Finite Group Databasebeta

← #12307117

Subgroups — #12307117

Order 1280.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2441C211yesmaximal, characteristic, complemented
2#10614785C211yesmaximal, characteristic, complemented
3#10614782C211yesmaximal, characteristic, complemented
4#10613999C211yesmaximal, characteristic
5#10613978C211yesmaximal, characteristic, complemented
6#10609850C211yesmaximal, characteristic
7#10609816C211yesmaximal, characteristic
8#10609811C211yesmaximal, characteristic, complemented
9#10609811C211yesmaximal, characteristic, complemented
10#10609176C211yesmaximal, characteristic
11#10609125C211yesmaximal, characteristic, complemented
12#10609108C211yesmaximal, characteristic
13#10609083C211yesmaximal, characteristic, complemented
14#10608018C211yesmaximal, characteristic, complemented
15#10608013C211yesmaximal, characteristic, complemented
16#10607987C211yesmaximal, characteristic, complemented
17#10607905C211yesmaximal, characteristic, complemented
18#10607875C211yesmaximal, characteristic, complemented
19#10607867C211yesmaximal, characteristic, complemented
20#10607830C211yesmaximal, characteristic, complemented
21#10607829C211yesmaximal, characteristic, complemented
22#10607176C211yesmaximal, characteristic, complemented
23#10606879C211yesmaximal, characteristic, complemented
24#10606864C211yesmaximal, characteristic, complemented
25#10606809C211yesmaximal, characteristic, complemented
26#10606104C211yesmaximal, characteristic, complemented
27#10606080C211yesmaximal, characteristic, complemented
28#10605676C211yesmaximal, characteristic, complemented
29#10605601C211yesmaximal, characteristic
30#10605299C211yesmaximal, characteristic
31#10605285C211yesmaximal, characteristic, complemented
32C2×C5×#125C2211yescharacteristic
33C2×C5×#117C2211yescharacteristic
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4043C2211yescharacteristic
36C2×#4035C2211yescharacteristic
37C2×#4024C2211yescharacteristic
38C2×C42×D5C2211yescharacteristic
39C5×#399C2211yescharacteristic
40C5×#399C2211yescharacteristic
41C5×#396C2211yescharacteristic
42C5×#396C2211yescharacteristic
43C5×#389C2211yescharacteristic
44C5×#389C2211yescharacteristic
45C5×#389C2211yescharacteristic
46C5×#389C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C5×#384C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C22⋊C4C2211yescharacteristic
52#65500C2211yescharacteristic
53C4×C22⋊Dic5C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65283C2211yescharacteristic
56#65283C2211yescharacteristic
57#65283C2211yescharacteristic
58#65281C2211yescharacteristic
59#65281C2211yescharacteristic
60#65281C2211yescharacteristic
61#65279C2211yescharacteristic
62#65279C2211yescharacteristic
63#65278C2211yescharacteristic
64#65278C2211yescharacteristic
65#65278C2211yescharacteristic
66#65278C2211yescharacteristic
67#65278C2211yescharacteristic
68#65278C2211yescharacteristic
69#65276C2211yescharacteristic
70#65275C2211yescharacteristic
71#65275C2211yescharacteristic
72#65275C2211yescharacteristic
73#65274C2211yescharacteristic
74#65274C2211yescharacteristic
75#65273C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65273C2211yescharacteristic
82#65273C2211yescharacteristic
83#65273C2211yescharacteristic
84#65273C2211yescharacteristic
85#65272C2211yescharacteristic
86#65272C2211yescharacteristic
87#65272C2211yescharacteristic
88#65272C2211yescharacteristic
89#65272C2211yescharacteristic
90#65272C2211yescharacteristic
91#65272C2211yescharacteristic
92#65270C2211yescharacteristic
93#65270C2211yescharacteristic
94#65270C2211yescharacteristic
95#65270C2211yescharacteristic
96#65269C2211yescharacteristic
97#65269C2211yescharacteristic
98#65269C2211yescharacteristic
99#65269C2211yescharacteristic
100#65268C2211yescharacteristic
101#65268C2211yescharacteristic
102#65267C2211yescharacteristic
103#65267C2211yescharacteristic
104#65267C2211yescharacteristic
105#65267C2211yescharacteristic
106#65267C2211yescharacteristic
107#65265C2211yescharacteristic
108#65263C2211yescharacteristic
109#65262C2211yescharacteristic
110#65262C2211yescharacteristic
111#65261C2211yescharacteristic
112#65261C2211yescharacteristic
113#65261C2211yescharacteristic
114#65261C2211yescharacteristic
115#65261C2211yescharacteristic
116#65261C2211yescharacteristic
117#65247C2211yescharacteristic
118#65247C2211yescharacteristic
119#65246C2211yescharacteristic
120#65246C2211yescharacteristic
121#65245C2211yescharacteristic
122#65245C2211yescharacteristic
123#65239C2211yescharacteristic
124#65239C2211yescharacteristic
125#65239C2211yescharacteristic
126#65237C2211yescharacteristic
127#65237C2211yescharacteristic
128#65237C2211yescharacteristic
129#65237C2211yescharacteristic
130#65235C2211yescharacteristic
131#65235C2211yescharacteristic
132#65235C2211yescharacteristic
133#65233C2211yescharacteristic
134#65233C2211yescharacteristic
135#65233C2211yescharacteristic
136#65233C2211yescharacteristic
137#65231C2211yescharacteristic
138#65231C2211yescharacteristic
139#65231C2211yescharacteristic
140#65229C2211yescharacteristic
141#65229C2211yescharacteristic
142C4×#685C2211yescharacteristic
143#65222C2211yescharacteristic
144#65222C2211yescharacteristic
145#65222C2211yescharacteristic
146#65222C2211yescharacteristic
147#65222C2211yescharacteristic
148#65222C2211yescharacteristic
149#65221C2211yescharacteristic
150C4×#683C2211yescharacteristic
151#65218C2211yescharacteristic
152#65217C2211yescharacteristic
153#65217C2211yescharacteristic
154#65217C2211yescharacteristic
155#64966C2211yescharacteristic
156#64965C2211yescharacteristic
157#64957C2211yescharacteristic
158#64957C2211yescharacteristic
159#64956C2211yescharacteristic
160#64956C2211yescharacteristic
161#64953C2211yescharacteristic
162#64953C2211yescharacteristic
163#64948C2211yescharacteristic
164#64947C2211yescharacteristic
165#64947C2211yescharacteristic
166#64946C2211yescharacteristic
167#64946C2211yescharacteristic
168#64946C2211yescharacteristic
169#64944C2211yescharacteristic
170#64944C2211yescharacteristic
171#64944C2211yescharacteristic
172#64944C2211yescharacteristic
173#64943C2211yescharacteristic
174#64943C2211yescharacteristic
175#64941C2211yescharacteristic
176#64940C2211yescharacteristic
177#64939C2211yescharacteristic
178#64939C2211yescharacteristic
179#64939C2211yescharacteristic
180#64938C2211yescharacteristic
181#64937C2211yescharacteristic
182#64936C2211yescharacteristic
183#64936C2211yescharacteristic
184#64936C2211yescharacteristic
185#64936C2211yescharacteristic
186#64935C2211yescharacteristic
187#36756—51nomaximal, Sylow
188C23×C4×C5C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C23×Dic5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C5×#125—42no—
197C5×#117—42no—
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×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C5×C4⋊C4C2311yescharacteristic
213C2×C5×C4⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
223C2×C42×C5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C4×C22⋊D5Q818yescomplemented
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
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×#683C2311yescharacteristic
275C2×#683C2311yescharacteristic
276C2×#683C2311yescharacteristic
277C2×#683C2311yescharacteristic
278C2×#683C2311yescharacteristic
279C2×#683C2311yescharacteristic
280C2×#683C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290#4043—42no—
291#4035—42no—
292#4024—42no—
293C42×D5—42no—
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#2855—51no—
351#2851—51no—
352#2807—51no—
353#2802—51no—
354#2791—51no—
355#2790—51no—
356#2790—51no—
357#2780—51no—
358#2780—51no—
359#2768—51no—
360#2768—51no—
361#2768—51no—
362#2755—51no—
363#2748—51no—
364#2732—51no—
365#2726—51no—
366#2720—51no—
367#2704—51no—
368#2667—51no—
369#2667—51no—
370#2612—51no—
371#2608—51no—
372#2606—51no—
373#2606—51no—
374#2570—51no—
375#2569—51no—
376#2441D511yescharacteristic, complemented
377#2438—51no—
378#2319—51no—
379#2318—51no—
380#2290—51no—
381C24×C5C2411yescharacteristic
382C23×D5C2411yescharacteristic
383C22×C4×C5—41no—
384C22×C4×C5—41no—
385C22×C4×C5C2×Q814yes—
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
399C22×C4×C5C2411yescharacteristic
400C2×C22⋊D5—41no—
401C2×C22⋊D5—41no—
402C2×C22⋊D5C2×Q814yes—
403C22×Dic5—41no—
404C22×Dic5—41no—
405C22×Dic5—41no—
406C22×Dic5—41no—
407C22×Dic5—41no—
408C22×Dic5—41no—
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C2×C4×D5—22no—
425C2×C4×D5—41no—
426C2×C4×D5—41no—
427C2×C4×D5—41no—
428C2×C4×D5—41no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×C4×D5C2×Q814yes—
433C2×Dic10—22no—
434C2×Dic10—41no—
435C2×Dic10—41no—
436C5×C4⋊C4—22no—
437C5×C4⋊C4—22no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—41no—
440C5×C4⋊C4—41no—
441C5×C4⋊C4—41no—
442C5×C4⋊C4—41no—
443C5×C4⋊C4—41no—
444C5×C4⋊C4—41no—
445C5×C4⋊C4—41no—
446C5×C4⋊C4—41no—
447C5×C4⋊C4—41no—
448C5×C4⋊C4—41no—
449C5×C4⋊C4—41no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C5×C22⋊C4—22no—
453C5×C22⋊C4—41no—
454C5×C22⋊C4—41no—
455C5×C22⋊C4—41no—
456C5×C22⋊C4—41no—
457C5×C22⋊C4—41no—
458C42×C5—22no—
459C42×C5—41no—
460C42×C5—41no—
461C42×C5—41no—
462C22⋊Dic5—41no—
463C22⋊Dic5—41no—
464C22⋊Dic5—41no—
465C22⋊Dic5—41no—
466C22⋊Dic5C2×Q814yes—
467#685—41no—
468#685—41no—
469#685—41no—
470#685—41no—
471#685—41no—
472#685—41no—
473#685—41no—
474#685—41no—
475#685—41no—
476#685—41no—
477#685C2×Q814yes—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489#683—22no—
490#683—41no—
491#683—41no—
492#683—41no—
493#683—41no—
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—
512#683—41no—
513#683—41no—
514#683—41no—
515#683—41no—
516#683—41no—
517#683C2×Q814yes—
518C4×Dic5—22no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C4×Dic5—41no—
522C4×Dic5—41no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5C2×Q814yes—
527C2×#125—51no—
528C2×#125C2×D511yescharacteristic
529C2×C22⋊Q8—51no—
530C2×C22⋊Q8—51no—
531C2×C4×D4—51no—
532C2×#117C2×D511yescharacteristic
533C22×C42—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#399—51no—
541#399—51no—
542#399—51no—
543#399—51no—
544#399C2×D511yescharacteristic
545#399C2×D511yescharacteristic
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#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#398—51no—
567#398—51no—
568#398—51no—
569#398—51no—
570#396—51no—
571#396—51no—
572#396—51no—
573#396—51no—
574#396—51no—
575#396—51no—
576#396—51no—
577#396—51no—
578#396C2×D511yescharacteristic
579#396C2×D511yescharacteristic
580#395—51no—
581#395—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#390—51no—
586#390—51no—
587#389—51no—
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#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—51no—
604#389C2×D511yescharacteristic
605#389C2×D511yescharacteristic
606#389C2×D511yescharacteristic
607#389C2×D511yescharacteristic
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388—51no—
613#388—51no—
614#388—51no—
615#388—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#387C2×D511yescharacteristic
639#387C2×D511yescharacteristic
640#386—51no—
641#386—51no—
642#386—51no—
643#386—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#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385—51no—
657#385—51no—
658#384—51no—
659#384C2×D511yescharacteristic
660#383—51no—
661#382—51no—
662#382—51no—
663#382—51no—
664#381—51no—
665#381—51no—
666#381—51no—
667#380—51no—
668#380—51no—
669#380—51no—
670#380—51no—
671#380—51no—
672#380—51no—
673#380C2×D511yescharacteristic
674C4×C4⋊C4—51no—
675C4×C4⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4C2×D511yescharacteristic
679#376—51no—
680#376—51no—
681C2×#95—51no—
682C23×C5—21no—
683C23×C5—21no—
684C23×C5—21no—
685C23×C5—21no—
686C23×C5—21no—
687C23×C5—21no—
688C23×C5C22×Q812yes—
689C23×C5C2511yescharacteristic
690C22×D5—21no—
691C22×D5—21no—
692C22×D5—21no—
693C22×D5—21no—
694C22×D5—21no—
695C22×D5—21no—
696C22×D5C22×Q812yes—
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—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—44no—
737C2×C4×C5C22×Q812yes—
738C2×C4×C5C22×Q812yes—
739C2×C4×C5H(5,𝔽2)12yes—
740C22⋊D5—44no—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—82no—
784C2×Dic5—82no—
785C2×Dic5C22×Q812yes—
786C2×Dic5C22×Q812yes—
787C2×Dic5C22×Q812yes—
788C4×D5—44no—
789C4×D5—44no—
790C4×D5—44no—
791Dic10—82no—
792C22×Q8—51no—
793C22×D4—51no—
794C23×C4—51no—
795C23×C4—51no—
796C23×C4—51no—
797C23×C4—51no—
798C23×C4—51no—
799C23×C4C22×D511yescharacteristic
800#125—42no—
801#125—202no—
802C22⋊Q8—202no—
803C22⋊Q8—202no—
804C4×D4—58no—
805#117—42no—
806C2×C4⋊C4—51no—
807C2×C4⋊C4—51no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—51no—
810C2×C4⋊C4—51no—
811C2×C4⋊C4—51no—
812C2×C4⋊C4—51no—
813C2×C4⋊C4—51no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4C22×D511yescharacteristic
847C2×C4⋊C4C22×D511yescharacteristic
848C2×C4⋊C4C22×D511yescharacteristic
849C2×C4⋊C4C22×D511yescharacteristic
850C2×C4⋊C4C22×D511yescharacteristic
851C2×C4⋊C4C22×D511yescharacteristic
852C2×C4⋊C4C22×D511yescharacteristic
853C2×C4⋊C4C22×D511yescharacteristic
854C2×C4⋊C4C22×D511yescharacteristic
855C2×C4⋊C4C22×D511yescharacteristic
856C2×C4⋊C4C22×D511yescharacteristic
857C2×C4⋊C4C22×D511yescharacteristic
858C2×C4⋊C4C22×D511yescharacteristic
859C2×C4⋊C4C22×D511yescharacteristic
860C2×C4⋊C4C22×D511yescharacteristic
861C2×C4⋊C4C22×D511yescharacteristic
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4—51no—
867C2×C22⋊C4—51no—
868C2×C22⋊C4—51no—
869C2×C22⋊C4—51no—
870C2×C22⋊C4—51no—
871C2×C22⋊C4—51no—
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4C22×D511yescharacteristic
879C2×C22⋊C4C22×D511yescharacteristic
880C2×C22⋊C4C22×D511yescharacteristic
881C2×C22⋊C4C22×D511yescharacteristic
882C2×C22⋊C4C22×D511yescharacteristic
883C2×C22⋊C4C22×D511yescharacteristic
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—51no—
891C2×C42—51no—
892C2×C42—51no—
893C2×C42—202no—
894C2×C42C22×D511yescharacteristic
895C2×C42C22×D511yescharacteristic
896C2×C42C22×D511yescharacteristic
897C2×C42C22×D511yescharacteristic
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954C22×C5—22no—
955C22×C5—22no—
956C22×C5—22no—
957C22×C5—41no—
958C22×C5—41no—
959C22×C5—41no—
960C22×C5—41no—
961C22×C5C23×Q811yescharacteristic
962C22×C5C2×H(5,𝔽2)11yescharacteristic
963C22×C5#58511yescharacteristic
964C22×C5#58511yescharacteristic
965C22×C5#58511yescharacteristic
966C22×C5#58511yescharacteristic
967C22×C5#58511yescharacteristic
968C2×D5—22no—
969C2×D5—22no—
970C2×D5—22no—
971C2×D5—41no—
972C2×D5—41no—
973C2×D5—41no—
974C2×D5—41no—
975C4×C5—22no—
976C4×C5—22no—
977C4×C5—22no—
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—
987C4×C5—41no—
988C4×C5—41no—
989Dic5—22no—
990Dic5—22no—
991Dic5—22no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000Dic5—41no—
1001Dic5—41no—
1002Dic5—41no—
1003Dic5—41no—
1004C24—51no—
1005C24C23×D511yescharacteristic
1006C2×Q8—102no—
1007C2×Q8—201no—
1008C2×Q8—201no—
1009C2×D4—54no—
1010C2×D4—201no—
1011C2×D4—201no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—51no—
1015C22×C4—51no—
1016C22×C4—51no—
1017C22×C4—54no—
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—102no—
1031C22×C4—201no—
1032C22×C4—201no—
1033C22×C4—201no—
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×C4Q8×D514yes—
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
1055C22×C4C23×D511yescharacteristic
1056C22×C4C23×D511yescharacteristic
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C4⋊C4—22no—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—54no—
1076C4⋊C4—102no—
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—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C22⋊C4—22no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—54no—
1122C22⋊C4—54no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C22⋊C4—201no—
1130C22⋊C4—201no—
1131C22⋊C4—201no—
1132C22⋊C4—201no—
1133C22⋊C4—201no—
1134C22⋊C4—201no—
1135C22⋊C4—201no—
1136C22⋊C4—201no—
1137C42—22no—
1138C42—41no—
1139C42—41no—
1140C42—41no—
1141C42—54no—
1142C42—102no—
1143C42—201no—
1144C42—201no—
1145C42—201no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C2×C5—42no—
1151C2×C5#345811yescharacteristic
1152C2×C5#350111yescharacteristic
1153C2×C5#350411yescharacteristic
1154C2×C5#353311yescharacteristic
1155C2×C5#353911yescharacteristic
1156C2×C5#356611yescharacteristic
1157C2×C5#356711yescharacteristic
1158D5—42no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—52no—
1166C23—101no—
1167C23—101no—
1168C23—101no—
1169C23—101no—
1170C23—101no—
1171C23—101no—
1172C23C2×Q8×D512yes—
1173C23C24×D511yescharacteristic
1174Q8—402no—
1175D4—204no—
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—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—44no—
1216C2×C4—52no—
1217C2×C4—52no—
1218C2×C4—52no—
1219C2×C4—101no—
1220C2×C4—101no—
1221C2×C4—101no—
1222C2×C4—101no—
1223C2×C4—101no—
1224C2×C4—101no—
1225C2×C4—101no—
1226C2×C4—101no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—204no—
1262C2×C4—204no—
1263C2×C4—204no—
1264C2×C4—402no—
1265C2×C4—402no—
1266C2×C4#414412yes—
1267C2×C4C2×Q8×D512yes—
1268C2×C4C2×Q8×D512yes—
1269C5#3675611yescharacteristic, complemented, Sylow
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—102no—
1278C22—102no—
1279C22—102no—
1280C22—201no—
1281C22—201no—
1282C22—201no—
1283C22—201no—
1284C22C2×#414411yescharacteristic
1285C22C22×Q8×D511yescharacteristic
1286C22#6628311yescharacteristic
1287C22#6628311yescharacteristic
1288C22#6628311yescharacteristic
1289C22#6628511yescharacteristic
1290C22#6628711yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—102no—
1306C4—102no—
1307C4—102no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C4—201no—
1313C4—201no—
1314C4—201no—
1315C4—201no—
1316C4—201no—
1317C4—201no—
1318C4—201no—
1319C4—201no—
1320C2—42no—
1321C2—202no—
1322C2#1061788711yescharacteristic
1323C2#1061817511yescharacteristic
1324C2#1061848811yescharacteristic
1325C2#1061860511yescharacteristic
1326C2#1061868711yescharacteristic
1327C2#1061877311yescharacteristic
1328C2#1061880811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2441C2
prime radicalC22×C22⋊D5C23
hypercenter#2441D5
hypocenterC5#36756
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C5×#2441C2semidirect
2. #10614785C2semidirect
3. #10614782C2semidirect
5. #10613978C2semidirect
8. #10609811C2semidirect
9. #10609811C2semidirect
11. #10609125C2semidirect
13. #10609083C2semidirect
14. #10608018C2semidirect
15. #10608013C2semidirect
16. #10607987C2semidirect
17. #10607905C2semidirect
18. #10607875C2semidirect
19. #10607867C2semidirect
20. #10607830C2semidirect
21. #10607829C2semidirect
22. #10607176C2semidirect
23. #10606879C2semidirect
24. #10606864C2semidirect
25. #10606809C2semidirect
26. #10606104C2semidirect
27. #10606080C2semidirect
28. #10605676C2semidirect
31. #10605285C2semidirect
229. C4×C22⋊D5Q8semidirect
376. #2441D5semidirect
1269. C5#36756semidirect

Maximal subgroups

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

subgroupindex
C5×#24412
#106147852
#106147822
#106139992
#106139782
#106098502
#106098162
#106098112
#106091762
#106091252
#106091082
#106090832
#106080182
#106080132
#106079872
#106079052
#106078752
#106078672
#106078302
#106078292
#106071762
#106068792
#106068642
#106068092
#106061042
#106060802
#106056762
#106056012
#106052992
#106052852
#367565