Finite Group Databasebeta

← #12307499

Subgroups — #12307499

Order 1280.

1494 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2332C211yesmaximal, characteristic, complemented
2#10614554C211yesmaximal, characteristic
3#10614542C211yesmaximal, characteristic, complemented
4#10608312C211yesmaximal, characteristic, complemented
5#10608308C211yesmaximal, characteristic, complemented
6#10608301C211yesmaximal, characteristic, complemented
7#10608299C211yesmaximal, characteristic, complemented
8#10607514C211yesmaximal, characteristic, complemented
9#10607505C211yesmaximal, characteristic
10#10607503C211yesmaximal, characteristic
11#10607485C211yesmaximal, characteristic, complemented
12#10607460C211yesmaximal, characteristic, complemented
13#10607450C211yesmaximal, characteristic
14#10607412C211yesmaximal, characteristic
15#10607404C211yesmaximal, characteristic, complemented
16#10607002C211yesmaximal, characteristic, complemented
17#10606998C211yesmaximal, characteristic, complemented
18#10606991C211yesmaximal, characteristic, complemented
19#10606983C211yesmaximal, characteristic, complemented
20#10606841C211yesmaximal, characteristic, complemented
21#10606834C211yesmaximal, characteristic, complemented
22#10606747C211yesmaximal, characteristic, complemented
23#10606742C211yesmaximal, characteristic, complemented
24#10605848C211yesmaximal, characteristic, complemented
25#10605822C211yesmaximal, characteristic
26#10605543C211yesmaximal, characteristic, complemented
27#10605542C211yesmaximal, characteristic, complemented
28#10605440C211yesmaximal, characteristic, complemented
29#10605437C211yesmaximal, characteristic, complemented
30#10605179C211yesmaximal, characteristic, complemented
31#10605169C211yesmaximal, characteristic
32C2×C5×C22⋊Q8C2211yescharacteristic
33C2×#4090C2211yescharacteristic
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C2×#4044C2211yescharacteristic
38C2×#4035C2211yescharacteristic
39C2×#4024C2211yescharacteristic
40C2×#4018C2211yescharacteristic
41C5×#391C2211yescharacteristic
42C5×#391C2211yescharacteristic
43C5×#388C2211yescharacteristic
44C5×#388C2211yescharacteristic
45C5×#388C2211yescharacteristic
46C5×#388C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C5×#387C2211yescharacteristic
50C5×#387C2211yescharacteristic
51C5×#381C2211yescharacteristic
52C4×C5×C4⋊C4C2211yescharacteristic
53C4×C5×C4⋊C4C2211yescharacteristic
54C4×C5×C22⋊C4C2211yescharacteristic
55#65520C2211yescharacteristic
56#65519C2211yescharacteristic
57#65518C2211yescharacteristic
58#65500C2211yescharacteristic
59#65283C2211yescharacteristic
60#65282C2211yescharacteristic
61#65281C2211yescharacteristic
62#65279C2211yescharacteristic
63#65278C2211yescharacteristic
64#65278C2211yescharacteristic
65#65275C2211yescharacteristic
66#65273C2211yescharacteristic
67#65273C2211yescharacteristic
68#65272C2211yescharacteristic
69#65271C2211yescharacteristic
70#65271C2211yescharacteristic
71#65271C2211yescharacteristic
72#65271C2211yescharacteristic
73#65269C2211yescharacteristic
74#65269C2211yescharacteristic
75#65268C2211yescharacteristic
76#65267C2211yescharacteristic
77#65267C2211yescharacteristic
78#65265C2211yescharacteristic
79#65263C2211yescharacteristic
80#65261C2211yescharacteristic
81#65261C2211yescharacteristic
82#65261C2211yescharacteristic
83#65261C2211yescharacteristic
84#65261C2211yescharacteristic
85#65250C2211yescharacteristic
86#65250C2211yescharacteristic
87#65248C2211yescharacteristic
88#65248C2211yescharacteristic
89#65247C2211yescharacteristic
90#65247C2211yescharacteristic
91#65242C2211yescharacteristic
92#65242C2211yescharacteristic
93#65241C2211yescharacteristic
94#65241C2211yescharacteristic
95#65239C2211yescharacteristic
96#65235C2211yescharacteristic
97#65235C2211yescharacteristic
98#65235C2211yescharacteristic
99#65234C2211yescharacteristic
100#65234C2211yescharacteristic
101#65233C2211yescharacteristic
102#65233C2211yescharacteristic
103#65231C2211yescharacteristic
104#65231C2211yescharacteristic
105#65231C2211yescharacteristic
106#65231C2211yescharacteristic
107#65231C2211yescharacteristic
108#65229C2211yescharacteristic
109#65229C2211yescharacteristic
110#65229C2211yescharacteristic
111#65229C2211yescharacteristic
112C4×#685C2211yescharacteristic
113#65226C2211yescharacteristic
114#65225C2211yescharacteristic
115#65222C2211yescharacteristic
116#65222C2211yescharacteristic
117#65222C2211yescharacteristic
118#65222C2211yescharacteristic
119#65222C2211yescharacteristic
120#65222C2211yescharacteristic
121#65222C2211yescharacteristic
122#65222C2211yescharacteristic
123#65222C2211yescharacteristic
124#65221C2211yescharacteristic
125C4×#683C2211yescharacteristic
126C4×#683C2211yescharacteristic
127C4×#683C2211yescharacteristic
128#65218C2211yescharacteristic
129#65217C2211yescharacteristic
130#65217C2211yescharacteristic
131#64965C2211yescharacteristic
132#64965C2211yescharacteristic
133#64964C2211yescharacteristic
134#64964C2211yescharacteristic
135#64964C2211yescharacteristic
136#64963C2211yescharacteristic
137#64962C2211yescharacteristic
138#64962C2211yescharacteristic
139#64959C2211yescharacteristic
140#64958C2211yescharacteristic
141#64958C2211yescharacteristic
142#64958C2211yescharacteristic
143#64957C2211yescharacteristic
144#64957C2211yescharacteristic
145C5⋊#401C2211yescharacteristic
146#64950C2211yescharacteristic
147#64949C2211yescharacteristic
148#64949C2211yescharacteristic
149#64948C2211yescharacteristic
150#64947C2211yescharacteristic
151#64947C2211yescharacteristic
152#64947C2211yescharacteristic
153#64947C2211yescharacteristic
154#64946C2211yescharacteristic
155#64946C2211yescharacteristic
156#64946C2211yescharacteristic
157#64946C2211yescharacteristic
158#64946C2211yescharacteristic
159#64946C2211yescharacteristic
160#64945C2211yescharacteristic
161#64944C2211yescharacteristic
162#64944C2211yescharacteristic
163#64944C2211yescharacteristic
164#64943C2211yescharacteristic
165#64943C2211yescharacteristic
166#64943C2211yescharacteristic
167#64942C2211yescharacteristic
168#64942C2211yescharacteristic
169#64942C2211yescharacteristic
170#64942C2211yescharacteristic
171#64942C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64941C2211yescharacteristic
176#64941C2211yescharacteristic
177#64941C2211yescharacteristic
178#64941C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36772—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×Dic10C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C5×C22⋊Q8—24no—
197C2×C5×C4⋊C4C2311yescharacteristic
198C2×C5×C4⋊C4C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C22⋊C4C2311yescharacteristic
205C2×C5×C22⋊C4C2311yescharacteristic
206C2×C5×C22⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C42×C5C2311yescharacteristic
211C2×C42×C5C2311yescharacteristic
212C2×C42×C5C2311yescharacteristic
213C2×C42×C5C2311yescharacteristic
214C2×C42×C5C2311yescharacteristic
215C2×C42×C5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221#4090—42no—
222C4×C22⋊D5—24no—
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244#4070—24no—
245C2×#683C2311yescharacteristic
246C2×#683C2311yescharacteristic
247C2×#683C2311yescharacteristic
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×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×C4×Dic5—42no—
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284#4044—42no—
285#4035—42no—
286#4024—42no—
287#4018—42no—
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
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#2857—51no—
353#2855—51no—
354#2799—51no—
355#2798—51no—
356#2793—51no—
357#2791—51no—
358#2787—51no—
359#2781—51no—
360#2779—51no—
361#2770—51no—
362#2759—51no—
363#2755—51no—
364#2747—51no—
365#2741—51no—
366#2716—51no—
367#2713—51no—
368#2702—51no—
369#2690—51no—
370#2638—51no—
371#2638—51no—
372#2590—51no—
373#2589—51no—
374#2588—51no—
375#2587—51no—
376#2533—51no—
377#2528—51no—
378#2478—51no—
379#2475—51no—
380#2332—51no—
381#2332D511yescharacteristic, complemented
382#2290—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C22×C4×C5—41no—
389C22×C4×C5—41no—
390C22×C4×C5#4114yes—
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C2×C22⋊D5—22no—
406C2×C22⋊D5—41no—
407C2×C22⋊D5—41no—
408C22×Dic5—22no—
409C22×Dic5—22no—
410C22×Dic5—22no—
411C22×Dic5—41no—
412C22×Dic5—41no—
413C22×Dic5—41no—
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C2×C4×D5—22no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×Dic10—22no—
433C2×Dic10—22no—
434C2×Dic10—41no—
435C2×Dic10—41no—
436C2×Dic10—41no—
437C2×Dic10—41no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—22no—
440C5×C4⋊C4—22no—
441C5×C4⋊C4—41no—
442C5×C4⋊C4—41no—
443C5×C4⋊C4—41no—
444C5×C4⋊C4—41no—
445C5×C22⋊C4—22no—
446C5×C22⋊C4—22no—
447C5×C22⋊C4—41no—
448C5×C22⋊C4—41no—
449C5×C22⋊C4—41no—
450C5×C22⋊C4—41no—
451C42×C5—41no—
452C42×C5—41no—
453C42×C5—41no—
454C42×C5—41no—
455C42×C5—41no—
456C42×C5—41no—
457C22⋊Dic5—22no—
458C22⋊Dic5—22no—
459C22⋊Dic5—22no—
460C22⋊Dic5—41no—
461C22⋊Dic5—41no—
462#685—22no—
463#685—22no—
464#685—22no—
465#685—22no—
466#685—41no—
467#685—41no—
468#685—41no—
469#685—41no—
470#685—41no—
471#685—41no—
472#685—41no—
473#685—41no—
474#685—41no—
475C4⋊Dic5—22no—
476C4⋊Dic5—22no—
477C4⋊Dic5—22no—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483#683—22no—
484#683—22no—
485#683—22no—
486#683—22no—
487#683—22no—
488#683—22no—
489#683—22no—
490#683—22no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—41no—
495#683—41no—
496#683—41no—
497#683—41no—
498#683—41no—
499#683—41no—
500#683—41no—
501#683—41no—
502#683—41no—
503#683—41no—
504#683—41no—
505#683—41no—
506#683—41no—
507#683—41no—
508#683—41no—
509#683—41no—
510#683—41no—
511#683—41no—
512C4×Dic5—22no—
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×C4⋊Q8—51no—
522C2×#126—51no—
523C2×#125—51no—
524C2×C22⋊Q8—51no—
525C2×C22⋊Q8—51no—
526C2×C22⋊Q8C2×D511yescharacteristic
527C2×C4×D4—51no—
528C2×#117—51no—
529C22×C42—51no—
530#401—51no—
531#400—51no—
532#400—51no—
533#400—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#399—51no—
544#398—51no—
545#398—51no—
546#398—51no—
547#398—51no—
548#398—51no—
549#398—51no—
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#397—51no—
557#397—51no—
558#397—51no—
559#397—51no—
560#397—51no—
561#397—51no—
562#397—51no—
563#397—51no—
564#397—51no—
565#396—51no—
566#396—51no—
567#396—51no—
568#395—51no—
569#395—51no—
570#395—51no—
571#394—51no—
572#394—51no—
573#394—51no—
574#394—51no—
575#393—51no—
576#393—51no—
577#393—51no—
578#391—51no—
579#391—51no—
580#391—51no—
581#391—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#391—51no—
586#391C2×D511yescharacteristic
587#391C2×D511yescharacteristic
588#389—51no—
589#389—51no—
590#389—51no—
591#389—51no—
592#389—51no—
593#389—51no—
594#389—51no—
595#389—51no—
596#389—51no—
597#389—51no—
598#388—51no—
599#388—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#388—51no—
604#388—51no—
605#388—51no—
606#388—51no—
607#388—51no—
608#388—51no—
609#388—51no—
610#388—51no—
611#388C2×D511yescharacteristic
612#388C2×D511yescharacteristic
613#388C2×D511yescharacteristic
614#388C2×D511yescharacteristic
615#387—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387C2×D511yescharacteristic
645#387C2×D511yescharacteristic
646#387C2×D511yescharacteristic
647#387C2×D511yescharacteristic
648#386—51no—
649#386—51no—
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385—51no—
657#385—51no—
658#384—51no—
659#383—51no—
660#382—51no—
661#381—51no—
662#381C2×D511yescharacteristic
663#380—51no—
664#380—51no—
665#380—51no—
666#380—51no—
667#380—51no—
668C4×C4⋊C4—51no—
669C4×C4⋊C4—51no—
670C4×C4⋊C4—51no—
671C4×C4⋊C4C2×D511yescharacteristic
672C4×C4⋊C4C2×D511yescharacteristic
673C4×C22⋊C4—51no—
674C4×C22⋊C4C2×D511yescharacteristic
675#376—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5C2×#4112yes—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5—21no—
691C5×Q8—82no—
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×C5—21no—
732C2×C4×C5—44no—
733C2×C4×C5C2×#4112yes—
734C2×C4×C5C2×#4112yes—
735C22⋊D5—44no—
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—44no—
779C2×Dic5—44no—
780C2×Dic5H(5,𝔽2)12yes—
781C2×Dic52−1+412yes—
782C2×Dic52−1+412yes—
783C4×D5—44no—
784Dic10—82no—
785Dic10—82no—
786C22×Q8—51no—
787C22×Q8—51no—
788C22×Q8C22×D511yescharacteristic
789C22×D4—51no—
790C23×C4—51no—
791C23×C4—51no—
792C23×C4—51no—
793C23×C4C22×D511yescharacteristic
794C4⋊Q8—202no—
795#126—202no—
796#125—202no—
797C22⋊Q8—24no—
798C22⋊Q8—104no—
799C22⋊Q8—202no—
800C4×D4—104no—
801#117—202no—
802C2×C4⋊C4—51no—
803C2×C4⋊C4—51no—
804C2×C4⋊C4—51no—
805C2×C4⋊C4—51no—
806C2×C4⋊C4—51no—
807C2×C4⋊C4—51no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—51no—
810C2×C4⋊C4—51no—
811C2×C4⋊C4—51no—
812C2×C4⋊C4—51no—
813C2×C4⋊C4—51no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊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⋊C4C22×D511yescharacteristic
840C2×C4⋊C4C22×D511yescharacteristic
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
846C2×C22⋊C4—51no—
847C2×C22⋊C4—51no—
848C2×C22⋊C4—51no—
849C2×C22⋊C4—51no—
850C2×C22⋊C4—51no—
851C2×C22⋊C4—51no—
852C2×C22⋊C4—51no—
853C2×C22⋊C4—51no—
854C2×C22⋊C4—51no—
855C2×C22⋊C4—51no—
856C2×C22⋊C4—51no—
857C2×C22⋊C4—51no—
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4C22×D511yescharacteristic
865C2×C22⋊C4C22×D511yescharacteristic
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C42—51no—
871C2×C42—51no—
872C2×C42—51no—
873C2×C42—51no—
874C2×C42—51no—
875C2×C42—51no—
876C2×C42—51no—
877C2×C42—51no—
878C2×C42—51no—
879C2×C42—202no—
880C2×C42C22×D511yescharacteristic
881C2×C42C22×D511yescharacteristic
882C2×C42C22×D511yescharacteristic
883C2×C42C22×D511yescharacteristic
884C2×C42C22×D511yescharacteristic
885C2×C42C22×D511yescharacteristic
886#95—51no—
887#95—51no—
888#95—51no—
889#95—51no—
890#95—51no—
891#95—51no—
892#95—51no—
893#95—51no—
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95C22×D511yescharacteristic
937#95C22×D511yescharacteristic
938#95C22×D511yescharacteristic
939#95C22×D511yescharacteristic
940#95C22×D511yescharacteristic
941#95C22×D511yescharacteristic
942#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950C22×C5—22no—
951C22×C5—22no—
952C22×C5—22no—
953C22×C5—41no—
954C22×C5—41no—
955C22×C5—41no—
956C22×C5—41no—
957C22×C5C22×#4111yescharacteristic
958C22×C5C2×H(5,𝔽2)11yescharacteristic
959C22×C5C2×2−1+411yescharacteristic
960C22×C5C2×2−1+411yescharacteristic
961C22×C5#58511yescharacteristic
962C22×C5#58511yescharacteristic
963C22×C5#58511yescharacteristic
964C2×D5—41no—
965C2×D5—41no—
966C2×D5—41no—
967C2×D5—41no—
968C2×D5—41no—
969C2×D5—41no—
970C2×D5—41no—
971C4×C5—22no—
972C4×C5—22no—
973C4×C5—41no—
974C4×C5—41no—
975C4×C5—41no—
976C4×C5—41no—
977C4×C5—41no—
978C4×C5—41no—
979C4×C5—41no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985Dic5—22no—
986Dic5—22no—
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—
1000C24—51no—
1001C24C23×D511yescharacteristic
1002C2×Q8—22no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—102no—
1006C2×Q8—102no—
1007C2×Q8—201no—
1008C2×Q8—201no—
1009C2×Q8—201no—
1010C2×Q8—201no—
1011C2×D4—102no—
1012C2×D4—201no—
1013C2×D4—201no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—51no—
1017C22×C4—51no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—51no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—102no—
1032C22×C4—102no—
1033C22×C4—102no—
1034C22×C4—102no—
1035C22×C4—201no—
1036C22×C4—201no—
1037C22×C4—201no—
1038C22×C4—201no—
1039C22×C4—201no—
1040C22×C4#70914yes—
1041C22×C4C23×D511yescharacteristic
1042C22×C4C23×D511yescharacteristic
1043C22×C4C23×D511yescharacteristic
1044C22×C4C23×D511yescharacteristic
1045C22×C4C23×D511yescharacteristic
1046C22×C4C23×D511yescharacteristic
1047C22×C4C23×D511yescharacteristic
1048C22×C4C23×D511yescharacteristic
1049C22×C4C23×D511yescharacteristic
1050C22×C4C23×D511yescharacteristic
1051C22×C4C23×D511yescharacteristic
1052C22×C4C23×D511yescharacteristic
1053C22×C4C23×D511yescharacteristic
1054C22×C4C23×D511yescharacteristic
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—102no—
1063C4⋊C4—102no—
1064C4⋊C4—102no—
1065C4⋊C4—102no—
1066C4⋊C4—102no—
1067C4⋊C4—102no—
1068C4⋊C4—102no—
1069C4⋊C4—102no—
1070C4⋊C4—102no—
1071C4⋊C4—102no—
1072C4⋊C4—102no—
1073C4⋊C4—102no—
1074C4⋊C4—102no—
1075C4⋊C4—102no—
1076C4⋊C4—201no—
1077C4⋊C4—201no—
1078C4⋊C4—201no—
1079C4⋊C4—201no—
1080C4⋊C4—201no—
1081C4⋊C4—201no—
1082C4⋊C4—201no—
1083C4⋊C4—201no—
1084C4⋊C4—201no—
1085C4⋊C4—201no—
1086C4⋊C4—201no—
1087C4⋊C4—201no—
1088C4⋊C4—201no—
1089C4⋊C4—201no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—102no—
1106C22⋊C4—102no—
1107C22⋊C4—102no—
1108C22⋊C4—102no—
1109C22⋊C4—102no—
1110C22⋊C4—102no—
1111C22⋊C4—102no—
1112C22⋊C4—201no—
1113C22⋊C4—201no—
1114C22⋊C4—201no—
1115C22⋊C4—201no—
1116C22⋊C4—201no—
1117C22⋊C4—201no—
1118C22⋊C4—201no—
1119C22⋊C4—201no—
1120C22⋊C4—201no—
1121C22⋊C4—201no—
1122C22⋊C4—201no—
1123C42—41no—
1124C42—41no—
1125C42—41no—
1126C42—41no—
1127C42—41no—
1128C42—41no—
1129C42—102no—
1130C42—102no—
1131C42—102no—
1132C42—201no—
1133C42—201no—
1134C42—201no—
1135C42—201no—
1136C42—201no—
1137C42—201no—
1138C2×C5—42no—
1139C2×C5#345511yescharacteristic
1140C2×C5#350511yescharacteristic
1141C2×C5#350911yescharacteristic
1142C2×C5#353511yescharacteristic
1143C2×C5#354111yescharacteristic
1144C2×C5#355711yescharacteristic
1145C2×C5#356511yescharacteristic
1146D5—81no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—101no—
1154C23—101no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23—101no—
1160C23C2×#70912yes—
1161C23C24×D511yescharacteristic
1162Q8—82no—
1163Q8—402no—
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—44no—
1207C2×C4—52no—
1208C2×C4—52no—
1209C2×C4—52no—
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—204no—
1253C2×C4—204no—
1254C2×C4—204no—
1255C2×C4C2×#70912yes—
1256C2×C4C2×#70912yes—
1257C5#3677211yescharacteristic, complemented, Sylow
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—201no—
1266C22—201no—
1267C22—201no—
1268C22—201no—
1269C22—201no—
1270C22—201no—
1271C22—201no—
1272C22C22×#70911yescharacteristic
1273C22#6628311yescharacteristic
1274C22#6628311yescharacteristic
1275C22D5×H(5,𝔽2)11yescharacteristic
1276C22#6628511yescharacteristic
1277C22D5×2−1+411yescharacteristic
1278C22D5×2−1+411yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—102no—
1294C4—102no—
1295C4—102no—
1296C4—201no—
1297C4—201no—
1298C4—201no—
1299C4—201no—
1300C4—201no—
1301C4—201no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C2—42no—
1309C2—401no—
1310C2#1061773811yescharacteristic
1311C2#1061776211yescharacteristic
1312C2#1061777711yescharacteristic
1313C2#1061834211yescharacteristic
1314C2#1061834811yescharacteristic
1315C2#1061843211yescharacteristic
1316C2#1061846111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2332C2
prime radicalC22×C22⋊D5C23
hypercenter#2332D5
hypocenterC5#36772
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
1. C5×#2332C2semidirect
3. #10614542C2semidirect
4. #10608312C2semidirect
5. #10608308C2semidirect
6. #10608301C2semidirect
7. #10608299C2semidirect
8. #10607514C2semidirect
11. #10607485C2semidirect
12. #10607460C2semidirect
15. #10607404C2semidirect
16. #10607002C2semidirect
17. #10606998C2semidirect
18. #10606991C2semidirect
19. #10606983C2semidirect
20. #10606841C2semidirect
21. #10606834C2semidirect
22. #10606747C2semidirect
23. #10606742C2semidirect
24. #10605848C2semidirect
26. #10605543C2semidirect
27. #10605542C2semidirect
28. #10605440C2semidirect
29. #10605437C2semidirect
30. #10605179C2semidirect
381. #2332D5semidirect
1257. C5#36772semidirect

Maximal subgroups

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

subgroupindex
C5×#23322
#106145542
#106145422
#106083122
#106083082
#106083012
#106082992
#106075142
#106075052
#106075032
#106074852
#106074602
#106074502
#106074122
#106074042
#106070022
#106069982
#106069912
#106069832
#106068412
#106068342
#106067472
#106067422
#106058482
#106058222
#106055432
#106055422
#106054402
#106054372
#106051792
#106051692
#367725