Finite Group Databasebeta

← #12269210

Subgroups — #12269210

Order 1280.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2510C211yesmaximal, characteristic, complemented
2#10610144C211yesmaximal, characteristic, complemented
3#10610140C211yesmaximal, characteristic, complemented
4#10609898C211yesmaximal, characteristic, complemented
5#10609864C211yesmaximal, characteristic, complemented
6#10609238C211yesmaximal, characteristic, complemented
7#10609236C211yesmaximal, characteristic, complemented
8#10609192C211yesmaximal, characteristic, complemented
9#10609191C211yesmaximal, characteristic, complemented
10#10607611C211yesmaximal, characteristic, complemented
11#10607318C211yesmaximal, characteristic, complemented
12#10607182C211yesmaximal, characteristic, complemented
13#10607180C211yesmaximal, characteristic, complemented
14#10607086C211yesmaximal, characteristic, complemented
15#10606669C211yesmaximal, characteristic, complemented
16#10606471C211yesmaximal, characteristic, complemented
17#10606438C211yesmaximal, characteristic
18#10606427C211yesmaximal, characteristic
19#10606392C211yesmaximal, characteristic, complemented
20#10606391C211yesmaximal, characteristic
21#10606388C211yesmaximal, characteristic, complemented
22#10606194C211yesmaximal, characteristic, complemented
23#10606111C211yesmaximal, characteristic, complemented
24#10606005C211yesmaximal, characteristic, complemented
25#10605989C211yesmaximal, characteristic, complemented
26#10605621C211yesmaximal, characteristic, complemented
27#10605597C211yesmaximal, characteristic, complemented
28#10605240C211yesmaximal, characteristic, complemented
29C4×#4027C211yesmaximal, characteristic, complemented
30#10605082C211yesmaximal, characteristic, complemented
31C2×#64937C211yesmaximal, characteristic, complemented
32C2×#4085C2211yescharacteristic
33C2×#4081C2211yescharacteristic
34C2×D4×Dic5C2211yescharacteristic
35C2×C4×C22⋊D5C2211yescharacteristic
36C2×#4070C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4033C2211yescharacteristic
41C2×#4032C2211yescharacteristic
42C2×#4027C2211yescharacteristic
43C2×#4027C2211yescharacteristic
44C2×#4027C2211yescharacteristic
45C2×#4023C2211yescharacteristic
46C2×C42×D5C2211yescharacteristic
47C5×#401C2211yescharacteristic
48C5×#400C2211yescharacteristic
49C5×#397C2211yescharacteristic
50C5×#397C2211yescharacteristic
51C5×#388C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#387C2211yescharacteristic
54C5×#386C2211yescharacteristic
55C5×#386C2211yescharacteristic
56C5×#386C2211yescharacteristic
57C5×#385C2211yescharacteristic
58C5×#383C2211yescharacteristic
59C5×#380C2211yescharacteristic
60C4×C5×C22⋊C4C2211yescharacteristic
61C2×C5×#95C2211yescharacteristic
62#65509C2211yescharacteristic
63#65502C2211yescharacteristic
64#65502C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67C2×#3963C2211yescharacteristic
68C2×#3963C2211yescharacteristic
69C2×#3963C2211yescharacteristic
70#65282C2211yescharacteristic
71#65279C2211yescharacteristic
72#65279C2211yescharacteristic
73#65278C2211yescharacteristic
74#65273C2211yescharacteristic
75#65271C2211yescharacteristic
76#65270C2211yescharacteristic
77#65269C2211yescharacteristic
78#65267C2211yescharacteristic
79C4⋊C4×Dic5C2211yescharacteristic
80C4⋊C4×Dic5C2211yescharacteristic
81C4⋊C4×Dic5C2211yescharacteristic
82#65263C2211yescharacteristic
83#65262C2211yescharacteristic
84#65261C2211yescharacteristic
85#65248C2211yescharacteristic
86#65248C2211yescharacteristic
87#65246C2211yescharacteristic
88#65245C2211yescharacteristic
89#65245C2211yescharacteristic
90#65241C2211yescharacteristic
91#65241C2211yescharacteristic
92#65240C2211yescharacteristic
93#65240C2211yescharacteristic
94#65237C2211yescharacteristic
95#65236C2211yescharacteristic
96#65235C2211yescharacteristic
97#65235C2211yescharacteristic
98#65235C2211yescharacteristic
99#65234C2211yescharacteristic
100#65234C2211yescharacteristic
101#65234C2211yescharacteristic
102#65234C2211yescharacteristic
103#65233C2211yescharacteristic
104#65233C2211yescharacteristic
105#65233C2211yescharacteristic
106#65232C2211yescharacteristic
107#65232C2211yescharacteristic
108#65231C2211yescharacteristic
109C22⋊C4×Dic5C2211yescharacteristic
110C22⋊C4×Dic5C2211yescharacteristic
111C22⋊C4×Dic5C2211yescharacteristic
112C22⋊C4×Dic5C2211yescharacteristic
113C22⋊C4×Dic5C2211yescharacteristic
114C22⋊C4×Dic5C2211yescharacteristic
115C22⋊C4×Dic5C2211yescharacteristic
116C4×#685C2211yescharacteristic
117#65226C2211yescharacteristic
118#65222C2211yescharacteristic
119#65222C2211yescharacteristic
120#65222C2211yescharacteristic
121C4×#683C2211yescharacteristic
122C42×Dic5C2211yescharacteristic
123#64965C2211yescharacteristic
124#64964C2211yescharacteristic
125#64964C2211yescharacteristic
126#64964C2211yescharacteristic
127#64962C2211yescharacteristic
128#64959C2211yescharacteristic
129#64957C2211yescharacteristic
130#64956C2211yescharacteristic
131#64956C2211yescharacteristic
132#64955C2211yescharacteristic
133#64955C2211yescharacteristic
134#64955C2211yescharacteristic
135#64955C2211yescharacteristic
136#64955C2211yescharacteristic
137#64953C2211yescharacteristic
138#64953C2211yescharacteristic
139C5⋊#401C2211yescharacteristic
140#64949C2211yescharacteristic
141#64949C2211yescharacteristic
142#64947C2211yescharacteristic
143#64947C2211yescharacteristic
144#64947C2211yescharacteristic
145#64947C2211yescharacteristic
146#64947C2211yescharacteristic
147#64947C2211yescharacteristic
148#64947C2211yescharacteristic
149#64947C2211yescharacteristic
150#64946C2211yescharacteristic
151#64946C2211yescharacteristic
152#64944C2211yescharacteristic
153#64944C2211yescharacteristic
154#64944C2211yescharacteristic
155#64943C2211yescharacteristic
156#64943C2211yescharacteristic
157#64943C2211yescharacteristic
158#64942C2211yescharacteristic
159#64941C2211yescharacteristic
160#64941C2211yescharacteristic
161#64941C2211yescharacteristic
162#64941C2211yescharacteristic
163#64941C2211yescharacteristic
164#64939C2211yescharacteristic
165#64939C2211yescharacteristic
166#64938C2211yescharacteristic
167#64938C2211yescharacteristic
168#64938C2211yescharacteristic
169#64938C2211yescharacteristic
170#64938C2211yescharacteristic
171#64938C2211yescharacteristic
172#64938C2211yescharacteristic
173#64938C2211yescharacteristic
174#64937C2211yescharacteristic
175#64937C2211yescharacteristic
176#64937C2211yescharacteristic
177#64937C2211yescharacteristic
178#64937C2211yescharacteristic
179#64937C2211yescharacteristic
180#64937C2211yescharacteristic
181#64937C2211yescharacteristic
182#64937C2211yescharacteristic
183#64936C2211yescharacteristic
184#64936C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#34811—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C22×C22⋊D5C2311yescharacteristic
193C22×C22⋊D5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C23×Dic5C2311yescharacteristic
198C23×Dic5C2311yescharacteristic
199C22×C4×D5C2311yescharacteristic
200C22×C4×D5C2311yescharacteristic
201C22×C4×D5C2311yescharacteristic
202C22×Dic10C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227#4085—24no—
228#4081—24no—
229D4×Dic5—24no—
230C4×C22⋊D5—24no—
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
245#4070—24no—
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×C4×Dic5—24no—
267C2×C4×Dic5—24no—
268C2×C4×Dic5—24no—
269C2×C4×Dic5C2311yescharacteristic
270C2×C4×Dic5C2311yescharacteristic
271C2×C4×Dic5C2311yescharacteristic
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
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
290C2×C4×Dic5C2311yescharacteristic
291#4033—24no—
292#4032—24no—
293#4027—24no—
294#4027—24no—
295#4027—24no—
296#4023—24no—
297C42×D5—24no—
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312C5×#95C2311yescharacteristic
313C5×#95C2311yescharacteristic
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#3963C2311yescharacteristic
357#3963C2311yescharacteristic
358#2533—51no—
359#2532—51no—
360#2531—51no—
361#2530—51no—
362#2529—51no—
363#2528—51no—
364#2527—51no—
365#2526—51no—
366#2510D511yescharacteristic, complemented
367#2505—51no—
368#2493—51no—
369#2488—51no—
370#2450—51no—
371#2444—51no—
372#2425—51no—
373#2419—51no—
374#2402—51no—
375#2401—51no—
376#2401—51no—
377#2398—51no—
378C4×C22⋊Q8—51no—
379C4×#123—51no—
380C4×#123—51no—
381C4×#121—51no—
382#2298—51no—
383#2295—51no—
384#2290—51no—
385#2290—51no—
386#2283—51no—
387C42×D4—51no—
388C2×#376—51no—
389C24×C5C2411yescharacteristic
390C24×C5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C2×C5×D4—22no—
393C2×C5×D4—22no—
394C2×C5×D4—22no—
395C22×C4×C5—22no—
396C22×C4×C5—22no—
397C22×C4×C5—22no—
398C22×C4×C5—22no—
399C22×C4×C5—22no—
400C22×C4×C5—41no—
401C22×C4×C5—41no—
402C22×C4×C5—41no—
403C22×C4×C5—41no—
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C22×C4×C5C2411yescharacteristic
417C2×C22⋊D5—22no—
418C2×C22⋊D5—22no—
419C2×C22⋊D5—22no—
420C2×C22⋊D5—22no—
421C2×C22⋊D5—41no—
422C2×C22⋊D5#4114yes—
423C22×Dic5—22no—
424C22×Dic5—22no—
425C22×Dic5—22no—
426C22×Dic5—22no—
427C22×Dic5—22no—
428C22×Dic5—22no—
429C22×Dic5—22no—
430C22×Dic5—22no—
431C22×Dic5—22no—
432C22×Dic5—22no—
433C22×Dic5—22no—
434C22×Dic5—22no—
435C22×Dic5—41no—
436C22×Dic5—41no—
437C22×Dic5#4114yes—
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C22×Dic5C2411yescharacteristic
443C22×Dic5C2411yescharacteristic
444C22×Dic5C2411yescharacteristic
445C22×Dic5C2411yescharacteristic
446C22×Dic5C2411yescharacteristic
447C22×Dic5C2411yescharacteristic
448C22×Dic5C2411yescharacteristic
449C22×Dic5C2411yescharacteristic
450C22×Dic5C2411yescharacteristic
451C22×Dic5C2411yescharacteristic
452C22×Dic5C2411yescharacteristic
453C2×C4×D5—22no—
454C2×C4×D5—22no—
455C2×C4×D5—22no—
456C2×C4×D5—22no—
457C2×C4×D5—22no—
458C2×C4×D5—22no—
459C2×C4×D5—22no—
460C2×C4×D5—41no—
461C2×C4×D5—41no—
462C2×Dic10—22no—
463C2×Dic10—22no—
464C2×Dic10—41no—
465C5×C4⋊C4—22no—
466C5×C4⋊C4—41no—
467C5×C4⋊C4—41no—
468C5×C4⋊C4—41no—
469C5×C22⋊C4—22no—
470C5×C22⋊C4—22no—
471C5×C22⋊C4—22no—
472C5×C22⋊C4—22no—
473C5×C22⋊C4—22no—
474C5×C22⋊C4—41no—
475C5×C22⋊C4—41no—
476C5×C22⋊C4—41no—
477C5×C22⋊C4—41no—
478C42×C5—22no—
479C42×C5—41no—
480C22⋊Dic5—22no—
481C22⋊Dic5—22no—
482C22⋊Dic5—22no—
483C22⋊Dic5—22no—
484C22⋊Dic5—22no—
485C22⋊Dic5—22no—
486C22⋊Dic5—22no—
487C22⋊Dic5—41no—
488C22⋊Dic5#4114yes—
489#685—22no—
490#685—22no—
491#685—22no—
492#685—22no—
493#685—22no—
494#685—22no—
495#685—22no—
496#685—41no—
497#685—41no—
498#685—41no—
499C4⋊Dic5—22no—
500C4⋊Dic5—22no—
501C4⋊Dic5—22no—
502C4⋊Dic5—22no—
503#683—22no—
504#683—22no—
505#683—22no—
506#683—22no—
507#683—22no—
508#683—22no—
509#683—22no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521#683—41no—
522#683—41no—
523C4×Dic5—22no—
524C4×Dic5—22no—
525C4×Dic5—22no—
526C4×Dic5—22no—
527C4×Dic5—22no—
528C4×Dic5—22no—
529C4×Dic5—22no—
530C4×Dic5—22no—
531C4×Dic5—22no—
532C4×Dic5—22no—
533C4×Dic5—22no—
534C4×Dic5—22no—
535C4×Dic5—22no—
536C4×Dic5—22no—
537C4×Dic5—22no—
538C4×Dic5—22no—
539C4×Dic5—22no—
540C4×Dic5—22no—
541C4×Dic5—22no—
542C4×Dic5—41no—
543C4×Dic5#4114yes—
544C4×Dic5#4114yes—
545C2×#123—51no—
546C2×#123—51no—
547C2×C22⋊Q8—51no—
548C2×#121—51no—
549C2×C4×Q8—51no—
550C2×C4×D4—51no—
551C2×C4×D4—51no—
552C2×C4×D4—51no—
553C2×C4×D4—51no—
554C2×C4×D4—51no—
555C2×#117—51no—
556C22×C42—51no—
557C22×C42—51no—
558C22×C42—51no—
559C22×C42—51no—
560#401—51no—
561#401C2×D511yescharacteristic
562#400—51no—
563#400—51no—
564#400—51no—
565#400—51no—
566#400—51no—
567#400—51no—
568#400—51no—
569#400—51no—
570#400—51no—
571#400—51no—
572#400—51no—
573#400C2×D511yescharacteristic
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#397—51no—
579#397—51no—
580#397—51no—
581#397—51no—
582#397—51no—
583#397—51no—
584#397C2×D511yescharacteristic
585#397C2×D511yescharacteristic
586#396—51no—
587#396—51no—
588#394—51no—
589#394—51no—
590#393—51no—
591#393—51no—
592#391—51no—
593#391—51no—
594#391—51no—
595#390—51no—
596#389—51no—
597#389—51no—
598#389—51no—
599#389—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#388—51no—
604#388—51no—
605#388—51no—
606#388—51no—
607#388—51no—
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388C2×D511yescharacteristic
613#388C2×D511yescharacteristic
614#387—51no—
615#387—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387C2×D511yescharacteristic
632#386—51no—
633#386—51no—
634#386—51no—
635#386—51no—
636#386—51no—
637#386C2×D511yescharacteristic
638#386C2×D511yescharacteristic
639#386C2×D511yescharacteristic
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#385—51no—
645#385—51no—
646#385—51no—
647#385C2×D511yescharacteristic
648#383—51no—
649#383C2×D511yescharacteristic
650#382—51no—
651#382—51no—
652#381—51no—
653#381—51no—
654#381—51no—
655#381—51no—
656#380—51no—
657#380—51no—
658#380—51no—
659#380C2×D511yescharacteristic
660C4×C4⋊C4—51no—
661C4×C4⋊C4—51no—
662C4×C4⋊C4—51no—
663C4×C4⋊C4—51no—
664C4×C4⋊C4—51no—
665C4×C4⋊C4—51no—
666C4×C4⋊C4—51no—
667C4×C4⋊C4—51no—
668C4×C4⋊C4—51no—
669C4×C4⋊C4—51no—
670C4×C4⋊C4—51no—
671C4×C4⋊C4—51no—
672C4×C22⋊C4—51no—
673C4×C22⋊C4—51no—
674C4×C22⋊C4—51no—
675C4×C22⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4—51no—
679C4×C22⋊C4—51no—
680C4×C22⋊C4—51no—
681C4×C22⋊C4—51no—
682C4×C22⋊C4—51no—
683C4×C22⋊C4—51no—
684C4×C22⋊C4—51no—
685C4×C22⋊C4C2×D511yescharacteristic
686#376—51no—
687#376—51no—
688#376—51no—
689#376—51no—
690#376—51no—
691#376—51no—
692#376—51no—
693#376—51no—
694#376—51no—
695C2×#95—51no—
696C2×#95—51no—
697C2×#95—51no—
698C2×#95C2×D511yescharacteristic
699C43—51no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5—21no—
707C23×C5—21no—
708C23×C5—21no—
709C23×C5—21no—
710C23×C5—21no—
711C23×C5C2×#4112yes—
712C23×C5C2×#4112yes—
713C23×C5C2×#4112yes—
714C23×C5C2511yescharacteristic
715C22×D5—21no—
716C22×D5—21no—
717C22×D5—21no—
718C22×D5—21no—
719C22×D5—21no—
720C22×D5—21no—
721C22×D5C2×#4112yes—
722C5×D4—44no—
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×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—21no—
747C2×C4×C5—21no—
748C2×C4×C5—21no—
749C2×C4×C5—21no—
750C2×C4×C5—21no—
751C2×C4×C5—21no—
752C2×C4×C5—21no—
753C2×C4×C5—21no—
754C2×C4×C5—21no—
755C2×C4×C5—21no—
756C2×C4×C5—21no—
757C2×C4×C5—21no—
758C2×C4×C5—21no—
759C2×C4×C5—21no—
760C2×C4×C5—44no—
761C2×C4×C5—44no—
762C2×C4×C5—44no—
763C2×C4×C5C2×#4112yes—
764C2×C4×C5C2×#4112yes—
765C22⋊D5—28no—
766C22⋊D5—44no—
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—28no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5—21no—
786C2×Dic5—21no—
787C2×Dic5—21no—
788C2×Dic5—21no—
789C2×Dic5—21no—
790C2×Dic5—21no—
791C2×Dic5—21no—
792C2×Dic5—21no—
793C2×Dic5—21no—
794C2×Dic5—21no—
795C2×Dic5—21no—
796C2×Dic5—21no—
797C2×Dic5—21no—
798C2×Dic5—21no—
799C2×Dic5—21no—
800C2×Dic5—21no—
801C2×Dic5—21no—
802C2×Dic5—21no—
803C2×Dic5—21no—
804C2×Dic5—44no—
805C2×Dic5—44no—
806C2×Dic5—44no—
807C2×Dic5—44no—
808C2×Dic5C2×#4112yes—
809C2×Dic5C2×#4112yes—
810C2×Dic5C2×#4112yes—
811C2×Dic5C2×#4112yes—
812C2×Dic5C2×#4112yes—
813C2×Dic5C2×#4112yes—
814C2×Dic5C2×#4112yes—
815C2×Dic5C2×#4112yes—
816C2×Dic5C2×#4112yes—
817C4×D5—44no—
818C4×D5—44no—
819C4×D5—44no—
820Dic10—44no—
821C22×Q8—51no—
822C22×D4—51no—
823C22×D4—51no—
824C22×D4C22×D511yescharacteristic
825C23×C4—51no—
826C23×C4—51no—
827C23×C4—51no—
828C23×C4—51no—
829C23×C4—51no—
830C23×C4—51no—
831C23×C4—51no—
832C23×C4—51no—
833C23×C4C22×D511yescharacteristic
834C23×C4C22×D511yescharacteristic
835C23×C4C22×D511yescharacteristic
836#123—104no—
837#123—104no—
838C22⋊Q8—104no—
839#121—104no—
840C4×Q8—104no—
841C4×D4—104no—
842C4×D4—104no—
843C4×D4—104no—
844C4×D4—104no—
845C4×D4—104no—
846#117—104no—
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—51no—
864C2×C4⋊C4—51no—
865C2×C4⋊C4—51no—
866C2×C4⋊C4—51no—
867C2×C4⋊C4—51no—
868C2×C4⋊C4—51no—
869C2×C4⋊C4—51no—
870C2×C4⋊C4—51no—
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
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×C22⋊C4—51no—
887C2×C22⋊C4—51no—
888C2×C22⋊C4—51no—
889C2×C22⋊C4—51no—
890C2×C22⋊C4—51no—
891C2×C22⋊C4—51no—
892C2×C22⋊C4—51no—
893C2×C22⋊C4—51no—
894C2×C22⋊C4C22×D511yescharacteristic
895C2×C22⋊C4C22×D511yescharacteristic
896C2×C22⋊C4C22×D511yescharacteristic
897C2×C22⋊C4C22×D511yescharacteristic
898C2×C22⋊C4C22×D511yescharacteristic
899C2×C22⋊C4C22×D511yescharacteristic
900C2×C22⋊C4C22×D511yescharacteristic
901C2×C22⋊C4C22×D511yescharacteristic
902C2×C22⋊C4C22×D511yescharacteristic
903C2×C42—51no—
904C2×C42—51no—
905C2×C42—51no—
906C2×C42—51no—
907C2×C42—51no—
908C2×C42—51no—
909C2×C42—51no—
910C2×C42—51no—
911C2×C42—51no—
912C2×C42—51no—
913C2×C42—51no—
914C2×C42—51no—
915C2×C42—51no—
916C2×C42—51no—
917C2×C42—51no—
918C2×C42—51no—
919C2×C42—51no—
920C2×C42—51no—
921C2×C42—51no—
922C2×C42—51no—
923C2×C42—51no—
924C2×C42—51no—
925C2×C42—104no—
926C2×C42—104no—
927C2×C42—104no—
928C2×C42—104no—
929C2×C42C22×D511yescharacteristic
930C2×C42C22×D511yescharacteristic
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#95—51no—
950#95—51no—
951#95—51no—
952#95—51no—
953#95—51no—
954#95—51no—
955#95—51no—
956#95—51no—
957#95—51no—
958#95—51no—
959#95—51no—
960#95—51no—
961#95—51no—
962#95—51no—
963#95—51no—
964#95—51no—
965#95—51no—
966#95—51no—
967#95—51no—
968#95—51no—
969#95—51no—
970#95—51no—
971#95—51no—
972#95—51no—
973#95—51no—
974#95—51no—
975#95C22×D511yescharacteristic
976#95C22×D511yescharacteristic
977#95C22×D511yescharacteristic
978#95C22×D511yescharacteristic
979#95C22×D511yescharacteristic
980#95C22×D511yescharacteristic
981#95C22×D511yescharacteristic
982#95C22×D511yescharacteristic
983#95C22×D511yescharacteristic
984#95C22×D511yescharacteristic
985#95C22×D511yescharacteristic
986#95C22×D511yescharacteristic
987#95C22×D511yescharacteristic
988#95C22×D511yescharacteristic
989#95C22×D511yescharacteristic
990#95C22×D511yescharacteristic
991C22×C5—22no—
992C22×C5—22no—
993C22×C5—22no—
994C22×C5—22no—
995C22×C5—22no—
996C22×C5—22no—
997C22×C5—41no—
998C22×C5—41no—
999C22×C5—41no—
1000C22×C5—41no—
1001C22×C5—41no—
1002C22×C5—41no—
1003C22×C5—41no—
1004C22×C5#52914yes—
1005C22×C5C22×#4111yescharacteristic
1006C22×C5C22×#4111yescharacteristic
1007C22×C5C22×#4111yescharacteristic
1008C22×C5C22×#4111yescharacteristic
1009C22×C5C22×#4111yescharacteristic
1010C22×C5#58511yescharacteristic
1011C22×C5#58511yescharacteristic
1012C2×D5—22no—
1013C2×D5—22no—
1014C2×D5—22no—
1015C2×D5—41no—
1016C2×D5—41no—
1017C2×D5—41no—
1018C2×D5—41no—
1019C4×C5—22no—
1020C4×C5—22no—
1021C4×C5—41no—
1022C4×C5—41no—
1023C4×C5—41no—
1024C4×C5—41no—
1025C4×C5—41no—
1026C4×C5—41no—
1027C4×C5—41no—
1028C4×C5—41no—
1029C4×C5—41no—
1030C4×C5—41no—
1031C4×C5—41no—
1032Dic5—22no—
1033Dic5—22no—
1034Dic5—22no—
1035Dic5—22no—
1036Dic5—22no—
1037Dic5—22no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045Dic5—41no—
1046Dic5#52914yes—
1047C24—51no—
1048C24C23×D511yescharacteristic
1049C24C23×D511yescharacteristic
1050C2×Q8—102no—
1051C2×Q8—102no—
1052C2×Q8—201no—
1053C2×D4—22no—
1054C2×D4—22no—
1055C2×D4—22no—
1056C2×D4—54no—
1057C2×D4—102no—
1058C2×D4—102no—
1059C2×D4—102no—
1060C2×D4—102no—
1061C2×D4—201no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—51no—
1072C22×C4—54no—
1073C22×C4—51no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—51no—
1079C22×C4—51no—
1080C22×C4—51no—
1081C22×C4—51no—
1082C22×C4—51no—
1083C22×C4—51no—
1084C22×C4—51no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—102no—
1088C22×C4—102no—
1089C22×C4—102no—
1090C22×C4—102no—
1091C22×C4—102no—
1092C22×C4—102no—
1093C22×C4—102no—
1094C22×C4—102no—
1095C22×C4—102no—
1096C22×C4—102no—
1097C22×C4—102no—
1098C22×C4—102no—
1099C22×C4—102no—
1100C22×C4—102no—
1101C22×C4—102no—
1102C22×C4—102no—
1103C22×C4—102no—
1104C22×C4—102no—
1105C22×C4—102no—
1106C22×C4—201no—
1107C22×C4—201no—
1108C22×C4—201no—
1109C22×C4—201no—
1110C22×C4C23×D511yescharacteristic
1111C22×C4C23×D511yescharacteristic
1112C22×C4C23×D511yescharacteristic
1113C22×C4C23×D511yescharacteristic
1114C22×C4C23×D511yescharacteristic
1115C22×C4C23×D511yescharacteristic
1116C22×C4C23×D511yescharacteristic
1117C22×C4C23×D511yescharacteristic
1118C22×C4C23×D511yescharacteristic
1119C22×C4C23×D511yescharacteristic
1120C22×C4C23×D511yescharacteristic
1121C22×C4C23×D511yescharacteristic
1122C22×C4C23×D511yescharacteristic
1123C4⋊C4—22no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—102no—
1128C4⋊C4—102no—
1129C4⋊C4—102no—
1130C4⋊C4—102no—
1131C4⋊C4—102no—
1132C4⋊C4—102no—
1133C4⋊C4—102no—
1134C4⋊C4—102no—
1135C4⋊C4—102no—
1136C4⋊C4—102no—
1137C4⋊C4—102no—
1138C4⋊C4—102no—
1139C4⋊C4—102no—
1140C4⋊C4—102no—
1141C4⋊C4—102no—
1142C4⋊C4—102no—
1143C4⋊C4—102no—
1144C4⋊C4—201no—
1145C4⋊C4—201no—
1146C4⋊C4—201no—
1147C4⋊C4—201no—
1148C4⋊C4—201no—
1149C4⋊C4—201no—
1150C4⋊C4—201no—
1151C22⋊C4—22no—
1152C22⋊C4—22no—
1153C22⋊C4—22no—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—41no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—54no—
1161C22⋊C4—102no—
1162C22⋊C4—102no—
1163C22⋊C4—102no—
1164C22⋊C4—102no—
1165C22⋊C4—102no—
1166C22⋊C4—102no—
1167C22⋊C4—102no—
1168C22⋊C4—102no—
1169C22⋊C4—102no—
1170C22⋊C4—102no—
1171C22⋊C4—102no—
1172C22⋊C4—102no—
1173C22⋊C4—102no—
1174C22⋊C4—102no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
1177C22⋊C4—201no—
1178C22⋊C4—201no—
1179C42—22no—
1180C42—41no—
1181C42—54no—
1182C42—54no—
1183C42—102no—
1184C42—102no—
1185C42—102no—
1186C42—102no—
1187C42—102no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—102no—
1195C42—102no—
1196C42—102no—
1197C42—102no—
1198C42—102no—
1199C42—102no—
1200C42—102no—
1201C42—102no—
1202C42—201no—
1203C2×C5—24no—
1204C2×C5—81no—
1205C2×C5C2×#52911yescharacteristic
1206C2×C5C2×#52911yescharacteristic
1207C2×C5#345511yescharacteristic
1208C2×C5#347511yescharacteristic
1209C2×C5#347511yescharacteristic
1210C2×C5#347511yescharacteristic
1211C2×C5#347511yescharacteristic
1212D5—42no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—52no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23—101no—
1230C23—101no—
1231C23D5×#4112yes—
1232C23D5×#4112yes—
1233C23D5×#4112yes—
1234C23C24×D511yescharacteristic
1235Q8—204no—
1236D4—44no—
1237D4—108no—
1238D4—204no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—44no—
1277C2×C4—44no—
1278C2×C4—44no—
1279C2×C4—52no—
1280C2×C4—52no—
1281C2×C4—52no—
1282C2×C4—52no—
1283C2×C4—52no—
1284C2×C4—52no—
1285C2×C4—52no—
1286C2×C4—52no—
1287C2×C4—52no—
1288C2×C4—108no—
1289C2×C4—101no—
1290C2×C4—101no—
1291C2×C4—101no—
1292C2×C4—101no—
1293C2×C4—101no—
1294C2×C4—101no—
1295C2×C4—101no—
1296C2×C4—101no—
1297C2×C4—101no—
1298C2×C4—101no—
1299C2×C4—101no—
1300C2×C4—101no—
1301C2×C4—101no—
1302C2×C4—101no—
1303C2×C4—101no—
1304C2×C4—101no—
1305C2×C4—101no—
1306C2×C4—101no—
1307C2×C4—101no—
1308C2×C4—101no—
1309C2×C4—101no—
1310C2×C4—101no—
1311C2×C4—101no—
1312C2×C4—101no—
1313C2×C4—101no—
1314C2×C4—101no—
1315C2×C4—101no—
1316C2×C4—101no—
1317C2×C4—101no—
1318C2×C4—101no—
1319C2×C4—101no—
1320C2×C4—101no—
1321C2×C4—101no—
1322C2×C4—101no—
1323C2×C4—101no—
1324C2×C4—101no—
1325C2×C4—204no—
1326C2×C4—204no—
1327C2×C4—204no—
1328C2×C4—204no—
1329C2×C4—204no—
1330C2×C4—204no—
1331C2×C4—204no—
1332C2×C4D5×#4112yes—
1333C2×C4D5×#4112yes—
1334C5#3481111yescharacteristic, complemented, Sylow
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—102no—
1349C22—102no—
1350C22—102no—
1351C22—201no—
1352C22—201no—
1353C22—201no—
1354C22—201no—
1355C22#6604014yes—
1356C22C2×D5×#4111yescharacteristic
1357C22C2×D5×#4111yescharacteristic
1358C22C2×D5×#4111yescharacteristic
1359C22C2×D5×#4111yescharacteristic
1360C22C2×D5×#4111yescharacteristic
1361C22#6628511yescharacteristic
1362C22#6628511yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—54no—
1377C4—102no—
1378C4—102no—
1379C4—102no—
1380C4—102no—
1381C4—102no—
1382C4—102no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C4—201no—
1388C4—201no—
1389C4—201no—
1390C4—201no—
1391C2—24no—
1392C2—81no—
1393C2—202no—
1394C2C2×#6604011yescharacteristic
1395C2D5×#52911yescharacteristic
1396C2#1061828811yescharacteristic
1397C2#1061869111yescharacteristic
1398C2#1061869111yescharacteristic
1399C2#1061877511yescharacteristic
1400C2#1061877511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2510C2
prime radicalC2×#4085C22
hypercenter#2510D5
hypocenterC5#34811
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2510

Complements

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

NH ≅ G/Ntype
1. C5×#2510C2semidirect
2. #10610144C2semidirect
3. #10610140C2semidirect
4. #10609898C2semidirect
5. #10609864C2semidirect
6. #10609238C2semidirect
7. #10609236C2semidirect
8. #10609192C2semidirect
9. #10609191C2semidirect
10. #10607611C2semidirect
11. #10607318C2semidirect
12. #10607182C2semidirect
13. #10607180C2semidirect
14. #10607086C2semidirect
15. #10606669C2semidirect
16. #10606471C2semidirect
19. #10606392C2semidirect
21. #10606388C2semidirect
22. #10606194C2semidirect
23. #10606111C2semidirect
24. #10606005C2semidirect
25. #10605989C2semidirect
26. #10605621C2semidirect
27. #10605597C2semidirect
28. #10605240C2semidirect
29. C4×#4027C2semidirect
30. #10605082C2semidirect
31. C2×#64937C2semidirect
366. #2510D5semidirect
1334. C5#34811semidirect

Maximal subgroups

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

subgroupindex
C5×#25102
#106101442
#106101402
#106098982
#106098642
#106092382
#106092362
#106091922
#106091912
#106076112
#106073182
#106071822
#106071802
#106070862
#106066692
#106064712
#106064382
#106064272
#106063922
#106063912
#106063882
#106061942
#106061112
#106060052
#106059892
#106056212
#106055972
#106052402
C4×#40272
#106050822
C2×#649372
#348115