Finite Group Databasebeta

← #12306986

Subgroups — #12306986

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×#2792C211yesmaximal, characteristic, complemented
2#10609696C211yesmaximal, characteristic
3#10609690C211yesmaximal, characteristic
4#10609681C211yesmaximal, characteristic
5#10609641C211yesmaximal, characteristic, complemented
6#10609607C211yesmaximal, characteristic, complemented
7#10609603C211yesmaximal, characteristic, complemented
8#10608989C211yesmaximal, characteristic
9#10608982C211yesmaximal, characteristic
10#10608969C211yesmaximal, characteristic, complemented
11#10608955C211yesmaximal, characteristic, complemented
12#10608949C211yesmaximal, characteristic, complemented
13#10608905C211yesmaximal, characteristic
14#10608019C211yesmaximal, characteristic
15#10608016C211yesmaximal, characteristic
16#10607953C211yesmaximal, characteristic
17#10607926C211yesmaximal, characteristic
18#10607912C211yesmaximal, characteristic, complemented
19#10607906C211yesmaximal, characteristic, complemented
20#10607899C211yesmaximal, characteristic, complemented
21#10607846C211yesmaximal, characteristic, complemented
22#10607092C211yesmaximal, characteristic
23#10607049C211yesmaximal, characteristic
24#10607027C211yesmaximal, characteristic
25D5×#387C211yesmaximal, characteristic
26#10607005C211yesmaximal, characteristic, complemented
27#10606984C211yesmaximal, characteristic, complemented
28#10606983C211yesmaximal, characteristic, complemented
29#10606918C211yesmaximal, characteristic, complemented
30#10606080C211yesmaximal, characteristic, complemented
31#10606057C211yesmaximal, characteristic
32C2×#4092C2211yescharacteristic
33C2×#4090C2211yescharacteristic
34C2×#4042C2211yescharacteristic
35C2×#4042C2211yescharacteristic
36C2×#4042C2211yescharacteristic
37C2×#4038C2211yescharacteristic
38C2×D5×C4⋊C4C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×#4036C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4018C2211yescharacteristic
44C2×C42×D5C2211yescharacteristic
45C5×#398C2211yescharacteristic
46C5×#398C2211yescharacteristic
47C5×#398C2211yescharacteristic
48C5×#395C2211yescharacteristic
49C5×#395C2211yescharacteristic
50C5×#395C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#389C2211yescharacteristic
53C5×#389C2211yescharacteristic
54C5×#389C2211yescharacteristic
55C5×#387C2211yescharacteristic
56C5×#387C2211yescharacteristic
57C5×#387C2211yescharacteristic
58C5×#387C2211yescharacteristic
59C5×#384C2211yescharacteristic
60#65519C2211yescharacteristic
61#65518C2211yescharacteristic
62#65278C2211yescharacteristic
63#65278C2211yescharacteristic
64#65278C2211yescharacteristic
65#65278C2211yescharacteristic
66#65278C2211yescharacteristic
67#65276C2211yescharacteristic
68#65276C2211yescharacteristic
69#65276C2211yescharacteristic
70#65276C2211yescharacteristic
71#65276C2211yescharacteristic
72#65276C2211yescharacteristic
73#65275C2211yescharacteristic
74#65274C2211yescharacteristic
75#65273C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65272C2211yescharacteristic
80#65272C2211yescharacteristic
81#65272C2211yescharacteristic
82#65271C2211yescharacteristic
83#65271C2211yescharacteristic
84#65271C2211yescharacteristic
85#65270C2211yescharacteristic
86#65270C2211yescharacteristic
87#65270C2211yescharacteristic
88#65270C2211yescharacteristic
89#65270C2211yescharacteristic
90#65270C2211yescharacteristic
91#65270C2211yescharacteristic
92#65269C2211yescharacteristic
93#65269C2211yescharacteristic
94#65269C2211yescharacteristic
95#65269C2211yescharacteristic
96#65269C2211yescharacteristic
97#65269C2211yescharacteristic
98#65268C2211yescharacteristic
99#65268C2211yescharacteristic
100#65268C2211yescharacteristic
101#65268C2211yescharacteristic
102#65268C2211yescharacteristic
103#65268C2211yescharacteristic
104#65267C2211yescharacteristic
105#65267C2211yescharacteristic
106#65267C2211yescharacteristic
107#65267C2211yescharacteristic
108#65266C2211yescharacteristic
109#65265C2211yescharacteristic
110#65265C2211yescharacteristic
111#65263C2211yescharacteristic
112#65262C2211yescharacteristic
113#65262C2211yescharacteristic
114#65261C2211yescharacteristic
115#65261C2211yescharacteristic
116#65261C2211yescharacteristic
117#65261C2211yescharacteristic
118#65261C2211yescharacteristic
119#65261C2211yescharacteristic
120#65261C2211yescharacteristic
121C4×#685C2211yescharacteristic
122#65222C2211yescharacteristic
123#65222C2211yescharacteristic
124#65222C2211yescharacteristic
125#65222C2211yescharacteristic
126#65218C2211yescharacteristic
127#65217C2211yescharacteristic
128#65217C2211yescharacteristic
129#65217C2211yescharacteristic
130#65217C2211yescharacteristic
131#64957C2211yescharacteristic
132#64957C2211yescharacteristic
133#64957C2211yescharacteristic
134#64956C2211yescharacteristic
135#64956C2211yescharacteristic
136#64956C2211yescharacteristic
137#64956C2211yescharacteristic
138#64955C2211yescharacteristic
139#64953C2211yescharacteristic
140#64953C2211yescharacteristic
141D5×#95C2211yescharacteristic
142D5×#95C2211yescharacteristic
143D5×#95C2211yescharacteristic
144D5×#95C2211yescharacteristic
145#64950C2211yescharacteristic
146#64950C2211yescharacteristic
147#64950C2211yescharacteristic
148#64949C2211yescharacteristic
149#64949C2211yescharacteristic
150#64949C2211yescharacteristic
151#64949C2211yescharacteristic
152#64949C2211yescharacteristic
153#64948C2211yescharacteristic
154#64947C2211yescharacteristic
155#64947C2211yescharacteristic
156#64946C2211yescharacteristic
157#64946C2211yescharacteristic
158#64946C2211yescharacteristic
159#64946C2211yescharacteristic
160#64946C2211yescharacteristic
161#64945C2211yescharacteristic
162#64945C2211yescharacteristic
163#64944C2211yescharacteristic
164#64944C2211yescharacteristic
165#64944C2211yescharacteristic
166#64944C2211yescharacteristic
167#64943C2211yescharacteristic
168#64943C2211yescharacteristic
169#64943C2211yescharacteristic
170#64943C2211yescharacteristic
171#64942C2211yescharacteristic
172#64942C2211yescharacteristic
173#64942C2211yescharacteristic
174#64942C2211yescharacteristic
175#64941C2211yescharacteristic
176#64941C2211yescharacteristic
177#64941C2211yescharacteristic
178#64941C2211yescharacteristic
179#64941C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64936C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36752—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C4×D5C2311yescharacteristic
190C22×C4×D5C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×Dic10C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
215C2×C5×C4⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
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×#683C2311yescharacteristic
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×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281#4042—42no—
282#4042—42no—
283#4042—42no—
284#4038—42no—
285D5×C4⋊C4—42no—
286D5×C4⋊C4Q818yescomplemented
287#4036—42no—
288#4034—42no—
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
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#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#2792D511yescharacteristic, complemented
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#2713—51no—
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—41no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C2×C4×D5—22no—
422C2×C4×D5—22no—
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—22no—
427C2×C4×D5—22no—
428C2×C4×D5—22no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×C4×D5—41no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×C4×D5—41no—
436C2×C4×D5—41no—
437C2×C4×D5—41no—
438C2×C4×D5—41no—
439C2×C4×D5C2×Q814yes—
440C2×C4×D5C2×Q814yes—
441C2×C4×D5C2×Q814yes—
442C2×Dic10—22no—
443C2×Dic10—22no—
444C2×Dic10—41no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C2×Dic10—41no—
449C2×Dic10—41no—
450C2×Dic10—41no—
451C5×C4⋊C4—22no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4—41no—
461C5×C4⋊C4—41no—
462C5×C4⋊C4—41no—
463C5×C4⋊C4—41no—
464C5×C4⋊C4—41no—
465C5×C4⋊C4—41no—
466C5×C4⋊C4—41no—
467C5×C4⋊C4C2×Q814yes—
468C42×C5—41no—
469C42×C5—41no—
470C42×C5—41no—
471#685—22no—
472#685—22no—
473#685—22no—
474#685—22no—
475#685—22no—
476#685—22no—
477#685—22no—
478#685—22no—
479C4⋊Dic5—22no—
480C4⋊Dic5—22no—
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⋊Dic5—41no—
490C4⋊Dic5—41no—
491C4⋊Dic5C2×Q814yes—
492#683—22no—
493#683—22no—
494#683—22no—
495#683—22no—
496#683—22no—
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—22no—
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⋊Q8—51no—
534C2×#125—51no—
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#400—51no—
555#400—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#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398C2×D511yescharacteristic
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#395C2×D511yescharacteristic
590#395C2×D511yescharacteristic
591#395C2×D511yescharacteristic
592#391—51no—
593#391—51no—
594#391—51no—
595#391—51no—
596#391—51no—
597#391—51no—
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#389C2×D511yescharacteristic
617#389C2×D511yescharacteristic
618#389C2×D511yescharacteristic
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#384C2×D511yescharacteristic
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—
695C2×C4×C5—21no—
696C2×C4×C5—21no—
697C2×C4×C5—21no—
698C2×C4×C5—21no—
699C2×C4×C5—21no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5C22×Q812yes—
737C2×C4×C5C22×Q812yes—
738C2×C4×C5C22×Q812yes—
739C2×C4×C52−1+412yes—
740C2×Dic5—21no—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5C22×Q812yes—
782C2×Dic5C22×Q812yes—
783C2×Dic5C22×Q812yes—
784C2×Dic5H(5,𝔽2)12yes—
785C4×D5—28no—
786C4×D5—44no—
787C4×D5—44no—
788C4×D5—44no—
789C4×D5—44no—
790C4×D5—82no—
791C4×D5—82no—
792Dic10—82no—
793Dic10—82no—
794Dic10—82no—
795C22×Q8—51no—
796C22×Q8—51no—
797C22×Q8—51no—
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—202no—
807C4⋊Q8—202no—
808C4⋊Q8—202no—
809#125—202no—
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—202no—
861C2×C4⋊C4C22×D511yescharacteristic
862C2×C4⋊C4C22×D511yescharacteristic
863C2×C4⋊C4C22×D511yescharacteristic
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#95—51no—
948#95—51no—
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—41no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—102no—
1012C2×Q8—102no—
1013C2×Q8—201no—
1014C2×Q8—201no—
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—41no—
1073C4⋊C4—41no—
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—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—54no—
1088C4⋊C4—54no—
1089C4⋊C4—54no—
1090C4⋊C4—102no—
1091C4⋊C4—102no—
1092C4⋊C4—102no—
1093C4⋊C4—102no—
1094C4⋊C4—102no—
1095C4⋊C4—102no—
1096C4⋊C4—102no—
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—41no—
1140C42—41no—
1141C42—41no—
1142C42—102no—
1143C42—102no—
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—402no—
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×C4C2×Q8×D512yes—
1265C2×C4C2×Q8×D512yes—
1266C2×C4C2×Q8×D512yes—
1267C2×C4#414712yes—
1268C5#3675211yescharacteristic, complemented, Sylow
1269C22—54no—
1270C22—102no—
1271C22—102no—
1272C22—102no—
1273C22—102no—
1274C22—102no—
1275C22—102no—
1276C22C22×Q8×D511yescharacteristic
1277C22C2×#414711yescharacteristic
1278C22#6628311yescharacteristic
1279C22D5×H(5,𝔽2)11yescharacteristic
1280C22D5×H(5,𝔽2)11yescharacteristic
1281C22#6628511yescharacteristic
1282C22D5×2−1+411yescharacteristic
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#1061836711yescharacteristic
1315C2#1061848911yescharacteristic
1316C2D5×#54411yescharacteristic
1317C2#1061885011yescharacteristic
1318C2#1061885811yescharacteristic
1319C2#1061894711yescharacteristic
1320C2#1061898311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2792C2
prime radicalC23×D5C24
hypercenter#2792D5
hypocenterC5#36752
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2792

Complements

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

NH ≅ G/Ntype
1. C5×#2792C2semidirect
5. #10609641C2semidirect
6. #10609607C2semidirect
7. #10609603C2semidirect
10. #10608969C2semidirect
11. #10608955C2semidirect
12. #10608949C2semidirect
18. #10607912C2semidirect
19. #10607906C2semidirect
20. #10607899C2semidirect
21. #10607846C2semidirect
26. #10607005C2semidirect
27. #10606984C2semidirect
28. #10606983C2semidirect
29. #10606918C2semidirect
30. #10606080C2semidirect
286. D5×C4⋊C4Q8semidirect
363. #2792D5semidirect
1268. C5#36752semidirect

Maximal subgroups

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

subgroupindex
C5×#27922
#106096962
#106096902
#106096812
#106096412
#106096072
#106096032
#106089892
#106089822
#106089692
#106089552
#106089492
#106089052
#106080192
#106080162
#106079532
#106079262
#106079122
#106079062
#106078992
#106078462
#106070922
#106070492
#106070272
D5×#3872
#106070052
#106069842
#106069832
#106069182
#106060802
#106060572
#367525