Finite Group Databasebeta

← #12306990

Subgroups — #12306990

Order 1280.

1570 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2713C211yesmaximal, characteristic, complemented
2#10614981C211yesmaximal, characteristic, complemented
3#10614964C211yesmaximal, characteristic
4#10614803C211yesmaximal, characteristic
5#10614779C211yesmaximal, characteristic, complemented
6#10610094C211yesmaximal, characteristic
7#10610088C211yesmaximal, characteristic
8#10610039C211yesmaximal, characteristic, complemented
9#10610029C211yesmaximal, characteristic, complemented
10#10609681C211yesmaximal, characteristic
11#10609639C211yesmaximal, characteristic, complemented
12#10609638C211yesmaximal, characteristic, complemented
13#10609476C211yesmaximal, characteristic
14#10608989C211yesmaximal, characteristic
15#10608982C211yesmaximal, characteristic
16#10608967C211yesmaximal, characteristic, complemented
17#10608955C211yesmaximal, characteristic, complemented
18#10608395C211yesmaximal, characteristic
19#10608358C211yesmaximal, characteristic
20#10608328C211yesmaximal, characteristic, complemented
21#10608308C211yesmaximal, characteristic, complemented
22#10607926C211yesmaximal, characteristic
23#10607900C211yesmaximal, characteristic, complemented
24#10607092C211yesmaximal, characteristic
25#10607048C211yesmaximal, characteristic
26#10607027C211yesmaximal, characteristic
27D5×#387C211yesmaximal, characteristic
28#10607010C211yesmaximal, characteristic, complemented
29#10607007C211yesmaximal, characteristic, complemented
30#10606982C211yesmaximal, characteristic, complemented
31#10606917C211yesmaximal, characteristic, complemented
32C2×C5×C4⋊Q8C2211yescharacteristic
33C2×C5×#125C2211yescharacteristic
34C2×#4092C2211yescharacteristic
35C2×#4092C2211yescharacteristic
36C2×#4090C2211yescharacteristic
37C2×#4043C2211yescharacteristic
38C2×#4042C2211yescharacteristic
39C2×#4038C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4018C2211yescharacteristic
44C2×C42×D5C2211yescharacteristic
45C5×#400C2211yescharacteristic
46C5×#400C2211yescharacteristic
47C5×#398C2211yescharacteristic
48C5×#398C2211yescharacteristic
49C5×#395C2211yescharacteristic
50C5×#395C2211yescharacteristic
51C5×#391C2211yescharacteristic
52C5×#391C2211yescharacteristic
53C5×#389C2211yescharacteristic
54C5×#387C2211yescharacteristic
55C5×#387C2211yescharacteristic
56C5×#387C2211yescharacteristic
57C5×#387C2211yescharacteristic
58#65519C2211yescharacteristic
59#65518C2211yescharacteristic
60#65518C2211yescharacteristic
61#65518C2211yescharacteristic
62#65518C2211yescharacteristic
63#65278C2211yescharacteristic
64#65278C2211yescharacteristic
65#65278C2211yescharacteristic
66#65278C2211yescharacteristic
67#65278C2211yescharacteristic
68#65276C2211yescharacteristic
69#65276C2211yescharacteristic
70#65276C2211yescharacteristic
71#65276C2211yescharacteristic
72#65275C2211yescharacteristic
73#65274C2211yescharacteristic
74#65274C2211yescharacteristic
75#65273C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65272C2211yescharacteristic
82#65272C2211yescharacteristic
83#65271C2211yescharacteristic
84#65270C2211yescharacteristic
85#65270C2211yescharacteristic
86#65270C2211yescharacteristic
87#65269C2211yescharacteristic
88#65268C2211yescharacteristic
89#65268C2211yescharacteristic
90#65268C2211yescharacteristic
91#65268C2211yescharacteristic
92#65268C2211yescharacteristic
93#65267C2211yescharacteristic
94#65267C2211yescharacteristic
95#65267C2211yescharacteristic
96#65267C2211yescharacteristic
97#65267C2211yescharacteristic
98#65267C2211yescharacteristic
99#65267C2211yescharacteristic
100#65267C2211yescharacteristic
101#65265C2211yescharacteristic
102#65265C2211yescharacteristic
103#65265C2211yescharacteristic
104#65263C2211yescharacteristic
105#65262C2211yescharacteristic
106#65262C2211yescharacteristic
107#65262C2211yescharacteristic
108#65261C2211yescharacteristic
109#65261C2211yescharacteristic
110#65261C2211yescharacteristic
111#65261C2211yescharacteristic
112#65261C2211yescharacteristic
113C4×#685C2211yescharacteristic
114#65225C2211yescharacteristic
115#65222C2211yescharacteristic
116#65222C2211yescharacteristic
117#65222C2211yescharacteristic
118#65222C2211yescharacteristic
119#65218C2211yescharacteristic
120#65217C2211yescharacteristic
121#65217C2211yescharacteristic
122#65217C2211yescharacteristic
123#64957C2211yescharacteristic
124#64957C2211yescharacteristic
125#64957C2211yescharacteristic
126#64956C2211yescharacteristic
127#64956C2211yescharacteristic
128#64956C2211yescharacteristic
129#64956C2211yescharacteristic
130#64956C2211yescharacteristic
131#64956C2211yescharacteristic
132#64955C2211yescharacteristic
133#64953C2211yescharacteristic
134#64953C2211yescharacteristic
135D5×#95C2211yescharacteristic
136D5×#95C2211yescharacteristic
137D5×#95C2211yescharacteristic
138D5×#95C2211yescharacteristic
139#64950C2211yescharacteristic
140#64950C2211yescharacteristic
141#64950C2211yescharacteristic
142#64950C2211yescharacteristic
143#64949C2211yescharacteristic
144#64949C2211yescharacteristic
145#64949C2211yescharacteristic
146#64948C2211yescharacteristic
147#64948C2211yescharacteristic
148#64948C2211yescharacteristic
149#64947C2211yescharacteristic
150#64947C2211yescharacteristic
151#64946C2211yescharacteristic
152#64946C2211yescharacteristic
153#64946C2211yescharacteristic
154#64946C2211yescharacteristic
155#64946C2211yescharacteristic
156#64946C2211yescharacteristic
157#64946C2211yescharacteristic
158#64946C2211yescharacteristic
159#64946C2211yescharacteristic
160#64945C2211yescharacteristic
161#64944C2211yescharacteristic
162#64944C2211yescharacteristic
163#64944C2211yescharacteristic
164#64944C2211yescharacteristic
165#64944C2211yescharacteristic
166#64944C2211yescharacteristic
167#64943C2211yescharacteristic
168#64943C2211yescharacteristic
169#64942C2211yescharacteristic
170#64942C2211yescharacteristic
171#64942C2211yescharacteristic
172#64942C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64941C2211yescharacteristic
176#64941C2211yescharacteristic
177#64941C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64936C2211yescharacteristic
184#64936C2211yescharacteristic
185#64936C2211yescharacteristic
186#64935C2211yescharacteristic
187#36752—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×C4×D5C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C5×C4⋊Q8—42no—
200C5×#125—42no—
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C5×C4⋊C4C2311yescharacteristic
213C2×C5×C4⋊C4C2311yescharacteristic
214C2×C5×C4⋊C4C2311yescharacteristic
215C2×C42×C5C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218#4092—42no—
219#4092—42no—
220#4090—42no—
221C2×#685C2311yescharacteristic
222C2×#685C2311yescharacteristic
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×C4⋊Dic5C2311yescharacteristic
230C2×C4⋊Dic5C2311yescharacteristic
231C2×C4⋊Dic5C2311yescharacteristic
232C2×C4⋊Dic5C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×#683C2311yescharacteristic
244C2×#683C2311yescharacteristic
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×#683C2311yescharacteristic
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#4043—42no—
285#4042—42no—
286#4038—42no—
287D5×C4⋊C4—42no—
288D5×C4⋊C4Q818yescomplemented
289#4034—42no—
290#4018—42no—
291C42×D5—42no—
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
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#3963C2311yescharacteristic
353#3963C2311yescharacteristic
354#3963C2311yescharacteristic
355#3963C2311yescharacteristic
356#2857—51no—
357#2851—51no—
358#2805—51no—
359#2805—51no—
360#2802—51no—
361#2802—51no—
362#2792—51no—
363#2792—51no—
364#2791—51no—
365#2791—51no—
366#2791—51no—
367#2791—51no—
368#2755—51no—
369#2755—51no—
370#2734—51no—
371#2734—51no—
372#2713—51no—
373#2713D511yescharacteristic, complemented
374#2659—51no—
375#2646—51no—
376#2569—51no—
377#2569—51no—
378#2440—51no—
379#2440—51no—
380#2438—51no—
381#2438—51no—
382#2438—51no—
383#2438—51no—
384#2316—51no—
385#2313—51no—
386C2×#387—51no—
387C23×D5C2411yescharacteristic
388C2×C5×Q8—22no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
391C2×C5×Q8—41no—
392C2×C5×Q8—41no—
393C2×C5×Q8—41no—
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
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
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—22no—
426C2×C4×D5—22no—
427C2×C4×D5—22no—
428C2×C4×D5—22no—
429C2×C4×D5—22no—
430C2×C4×D5—22no—
431C2×C4×D5—22no—
432C2×C4×D5—41no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×C4×D5—41no—
436C2×C4×D5—41no—
437C2×C4×D5—41no—
438C2×C4×D5—41no—
439C2×C4×D5—41no—
440C2×C4×D5—41no—
441C2×C4×D5—41no—
442C2×C4×D5C2×Q814yes—
443C2×C4×D5C2×Q814yes—
444C2×C4×D5C2×Q814yes—
445C2×Dic10—22no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C2×Dic10—41no—
449C2×Dic10—41no—
450C2×Dic10—41no—
451C5×C4⋊C4—22no—
452C5×C4⋊C4—22no—
453C5×C4⋊C4—22no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4—41no—
461C5×C4⋊C4—41no—
462C5×C4⋊C4—41no—
463C5×C4⋊C4—41no—
464C5×C4⋊C4C2×Q814yes—
465C42×C5—22no—
466C42×C5—41no—
467C42×C5—41no—
468#685—22no—
469#685—22no—
470#685—22no—
471#685—22no—
472#685—22no—
473#685—22no—
474#685—22no—
475#685—22no—
476C4⋊Dic5—41no—
477C4⋊Dic5—41no—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489C4⋊Dic5C2×Q814yes—
490#683—22no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—22no—
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#683—41no—
518#683—41no—
519#683—41no—
520#683C2×Q814yes—
521#683C2×Q814yes—
522C4×Dic5—22no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5—41no—
527C4×Dic5—41no—
528C4×Dic5—41no—
529C4×Dic5—41no—
530C4×Dic5—41no—
531C2×C4⋊Q8—51no—
532C2×C4⋊Q8—51no—
533C2×C4⋊Q8C2×D511yescharacteristic
534C2×#125C2×D511yescharacteristic
535C2×C22⋊Q8—51no—
536C2×C22⋊Q8—51no—
537C2×C22⋊Q8—51no—
538C2×C22⋊Q8—51no—
539C2×#117—51no—
540C2×#117—51no—
541C22×C4⋊C4—51no—
542C22×C4⋊C4—51no—
543C22×C42—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#400—51no—
551#400—51no—
552#400—51no—
553#400—51no—
554#400C2×D511yescharacteristic
555#400C2×D511yescharacteristic
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#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#398C2×D511yescharacteristic
579#398C2×D511yescharacteristic
580#395—51no—
581#395—51no—
582#395—51no—
583#395—51no—
584#395—51no—
585#395—51no—
586#395—51no—
587#395—51no—
588#395—51no—
589#395—51no—
590#395C2×D511yescharacteristic
591#395C2×D511yescharacteristic
592#391—51no—
593#391—51no—
594#391—51no—
595#391—51no—
596#391C2×D511yescharacteristic
597#391C2×D511yescharacteristic
598#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—51no—
604#389—51no—
605#389—51no—
606#389—51no—
607#389—51no—
608#389—51no—
609#389—51no—
610#389—51no—
611#389—51no—
612#389—51no—
613#389—51no—
614#389—51no—
615#389—51no—
616#389—51no—
617#389—51no—
618#389—51no—
619#389C2×D511yescharacteristic
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#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#387—51no—
649#387—51no—
650#387—51no—
651#387—51no—
652#387C2×D511yescharacteristic
653#387C2×D511yescharacteristic
654#387C2×D511yescharacteristic
655#387C2×D511yescharacteristic
656#385—51no—
657#385—51no—
658#385—51no—
659#385—51no—
660#385—51no—
661#385—51no—
662#385—51no—
663#385—51no—
664#384—51no—
665#384—51no—
666#384—51no—
667#382—51no—
668#381—51no—
669#381—51no—
670#380—51no—
671#380—51no—
672#380—51no—
673#380—51no—
674#380—51no—
675#380—51no—
676#380—51no—
677#380—51no—
678#380—51no—
679#380—51no—
680C4×C22⋊C4—51no—
681C4×C22⋊C4—51no—
682C2×#95—51no—
683C2×#95—51no—
684C2×#95—51no—
685C2×#95—51no—
686C23×C5C2511yescharacteristic
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5—21no—
691C22×D5C22×Q812yes—
692C22×D5H(5,𝔽2)12yes—
693C22×D52−1+412yes—
694C5×Q8—82no—
695C5×Q8—82no—
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—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5C22×Q812yes—
738C2×C4×C5C22×Q812yes—
739C2×C4×C5C22×Q812yes—
740C2×C4×C5H(5,𝔽2)12yes—
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×Dic5C22×Q812yes—
783C2×Dic5C22×Q812yes—
784C2×Dic5C22×Q812yes—
785C2×Dic52−1+412yes—
786C4×D5—28no—
787C4×D5—44no—
788C4×D5—44no—
789C4×D5—44no—
790C4×D5—44no—
791C4×D5—82no—
792C4×D5—82no—
793Dic10—82no—
794Dic10—82no—
795C22×Q8—51no—
796C22×Q8—51no—
797C22×Q8C22×D511yescharacteristic
798C22×Q8C22×D511yescharacteristic
799C23×C4—51no—
800C23×C4—51no—
801C23×C4—51no—
802C23×C4—51no—
803C23×C4—51no—
804C23×C4—51no—
805C23×C4—51no—
806C4⋊Q8—42no—
807C4⋊Q8—202no—
808C4⋊Q8—202no—
809#125—42no—
810C22⋊Q8—202no—
811C22⋊Q8—202no—
812C22⋊Q8—202no—
813C22⋊Q8—202no—
814#117—202no—
815#117—202no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—58no—
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⋊C4—51no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—51no—
852C2×C4⋊C4—51no—
853C2×C4⋊C4—51no—
854C2×C4⋊C4—51no—
855C2×C4⋊C4—51no—
856C2×C4⋊C4—51no—
857C2×C4⋊C4—51no—
858C2×C4⋊C4—51no—
859C2×C4⋊C4—51no—
860C2×C4⋊C4—51no—
861C2×C4⋊C4—51no—
862C2×C4⋊C4—51no—
863C2×C4⋊C4—202no—
864C2×C4⋊C4C22×D511yescharacteristic
865C2×C4⋊C4C22×D511yescharacteristic
866C2×C4⋊C4C22×D511yescharacteristic
867C2×C4⋊C4C22×D511yescharacteristic
868C2×C4⋊C4C22×D511yescharacteristic
869C2×C4⋊C4C22×D511yescharacteristic
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C4⋊C4C22×D511yescharacteristic
876C2×C4⋊C4C22×D511yescharacteristic
877C2×C4⋊C4C22×D511yescharacteristic
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—51no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—51no—
891C2×C42—51no—
892C2×C42—51no—
893C2×C42—51no—
894C2×C42—51no—
895C2×C42—202no—
896C2×C42C22×D511yescharacteristic
897C2×C42C22×D511yescharacteristic
898C2×C42C22×D511yescharacteristic
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#95—51no—
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954#95C22×D511yescharacteristic
955#95C22×D511yescharacteristic
956#95C22×D511yescharacteristic
957#95C22×D511yescharacteristic
958#95C22×D511yescharacteristic
959#95C22×D511yescharacteristic
960#95C22×D511yescharacteristic
961#95C22×D511yescharacteristic
962#95C22×D511yescharacteristic
963C22×C5C23×Q811yescharacteristic
964C22×C5C2×H(5,𝔽2)11yescharacteristic
965C22×C5C2×H(5,𝔽2)11yescharacteristic
966C22×C5C2×2−1+411yescharacteristic
967C22×C5C2×2−1+411yescharacteristic
968C22×C5#58511yescharacteristic
969C22×C5#58511yescharacteristic
970C2×D5—22no—
971C2×D5—22no—
972C2×D5—22no—
973C2×D5—22no—
974C2×D5—22no—
975C2×D5—22no—
976C2×D5#54414yes—
977C4×C5—22no—
978C4×C5—22no—
979C4×C5—22no—
980C4×C5—22no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985C4×C5—41no—
986C4×C5—41no—
987C4×C5—41no—
988C4×C5—41no—
989C4×C5—41no—
990C4×C5—41no—
991C4×C5—41no—
992Dic5—22no—
993Dic5—22no—
994Dic5—22no—
995Dic5—22no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000Dic5—41no—
1001Dic5—41no—
1002Dic5—41no—
1003Dic5—41no—
1004Dic5—41no—
1005Dic5—41no—
1006Dic5—41no—
1007C24—51no—
1008C2×Q8—22no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—102no—
1015C2×Q8—201no—
1016C2×Q8—201no—
1017C2×Q8—201no—
1018C2×Q8—201no—
1019C2×Q8—201no—
1020C22×C4—51no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—54no—
1025C22×C4—54no—
1026C22×C4—54no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—102no—
1039C22×C4—102no—
1040C22×C4—102no—
1041C22×C4—102no—
1042C22×C4—102no—
1043C22×C4—102no—
1044C22×C4—102no—
1045C22×C4—102no—
1046C22×C4—201no—
1047C22×C4—201no—
1048C22×C4—201no—
1049C22×C4—201no—
1050C22×C4—201no—
1051C22×C4—201no—
1052C22×C4—201no—
1053C22×C4—201no—
1054C22×C4—201no—
1055C22×C4—201no—
1056C22×C4C23×D511yescharacteristic
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C22×C4C23×D511yescharacteristic
1060C22×C4C23×D511yescharacteristic
1061C22×C4C23×D511yescharacteristic
1062C22×C4C23×D511yescharacteristic
1063C22×C4C23×D511yescharacteristic
1064C22×C4C23×D511yescharacteristic
1065C22×C4C23×D511yescharacteristic
1066C22×C4C23×D511yescharacteristic
1067C22×C4C23×D511yescharacteristic
1068C22×C4C23×D511yescharacteristic
1069C22×C4C23×D511yescharacteristic
1070C22×C4C23×D511yescharacteristic
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—54no—
1085C4⋊C4—54no—
1086C4⋊C4—54no—
1087C4⋊C4—102no—
1088C4⋊C4—102no—
1089C4⋊C4—102no—
1090C4⋊C4—102no—
1091C4⋊C4—102no—
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—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
1119C4⋊C4—201no—
1120C4⋊C4—201no—
1121C4⋊C4—201no—
1122C4⋊C4—201no—
1123C4⋊C4—201no—
1124C4⋊C4—201no—
1125C4⋊C4—201no—
1126C4⋊C4—201no—
1127C4⋊C4—201no—
1128C4⋊C4—201no—
1129C4⋊C4—201no—
1130C4⋊C4Q8×D514yes—
1131C22⋊C4—102no—
1132C22⋊C4—102no—
1133C22⋊C4—102no—
1134C22⋊C4—102no—
1135C22⋊C4—102no—
1136C22⋊C4—102no—
1137C22⋊C4—102no—
1138C22⋊C4—102no—
1139C42—22no—
1140C42—41no—
1141C42—41no—
1142C42—102no—
1143C42—201no—
1144C42—201no—
1145C42—201no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C42—201no—
1151C2×C5C2×#54411yescharacteristic
1152C2×C5#350111yescharacteristic
1153C2×C5#350211yescharacteristic
1154C2×C5#353411yescharacteristic
1155C2×C5#353811yescharacteristic
1156C2×C5#355911yescharacteristic
1157C2×C5#356411yescharacteristic
1158D5—24no—
1159C23—52no—
1160C23—52no—
1161C23—52no—
1162C23—101no—
1163C23—101no—
1164C23—101no—
1165C23—101no—
1166C23C24×D511yescharacteristic
1167Q8—82no—
1168Q8—82no—
1169Q8—402no—
1170Q8—402no—
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—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—52no—
1213C2×C4—52no—
1214C2×C4—52no—
1215C2×C4—52no—
1216C2×C4—108no—
1217C2×C4—101no—
1218C2×C4—101no—
1219C2×C4—101no—
1220C2×C4—101no—
1221C2×C4—101no—
1222C2×C4—101no—
1223C2×C4—101no—
1224C2×C4—101no—
1225C2×C4—101no—
1226C2×C4—101no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—204no—
1259C2×C4—204no—
1260C2×C4—204no—
1261C2×C4—204no—
1262C2×C4—402no—
1263C2×C4—402no—
1264C2×C4#414412yes—
1265C2×C4C2×Q8×D512yes—
1266C2×C4C2×Q8×D512yes—
1267C2×C4C2×Q8×D512yes—
1268C5#3675211yescharacteristic, complemented, Sylow
1269C22—54no—
1270C22—102no—
1271C22—102no—
1272C22—102no—
1273C22—102no—
1274C22—102no—
1275C22—102no—
1276C22C2×#414411yescharacteristic
1277C22C22×Q8×D511yescharacteristic
1278C22#6628311yescharacteristic
1279C22D5×H(5,𝔽2)11yescharacteristic
1280C22D5×2−1+411yescharacteristic
1281C22D5×2−1+411yescharacteristic
1282C22#6628711yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—22no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—102no—
1299C4—102no—
1300C4—102no—
1301C4—102no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C4—201no—
1313C2—104no—
1314C2#1061826011yescharacteristic
1315C2#1061842211yescharacteristic
1316C2D5×#54411yescharacteristic
1317C2#1061854611yescharacteristic
1318C2#1061866211yescharacteristic
1319C2#1061893311yescharacteristic
1320C2#1061903511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2713C2
prime radicalC23×D5C24
hypercenter#2713D5
hypocenterC5#36752
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2713

Complements

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

NH ≅ G/Ntype
1. C5×#2713C2semidirect
2. #10614981C2semidirect
5. #10614779C2semidirect
8. #10610039C2semidirect
9. #10610029C2semidirect
11. #10609639C2semidirect
12. #10609638C2semidirect
16. #10608967C2semidirect
17. #10608955C2semidirect
20. #10608328C2semidirect
21. #10608308C2semidirect
23. #10607900C2semidirect
28. #10607010C2semidirect
29. #10607007C2semidirect
30. #10606982C2semidirect
31. #10606917C2semidirect
288. D5×C4⋊C4Q8semidirect
373. #2713D5semidirect
1268. C5#36752semidirect

Maximal subgroups

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

subgroupindex
C5×#27132
#106149812
#106149642
#106148032
#106147792
#106100942
#106100882
#106100392
#106100292
#106096812
#106096392
#106096382
#106094762
#106089892
#106089822
#106089672
#106089552
#106083952
#106083582
#106083282
#106083082
#106079262
#106079002
#106070922
#106070482
#106070272
D5×#3872
#106070102
#106070072
#106069822
#106069172
#367525