
140#65222C2211yescharacteristic
141#65222C2211yescharacteristic
142#65222C2211yescharacteristic
143#65222C2211yescharacteristic
144#65218C2211yescharacteristic
145#65217C2211yescharacteristic
146#65217C2211yescharacteristic
147#64957C2211yescharacteristic
148#64957C2211yescharacteristic
149#64957C2211yescharacteristic
150#64956C2211yescharacteristic
151#64956C2211yescharacteristic
152#64955C2211yescharacteristic
153D5×#95C2211yescharacteristic
154D5×#95C2211yescharacteristic
155D5×#95C2211yescharacteristic
156D5×#95C2211yescharacteristic
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#64947C2211yescharacteristic
170#64945C2211yescharacteristic
171#64944C2211yescharacteristic
172#64943C2211yescharacteristic
173#64943C2211yescharacteristic
174#64943C2211yescharacteristic
175#64943C2211yescharacteristic
176#64943C2211yescharacteristic
177#64942C2211yescharacteristic
178#64942C2211yescharacteristic
179#64941C2211yescharacteristic
180#64941C2211yescharacteristic
181#64941C2211yescharacteristic
182#64941C2211yescharacteristic
183#64940C2211yescharacteristic
184#64940C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36798—51nomaximal, Sylow
188C22×C22⋊D5C2311yescharacteristic
189C23×Dic5C2311yescharacteristic
190C22×C4×D5C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C5×#126—42no—
199C5×#125—42no—
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×C4⋊C4C2311yescharacteristic
214C2×C5×C4⋊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×C42×C5C2311yescharacteristic
224C2×C42×C5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
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×#683C2311yescharacteristic
249C2×#683C2311yescharacteristic
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×C4×Dic5C2311yescharacteristic
270C2×C4×Dic5C2311yescharacteristic
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277#4043—24no—
278D5×C4⋊C4—24no—
279D5×C4⋊C4—42no—
280#4036—42no—
281#4027—24no—
282#4025—42no—
283C42×D5—42no—
284C5×#95C2311yescharacteristic
285C5×#95C2311yescharacteristic
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
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#2798—51no—
355#2794—51no—
356#2794—51no—
357#2789—51no—
358#2776—51no—
359#2769—51no—
360#2766—51no—
361#2758—51no—
362#2754—51no—
363#2747—51no—
364#2744—51no—
365#2739—51no—
366#2722—51no—
367#2721—51no—
368#2721D511yescharacteristic, complemented
369#2719—51no—
370#2646—51no—
371#2643—51no—
372#2569—51no—
373#2564—51no—
374#2510—51no—
375#2505—51no—
376#2502—51no—
377#2487—51no—
378#2481—51no—
379#2473—51no—
380#2329—51no—
381#2318—51no—
382C2×#387—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C22×C4×C5C2411yescharacteristic
386C22×C4×C5C2411yescharacteristic
387C22×C4×C5C2411yescharacteristic
388C22×C4×C5C2411yescharacteristic
389C22×C4×C5C2411yescharacteristic
390C22×C4×C5C2411yescharacteristic
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C2×C22⋊D5—22no—
400C2×C22⋊D5—22no—
401C2×C22⋊D5—22no—
402C22×Dic5—22no—
403C22×Dic5—41no—
404C22×Dic5—41no—
405C22×Dic5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C2×C4×D5—22no—
421C2×C4×D5—22no—
422C2×C4×D5—22no—
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—22no—
427C2×C4×D5—41no—
428C2×C4×D5—41no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×C4×D5—41no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×C4×D5—41no—
436C2×C4×D5—41no—
437C2×C4×D5—41no—
438C2×C4×D5—41no—
439C2×C4×D5—41no—
440C2×C4×D5#4114yes—
441C2×Dic10—22no—
442C2×Dic10—41no—
443C2×Dic10—41no—
444C5×C4⋊C4—22no—
445C5×C4⋊C4—22no—
446C5×C4⋊C4—22no—
447C5×C4⋊C4—22no—
448C5×C4⋊C4—22no—
449C5×C4⋊C4—41no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C22⋊C4—22no—
460C5×C22⋊C4—22no—
461C5×C22⋊C4—41no—
462C5×C22⋊C4—41no—
463C5×C22⋊C4—41no—
464C5×C22⋊C4—41no—
465C5×C22⋊C4—41no—
466C42×C5—22no—
467C42×C5—41no—
468C42×C5—41no—
469C22⋊Dic5—41no—
470C22⋊Dic5—41no—
471C22⋊Dic5—41no—
472C22⋊Dic5—41no—
473C22⋊Dic5—41no—
474C22⋊Dic5—41no—
475#685—22no—
476#685—22no—
477#685—22no—
478#685—22no—
479#685—22no—
480#685—22no—
481#685—22no—
482C4⋊Dic5—22no—
483C4⋊Dic5—22no—
484C4⋊Dic5—22no—
485C4⋊Dic5—22no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489C4⋊Dic5—41no—
490C4⋊Dic5—41no—
491C4⋊Dic5—41no—
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—
511#683—41no—
512#683—41no—
513C4×Dic5—22no—
514C4×Dic5—22no—
515C4×Dic5—41no—
516C4×Dic5—41no—
517C4×Dic5—41no—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C2×#126—51no—
522C2×#126C2×D511yescharacteristic
523C2×#125—51no—
524C2×#125C2×D511yescharacteristic
525C2×C22⋊Q8—51no—
526C2×C4×D4—51no—
527C22×C4⋊C4—51no—
528C22×C4⋊C4—51no—
529C22×C42—51no—
530#401—51no—
531#401—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#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#400—51no—
551#399—51no—
552#399C2×D511yescharacteristic
553#399C2×D511yescharacteristic
554#398—51no—
555#398—51no—
556#398—51no—
557#398—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398C2×D511yescharacteristic
567#398C2×D511yescharacteristic
568#397—51no—
569#397—51no—
570#397—51no—
571#397—51no—
572#397—51no—
573#397C2×D511yescharacteristic
574#396—51no—
575#396C2×D511yescharacteristic
576#395—51no—
577#393—51no—
578#391—51no—
579#391—51no—
580#391—51no—
581#391—51no—
582#389—51no—
583#389—51no—
584#389—51no—
585#389—51no—
586#389—51no—
587#389—51no—
588#389—51no—
589#389C2×D511yescharacteristic
590#388—51no—
591#388—51no—
592#388—51no—
593#388—51no—
594#388—51no—
595#388—51no—
596#388C2×D511yescharacteristic
597#388C2×D511yescharacteristic
598#387—51no—
599#387—51no—
600#387—51no—
601#387—51no—
602#387—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#387C2×D511yescharacteristic
630#387C2×D511yescharacteristic
631#387C2×D511yescharacteristic
632#386—51no—
633#386—51no—
634#386—51no—
635#386—51no—
636#386—51no—
637#386—51no—
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#384—51no—
653#384C2×D511yescharacteristic
654#383—51no—
655#383—51no—
656#383—51no—
657#382—51no—
658#382—51no—
659#382—51no—
660#381—51no—
661#380—51no—
662#380—51no—
663#380—51no—
664#380—51no—
665#380—51no—
666#380—51no—
667#380—51no—
668#380—51no—
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C2×#95—51no—
673C2×#95—51no—
674C2×#95—51no—
675C2×#95—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5—21no—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5C2×#4112yes—
689C22×D52−1+412yes—
690C22×D52−1+412yes—
691C2×C4×C5—21no—
692C2×C4×C5—21no—
693C2×C4×C5—21no—
694C2×C4×C5—21no—
695C2×C4×C5—21no—
696C2×C4×C5—21no—
697C2×C4×C5—21no—
698C2×C4×C5—21no—
699C2×C4×C5—21no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5C2×#4112yes—
732C2×C4×C5H(5,𝔽2)12yes—
733C22⋊D5—44no—
734C2×Dic5—21no—
735C2×Dic5—21no—
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—82no—
779C2×Dic5C2×#4112yes—
780C4×D5—44no—
781C4×D5—44no—
782C4×D5—44no—
783C4×D5—44no—
784C4×D5—44no—
785C4×D5—82no—
786C4×D5—82no—
787Dic10—82no—
788C22×Q8—51no—
789C22×D4—51no—
790C23×C4—51no—
791C23×C4—51no—
792C23×C4—51no—
793C23×C4—51no—
794C23×C4—51no—
795C23×C4—51no—
796C23×C4—51no—
797C23×C4—51no—
798#126—42no—
799#126—202no—
800#125—42no—
801#125—202no—
802C22⋊Q8—104no—
803C4×D4—104no—
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⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—104no—
836C2×C4⋊C4—202no—
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×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⋊C4—51no—
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—202no—
881C2×C42C22×D511yescharacteristic
882C2×C42C22×D511yescharacteristic
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#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952C22×C5—41no—
953C22×C5—41no—
954C22×C5—41no—
955C22×C5—41no—
956C22×C5—41no—
957C22×C5—41no—
958C22×C5—41no—
959C22×C5C22×#4111yescharacteristic
960C22×C5C2×H(5,𝔽2)11yescharacteristic
961C22×C5C2×2−1+411yescharacteristic
962C22×C5C2×2−1+411yescharacteristic
963C22×C5#58511yescharacteristic
964C22×C5#58511yescharacteristic
965C22×C5#58511yescharacteristic
966C2×D5—22no—
967C2×D5—22no—
968C2×D5—22no—
969C2×D5—22no—
970C2×D5—22no—
971C2×D5—22no—
972C2×D5#54114yes—
973C4×C5—22no—
974C4×C5—22no—
975C4×C5—41no—
976C4×C5—41no—
977C4×C5—41no—
978C4×C5—41no—
979C4×C5—41no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985C4×C5—41no—
986C4×C5—41no—
987Dic5—22no—
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—
1002C24—51no—
1003C24C23×D511yescharacteristic
1004C2×Q8—102no—
1005C2×Q8—201no—
1006C2×Q8—201no—
1007C2×D4—102no—
1008C2×D4—102no—
1009C2×D4—102no—
1010C22×C4—51no—
1011C22×C4—54no—
1012C22×C4—51no—
1013C22×C4—51no—
1014C22×C4—51no—
1015C22×C4—51no—
1016C22×C4—51no—
1017C22×C4—51no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—51no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—102no—
1027C22×C4—102no—
1028C22×C4—102no—
1029C22×C4—102no—
1030C22×C4—102no—
1031C22×C4—102no—
1032C22×C4—102no—
1033C22×C4—102no—
1034C22×C4—201no—
1035C22×C4—201no—
1036C22×C4—201no—
1037C22×C4—201no—
1038C22×C4—201no—
1039C22×C4—201no—
1040C22×C4—201no—
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×C4C23×D511yescharacteristic
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—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—102no—
1079C4⋊C4—102no—
1080C4⋊C4—102no—
1081C4⋊C4—102no—
1082C4⋊C4—102no—
1083C4⋊C4—102no—
1084C4⋊C4—102no—
1085C4⋊C4—102no—
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—41no—
1112C22⋊C4—41no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—41no—
1116C22⋊C4—102no—
1117C22⋊C4—102no—
1118C22⋊C4—102no—
1119C22⋊C4—102no—
1120C22⋊C4—102no—
1121C22⋊C4—102no—
1122C22⋊C4—102no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C42—22no—
1130C42—41no—
1131C42—41no—
1132C42—102no—
1133C42—102no—
1134C42—201no—
1135C42—201no—
1136C42—201no—
1137C42—201no—
1138C42—201no—
1139C42—201no—
1140C2×C5—81no—
1141C2×C5C2×#54111yescharacteristic
1142C2×C5#349111yescharacteristic
1143C2×C5#350611yescharacteristic
1144C2×C5#353511yescharacteristic
1145C2×C5#354111yescharacteristic
1146C2×C5#355311yescharacteristic
1147C2×C5#356411yescharacteristic
1148D5—24no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—52no—
1157C23—52no—
1158C23—52no—
1159C23—101no—
1160C23—101no—
1161C23—101no—
1162C23—101no—
1163C23C24×D511yescharacteristic
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—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—52no—
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×C4—204no—
1253C2×C4—204no—
1254C2×C4—204no—
1255C2×C4—204no—
1256C2×C4—402no—
1257C2×C4—402no—
1258C2×C4—402no—
1259C2×C4#414412yes—
1260C2×C4D5×#4112yes—
1261C5#3679811yescharacteristic, complemented, Sylow
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—54no—
1270C22—102no—
1271C22—102no—
1272C22—102no—
1273C22—102no—
1274C22—102no—
1275C22—102no—
1276C22C2×#414411yescharacteristic
1277C22C2×D5×#4111yescharacteristic
1278C22#6628311yescharacteristic
1279C22#6628511yescharacteristic
1280C22D5×2−1+411yescharacteristic
1281C22D5×2−1+411yescharacteristic
1282C22#6628711yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—102no—
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—81no—
1313C2—104no—
1314C2#1061826111yescharacteristic
1315C2#1061836411yescharacteristic
1316C2D5×#54111yescharacteristic
1317C2#1061859011yescharacteristic
1318C2#1061868611yescharacteristic
1319C2#1061876011yescharacteristic
1320C2#1061903911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2721C2
prime radicalC22×C22⋊D5C23
hypercenter#2721D5
hypocenterC5#36798
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2721

Complements

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

NH ≅ G/Ntype
1. C5×#2721C2semidirect
3. #10614830C2semidirect
4. #10614780C2semidirect
5. #10614763C2semidirect
7. #10609810C2semidirect
8. #10609801C2semidirect
10. #10609696C2semidirect
11. #10609687C2semidirect
12. #10609630C2semidirect
13. #10609614C2semidirect
15. #10609334C2semidirect
16. #10609107C2semidirect
18. #10608016C2semidirect
19. #10607876C2semidirect
21. #10607530C2semidirect
22. #10607447C2semidirect
24. #10607093C2semidirect
25. #10607031C2semidirect
26. D5×#387C2semidirect
27. #10606995C2semidirect
28. #10606977C2semidirect
29. #10606923C2semidirect
30. #10606083C2semidirect
31. #10606060C2semidirect
368. #2721D5semidirect
1261. C5#36798semidirect

Maximal subgroups

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

subgroupindex
C5×#27212
#106148512
#106148302
#106147802
#106147632
#106098392
#106098102
#106098012
#106097602
#106096962
#106096872
#106096302
#106096142
#106094192
#106093342
#106091072
#106090352
#106080162
#106078762
#106076022
#106075302
#106074472
#106071882
#106070932
#106070312
D5×#3872
#106069952
#106069772
#106069232
#106060832
#106060602
#367985