Finite Group Databasebeta

← #12313922

Subgroups — #12313922

Order 1280.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2650C211yesmaximal, characteristic
2#10610038C211yesmaximal, characteristic, complemented
3#10610032C211yesmaximal, characteristic, complemented
4#10610029C211yesmaximal, characteristic, complemented
5#10610027C211yesmaximal, characteristic, complemented
6#10610003C211yesmaximal, characteristic, complemented
7#10609990C211yesmaximal, characteristic, complemented
8#10609372C211yesmaximal, characteristic
9#10609347C211yesmaximal, characteristic
10#10609346C211yesmaximal, characteristic
11#10609337C211yesmaximal, characteristic
12#10609127C211yesmaximal, characteristic
13#10609124C211yesmaximal, characteristic
14#10608967C211yesmaximal, characteristic, complemented
15#10608959C211yesmaximal, characteristic, complemented
16#10608580C211yesmaximal, characteristic
17#10608572C211yesmaximal, characteristic
18#10608287C211yesmaximal, characteristic, complemented
19#10608283C211yesmaximal, characteristic, complemented
20#10607554C211yesmaximal, characteristic
21#10607382C211yesmaximal, characteristic
22#10607373C211yesmaximal, characteristic
23#10607358C211yesmaximal, characteristic
24#10607322C211yesmaximal, characteristic
25#10607187C211yesmaximal, characteristic
26#10607022C211yesmaximal, characteristic, complemented
27#10606807C211yesmaximal, characteristic, complemented
28#10606803C211yesmaximal, characteristic, complemented
29#10606688C211yesmaximal, characteristic, complemented
30#10605477C211yesmaximal, characteristic, complemented
31#10605350C211yesmaximal, characteristic, complemented
32C2×#4035C2211yescharacteristic
33C2×#4023C2211yescharacteristic
34C2×C4×Dic10C2211yescharacteristic
35C5×#400C2211yescharacteristic
36C5×#400C2211yescharacteristic
37C5×#400C2211yescharacteristic
38C5×#397C2211yescharacteristic
39C5×#397C2211yescharacteristic
40C5×#396C2211yescharacteristic
41C5×#395C2211yescharacteristic
42C5×#393C2211yescharacteristic
43C5×#391C2211yescharacteristic
44C5×#388C2211yescharacteristic
45C5×#388C2211yescharacteristic
46C5×#388C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C4×C5×C4⋊C4C2211yescharacteristic
50#65519C2211yescharacteristic
51#65519C2211yescharacteristic
52#65518C2211yescharacteristic
53#65518C2211yescharacteristic
54#65275C2211yescharacteristic
55#65275C2211yescharacteristic
56#65273C2211yescharacteristic
57#65272C2211yescharacteristic
58#65271C2211yescharacteristic
59#65271C2211yescharacteristic
60#65270C2211yescharacteristic
61#65270C2211yescharacteristic
62#65270C2211yescharacteristic
63#65270C2211yescharacteristic
64#65269C2211yescharacteristic
65#65269C2211yescharacteristic
66#65268C2211yescharacteristic
67#65268C2211yescharacteristic
68#65267C2211yescharacteristic
69#65267C2211yescharacteristic
70#65267C2211yescharacteristic
71#65267C2211yescharacteristic
72#65267C2211yescharacteristic
73#65267C2211yescharacteristic
74#65267C2211yescharacteristic
75#65265C2211yescharacteristic
76#65265C2211yescharacteristic
77C4⋊C4×Dic5C2211yescharacteristic
78#65263C2211yescharacteristic
79#65262C2211yescharacteristic
80#65261C2211yescharacteristic
81#65261C2211yescharacteristic
82#65261C2211yescharacteristic
83#65261C2211yescharacteristic
84#65261C2211yescharacteristic
85#65241C2211yescharacteristic
86#65241C2211yescharacteristic
87#65241C2211yescharacteristic
88#65241C2211yescharacteristic
89#65240C2211yescharacteristic
90#65240C2211yescharacteristic
91#65240C2211yescharacteristic
92#65239C2211yescharacteristic
93#65239C2211yescharacteristic
94#65238C2211yescharacteristic
95#65237C2211yescharacteristic
96#65236C2211yescharacteristic
97#65236C2211yescharacteristic
98#65235C2211yescharacteristic
99#65235C2211yescharacteristic
100#65234C2211yescharacteristic
101#65234C2211yescharacteristic
102#65234C2211yescharacteristic
103#65234C2211yescharacteristic
104#65233C2211yescharacteristic
105#65233C2211yescharacteristic
106#65233C2211yescharacteristic
107#65233C2211yescharacteristic
108#65233C2211yescharacteristic
109#65233C2211yescharacteristic
110#65231C2211yescharacteristic
111#65231C2211yescharacteristic
112#65222C2211yescharacteristic
113#65222C2211yescharacteristic
114#65222C2211yescharacteristic
115#65222C2211yescharacteristic
116#65222C2211yescharacteristic
117#65221C2211yescharacteristic
118#65221C2211yescharacteristic
119C4×#683C2211yescharacteristic
120C4×#683C2211yescharacteristic
121C42×Dic5C2211yescharacteristic
122#65217C2211yescharacteristic
123C5⋊#401C2211yescharacteristic
124C5⋊#401C2211yescharacteristic
125#64950C2211yescharacteristic
126#64950C2211yescharacteristic
127#64949C2211yescharacteristic
128#64949C2211yescharacteristic
129#64949C2211yescharacteristic
130#64948C2211yescharacteristic
131#64948C2211yescharacteristic
132#64948C2211yescharacteristic
133#64947C2211yescharacteristic
134#64947C2211yescharacteristic
135#64947C2211yescharacteristic
136#64947C2211yescharacteristic
137#64946C2211yescharacteristic
138#64946C2211yescharacteristic
139#64946C2211yescharacteristic
140#64946C2211yescharacteristic
141#64946C2211yescharacteristic
142#64946C2211yescharacteristic
143#64944C2211yescharacteristic
144#64944C2211yescharacteristic
145#64944C2211yescharacteristic
146#64944C2211yescharacteristic
147#64944C2211yescharacteristic
148#64944C2211yescharacteristic
149#64944C2211yescharacteristic
150#64943C2211yescharacteristic
151#64943C2211yescharacteristic
152#64943C2211yescharacteristic
153#64942C2211yescharacteristic
154#64942C2211yescharacteristic
155#64942C2211yescharacteristic
156#64942C2211yescharacteristic
157#64942C2211yescharacteristic
158#64941C2211yescharacteristic
159#64941C2211yescharacteristic
160#64941C2211yescharacteristic
161#64941C2211yescharacteristic
162#64941C2211yescharacteristic
163#64941C2211yescharacteristic
164#64941C2211yescharacteristic
165#64941C2211yescharacteristic
166#64941C2211yescharacteristic
167#64940C2211yescharacteristic
168#64940C2211yescharacteristic
169#64940C2211yescharacteristic
170#64940C2211yescharacteristic
171#64940C2211yescharacteristic
172#64939C2211yescharacteristic
173#64939C2211yescharacteristic
174#64938C2211yescharacteristic
175#64938C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64935C2211yescharacteristic
180#64935C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#37001—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C23×Dic5C2311yescharacteristic
190C22×Dic10C2311yescharacteristic
191C22×Dic10C2311yescharacteristic
192C2×C5×C4⋊C4C2311yescharacteristic
193C2×C5×C4⋊C4C2311yescharacteristic
194C2×C5×C4⋊C4C2311yescharacteristic
195C2×C5×C4⋊C4C2311yescharacteristic
196C2×C5×C4⋊C4C2311yescharacteristic
197C2×C5×C4⋊C4C2311yescharacteristic
198C2×C5×C4⋊C4C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C22⋊C4C2311yescharacteristic
201C2×C5×C22⋊C4C2311yescharacteristic
202C2×C5×C22⋊C4C2311yescharacteristic
203C2×C5×C22⋊C4C2311yescharacteristic
204C2×C5×C22⋊C4C2311yescharacteristic
205C2×C5×C22⋊C4C2311yescharacteristic
206C2×C5×C22⋊C4C2311yescharacteristic
207C2×C42×C5C2311yescharacteristic
208C2×C42×C5C2311yescharacteristic
209C2×C42×C5C2311yescharacteristic
210C2×C22⋊Dic5C2311yescharacteristic
211C2×C22⋊Dic5C2311yescharacteristic
212C2×C22⋊Dic5C2311yescharacteristic
213C2×C22⋊Dic5C2311yescharacteristic
214C2×C22⋊Dic5C2311yescharacteristic
215C2×C22⋊Dic5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C4⋊Dic5C2311yescharacteristic
218C2×C4⋊Dic5C2311yescharacteristic
219C2×C4⋊Dic5C2311yescharacteristic
220C2×C4⋊Dic5C2311yescharacteristic
221C2×C4⋊Dic5C2311yescharacteristic
222C2×C4⋊Dic5C2311yescharacteristic
223C2×C4⋊Dic5C2311yescharacteristic
224C2×C4⋊Dic5C2311yescharacteristic
225C2×C4⋊Dic5C2311yescharacteristic
226C2×#683C2311yescharacteristic
227C2×#683C2311yescharacteristic
228C2×#683C2311yescharacteristic
229C2×#683C2311yescharacteristic
230C2×#683C2311yescharacteristic
231C2×#683C2311yescharacteristic
232C2×#683C2311yescharacteristic
233C2×#683C2311yescharacteristic
234C2×#683C2311yescharacteristic
235C2×#683C2311yescharacteristic
236C2×#683C2311yescharacteristic
237C2×#683C2311yescharacteristic
238C2×#683C2311yescharacteristic
239C2×#683C2311yescharacteristic
240C2×#683C2311yescharacteristic
241C2×#683C2311yescharacteristic
242C2×#683C2311yescharacteristic
243C2×#683C2311yescharacteristic
244C2×#683C2311yescharacteristic
245C2×#683C2311yescharacteristic
246C2×#683C2311yescharacteristic
247C2×#683C2311yescharacteristic
248C2×#683C2311yescharacteristic
249C2×#683C2311yescharacteristic
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
254C2×C4×Dic5C2311yescharacteristic
255C2×C4×Dic5C2311yescharacteristic
256C2×C4×Dic5C2311yescharacteristic
257C2×C4×Dic5C2311yescharacteristic
258C2×C4×Dic5C2311yescharacteristic
259C2×C4×Dic5C2311yescharacteristic
260C2×C4×Dic5C2311yescharacteristic
261C2×C4×Dic5C2311yescharacteristic
262C2×C4×Dic5C2311yescharacteristic
263C2×C4×Dic5C2311yescharacteristic
264C2×C4×Dic5C2311yescharacteristic
265C2×C4×Dic5C2311yescharacteristic
266C2×C4×Dic5C2311yescharacteristic
267C2×C4×Dic5C2311yescharacteristic
268C2×C4×Dic5C2311yescharacteristic
269#4035—24no—
270#4023—24no—
271C4×Dic10—24no—
272C5×#95C2311yescharacteristic
273C5×#95C2311yescharacteristic
274C5×#95C2311yescharacteristic
275C5×#95C2311yescharacteristic
276C5×#95C2311yescharacteristic
277C5×#95C2311yescharacteristic
278C5×#95C2311yescharacteristic
279C5×#95C2311yescharacteristic
280C5×#95C2311yescharacteristic
281C5×#95C2311yescharacteristic
282C5×#95C2311yescharacteristic
283C5×#95C2311yescharacteristic
284C5×#95C2311yescharacteristic
285C5×#95C2311yescharacteristic
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288#3963C2311yescharacteristic
289#3963C2311yescharacteristic
290#3963C2311yescharacteristic
291#3963C2311yescharacteristic
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#2866—51no—
347#2863—51no—
348#2799—51no—
349#2798—51no—
350#2794—51no—
351#2793—51no—
352#2792—51no—
353#2791—51no—
354#2789—51no—
355#2788—51no—
356#2788—51no—
357#2770—51no—
358#2770—51no—
359#2769—51no—
360#2762—51no—
361#2759—51no—
362#2758—51no—
363#2754—51no—
364#2655—51no—
365#2650D511yescharacteristic
366#2611—51no—
367#2605—51no—
368#2599—51no—
369#2594—51no—
370#2588—51no—
371#2565—51no—
372#2533—51no—
373#2532—51no—
374#2336—51no—
375#2314—51no—
376#2295—51no—
377C24×C5C2411yescharacteristic
378C2×C5×Q8—41no—
379C2×C5×Q8—41no—
380C2×C5×Q8—41no—
381C22×C4×C5C2411yescharacteristic
382C22×C4×C5C2411yescharacteristic
383C22×C4×C5C2411yescharacteristic
384C22×C4×C5C2411yescharacteristic
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×Dic5—22no—
396C22×Dic5—41no—
397C22×Dic5—41no—
398C22×Dic5C2411yescharacteristic
399C22×Dic5C2411yescharacteristic
400C22×Dic5C2411yescharacteristic
401C22×Dic5C2411yescharacteristic
402C22×Dic5C2411yescharacteristic
403C22×Dic5C2411yescharacteristic
404C22×Dic5C2411yescharacteristic
405C22×Dic5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C2×Dic10—22no—
415C2×Dic10—22no—
416C2×Dic10—22no—
417C2×Dic10—41no—
418C2×Dic10—41no—
419C2×Dic10—41no—
420C5×C4⋊C4—22no—
421C5×C4⋊C4—41no—
422C5×C4⋊C4—41no—
423C5×C4⋊C4—41no—
424C5×C4⋊C4—41no—
425C5×C4⋊C4—41no—
426C5×C4⋊C4—41no—
427C5×C4⋊C4—41no—
428C5×C22⋊C4—22no—
429C5×C22⋊C4—41no—
430C5×C22⋊C4—41no—
431C5×C22⋊C4—41no—
432C5×C22⋊C4—41no—
433C5×C22⋊C4—41no—
434C5×C22⋊C4—41no—
435C42×C5—22no—
436C42×C5—41no—
437C42×C5—41no—
438C22⋊Dic5—22no—
439C22⋊Dic5—22no—
440C22⋊Dic5—22no—
441C22⋊Dic5—41no—
442C22⋊Dic5—41no—
443C22⋊Dic5—41no—
444C22⋊Dic5—41no—
445C4⋊Dic5—22no—
446C4⋊Dic5—22no—
447C4⋊Dic5—41no—
448C4⋊Dic5—41no—
449C4⋊Dic5—41no—
450C4⋊Dic5—41no—
451C4⋊Dic5—41no—
452C4⋊Dic5—41no—
453C4⋊Dic5—41no—
454#683—22no—
455#683—22no—
456#683—22no—
457#683—22no—
458#683—22no—
459#683—22no—
460#683—22no—
461#683—22no—
462#683—22no—
463#683—22no—
464#683—22no—
465#683—22no—
466#683—41no—
467#683—41no—
468#683—41no—
469#683—41no—
470#683—41no—
471#683—41no—
472#683—41no—
473#683—41no—
474#683—41no—
475#683—41no—
476#683—41no—
477#683—41no—
478#683—41no—
479#683—41no—
480#683—41no—
481#683—41no—
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—
492C4×Dic5—41no—
493C4×Dic5—41no—
494C4×Dic5—41no—
495C4×Dic5—41no—
496C4×Dic5#4114yes—
497C2×#125—51no—
498C2×C4×Q8—51no—
499C2×#117—51no—
500#401—51no—
501#401—51no—
502#400—51no—
503#400—51no—
504#400—51no—
505#400—51no—
506#400—51no—
507#400—51no—
508#400—51no—
509#400—51no—
510#400—51no—
511#400—51no—
512#400—51no—
513#400—51no—
514#400—51no—
515#400—51no—
516#400C2×D511yescharacteristic
517#400C2×D511yescharacteristic
518#400C2×D511yescharacteristic
519#399—51no—
520#398—51no—
521#398—51no—
522#398—51no—
523#398—51no—
524#398—51no—
525#398—51no—
526#398—51no—
527#398—51no—
528#398—51no—
529#398—51no—
530#398—51no—
531#398—51no—
532#397—51no—
533#397—51no—
534#397—51no—
535#397—51no—
536#397C2×D511yescharacteristic
537#397C2×D511yescharacteristic
538#396—51no—
539#396C2×D511yescharacteristic
540#395—51no—
541#395—51no—
542#395—51no—
543#395—51no—
544#395C2×D511yescharacteristic
545#393—51no—
546#393—51no—
547#393C2×D511yescharacteristic
548#391—51no—
549#391—51no—
550#391—51no—
551#391—51no—
552#391—51no—
553#391—51no—
554#391—51no—
555#391—51no—
556#391—51no—
557#391—51no—
558#391—51no—
559#391C2×D511yescharacteristic
560#389—51no—
561#389—51no—
562#389—51no—
563#389—51no—
564#389—51no—
565#389—51no—
566#389—51no—
567#389—51no—
568#389—51no—
569#389—51no—
570#388—51no—
571#388—51no—
572#388—51no—
573#388—51no—
574#388—51no—
575#388—51no—
576#388—51no—
577#388—51no—
578#388—51no—
579#388—51no—
580#388—51no—
581#388—51no—
582#388—51no—
583#388C2×D511yescharacteristic
584#388C2×D511yescharacteristic
585#388C2×D511yescharacteristic
586#387—51no—
587#387—51no—
588#387—51no—
589#387—51no—
590#387—51no—
591#387—51no—
592#387—51no—
593#387—51no—
594#387—51no—
595#387—51no—
596#387—51no—
597#387—51no—
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#387C2×D511yescharacteristic
627#387C2×D511yescharacteristic
628#385—51no—
629#385—51no—
630#385—51no—
631#385—51no—
632#384—51no—
633#384—51no—
634#383—51no—
635#383—51no—
636#383—51no—
637#383—51no—
638#383—51no—
639#382—51no—
640#382—51no—
641#380—51no—
642#380—51no—
643C4×C4⋊C4—51no—
644C4×C4⋊C4—51no—
645C4×C4⋊C4—51no—
646C4×C4⋊C4—51no—
647C4×C4⋊C4—51no—
648C4×C4⋊C4C2×D511yescharacteristic
649#376—51no—
650#376—51no—
651C43—51no—
652C23×C5—21no—
653C23×C5—21no—
654C23×C5—21no—
655C23×C5—21no—
656C23×C5—21no—
657C23×C5—21no—
658C23×C5—21no—
659C23×C5C2511yescharacteristic
660C5×Q8—82no—
661C2×C4×C5—21no—
662C2×C4×C5—21no—
663C2×C4×C5—21no—
664C2×C4×C5—21no—
665C2×C4×C5—21no—
666C2×C4×C5—21no—
667C2×C4×C5—21no—
668C2×C4×C5—21no—
669C2×C4×C5—21no—
670C2×C4×C5—21no—
671C2×C4×C5—21no—
672C2×C4×C5—21no—
673C2×C4×C5—21no—
674C2×C4×C5—21no—
675C2×C4×C5—21no—
676C2×C4×C5—21no—
677C2×C4×C5—21no—
678C2×C4×C5—21no—
679C2×C4×C5—21no—
680C2×C4×C5—21no—
681C2×C4×C5—21no—
682C2×C4×C5—21no—
683C2×C4×C5—21no—
684C2×C4×C5—21no—
685C2×C4×C5—21no—
686C2×C4×C5—21no—
687C2×C4×C5—21no—
688C2×C4×C5—21no—
689C2×C4×C5—21no—
690C2×C4×C5—21no—
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×C5C2×#4112yes—
703C2×Dic5—21no—
704C2×Dic5—21no—
705C2×Dic5—21no—
706C2×Dic5—21no—
707C2×Dic5—21no—
708C2×Dic5—21no—
709C2×Dic5—21no—
710C2×Dic5—21no—
711C2×Dic5—21no—
712C2×Dic5—21no—
713C2×Dic5—21no—
714C2×Dic5—21no—
715C2×Dic5—21no—
716C2×Dic5—21no—
717C2×Dic5—21no—
718C2×Dic5—21no—
719C2×Dic5—21no—
720C2×Dic5—21no—
721C2×Dic5—21no—
722C2×Dic5—21no—
723C2×Dic5—21no—
724C2×Dic5—21no—
725C2×Dic5—21no—
726C2×Dic5—21no—
727C2×Dic5—21no—
728C2×Dic5—21no—
729C2×Dic5—21no—
730C2×Dic5—21no—
731C2×Dic5—21no—
732C2×Dic5—21no—
733C2×Dic5—21no—
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—44no—
748C2×Dic5C2×#4112yes—
749C2×Dic5C2×#4112yes—
750C2×Dic52−1+412yes—
751C2×Dic52−1+412yes—
752Dic10—44no—
753Dic10—82no—
754C22×Q8—51no—
755C22×Q8—51no—
756C22×Q8C22×D511yescharacteristic
757C23×C4—51no—
758#125—104no—
759C4×Q8—104no—
760#117—104no—
761C2×C4⋊C4—51no—
762C2×C4⋊C4—51no—
763C2×C4⋊C4—51no—
764C2×C4⋊C4—51no—
765C2×C4⋊C4—51no—
766C2×C4⋊C4—51no—
767C2×C4⋊C4—51no—
768C2×C4⋊C4—51no—
769C2×C4⋊C4—51no—
770C2×C4⋊C4—51no—
771C2×C4⋊C4—51no—
772C2×C4⋊C4—51no—
773C2×C4⋊C4—51no—
774C2×C4⋊C4—51no—
775C2×C4⋊C4—51no—
776C2×C4⋊C4—51no—
777C2×C4⋊C4—51no—
778C2×C4⋊C4—51no—
779C2×C4⋊C4—51no—
780C2×C4⋊C4—51no—
781C2×C4⋊C4—51no—
782C2×C4⋊C4—51no—
783C2×C4⋊C4—51no—
784C2×C4⋊C4—51no—
785C2×C4⋊C4—51no—
786C2×C4⋊C4—51no—
787C2×C4⋊C4—51no—
788C2×C4⋊C4—51no—
789C2×C4⋊C4—51no—
790C2×C4⋊C4—51no—
791C2×C4⋊C4—51no—
792C2×C4⋊C4—51no—
793C2×C4⋊C4—51no—
794C2×C4⋊C4—51no—
795C2×C4⋊C4—51no—
796C2×C4⋊C4—51no—
797C2×C4⋊C4—51no—
798C2×C4⋊C4C22×D511yescharacteristic
799C2×C4⋊C4C22×D511yescharacteristic
800C2×C4⋊C4C22×D511yescharacteristic
801C2×C4⋊C4C22×D511yescharacteristic
802C2×C4⋊C4C22×D511yescharacteristic
803C2×C4⋊C4C22×D511yescharacteristic
804C2×C4⋊C4C22×D511yescharacteristic
805C2×C4⋊C4C22×D511yescharacteristic
806C2×C22⋊C4—51no—
807C2×C22⋊C4—51no—
808C2×C22⋊C4—51no—
809C2×C22⋊C4—51no—
810C2×C22⋊C4—51no—
811C2×C22⋊C4—51no—
812C2×C22⋊C4—51no—
813C2×C22⋊C4C22×D511yescharacteristic
814C2×C22⋊C4C22×D511yescharacteristic
815C2×C22⋊C4C22×D511yescharacteristic
816C2×C22⋊C4C22×D511yescharacteristic
817C2×C22⋊C4C22×D511yescharacteristic
818C2×C22⋊C4C22×D511yescharacteristic
819C2×C22⋊C4C22×D511yescharacteristic
820C2×C42—51no—
821C2×C42—51no—
822C2×C42—51no—
823C2×C42—51no—
824C2×C42—51no—
825C2×C42—51no—
826C2×C42—51no—
827C2×C42—51no—
828C2×C42—51no—
829C2×C42—51no—
830C2×C42—51no—
831C2×C42—51no—
832C2×C42—51no—
833C2×C42—51no—
834C2×C42—51no—
835C2×C42C22×D511yescharacteristic
836C2×C42C22×D511yescharacteristic
837C2×C42C22×D511yescharacteristic
838#95—51no—
839#95—51no—
840#95—51no—
841#95—51no—
842#95—51no—
843#95—51no—
844#95—51no—
845#95—51no—
846#95—51no—
847#95—51no—
848#95—51no—
849#95—51no—
850#95—51no—
851#95—51no—
852#95—51no—
853#95—51no—
854#95—51no—
855#95—51no—
856#95—51no—
857#95—51no—
858#95—51no—
859#95—51no—
860#95—51no—
861#95—51no—
862#95—51no—
863#95—51no—
864#95—51no—
865#95—51no—
866#95—51no—
867#95—51no—
868#95—51no—
869#95—51no—
870#95—51no—
871#95—51no—
872#95—51no—
873#95—51no—
874#95—51no—
875#95—51no—
876#95—51no—
877#95—51no—
878#95—51no—
879#95—51no—
880#95—51no—
881#95—51no—
882#95—51no—
883#95—51no—
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#95C22×D511yescharacteristic
897#95C22×D511yescharacteristic
898#95C22×D511yescharacteristic
899#95C22×D511yescharacteristic
900#95C22×D511yescharacteristic
901#95C22×D511yescharacteristic
902#95C22×D511yescharacteristic
903#95C22×D511yescharacteristic
904#95C22×D511yescharacteristic
905#95C22×D511yescharacteristic
906#95C22×D511yescharacteristic
907#95C22×D511yescharacteristic
908#95C22×D511yescharacteristic
909#95C22×D511yescharacteristic
910#95C22×D511yescharacteristic
911#95C22×D511yescharacteristic
912C22×C5—41no—
913C22×C5—41no—
914C22×C5—41no—
915C22×C5—41no—
916C22×C5—41no—
917C22×C5—41no—
918C22×C5—41no—
919C22×C5C22×#4111yescharacteristic
920C22×C5C2×2−1+411yescharacteristic
921C22×C5C2×2−1+411yescharacteristic
922C22×C5#58511yescharacteristic
923C22×C5#58511yescharacteristic
924C22×C5#58511yescharacteristic
925C22×C5#58511yescharacteristic
926C4×C5—22no—
927C4×C5—41no—
928C4×C5—41no—
929C4×C5—41no—
930C4×C5—41no—
931C4×C5—41no—
932C4×C5—41no—
933C4×C5—41no—
934C4×C5—41no—
935C4×C5—41no—
936C4×C5—41no—
937C4×C5—41no—
938C4×C5—41no—
939C4×C5—41no—
940Dic5—22no—
941Dic5—22no—
942Dic5—22no—
943Dic5—22no—
944Dic5—41no—
945Dic5—41no—
946Dic5—41no—
947Dic5—41no—
948Dic5—41no—
949Dic5—41no—
950Dic5—41no—
951Dic5—41no—
952Dic5—41no—
953Dic5—41no—
954Dic5—41no—
955Dic5—41no—
956C24C23×D511yescharacteristic
957C2×Q8—41no—
958C2×Q8—41no—
959C2×Q8—41no—
960C2×Q8—102no—
961C2×Q8—102no—
962C2×Q8—102no—
963C2×Q8—201no—
964C2×Q8—201no—
965C2×Q8—201no—
966C22×C4—51no—
967C22×C4—51no—
968C22×C4—51no—
969C22×C4—51no—
970C22×C4—51no—
971C22×C4—51no—
972C22×C4—51no—
973C22×C4—51no—
974C22×C4—51no—
975C22×C4—51no—
976C22×C4—51no—
977C22×C4—51no—
978C22×C4—51no—
979C22×C4—51no—
980C22×C4—51no—
981C22×C4—51no—
982C22×C4—102no—
983C22×C4—201no—
984C22×C4—201no—
985C22×C4C23×D511yescharacteristic
986C22×C4C23×D511yescharacteristic
987C22×C4C23×D511yescharacteristic
988C22×C4C23×D511yescharacteristic
989C22×C4C23×D511yescharacteristic
990C22×C4C23×D511yescharacteristic
991C22×C4C23×D511yescharacteristic
992C22×C4C23×D511yescharacteristic
993C22×C4C23×D511yescharacteristic
994C22×C4C23×D511yescharacteristic
995C22×C4C23×D511yescharacteristic
996C22×C4C23×D511yescharacteristic
997C22×C4C23×D511yescharacteristic
998C22×C4C23×D511yescharacteristic
999C4⋊C4—22no—
1000C4⋊C4—41no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—102no—
1008C4⋊C4—102no—
1009C4⋊C4—102no—
1010C4⋊C4—102no—
1011C4⋊C4—102no—
1012C4⋊C4—102no—
1013C4⋊C4—102no—
1014C4⋊C4—102no—
1015C4⋊C4—102no—
1016C4⋊C4—102no—
1017C4⋊C4—102no—
1018C4⋊C4—102no—
1019C4⋊C4—102no—
1020C4⋊C4—102no—
1021C4⋊C4—201no—
1022C4⋊C4—201no—
1023C4⋊C4—201no—
1024C4⋊C4—201no—
1025C4⋊C4—201no—
1026C4⋊C4—201no—
1027C4⋊C4—201no—
1028C4⋊C4—201no—
1029C4⋊C4—201no—
1030C4⋊C4—201no—
1031C4⋊C4—201no—
1032C4⋊C4—201no—
1033C4⋊C4—201no—
1034C4⋊C4—201no—
1035C4⋊C4—201no—
1036C4⋊C4—201no—
1037C4⋊C4—201no—
1038C4⋊C4—201no—
1039C4⋊C4—201no—
1040C4⋊C4—201no—
1041C4⋊C4—201no—
1042C4⋊C4—201no—
1043C4⋊C4—201no—
1044C22⋊C4—22no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—102no—
1052C22⋊C4—102no—
1053C22⋊C4—102no—
1054C22⋊C4—201no—
1055C22⋊C4—201no—
1056C22⋊C4—201no—
1057C22⋊C4—201no—
1058C42—22no—
1059C42—41no—
1060C42—41no—
1061C42—54no—
1062C42—102no—
1063C42—102no—
1064C42—102no—
1065C42—102no—
1066C42—201no—
1067C42—201no—
1068C42—201no—
1069C42—201no—
1070C42—201no—
1071C42—201no—
1072C42—201no—
1073C42—201no—
1074C42—201no—
1075C42—201no—
1076C2×C5—81no—
1077C2×C5#345511yescharacteristic
1078C2×C5#349511yescharacteristic
1079C2×C5#350711yescharacteristic
1080C2×C5#355511yescharacteristic
1081C2×C5#356411yescharacteristic
1082C2×C5#356511yescharacteristic
1083C2×C5#356611yescharacteristic
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23C24×D511yescharacteristic
1092Q8—82no—
1093Q8—204no—
1094Q8—402no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—52no—
1137C2×C4—52no—
1138C2×C4—52no—
1139C2×C4—52no—
1140C2×C4—101no—
1141C2×C4—101no—
1142C2×C4—101no—
1143C2×C4—101no—
1144C2×C4—101no—
1145C2×C4—101no—
1146C2×C4—101no—
1147C2×C4—101no—
1148C2×C4—101no—
1149C2×C4—101no—
1150C2×C4—101no—
1151C2×C4—101no—
1152C2×C4—101no—
1153C2×C4—101no—
1154C2×C4—101no—
1155C2×C4—101no—
1156C2×C4—101no—
1157C2×C4—101no—
1158C2×C4—101no—
1159C2×C4—101no—
1160C2×C4—101no—
1161C2×C4—101no—
1162C2×C4—101no—
1163C2×C4—101no—
1164C2×C4—101no—
1165C2×C4—101no—
1166C2×C4—101no—
1167C2×C4—101no—
1168C2×C4—101no—
1169C2×C4—101no—
1170C2×C4—101no—
1171C2×C4—101no—
1172C2×C4—101no—
1173C2×C4—101no—
1174C2×C4—101no—
1175C2×C4—101no—
1176C2×C4—101no—
1177C2×C4—101no—
1178C2×C4—101no—
1179C2×C4—101no—
1180C2×C4—101no—
1181C2×C4—101no—
1182C2×C4—101no—
1183C2×C4—101no—
1184C2×C4—204no—
1185C2×C4D5×#4112yes—
1186C5#3700111yescharacteristic, complemented, Sylow
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22C2×D5×#4111yescharacteristic
1195C22#6628311yescharacteristic
1196C22#6628311yescharacteristic
1197C22#6628511yescharacteristic
1198C22#6628511yescharacteristic
1199C22D5×2−1+411yescharacteristic
1200C22D5×2−1+411yescharacteristic
1201C4—22no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—102no—
1216C4—102no—
1217C4—102no—
1218C4—102no—
1219C4—201no—
1220C4—201no—
1221C4—201no—
1222C4—201no—
1223C4—201no—
1224C4—201no—
1225C4—201no—
1226C4—201no—
1227C4—201no—
1228C4—201no—
1229C4—201no—
1230C4—201no—
1231C2—81no—
1232C2#1061804711yescharacteristic
1233C2#1061831011yescharacteristic
1234C2#1061833211yescharacteristic
1235C2#1061840211yescharacteristic
1236C2#1061844511yescharacteristic
1237C2#1061845211yescharacteristic
1238C2#1061847111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2650C2
prime radicalC24×C5C24
hypercenter#2650D5
hypocenterC5#37001
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2650

Complements

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

NH ≅ G/Ntype
2. #10610038C2semidirect
3. #10610032C2semidirect
4. #10610029C2semidirect
5. #10610027C2semidirect
6. #10610003C2semidirect
7. #10609990C2semidirect
14. #10608967C2semidirect
15. #10608959C2semidirect
18. #10608287C2semidirect
19. #10608283C2semidirect
26. #10607022C2semidirect
27. #10606807C2semidirect
28. #10606803C2semidirect
29. #10606688C2semidirect
30. #10605477C2semidirect
31. #10605350C2semidirect
1186. C5#37001semidirect

Maximal subgroups

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

subgroupindex
C5×#26502
#106100382
#106100322
#106100292
#106100272
#106100032
#106099902
#106093722
#106093472
#106093462
#106093372
#106091272
#106091242
#106089672
#106089592
#106085802
#106085722
#106082872
#106082832
#106075542
#106073822
#106073732
#106073582
#106073222
#106071872
#106070222
#106068072
#106068032
#106066882
#106054772
#106053502
#370015