Finite Group Databasebeta

← #12269184

Subgroups — #12269184

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×#2530C211yesmaximal, characteristic, complemented
2#10610085C211yesmaximal, characteristic, complemented
3#10610077C211yesmaximal, characteristic, complemented
4#10609864C211yesmaximal, characteristic, complemented
5#10609863C211yesmaximal, characteristic, complemented
6#10609405C211yesmaximal, characteristic
7#10609401C211yesmaximal, characteristic, complemented
8#10609192C211yesmaximal, characteristic, complemented
9#10609191C211yesmaximal, characteristic, complemented
10#10607786C211yesmaximal, characteristic, complemented
11#10607696C211yesmaximal, characteristic, complemented
12#10607308C211yesmaximal, characteristic, complemented
13#10607305C211yesmaximal, characteristic, complemented
14#10607184C211yesmaximal, characteristic, complemented
15#10607183C211yesmaximal, characteristic
16#10607073C211yesmaximal, characteristic, complemented
17#10607067C211yesmaximal, characteristic, complemented
18#10606801C211yesmaximal, characteristic, complemented
19#10606793C211yesmaximal, characteristic, complemented
20#10606671C211yesmaximal, characteristic, complemented
21#10606670C211yesmaximal, characteristic, complemented
22#10606669C211yesmaximal, characteristic, complemented
23#10606668C211yesmaximal, characteristic, complemented
24#10606341C211yesmaximal, characteristic, complemented
25#10606108C211yesmaximal, characteristic, complemented
26#10605753C211yesmaximal, characteristic
27#10605594C211yesmaximal, characteristic, complemented
28#10605264C211yesmaximal, characteristic, complemented
29C4×#4027C211yesmaximal, characteristic, complemented
30D5×#376C211yesmaximal, characteristic, complemented
31#10605132C211yesmaximal, characteristic, complemented
32C2×C4×C22⋊D5C2211yescharacteristic
33C22×C4×Dic5C2211yescharacteristic
34C2×#4043C2211yescharacteristic
35C2×#4040C2211yescharacteristic
36C2×#4039C2211yescharacteristic
37C2×#4038C2211yescharacteristic
38C2×#4033C2211yescharacteristic
39C2×#4030C2211yescharacteristic
40C2×#4029C2211yescharacteristic
41C2×#4027C2211yescharacteristic
42C2×#4027C2211yescharacteristic
43C2×#4027C2211yescharacteristic
44C2×C42×D5C2211yescharacteristic
45C2×C42×D5C2211yescharacteristic
46C2×C42×D5C2211yescharacteristic
47C5×#400C2211yescharacteristic
48C5×#400C2211yescharacteristic
49C5×#397C2211yescharacteristic
50C5×#397C2211yescharacteristic
51C5×#389C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#388C2211yescharacteristic
54C5×#387C2211yescharacteristic
55C5×#387C2211yescharacteristic
56C5×#387C2211yescharacteristic
57C5×#387C2211yescharacteristic
58C5×#385C2211yescharacteristic
59C5×#380C2211yescharacteristic
60C4×C5×C22⋊C4C2211yescharacteristic
61C5×#376C2211yescharacteristic
62#65502C2211yescharacteristic
63#65501C2211yescharacteristic
64#65283C2211yescharacteristic
65#65282C2211yescharacteristic
66#65282C2211yescharacteristic
67#65279C2211yescharacteristic
68#65279C2211yescharacteristic
69#65278C2211yescharacteristic
70#65278C2211yescharacteristic
71#65278C2211yescharacteristic
72#65278C2211yescharacteristic
73#65276C2211yescharacteristic
74#65273C2211yescharacteristic
75#65271C2211yescharacteristic
76#65270C2211yescharacteristic
77#65270C2211yescharacteristic
78#65270C2211yescharacteristic
79#65269C2211yescharacteristic
80#65267C2211yescharacteristic
81#65267C2211yescharacteristic
82#65266C2211yescharacteristic
83#65266C2211yescharacteristic
84C4⋊C4×Dic5C2211yescharacteristic
85C4⋊C4×Dic5C2211yescharacteristic
86C4⋊C4×Dic5C2211yescharacteristic
87C4⋊C4×Dic5C2211yescharacteristic
88C4⋊C4×Dic5C2211yescharacteristic
89#65261C2211yescharacteristic
90#65261C2211yescharacteristic
91#65248C2211yescharacteristic
92#65248C2211yescharacteristic
93#65247C2211yescharacteristic
94#65246C2211yescharacteristic
95#65245C2211yescharacteristic
96#65245C2211yescharacteristic
97#65241C2211yescharacteristic
98#65241C2211yescharacteristic
99#65239C2211yescharacteristic
100#65237C2211yescharacteristic
101#65236C2211yescharacteristic
102#65233C2211yescharacteristic
103#65232C2211yescharacteristic
104#65232C2211yescharacteristic
105C22⋊C4×Dic5C2211yescharacteristic
106C22⋊C4×Dic5C2211yescharacteristic
107C22⋊C4×Dic5C2211yescharacteristic
108C22⋊C4×Dic5C2211yescharacteristic
109C22⋊C4×Dic5C2211yescharacteristic
110#65229C2211yescharacteristic
111#65229C2211yescharacteristic
112#65229C2211yescharacteristic
113#65229C2211yescharacteristic
114C4×#685C2211yescharacteristic
115#65222C2211yescharacteristic
116#65222C2211yescharacteristic
117#65221C2211yescharacteristic
118#65221C2211yescharacteristic
119#65221C2211yescharacteristic
120C4×#683C2211yescharacteristic
121C42×Dic5C2211yescharacteristic
122#65218C2211yescharacteristic
123#64964C2211yescharacteristic
124#64963C2211yescharacteristic
125#64962C2211yescharacteristic
126#64959C2211yescharacteristic
127#64959C2211yescharacteristic
128#64959C2211yescharacteristic
129#64958C2211yescharacteristic
130#64958C2211yescharacteristic
131#64957C2211yescharacteristic
132#64957C2211yescharacteristic
133#64956C2211yescharacteristic
134#64955C2211yescharacteristic
135#64955C2211yescharacteristic
136#64955C2211yescharacteristic
137#64955C2211yescharacteristic
138#64955C2211yescharacteristic
139#64955C2211yescharacteristic
140#64955C2211yescharacteristic
141#64954C2211yescharacteristic
142#64954C2211yescharacteristic
143#64954C2211yescharacteristic
144#64954C2211yescharacteristic
145#64953C2211yescharacteristic
146#64953C2211yescharacteristic
147D5×#95C2211yescharacteristic
148D5×#95C2211yescharacteristic
149D5×#95C2211yescharacteristic
150D5×#95C2211yescharacteristic
151C5⋊#401C2211yescharacteristic
152C5⋊#401C2211yescharacteristic
153#64949C2211yescharacteristic
154#64949C2211yescharacteristic
155#64949C2211yescharacteristic
156#64948C2211yescharacteristic
157#64947C2211yescharacteristic
158#64947C2211yescharacteristic
159#64947C2211yescharacteristic
160#64947C2211yescharacteristic
161#64947C2211yescharacteristic
162#64946C2211yescharacteristic
163#64946C2211yescharacteristic
164#64944C2211yescharacteristic
165#64943C2211yescharacteristic
166#64943C2211yescharacteristic
167#64943C2211yescharacteristic
168#64942C2211yescharacteristic
169#64942C2211yescharacteristic
170#64941C2211yescharacteristic
171#64940C2211yescharacteristic
172#64940C2211yescharacteristic
173#64938C2211yescharacteristic
174#64938C2211yescharacteristic
175#64938C2211yescharacteristic
176#64938C2211yescharacteristic
177#64938C2211yescharacteristic
178#64938C2211yescharacteristic
179#64937C2211yescharacteristic
180#64937C2211yescharacteristic
181#64937C2211yescharacteristic
182#64937C2211yescharacteristic
183#64937C2211yescharacteristic
184#64936C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#34811—51nomaximal, Sylow
188C23×C4×C5C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C22×D20C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×C4×D5C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C4×C22⋊D5—24no—
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
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×C4×Dic5—24no—
265C2×C4×Dic5C2311yescharacteristic
266C2×C4×Dic5C2311yescharacteristic
267C2×C4×Dic5C2311yescharacteristic
268C2×C4×Dic5C2311yescharacteristic
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
285#4043—24no—
286#4040—24no—
287#4039—24no—
288#4038—24no—
289#4033—24no—
290#4030—24no—
291#4029—24no—
292#4027—24no—
293#4027—24no—
294#4027—24no—
295C42×D5—24no—
296C42×D5—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#2530D511yescharacteristic, complemented
362#2529—51no—
363#2528—51no—
364#2527—51no—
365#2526—51no—
366#2510—51no—
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
390C23×D5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C22×C4×C5—22no—
393C22×C4×C5—22no—
394C22×C4×C5—41no—
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
409C2×C22⋊D5—22no—
410C2×C22⋊D5—22no—
411C2×C22⋊D5—22no—
412C2×C22⋊D5—22no—
413C2×C22⋊D5—41no—
414C2×C22⋊D5#4114yes—
415C22×Dic5—22no—
416C22×Dic5—22no—
417C22×Dic5—22no—
418C22×Dic5—22no—
419C22×Dic5—22no—
420C22×Dic5—41no—
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C2×D20—22no—
436C2×D20—22no—
437C2×D20—22no—
438C2×C4×D5—22no—
439C2×C4×D5—22no—
440C2×C4×D5—22no—
441C2×C4×D5—22no—
442C2×C4×D5—22no—
443C2×C4×D5—22no—
444C2×C4×D5—22no—
445C2×C4×D5—22no—
446C2×C4×D5—22no—
447C2×C4×D5—22no—
448C2×C4×D5—22no—
449C2×C4×D5—22no—
450C2×C4×D5—22no—
451C2×C4×D5—22no—
452C2×C4×D5—22no—
453C2×C4×D5—22no—
454C2×C4×D5—22no—
455C2×C4×D5—41no—
456C2×C4×D5—41no—
457C2×C4×D5—41no—
458C2×C4×D5—41no—
459C2×C4×D5—41no—
460C2×C4×D5—41no—
461C2×C4×D5#4114yes—
462C2×Dic10—22no—
463C2×Dic10—22no—
464C2×Dic10—41no—
465C5×C4⋊C4—22no—
466C5×C4⋊C4—22no—
467C5×C4⋊C4—22no—
468C5×C4⋊C4—22no—
469C5×C4⋊C4—22no—
470C5×C4⋊C4—41no—
471C5×C4⋊C4—41no—
472C5×C4⋊C4—41no—
473C5×C22⋊C4—22no—
474C5×C22⋊C4—22no—
475C5×C22⋊C4—22no—
476C5×C22⋊C4—22no—
477C5×C22⋊C4—22no—
478C5×C22⋊C4—41no—
479C42×C5—22no—
480C42×C5—22no—
481C42×C5—22no—
482C42×C5—41no—
483C22⋊Dic5—22no—
484C22⋊Dic5—22no—
485C22⋊Dic5—41no—
486C22⋊Dic5—41no—
487#685—22no—
488#685—22no—
489#685—22no—
490#685—22no—
491#685—22no—
492#685—22no—
493#685—22no—
494#685—22no—
495#685—22no—
496#685—22no—
497#685—22no—
498#685—22no—
499#685—41no—
500#685—41no—
501#685—41no—
502#685—41no—
503#685—41no—
504#685#4114yes—
505C4⋊Dic5—22no—
506C4⋊Dic5—22no—
507C4⋊Dic5—22no—
508C4⋊Dic5—22no—
509C4⋊Dic5—41no—
510C4⋊Dic5—41no—
511#683—22no—
512#683—22no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—22no—
517#683—22no—
518#683—22no—
519#683—22no—
520#683—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
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#401—51no—
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#400C2×D511yescharacteristic
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#389C2×D511yescharacteristic
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#387C2×D511yescharacteristic
629#387C2×D511yescharacteristic
630#387C2×D511yescharacteristic
631#387C2×D511yescharacteristic
632#386—51no—
633#386—51no—
634#386—51no—
635#386—51no—
636#386—51no—
637#386—51no—
638#386—51no—
639#386—51no—
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#383—51no—
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#376C2×D511yescharacteristic
695C2×#95—51no—
696C2×#95—51no—
697C2×#95—51no—
698C2×#95—51no—
699C43—51no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5C2×#4112yes—
707C23×C5C2511yescharacteristic
708C22×D5—21no—
709C22×D5—21no—
710C22×D5—21no—
711C22×D5—21no—
712C22×D5—21no—
713C22×D5—21no—
714C22×D5—21no—
715C22×D5—21no—
716C22×D5—21no—
717C22×D5—21no—
718C22×D5—21no—
719C22×D5C2×#4112yes—
720C22×D5C2×#4112yes—
721C22×D5C2×#4112yes—
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×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×C5C2×#4112yes—
762C2×C4×C5C2×#4112yes—
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—21no—
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—44no—
803C2×Dic5—44no—
804C2×Dic5C2×#4112yes—
805C2×Dic5C2×#4112yes—
806C2×Dic5C2×#4112yes—
807C2×Dic5C2×#4112yes—
808C2×Dic5C2×#4112yes—
809C2×Dic5C2×#4112yes—
810C2×Dic5C2×#4112yes—
811D20—44no—
812C4×D5—28no—
813C4×D5—44no—
814C4×D5—44no—
815C4×D5—44no—
816C4×D5—44no—
817C4×D5—44no—
818C4×D5—44no—
819C4×D5—44no—
820Dic10—44no—
821C22×Q8—51no—
822C22×D4—51no—
823C22×D4—51no—
824C22×D4—51no—
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×C4—51no—
834C23×C4—51no—
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⋊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×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⋊C4—51no—
895C2×C22⋊C4—51no—
896C2×C22⋊C4—51no—
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—104no—
924C2×C42—104no—
925C2×C42—104no—
926C2×C42—104no—
927C2×C42C22×D511yescharacteristic
928C2×C42C22×D511yescharacteristic
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—41no—
995C22×C5—41no—
996C22×C5—41no—
997C22×C5—41no—
998C22×C5C22×#4111yescharacteristic
999C22×C5C22×#4111yescharacteristic
1000C22×C5C22×#4111yescharacteristic
1001C22×C5C22×#4111yescharacteristic
1002C22×C5C22×#4111yescharacteristic
1003C22×C5#58511yescharacteristic
1004C22×C5#58511yescharacteristic
1005C2×D5—22no—
1006C2×D5—22no—
1007C2×D5—22no—
1008C2×D5—22no—
1009C2×D5—22no—
1010C2×D5—22no—
1011C2×D5—41no—
1012C2×D5—41no—
1013C2×D5—41no—
1014C2×D5—41no—
1015C2×D5—41no—
1016C2×D5—41no—
1017C2×D5—41no—
1018C2×D5#52914yes—
1019C4×C5—22no—
1020C4×C5—22no—
1021C4×C5—22no—
1022C4×C5—22no—
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—
1032C4×C5—41no—
1033Dic5—22no—
1034Dic5—22no—
1035Dic5—22no—
1036Dic5—22no—
1037Dic5—41no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045Dic5—41no—
1046Dic5#52914yes—
1047C24—51no—
1048C24—51no—
1049C24C23×D511yescharacteristic
1050C2×Q8—102no—
1051C2×Q8—102no—
1052C2×Q8—201no—
1053C2×D4—54no—
1054C2×D4—102no—
1055C2×D4—102no—
1056C2×D4—102no—
1057C2×D4—102no—
1058C2×D4—102no—
1059C2×D4—102no—
1060C2×D4—102no—
1061C2×D4—201no—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—41no—
1065C22×C4—51no—
1066C22×C4—51no—
1067C22×C4—51no—
1068C22×C4—51no—
1069C22×C4—51no—
1070C22×C4—54no—
1071C22×C4—51no—
1072C22×C4—51no—
1073C22×C4—51no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—51no—
1079C22×C4—51no—
1080C22×C4—102no—
1081C22×C4—102no—
1082C22×C4—102no—
1083C22×C4—102no—
1084C22×C4—102no—
1085C22×C4—102no—
1086C22×C4—102no—
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—201no—
1103C22×C4—201no—
1104C22×C4—201no—
1105C22×C4—201no—
1106C22×C4—201no—
1107C22×C4—201no—
1108C22×C4—201no—
1109C22×C4C23×D511yescharacteristic
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—22no—
1125C4⋊C4—22no—
1126C4⋊C4—22no—
1127C4⋊C4—22no—
1128C4⋊C4—41no—
1129C4⋊C4—41no—
1130C4⋊C4—41no—
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—54no—
1158C22⋊C4—102no—
1159C22⋊C4—102no—
1160C22⋊C4—102no—
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—201no—
1173C22⋊C4—201no—
1174C22⋊C4—201no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
1177C22⋊C4—201no—
1178C22⋊C4—201no—
1179C42—22no—
1180C42—22no—
1181C42—22no—
1182C42—41no—
1183C42—54no—
1184C42—54no—
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—42no—
1204C2×C5C2×#52911yescharacteristic
1205C2×C5C2×#52911yescharacteristic
1206C2×C5#345511yescharacteristic
1207C2×C5#347511yescharacteristic
1208C2×C5#347511yescharacteristic
1209C2×C5#347511yescharacteristic
1210C2×C5#347511yescharacteristic
1211D5—24no—
1212D5—81no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—52no—
1220C23—52no—
1221C23—52no—
1222C23—101no—
1223C23—101no—
1224C23—101no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23—101no—
1230C23—101no—
1231C23—101no—
1232C23—101no—
1233C23D5×#4112yes—
1234C23C24×D511yescharacteristic
1235Q8—204no—
1236D4—108no—
1237D4—204no—
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—21no—
1277C2×C4—44no—
1278C2×C4—52no—
1279C2×C4—52no—
1280C2×C4—52no—
1281C2×C4—52no—
1282C2×C4—52no—
1283C2×C4—52no—
1284C2×C4—52no—
1285C2×C4—108no—
1286C2×C4—101no—
1287C2×C4—101no—
1288C2×C4—101no—
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—204no—
1322C2×C4—204no—
1323C2×C4—204no—
1324C2×C4—204no—
1325C2×C4—204no—
1326C2×C4—204no—
1327C2×C4—204no—
1328C2×C4—204no—
1329C2×C4—204no—
1330C2×C4D5×#4112yes—
1331C2×C4D5×#4112yes—
1332C2×C4D5×#4112yes—
1333C2×C4D5×#4112yes—
1334C5#3481111yescharacteristic, complemented, Sylow
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—54no—
1343C22—102no—
1344C22—102no—
1345C22—102no—
1346C22—102no—
1347C22—102no—
1348C22—102no—
1349C22—201no—
1350C22—201no—
1351C22—201no—
1352C22—201no—
1353C22—201no—
1354C22—201no—
1355C22—201no—
1356C22C2×D5×#4111yescharacteristic
1357C22C2×D5×#4111yescharacteristic
1358C22C2×D5×#4111yescharacteristic
1359C22C2×D5×#4111yescharacteristic
1360C22C2×D5×#4111yescharacteristic
1361C22#6628511yescharacteristic
1362C22#6628711yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—22no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—54no—
1378C4—102no—
1379C4—102no—
1380C4—102no—
1381C4—102no—
1382C4—201no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C4—201no—
1388C4—201no—
1389C4—201no—
1390C4—201no—
1391C2—42no—
1392C2—104no—
1393C2—401no—
1394C2D5×#52911yescharacteristic
1395C2D5×#52911yescharacteristic
1396C2#1061842411yescharacteristic
1397C2#1061869111yescharacteristic
1398C2#1061872711yescharacteristic
1399C2#1061872811yescharacteristic
1400C2#1061877511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2530C2
prime radicalC2×#4030C22
hypercenter#2530D5
hypocenterC5#34811
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2530

Complements

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

NH ≅ G/Ntype
1. C5×#2530C2semidirect
2. #10610085C2semidirect
3. #10610077C2semidirect
4. #10609864C2semidirect
5. #10609863C2semidirect
7. #10609401C2semidirect
8. #10609192C2semidirect
9. #10609191C2semidirect
10. #10607786C2semidirect
11. #10607696C2semidirect
12. #10607308C2semidirect
13. #10607305C2semidirect
14. #10607184C2semidirect
16. #10607073C2semidirect
17. #10607067C2semidirect
18. #10606801C2semidirect
19. #10606793C2semidirect
20. #10606671C2semidirect
21. #10606670C2semidirect
22. #10606669C2semidirect
23. #10606668C2semidirect
24. #10606341C2semidirect
25. #10606108C2semidirect
27. #10605594C2semidirect
28. #10605264C2semidirect
29. C4×#4027C2semidirect
30. D5×#376C2semidirect
31. #10605132C2semidirect
361. #2530D5semidirect
1334. C5#34811semidirect

Maximal subgroups

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

subgroupindex
C5×#25302
#106100852
#106100772
#106098642
#106098632
#106094052
#106094012
#106091922
#106091912
#106077862
#106076962
#106073082
#106073052
#106071842
#106071832
#106070732
#106070672
#106068012
#106067932
#106066712
#106066702
#106066692
#106066682
#106063412
#106061082
#106057532
#106055942
#106052642
C4×#40272
D5×#3762
#106051322
#348115