Finite Group Databasebeta

← #12307065

Subgroups — #12307065

Order 1280.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2692C211yesmaximal, characteristic
2#10614541C211yesmaximal, characteristic, complemented
3#10614536C211yesmaximal, characteristic, complemented
4#10614534C211yesmaximal, characteristic, complemented
5#10614493C211yesmaximal, characteristic, complemented
6#10609807C211yesmaximal, characteristic, complemented
7#10609777C211yesmaximal, characteristic, complemented
8#10609606C211yesmaximal, characteristic, complemented
9#10609524C211yesmaximal, characteristic, complemented
10#10609125C211yesmaximal, characteristic, complemented
11#10609077C211yesmaximal, characteristic, complemented
12#10608948C211yesmaximal, characteristic, complemented
13#10608929C211yesmaximal, characteristic, complemented
14#10608575C211yesmaximal, characteristic, complemented
15#10608574C211yesmaximal, characteristic, complemented
16#10608552C211yesmaximal, characteristic, complemented
17#10608513C211yesmaximal, characteristic, complemented
18#10608328C211yesmaximal, characteristic, complemented
19#10608287C211yesmaximal, characteristic, complemented
20#10608144C211yesmaximal, characteristic
21#10608026C211yesmaximal, characteristic
22#10606955C211yesmaximal, characteristic, complemented
23#10606865C211yesmaximal, characteristic, complemented
24#10606597C211yesmaximal, characteristic
25#10606592C211yesmaximal, characteristic
26#10606394C211yesmaximal, characteristic
27#10606388C211yesmaximal, characteristic
28#10606317C211yesmaximal, characteristic, complemented
29#10606304C211yesmaximal, characteristic, complemented
30#10605727C211yesmaximal, characteristic, complemented
31#10605675C211yesmaximal, characteristic, complemented
32C2×C5×C22⋊Q8C2211yescharacteristic
33C2×C5×C22⋊Q8C2211yescharacteristic
34C2×#4090C2211yescharacteristic
35C2×D4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C2×#4035C2211yescharacteristic
38C2×#4023C2211yescharacteristic
39C5×#399C2211yescharacteristic
40C5×#398C2211yescharacteristic
41C5×#396C2211yescharacteristic
42C5×#395C2211yescharacteristic
43C5×#393C2211yescharacteristic
44C5×#393C2211yescharacteristic
45C5×#391C2211yescharacteristic
46C5×#390C2211yescharacteristic
47C5×#387C2211yescharacteristic
48C5×#386C2211yescharacteristic
49C5×#386C2211yescharacteristic
50C5×#385C2211yescharacteristic
51C5×#380C2211yescharacteristic
52#65519C2211yescharacteristic
53#65519C2211yescharacteristic
54#65519C2211yescharacteristic
55#65519C2211yescharacteristic
56#65518C2211yescharacteristic
57#65518C2211yescharacteristic
58#65518C2211yescharacteristic
59#65510C2211yescharacteristic
60#65509C2211yescharacteristic
61#65509C2211yescharacteristic
62#65501C2211yescharacteristic
63#65499C2211yescharacteristic
64#65499C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67#65499C2211yescharacteristic
68C2×#3963C2211yescharacteristic
69#65275C2211yescharacteristic
70#65273C2211yescharacteristic
71#65273C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65272C2211yescharacteristic
75#65271C2211yescharacteristic
76#65271C2211yescharacteristic
77#65270C2211yescharacteristic
78#65270C2211yescharacteristic
79#65270C2211yescharacteristic
80#65270C2211yescharacteristic
81#65269C2211yescharacteristic
82#65269C2211yescharacteristic
83#65268C2211yescharacteristic
84#65268C2211yescharacteristic
85#65268C2211yescharacteristic
86#65267C2211yescharacteristic
87#65267C2211yescharacteristic
88#65267C2211yescharacteristic
89#65267C2211yescharacteristic
90#65267C2211yescharacteristic
91#65267C2211yescharacteristic
92#65267C2211yescharacteristic
93#65267C2211yescharacteristic
94#65265C2211yescharacteristic
95C4⋊C4×Dic5C2211yescharacteristic
96#65263C2211yescharacteristic
97#65263C2211yescharacteristic
98#65262C2211yescharacteristic
99#65262C2211yescharacteristic
100#65262C2211yescharacteristic
101#65261C2211yescharacteristic
102#65261C2211yescharacteristic
103#65261C2211yescharacteristic
104#65239C2211yescharacteristic
105#65239C2211yescharacteristic
106#65239C2211yescharacteristic
107#65238C2211yescharacteristic
108#65237C2211yescharacteristic
109#65237C2211yescharacteristic
110#65237C2211yescharacteristic
111#65237C2211yescharacteristic
112#65237C2211yescharacteristic
113#65236C2211yescharacteristic
114#65236C2211yescharacteristic
115#65236C2211yescharacteristic
116#65236C2211yescharacteristic
117#65236C2211yescharacteristic
118#65236C2211yescharacteristic
119#65235C2211yescharacteristic
120#65235C2211yescharacteristic
121#65235C2211yescharacteristic
122#65235C2211yescharacteristic
123#65235C2211yescharacteristic
124#65234C2211yescharacteristic
125#65234C2211yescharacteristic
126#65234C2211yescharacteristic
127#65234C2211yescharacteristic
128#65233C2211yescharacteristic
129#65233C2211yescharacteristic
130#65233C2211yescharacteristic
131#65233C2211yescharacteristic
132#65232C2211yescharacteristic
133#65232C2211yescharacteristic
134#65232C2211yescharacteristic
135#65231C2211yescharacteristic
136#65231C2211yescharacteristic
137#65231C2211yescharacteristic
138#65231C2211yescharacteristic
139#65231C2211yescharacteristic
140C22⋊C4×Dic5C2211yescharacteristic
141C22⋊C4×Dic5C2211yescharacteristic
142C22⋊C4×Dic5C2211yescharacteristic
143#65222C2211yescharacteristic
144#65221C2211yescharacteristic
145#65217C2211yescharacteristic
146#65217C2211yescharacteristic
147#64949C2211yescharacteristic
148#64949C2211yescharacteristic
149#64949C2211yescharacteristic
150#64948C2211yescharacteristic
151#64948C2211yescharacteristic
152#64948C2211yescharacteristic
153#64947C2211yescharacteristic
154#64947C2211yescharacteristic
155#64947C2211yescharacteristic
156#64947C2211yescharacteristic
157#64947C2211yescharacteristic
158#64945C2211yescharacteristic
159#64945C2211yescharacteristic
160#64945C2211yescharacteristic
161#64944C2211yescharacteristic
162#64943C2211yescharacteristic
163#64943C2211yescharacteristic
164#64943C2211yescharacteristic
165#64942C2211yescharacteristic
166#64942C2211yescharacteristic
167#64942C2211yescharacteristic
168#64942C2211yescharacteristic
169#64941C2211yescharacteristic
170#64941C2211yescharacteristic
171#64940C2211yescharacteristic
172#64939C2211yescharacteristic
173#64939C2211yescharacteristic
174#64939C2211yescharacteristic
175#64939C2211yescharacteristic
176#64938C2211yescharacteristic
177#64937C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36755—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×C5×D4C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×C4×C5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C5×C22⋊Q8—42no—
201C5×C22⋊Q8—42no—
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×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C5×C22⋊C4C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233C2×C22⋊Dic5C2311yescharacteristic
234#4090—42no—
235D4×Dic5Q818yescomplemented
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
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×C4×Dic5—42no—
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
284#4035—42no—
285#4023—42no—
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296#3963C2311yescharacteristic
297#3963C2311yescharacteristic
298#3963C2311yescharacteristic
299#3963C2311yescharacteristic
300#3963C2311yescharacteristic
301#3963C2311yescharacteristic
302#3963C2311yescharacteristic
303#3963C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#2855—51no—
351#2851—51no—
352#2805—51no—
353#2804—51no—
354#2790—51no—
355#2788—51no—
356#2788—51no—
357#2784—51no—
358#2780—51no—
359#2774—51no—
360#2763—51no—
361#2763—51no—
362#2755—51no—
363#2742—51no—
364#2729—51no—
365#2720—51no—
366#2713—51no—
367#2692D511yescharacteristic
368#2665—51no—
369#2665—51no—
370#2612—51no—
371#2607—51no—
372#2605—51no—
373#2605—51no—
374#2570—51no—
375#2569—51no—
376#2439—51no—
377#2438—51no—
378#2319—51no—
379#2318—51no—
380#2290—51no—
381C24×C5C2411yescharacteristic
382C24×C5C2411yescharacteristic
383C2×C5×Q8—22no—
384C2×C5×Q8—41no—
385C2×C5×Q8—41no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C2×C5×Q8—41no—
389C2×C5×D4—41no—
390C2×C5×D4—41no—
391C2×C5×D4C2×Q814yes—
392C22×C4×C5—22no—
393C22×C4×C5—41no—
394C22×C4×C5—41no—
395C22×C4×C5—41no—
396C22×C4×C5—41no—
397C22×C4×C5—41no—
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×Dic5—41no—
412C22×Dic5—41no—
413C22×Dic5—41no—
414C22×Dic5—41no—
415C22×Dic5—41no—
416C22×Dic5—41no—
417C22×Dic5—41no—
418C22×Dic5—41no—
419C22×Dic5—41no—
420C22×Dic5—41no—
421C22×Dic5C2×Q814yes—
422C22×Dic5C2×Q814yes—
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C2×Dic10—41no—
440C2×Dic10—41no—
441C2×Dic10—41no—
442C2×Dic10—41no—
443C2×Dic10—41no—
444C2×Dic10—41no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C5×C4⋊C4—22no—
449C5×C4⋊C4—22no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C22⋊C4—22no—
458C5×C22⋊C4—41no—
459C5×C22⋊C4—41no—
460C5×C22⋊C4—41no—
461C5×C22⋊C4—41no—
462C5×C22⋊C4—41no—
463C5×C22⋊C4—41no—
464C5×C22⋊C4—41no—
465C5×C22⋊C4—41no—
466C5×C22⋊C4—41no—
467C42×C5—41no—
468C22⋊Dic5—41no—
469C22⋊Dic5—41no—
470C22⋊Dic5—41no—
471C22⋊Dic5—41no—
472C22⋊Dic5—41no—
473C22⋊Dic5—41no—
474C22⋊Dic5—41no—
475C22⋊Dic5—41no—
476C22⋊Dic5—41no—
477C22⋊Dic5—41no—
478C22⋊Dic5C2×Q814yes—
479C22⋊Dic5C2×Q814yes—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5C2×Q814yes—
489#683—22no—
490#683—22no—
491#683—41no—
492#683—41no—
493#683—41no—
494#683—41no—
495#683—41no—
496#683—41no—
497#683—41no—
498#683—41no—
499#683—41no—
500#683—41no—
501#683—41no—
502#683—41no—
503#683—41no—
504#683—41no—
505#683—41no—
506#683—41no—
507#683—41no—
508#683—41no—
509#683—41no—
510#683—41no—
511#683—41no—
512#683—41no—
513#683—41no—
514#683—41no—
515C4×Dic5—22no—
516C4×Dic5—22no—
517C4×Dic5—41no—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C4×Dic5—41no—
522C4×Dic5—41no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5C2×Q814yes—
527C2×C4⋊Q8—51no—
528C2×#125—51no—
529C2×C22⋊Q8C2×D511yescharacteristic
530C2×C22⋊Q8C2×D511yescharacteristic
531C2×C4×D4—51no—
532C2×#117—51no—
533C22×C42—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#399—51no—
549#399C2×D511yescharacteristic
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#398—51no—
557#398C2×D511yescharacteristic
558#396—51no—
559#396—51no—
560#396—51no—
561#396—51no—
562#396—51no—
563#396C2×D511yescharacteristic
564#395—51no—
565#395—51no—
566#395—51no—
567#395—51no—
568#395—51no—
569#395—51no—
570#395—51no—
571#395—51no—
572#395—51no—
573#395C2×D511yescharacteristic
574#393—51no—
575#393—51no—
576#393—51no—
577#393—51no—
578#393—51no—
579#393—51no—
580#393C2×D511yescharacteristic
581#393C2×D511yescharacteristic
582#391—51no—
583#391—51no—
584#391—51no—
585#391—51no—
586#391—51no—
587#391—51no—
588#391—51no—
589#391—51no—
590#391—51no—
591#391—51no—
592#391—51no—
593#391—51no—
594#391C2×D511yescharacteristic
595#390—51no—
596#390C2×D511yescharacteristic
597#389—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#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388—51no—
613#388—51no—
614#388—51no—
615#388—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387—51no—
639#387C2×D511yescharacteristic
640#386—51no—
641#386—51no—
642#386C2×D511yescharacteristic
643#386C2×D511yescharacteristic
644#385—51no—
645#385—51no—
646#385—51no—
647#385—51no—
648#385—51no—
649#385—51no—
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385—51no—
657#385C2×D511yescharacteristic
658#384—51no—
659#383—51no—
660#382—51no—
661#382—51no—
662#382—51no—
663#382—51no—
664#381—51no—
665#381—51no—
666#381—51no—
667#380—51no—
668#380—51no—
669#380—51no—
670#380—51no—
671#380—51no—
672#380—51no—
673#380C2×D511yescharacteristic
674C4×C4⋊C4—51no—
675C4×C4⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4—51no—
679#376—51no—
680#376—51no—
681C2×#95—51no—
682C23×C5—21no—
683C23×C5—21no—
684C23×C5—21no—
685C23×C5—21no—
686C23×C5—21no—
687C23×C5—21no—
688C23×C5—21no—
689C23×C5—21no—
690C23×C5—21no—
691C23×C5—21no—
692C23×C5—21no—
693C23×C5—21no—
694C23×C5C22×Q812yes—
695C23×C5C22×Q812yes—
696C23×C5C2511yescharacteristic
697C5×Q8—82no—
698C5×Q8—82no—
699C5×D4—44no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—44no—
738C2×C4×C5—82no—
739C2×C4×C5C22×Q812yes—
740C2×C4×C5H(5,𝔽2)12yes—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5—44no—
786C2×Dic5—44no—
787C2×Dic5—44no—
788C2×Dic5—82no—
789C2×Dic5C22×Q812yes—
790C2×Dic5C22×Q812yes—
791C2×Dic5C22×Q812yes—
792C2×Dic5C22×Q812yes—
793Dic10—82no—
794Dic10—82no—
795Dic10—82no—
796C22×Q8—51no—
797C22×Q8—51no—
798C22×Q8—51no—
799C22×Q8C22×D511yescharacteristic
800C22×Q8C22×D511yescharacteristic
801C22×D4C22×D511yescharacteristic
802C23×C4—51no—
803C23×C4—51no—
804C23×C4—51no—
805C23×C4—51no—
806C23×C4C22×D511yescharacteristic
807C23×C4C22×D511yescharacteristic
808C4⋊Q8—202no—
809#125—202no—
810C22⋊Q8—42no—
811C22⋊Q8—42no—
812C4×D4—58no—
813#117—202no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—51no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4C22×D511yescharacteristic
850C2×C4⋊C4C22×D511yescharacteristic
851C2×C4⋊C4C22×D511yescharacteristic
852C2×C4⋊C4C22×D511yescharacteristic
853C2×C4⋊C4C22×D511yescharacteristic
854C2×C4⋊C4C22×D511yescharacteristic
855C2×C4⋊C4C22×D511yescharacteristic
856C2×C4⋊C4C22×D511yescharacteristic
857C2×C4⋊C4C22×D511yescharacteristic
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4—51no—
867C2×C22⋊C4—51no—
868C2×C22⋊C4—51no—
869C2×C22⋊C4—51no—
870C2×C22⋊C4C22×D511yescharacteristic
871C2×C22⋊C4C22×D511yescharacteristic
872C2×C22⋊C4C22×D511yescharacteristic
873C2×C22⋊C4C22×D511yescharacteristic
874C2×C22⋊C4C22×D511yescharacteristic
875C2×C22⋊C4C22×D511yescharacteristic
876C2×C22⋊C4C22×D511yescharacteristic
877C2×C22⋊C4C22×D511yescharacteristic
878C2×C22⋊C4C22×D511yescharacteristic
879C2×C22⋊C4C22×D511yescharacteristic
880C2×C42—51no—
881C2×C42—51no—
882C2×C42—51no—
883C2×C42—51no—
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—51no—
891C2×C42—51no—
892C2×C42—202no—
893C2×C42C22×D511yescharacteristic
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954#95C22×D511yescharacteristic
955#95C22×D511yescharacteristic
956#95C22×D511yescharacteristic
957#95C22×D511yescharacteristic
958C22×C5—22no—
959C22×C5—22no—
960C22×C5—22no—
961C22×C5—22no—
962C22×C5—22no—
963C22×C5—22no—
964C22×C5—41no—
965C22×C5—41no—
966C22×C5—41no—
967C22×C5—41no—
968C22×C5—41no—
969C22×C5—41no—
970C22×C5—41no—
971C22×C5—41no—
972C22×C5C23×Q811yescharacteristic
973C22×C5C2×H(5,𝔽2)11yescharacteristic
974C22×C5#58511yescharacteristic
975C22×C5#58511yescharacteristic
976C22×C5#58511yescharacteristic
977C22×C5#58511yescharacteristic
978C22×C5#58511yescharacteristic
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—
1007Dic5—41no—
1008C24C23×D511yescharacteristic
1009C24C23×D511yescharacteristic
1010C2×Q8—22no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—201no—
1017C2×Q8—201no—
1018C2×Q8—201no—
1019C2×Q8—201no—
1020C2×Q8—201no—
1021C2×Q8—201no—
1022C2×Q8—201no—
1023C2×Q8—201no—
1024C2×Q8—201no—
1025C2×D4—41no—
1026C2×D4—41no—
1027C2×D4Q8×D514yes—
1028C22×C4—22no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—54no—
1039C22×C4—54no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—51no—
1044C22×C4—51no—
1045C22×C4—51no—
1046C22×C4—51no—
1047C22×C4—51no—
1048C22×C4—51no—
1049C22×C4—51no—
1050C22×C4—51no—
1051C22×C4—51no—
1052C22×C4—201no—
1053C22×C4—201no—
1054C22×C4—201no—
1055C22×C4—201no—
1056C22×C4—201no—
1057C22×C4—201no—
1058C22×C4—201no—
1059C22×C4—201no—
1060C22×C4—201no—
1061C22×C4—201no—
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
1071C22×C4C23×D511yescharacteristic
1072C22×C4C23×D511yescharacteristic
1073C22×C4C23×D511yescharacteristic
1074C22×C4C23×D511yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—54no—
1085C4⋊C4—102no—
1086C4⋊C4—102no—
1087C4⋊C4—201no—
1088C4⋊C4—201no—
1089C4⋊C4—201no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
1119C22⋊C4—22no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—41no—
1129C22⋊C4—54no—
1130C22⋊C4—54no—
1131C22⋊C4—201no—
1132C22⋊C4—201no—
1133C22⋊C4—201no—
1134C22⋊C4—201no—
1135C22⋊C4—201no—
1136C22⋊C4—201no—
1137C22⋊C4—201no—
1138C22⋊C4—201no—
1139C22⋊C4—201no—
1140C22⋊C4—201no—
1141C42—41no—
1142C42—54no—
1143C42—102no—
1144C42—102no—
1145C42—201no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C42—201no—
1151C42—201no—
1152C42—201no—
1153C42—201no—
1154C2×C5—42no—
1155C2×C5—42no—
1156C2×C5#345811yescharacteristic
1157C2×C5#350111yescharacteristic
1158C2×C5#350411yescharacteristic
1159C2×C5#353311yescharacteristic
1160C2×C5#354011yescharacteristic
1161C2×C5#356611yescharacteristic
1162C2×C5#356811yescharacteristic
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23C2×Q8×D512yes—
1176C23C2×Q8×D512yes—
1177C23C24×D511yescharacteristic
1178Q8—82no—
1179Q8—82no—
1180Q8—402no—
1181Q8—402no—
1182Q8—402no—
1183D4—44no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—44no—
1222C2×C4—52no—
1223C2×C4—52no—
1224C2×C4—52no—
1225C2×C4—52no—
1226C2×C4—82no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—101no—
1263C2×C4—101no—
1264C2×C4—101no—
1265C2×C4—101no—
1266C2×C4—101no—
1267C2×C4—101no—
1268C2×C4—101no—
1269C2×C4—101no—
1270C2×C4—101no—
1271C2×C4—204no—
1272C2×C4—204no—
1273C2×C4—204no—
1274C2×C4—402no—
1275C2×C4#414412yes—
1276C2×C4C2×Q8×D512yes—
1277C5#3675511yescharacteristic, complemented, Sylow
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22C2×#414411yescharacteristic
1293C22C22×Q8×D511yescharacteristic
1294C22#6628311yescharacteristic
1295C22#6628511yescharacteristic
1296C22#6628511yescharacteristic
1297C22#6628511yescharacteristic
1298C22#6628711yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—102no—
1313C4—102no—
1314C4—102no—
1315C4—102no—
1316C4—201no—
1317C4—201no—
1318C4—201no—
1319C4—201no—
1320C4—201no—
1321C4—201no—
1322C4—201no—
1323C4—201no—
1324C4—201no—
1325C4—201no—
1326C4—201no—
1327C4—201no—
1328C2—42no—
1329C2—42no—
1330C2#1061822211yescharacteristic
1331C2#1061844911yescharacteristic
1332C2#1061847211yescharacteristic
1333C2#1061857211yescharacteristic
1334C2#1061866211yescharacteristic
1335C2#1061882811yescharacteristic
1336C2#1061900511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2692C2
prime radicalC22×C5×D4C23
hypercenter#2692D5
hypocenterC5#36755
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2692

Complements

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

NH ≅ G/Ntype
2. #10614541C2semidirect
3. #10614536C2semidirect
4. #10614534C2semidirect
5. #10614493C2semidirect
6. #10609807C2semidirect
7. #10609777C2semidirect
8. #10609606C2semidirect
9. #10609524C2semidirect
10. #10609125C2semidirect
11. #10609077C2semidirect
12. #10608948C2semidirect
13. #10608929C2semidirect
14. #10608575C2semidirect
15. #10608574C2semidirect
16. #10608552C2semidirect
17. #10608513C2semidirect
18. #10608328C2semidirect
19. #10608287C2semidirect
22. #10606955C2semidirect
23. #10606865C2semidirect
28. #10606317C2semidirect
29. #10606304C2semidirect
30. #10605727C2semidirect
31. #10605675C2semidirect
235. D4×Dic5Q8semidirect
1277. C5#36755semidirect

Maximal subgroups

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

subgroupindex
C5×#26922
#106145412
#106145362
#106145342
#106144932
#106098072
#106097772
#106096062
#106095242
#106091252
#106090772
#106089482
#106089292
#106085752
#106085742
#106085522
#106085132
#106083282
#106082872
#106081442
#106080262
#106069552
#106068652
#106065972
#106065922
#106063942
#106063882
#106063172
#106063042
#106057272
#106056752
#367555