Finite Group Databasebeta

← #12306992

Subgroups — #12306992

Order 1280.

1570 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2438C211yesmaximal, characteristic
2#10614520C211yesmaximal, characteristic
3#10614494C211yesmaximal, characteristic
4#10613978C211yesmaximal, characteristic
5#10613963C211yesmaximal, characteristic
6#10610043C211yesmaximal, characteristic, complemented
7#10609985C211yesmaximal, characteristic, complemented
8#10609649C211yesmaximal, characteristic, complemented
9#10609641C211yesmaximal, characteristic, complemented
10#10609639C211yesmaximal, characteristic, complemented
11#10609587C211yesmaximal, characteristic, complemented
12#10608966C211yesmaximal, characteristic, complemented
13#10608955C211yesmaximal, characteristic, complemented
14#10608328C211yesmaximal, characteristic, complemented
15#10608299C211yesmaximal, characteristic, complemented
16#10607907C211yesmaximal, characteristic, complemented
17#10607866C211yesmaximal, characteristic, complemented
18#10606987C211yesmaximal, characteristic, complemented
19#10606984C211yesmaximal, characteristic, complemented
20#10606984C211yesmaximal, characteristic, complemented
21#10606920C211yesmaximal, characteristic, complemented
22#10606317C211yesmaximal, characteristic
23#10606235C211yesmaximal, characteristic
24#10606209C211yesmaximal, characteristic
25#10606147C211yesmaximal, characteristic
26#10605798C211yesmaximal, characteristic
27#10605785C211yesmaximal, characteristic
28#10605732C211yesmaximal, characteristic
29#10605675C211yesmaximal, characteristic
30#10605081C211yesmaximal, characteristic
31C2×#64943C211yesmaximal, characteristic
32C2×C5×C22⋊Q8C2211yescharacteristic
33C2×C5×#117C2211yescharacteristic
34C2×#4090C2211yescharacteristic
35C2×#4072C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4035C2211yescharacteristic
41C2×#4034C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4024C2211yescharacteristic
44C2×#4024C2211yescharacteristic
45C5×#400C2211yescharacteristic
46C5×#398C2211yescharacteristic
47C5×#398C2211yescharacteristic
48C5×#395C2211yescharacteristic
49C5×#391C2211yescharacteristic
50C5×#389C2211yescharacteristic
51C5×#387C2211yescharacteristic
52C5×#387C2211yescharacteristic
53C5×#385C2211yescharacteristic
54C5×#385C2211yescharacteristic
55C5×#381C2211yescharacteristic
56C5×#380C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58#65518C2211yescharacteristic
59#65518C2211yescharacteristic
60#65518C2211yescharacteristic
61#65501C2211yescharacteristic
62#65500C2211yescharacteristic
63#65499C2211yescharacteristic
64#65499C2211yescharacteristic
65C2×#3963C2211yescharacteristic
66C2×#3963C2211yescharacteristic
67C2×#3963C2211yescharacteristic
68#65275C2211yescharacteristic
69#65274C2211yescharacteristic
70#65273C2211yescharacteristic
71#65273C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65273C2211yescharacteristic
75#65272C2211yescharacteristic
76#65272C2211yescharacteristic
77#65272C2211yescharacteristic
78#65272C2211yescharacteristic
79#65272C2211yescharacteristic
80#65271C2211yescharacteristic
81#65271C2211yescharacteristic
82#65270C2211yescharacteristic
83#65270C2211yescharacteristic
84#65270C2211yescharacteristic
85#65269C2211yescharacteristic
86#65269C2211yescharacteristic
87#65269C2211yescharacteristic
88#65269C2211yescharacteristic
89#65269C2211yescharacteristic
90#65268C2211yescharacteristic
91#65268C2211yescharacteristic
92#65268C2211yescharacteristic
93#65268C2211yescharacteristic
94#65268C2211yescharacteristic
95#65267C2211yescharacteristic
96#65267C2211yescharacteristic
97#65267C2211yescharacteristic
98#65265C2211yescharacteristic
99#65265C2211yescharacteristic
100#65265C2211yescharacteristic
101#65262C2211yescharacteristic
102#65262C2211yescharacteristic
103#65262C2211yescharacteristic
104#65262C2211yescharacteristic
105#65262C2211yescharacteristic
106#65261C2211yescharacteristic
107#65261C2211yescharacteristic
108#65261C2211yescharacteristic
109#65239C2211yescharacteristic
110#65239C2211yescharacteristic
111#65235C2211yescharacteristic
112#65235C2211yescharacteristic
113#65231C2211yescharacteristic
114#65231C2211yescharacteristic
115#65231C2211yescharacteristic
116#65231C2211yescharacteristic
117#65231C2211yescharacteristic
118#65231C2211yescharacteristic
119#65231C2211yescharacteristic
120#65231C2211yescharacteristic
121C22⋊C4×Dic5C2211yescharacteristic
122C22⋊C4×Dic5C2211yescharacteristic
123#65222C2211yescharacteristic
124#65222C2211yescharacteristic
125#65218C2211yescharacteristic
126#65217C2211yescharacteristic
127#65217C2211yescharacteristic
128#65217C2211yescharacteristic
129#65217C2211yescharacteristic
130#65217C2211yescharacteristic
131#64950C2211yescharacteristic
132#64950C2211yescharacteristic
133#64949C2211yescharacteristic
134#64949C2211yescharacteristic
135#64948C2211yescharacteristic
136#64948C2211yescharacteristic
137#64947C2211yescharacteristic
138#64947C2211yescharacteristic
139#64947C2211yescharacteristic
140#64947C2211yescharacteristic
141#64946C2211yescharacteristic
142#64946C2211yescharacteristic
143#64946C2211yescharacteristic
144#64946C2211yescharacteristic
145#64946C2211yescharacteristic
146#64945C2211yescharacteristic
147#64945C2211yescharacteristic
148#64945C2211yescharacteristic
149#64944C2211yescharacteristic
150#64944C2211yescharacteristic
151#64943C2211yescharacteristic
152#64943C2211yescharacteristic
153#64943C2211yescharacteristic
154#64943C2211yescharacteristic
155#64943C2211yescharacteristic
156#64943C2211yescharacteristic
157#64943C2211yescharacteristic
158#64943C2211yescharacteristic
159#64943C2211yescharacteristic
160#64943C2211yescharacteristic
161#64943C2211yescharacteristic
162#64943C2211yescharacteristic
163#64943C2211yescharacteristic
164#64943C2211yescharacteristic
165#64942C2211yescharacteristic
166#64942C2211yescharacteristic
167#64942C2211yescharacteristic
168#64942C2211yescharacteristic
169#64942C2211yescharacteristic
170#64942C2211yescharacteristic
171#64942C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64939C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36752—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C22×Dic10C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C5×C22⋊Q8—42no—
200C5×#117—42no—
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C5×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
222#4090—42no—
223#4072—42no—
224C2×C4⋊Dic5Q818yescomplemented
225C2×C4⋊Dic5C2311yescharacteristic
226C2×C4⋊Dic5C2311yescharacteristic
227C2×C4⋊Dic5C2311yescharacteristic
228C2×C4⋊Dic5C2311yescharacteristic
229C2×C4⋊Dic5C2311yescharacteristic
230C2×C4⋊Dic5C2311yescharacteristic
231C2×C4⋊Dic5C2311yescharacteristic
232C2×C4⋊Dic5C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240#4070—42no—
241C2×#683—42no—
242C2×#683C2311yescharacteristic
243C2×#683C2311yescharacteristic
244C2×#683C2311yescharacteristic
245C2×#683C2311yescharacteristic
246C2×#683C2311yescharacteristic
247C2×#683C2311yescharacteristic
248C2×#683C2311yescharacteristic
249C2×#683C2311yescharacteristic
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×#683C2311yescharacteristic
275C2×#683C2311yescharacteristic
276C2×C4×Dic5—42no—
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
287#4035—42no—
288#4034—42no—
289#4034—42no—
290#4024—42no—
291#4024—42no—
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#3963C2311yescharacteristic
353#3963C2311yescharacteristic
354#3963C2311yescharacteristic
355#3963C2311yescharacteristic
356#2857—51no—
357#2851—51no—
358#2805—51no—
359#2805—51no—
360#2802—51no—
361#2802—51no—
362#2792—51no—
363#2792—51no—
364#2791—51no—
365#2791—51no—
366#2791—51no—
367#2791—51no—
368#2755—51no—
369#2755—51no—
370#2734—51no—
371#2734—51no—
372#2713—51no—
373#2713—51no—
374#2659—51no—
375#2646—51no—
376#2569—51no—
377#2569—51no—
378#2440—51no—
379#2440—51no—
380#2438—51no—
381#2438—51no—
382#2438—51no—
383#2438D511yescharacteristic
384#2316—51no—
385#2313—51no—
386C2×#387—51no—
387C24×C5C2411yescharacteristic
388C2×C5×Q8—41no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
391C22×C4×C5—22no—
392C22×C4×C5—22no—
393C22×C4×C5—22no—
394C22×C4×C5—22no—
395C22×C4×C5—22no—
396C22×C4×C5—41no—
397C22×C4×C5—41no—
398C22×C4×C5—41no—
399C22×C4×C5C2×Q814yes—
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×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C22×Dic5—22no—
415C22×Dic5—22no—
416C22×Dic5—22no—
417C22×Dic5—41no—
418C22×Dic5—41no—
419C22×Dic5—41no—
420C22×Dic5—41no—
421C22×Dic5—41no—
422C22×Dic5—41no—
423C22×Dic5—41no—
424C22×Dic5C2×Q814yes—
425C22×Dic5C2×Q814yes—
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
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C2×Dic10—22no—
443C2×Dic10—22no—
444C2×Dic10—41no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C2×Dic10—41no—
449C2×Dic10—41no—
450C2×Dic10—41no—
451C5×C4⋊C4—22no—
452C5×C4⋊C4—22no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4—41no—
461C5×C4⋊C4—41no—
462C5×C22⋊C4—22no—
463C5×C22⋊C4—22no—
464C5×C22⋊C4—22no—
465C5×C22⋊C4—22no—
466C42×C5—41no—
467C42×C5—41no—
468C22⋊Dic5—22no—
469C22⋊Dic5—22no—
470C22⋊Dic5—22no—
471C22⋊Dic5—22no—
472C4⋊Dic5—22no—
473C4⋊Dic5—22no—
474C4⋊Dic5—41no—
475C4⋊Dic5—41no—
476C4⋊Dic5—41no—
477C4⋊Dic5—41no—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5C2×Q814yes—
484C4⋊Dic5C2×Q814yes—
485C4⋊Dic5C2×Q814yes—
486C4⋊Dic5C2×Q814yes—
487#683—22no—
488#683—22no—
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—
515#683—41no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521C4×Dic5—22no—
522C4×Dic5—22no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5—41no—
527C4×Dic5—41no—
528C4×Dic5—41no—
529C4×Dic5—41no—
530C4×Dic5—41no—
531C2×C4⋊Q8—51no—
532C2×C4⋊Q8—51no—
533C2×C4⋊Q8—51no—
534C2×#125—51no—
535C2×C22⋊Q8—51no—
536C2×C22⋊Q8—51no—
537C2×C22⋊Q8—51no—
538C2×C22⋊Q8C2×D511yescharacteristic
539C2×#117—51no—
540C2×#117C2×D511yescharacteristic
541C22×C4⋊C4—51no—
542C22×C4⋊C4—51no—
543C22×C42—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#400—51no—
551#400—51no—
552#400—51no—
553#400—51no—
554#400—51no—
555#400C2×D511yescharacteristic
556#398—51no—
557#398—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398—51no—
567#398—51no—
568#398—51no—
569#398—51no—
570#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#398C2×D511yescharacteristic
579#398C2×D511yescharacteristic
580#395—51no—
581#395—51no—
582#395—51no—
583#395—51no—
584#395—51no—
585#395—51no—
586#395—51no—
587#395—51no—
588#395—51no—
589#395—51no—
590#395—51no—
591#395C2×D511yescharacteristic
592#391—51no—
593#391—51no—
594#391—51no—
595#391—51no—
596#391—51no—
597#391C2×D511yescharacteristic
598#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—51no—
604#389—51no—
605#389—51no—
606#389—51no—
607#389—51no—
608#389—51no—
609#389—51no—
610#389—51no—
611#389—51no—
612#389—51no—
613#389—51no—
614#389—51no—
615#389—51no—
616#389—51no—
617#389—51no—
618#389—51no—
619#389C2×D511yescharacteristic
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#387—51no—
649#387—51no—
650#387—51no—
651#387—51no—
652#387—51no—
653#387—51no—
654#387C2×D511yescharacteristic
655#387C2×D511yescharacteristic
656#385—51no—
657#385—51no—
658#385—51no—
659#385—51no—
660#385—51no—
661#385—51no—
662#385C2×D511yescharacteristic
663#385C2×D511yescharacteristic
664#384—51no—
665#384—51no—
666#384—51no—
667#382—51no—
668#381—51no—
669#381C2×D511yescharacteristic
670#380—51no—
671#380—51no—
672#380—51no—
673#380—51no—
674#380—51no—
675#380—51no—
676#380—51no—
677#380—51no—
678#380—51no—
679#380C2×D511yescharacteristic
680C4×C22⋊C4—51no—
681C4×C22⋊C4—51no—
682C2×#95—51no—
683C2×#95—51no—
684C2×#95—51no—
685C2×#95C2×D511yescharacteristic
686C23×C5—21no—
687C23×C5—21no—
688C23×C5—21no—
689C23×C5—21no—
690C23×C5C22×Q812yes—
691C23×C5H(5,𝔽2)12yes—
692C23×C52−1+412yes—
693C23×C5C2511yescharacteristic
694C5×Q8—82no—
695C2×C4×C5—28no—
696C2×C4×C5—21no—
697C2×C4×C5—21no—
698C2×C4×C5—21no—
699C2×C4×C5—21no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—44no—
736C2×C4×C5—82no—
737C2×C4×C5C22×Q812yes—
738C2×C4×C5C22×Q812yes—
739C2×C4×C52−1+412yes—
740C2×Dic5—21no—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—44no—
784C2×Dic5—44no—
785C2×Dic5—44no—
786C2×Dic5—82no—
787C2×Dic5C22×Q812yes—
788C2×Dic5C22×Q812yes—
789C2×Dic5C22×Q812yes—
790C2×Dic5C22×Q812yes—
791C2×Dic5H(5,𝔽2)12yes—
792Dic10—82no—
793Dic10—82no—
794Dic10—82no—
795C22×Q8—51no—
796C22×Q8—51no—
797C22×Q8—51no—
798C22×Q8C22×D511yescharacteristic
799C23×C4—51no—
800C23×C4—51no—
801C23×C4—51no—
802C23×C4—51no—
803C23×C4C22×D511yescharacteristic
804C23×C4C22×D511yescharacteristic
805C23×C4C22×D511yescharacteristic
806C4⋊Q8—202no—
807C4⋊Q8—202no—
808C4⋊Q8—202no—
809#125—202no—
810C22⋊Q8—42no—
811C22⋊Q8—202no—
812C22⋊Q8—202no—
813C22⋊Q8—202no—
814#117—42no—
815#117—202no—
816C2×C4⋊C4—58no—
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⋊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—202no—
867C2×C4⋊C4C22×D511yescharacteristic
868C2×C4⋊C4C22×D511yescharacteristic
869C2×C4⋊C4C22×D511yescharacteristic
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C4⋊C4C22×D511yescharacteristic
876C2×C4⋊C4C22×D511yescharacteristic
877C2×C4⋊C4C22×D511yescharacteristic
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4C22×D511yescharacteristic
883C2×C22⋊C4C22×D511yescharacteristic
884C2×C22⋊C4C22×D511yescharacteristic
885C2×C22⋊C4C22×D511yescharacteristic
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—51no—
891C2×C42—51no—
892C2×C42—51no—
893C2×C42—51no—
894C2×C42—51no—
895C2×C42—51no—
896C2×C42—202no—
897C2×C42C22×D511yescharacteristic
898C2×C42C22×D511yescharacteristic
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
948#95—51no—
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954#95C22×D511yescharacteristic
955#95C22×D511yescharacteristic
956#95C22×D511yescharacteristic
957#95C22×D511yescharacteristic
958#95C22×D511yescharacteristic
959#95C22×D511yescharacteristic
960#95C22×D511yescharacteristic
961#95C22×D511yescharacteristic
962#95C22×D511yescharacteristic
963C22×C5—22no—
964C22×C5—22no—
965C22×C5—22no—
966C22×C5—22no—
967C22×C5—22no—
968C22×C5—22no—
969C22×C5#54414yes—
970C22×C5C23×Q811yescharacteristic
971C22×C5C2×H(5,𝔽2)11yescharacteristic
972C22×C5C2×H(5,𝔽2)11yescharacteristic
973C22×C5C2×2−1+411yescharacteristic
974C22×C5C2×2−1+411yescharacteristic
975C22×C5#58511yescharacteristic
976C22×C5#58511yescharacteristic
977C4×C5—22no—
978C4×C5—22no—
979C4×C5—22no—
980C4×C5—41no—
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—
991Dic5—22no—
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—
1007C24C23×D511yescharacteristic
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—41no—
1011C2×Q8—102no—
1012C2×Q8—102no—
1013C2×Q8—201no—
1014C2×Q8—201no—
1015C2×Q8—201no—
1016C2×Q8—201no—
1017C2×Q8—201no—
1018C2×Q8—201no—
1019C2×Q8—201no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—54no—
1034C22×C4—54no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—51no—
1039C22×C4—51no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—51no—
1044C22×C4—51no—
1045C22×C4—51no—
1046C22×C4—102no—
1047C22×C4—102no—
1048C22×C4—102no—
1049C22×C4—201no—
1050C22×C4—201no—
1051C22×C4—201no—
1052C22×C4—201no—
1053C22×C4—201no—
1054C22×C4—201no—
1055C22×C4—201no—
1056C22×C4Q8×D514yes—
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C22×C4C23×D511yescharacteristic
1060C22×C4C23×D511yescharacteristic
1061C22×C4C23×D511yescharacteristic
1062C22×C4C23×D511yescharacteristic
1063C22×C4C23×D511yescharacteristic
1064C22×C4C23×D511yescharacteristic
1065C22×C4C23×D511yescharacteristic
1066C22×C4C23×D511yescharacteristic
1067C22×C4C23×D511yescharacteristic
1068C22×C4C23×D511yescharacteristic
1069C22×C4C23×D511yescharacteristic
1070C22×C4C23×D511yescharacteristic
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—54no—
1083C4⋊C4—54no—
1084C4⋊C4—54no—
1085C4⋊C4—54no—
1086C4⋊C4—102no—
1087C4⋊C4—102no—
1088C4⋊C4—102no—
1089C4⋊C4—102no—
1090C4⋊C4—102no—
1091C4⋊C4—102no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
1119C4⋊C4—201no—
1120C4⋊C4—201no—
1121C4⋊C4—201no—
1122C4⋊C4—201no—
1123C4⋊C4—201no—
1124C4⋊C4—201no—
1125C4⋊C4—201no—
1126C4⋊C4—201no—
1127C4⋊C4—201no—
1128C4⋊C4—201no—
1129C4⋊C4—201no—
1130C4⋊C4—201no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—102no—
1136C22⋊C4—102no—
1137C22⋊C4—102no—
1138C22⋊C4—102no—
1139C42—41no—
1140C42—41no—
1141C42—102no—
1142C42—102no—
1143C42—201no—
1144C42—201no—
1145C42—201no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C42—201no—
1151C2×C5—24no—
1152C2×C5C2×#54411yescharacteristic
1153C2×C5#350111yescharacteristic
1154C2×C5#350211yescharacteristic
1155C2×C5#353411yescharacteristic
1156C2×C5#353811yescharacteristic
1157C2×C5#355911yescharacteristic
1158C2×C5#356411yescharacteristic
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23#414412yes—
1164C23C2×Q8×D512yes—
1165C23#415012yes—
1166C23C24×D511yescharacteristic
1167Q8—82no—
1168Q8—402no—
1169Q8—402no—
1170Q8—402no—
1171C2×C4—28no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—44no—
1212C2×C4—52no—
1213C2×C4—52no—
1214C2×C4—52no—
1215C2×C4—52no—
1216C2×C4—52no—
1217C2×C4—82no—
1218C2×C4—101no—
1219C2×C4—101no—
1220C2×C4—101no—
1221C2×C4—101no—
1222C2×C4—101no—
1223C2×C4—101no—
1224C2×C4—101no—
1225C2×C4—101no—
1226C2×C4—101no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—204no—
1262C2×C4—204no—
1263C2×C4—204no—
1264C2×C4—402no—
1265C2×C4C2×Q8×D512yes—
1266C2×C4C2×Q8×D512yes—
1267C2×C4#415012yes—
1268C5#3675211yescharacteristic, complemented, Sylow
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22#6595714yes—
1276C22C2×#414411yescharacteristic
1277C22C22×Q8×D511yescharacteristic
1278C22C2×#415011yescharacteristic
1279C22C2×#415011yescharacteristic
1280C22#6628311yescharacteristic
1281C22D5×H(5,𝔽2)11yescharacteristic
1282C22#6628711yescharacteristic
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—102no—
1298C4—102no—
1299C4—102no—
1300C4—102no—
1301C4—102no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C4—201no—
1313C2—24no—
1314C2C2×#6595711yescharacteristic
1315C2#1061815911yescharacteristic
1316C2#1061850011yescharacteristic
1317C2#1061857011yescharacteristic
1318C2#1061859711yescharacteristic
1319C2#1061870411yescharacteristic
1320C2#1061875411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2438C2
prime radicalC24×C5C24
hypercenter#2438D5
hypocenterC5#36752
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2438

Complements

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

NH ≅ G/Ntype
6. #10610043C2semidirect
7. #10609985C2semidirect
8. #10609649C2semidirect
9. #10609641C2semidirect
10. #10609639C2semidirect
11. #10609587C2semidirect
12. #10608966C2semidirect
13. #10608955C2semidirect
14. #10608328C2semidirect
15. #10608299C2semidirect
16. #10607907C2semidirect
17. #10607866C2semidirect
18. #10606987C2semidirect
19. #10606984C2semidirect
20. #10606984C2semidirect
21. #10606920C2semidirect
224. C2×C4⋊Dic5Q8semidirect
1268. C5#36752semidirect

Maximal subgroups

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

subgroupindex
C5×#24382
#106145202
#106144942
#106139782
#106139632
#106100432
#106099852
#106096492
#106096412
#106096392
#106095872
#106089662
#106089552
#106083282
#106082992
#106079072
#106078662
#106069872
#106069842
#106069202
#106063172
#106062352
#106062092
#106061472
#106057982
#106057852
#106057322
#106056752
#106050812
C2×#649432
#367525