Finite Group Databasebeta

← #12266437

Subgroups — #12266437

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2650C211yesmaximal, characteristic, complemented
2#10609947C211yesmaximal, characteristic, complemented
3#10609946C211yesmaximal, characteristic, complemented
4#10609939C211yesmaximal, characteristic, complemented
5#10609863C211yesmaximal, characteristic, complemented
6#10609862C211yesmaximal, characteristic, complemented
7#10609860C211yesmaximal, characteristic, complemented
8#10609279C211yesmaximal, characteristic, complemented
9#10609270C211yesmaximal, characteristic
10#10609192C211yesmaximal, characteristic, complemented
11#10609190C211yesmaximal, characteristic, complemented
12#10609062C211yesmaximal, characteristic
13#10609013C211yesmaximal, characteristic, complemented
14#10608933C211yesmaximal, characteristic, complemented
15#10608901C211yesmaximal, characteristic, complemented
16#10608546C211yesmaximal, characteristic, complemented
17#10608510C211yesmaximal, characteristic, complemented
18#10608292C211yesmaximal, characteristic, complemented
19#10608212C211yesmaximal, characteristic, complemented
20#10607640C211yesmaximal, characteristic, complemented
21#10607636C211yesmaximal, characteristic, complemented
22#10607392C211yesmaximal, characteristic, complemented
23#10607185C211yesmaximal, characteristic, complemented
24#10607183C211yesmaximal, characteristic
25#10607181C211yesmaximal, characteristic, complemented
26#10607112C211yesmaximal, characteristic, complemented
27#10606869C211yesmaximal, characteristic, complemented
28#10606672C211yesmaximal, characteristic, complemented
29#10606669C211yesmaximal, characteristic, complemented
30#10605545C211yesmaximal, characteristic, complemented
31C4×#4038C211yesmaximal, characteristic, complemented
32C2×Q8×Dic5C2211yescharacteristic
33C2×#4090C2211yescharacteristic
34C2×#4042C2211yescharacteristic
35C2×#4039C2211yescharacteristic
36C2×#4038C2211yescharacteristic
37C2×#4038C2211yescharacteristic
38C2×#4038C2211yescharacteristic
39C2×#4033C2211yescharacteristic
40C2×#4033C2211yescharacteristic
41C2×#4031C2211yescharacteristic
42C2×#4030C2211yescharacteristic
43C2×#4027C2211yescharacteristic
44C2×#4027C2211yescharacteristic
45C2×#4023C2211yescharacteristic
46C2×C42×D5C2211yescharacteristic
47C5×#400C2211yescharacteristic
48C5×#400C2211yescharacteristic
49C5×#400C2211yescharacteristic
50C5×#397C2211yescharacteristic
51C5×#397C2211yescharacteristic
52C5×#396C2211yescharacteristic
53C5×#395C2211yescharacteristic
54C5×#393C2211yescharacteristic
55C5×#391C2211yescharacteristic
56C5×#388C2211yescharacteristic
57C5×#388C2211yescharacteristic
58C5×#388C2211yescharacteristic
59C5×#387C2211yescharacteristic
60C5×#387C2211yescharacteristic
61C4×C5×C4⋊C4C2211yescharacteristic
62#65520C2211yescharacteristic
63#65520C2211yescharacteristic
64#65283C2211yescharacteristic
65#65283C2211yescharacteristic
66#65283C2211yescharacteristic
67#65282C2211yescharacteristic
68#65281C2211yescharacteristic
69#65281C2211yescharacteristic
70#65280C2211yescharacteristic
71#65279C2211yescharacteristic
72#65278C2211yescharacteristic
73#65275C2211yescharacteristic
74#65273C2211yescharacteristic
75#65272C2211yescharacteristic
76#65272C2211yescharacteristic
77#65271C2211yescharacteristic
78#65271C2211yescharacteristic
79#65270C2211yescharacteristic
80#65268C2211yescharacteristic
81#65265C2211yescharacteristic
82C4⋊C4×Dic5C2211yescharacteristic
83C4⋊C4×Dic5C2211yescharacteristic
84C4⋊C4×Dic5C2211yescharacteristic
85C4⋊C4×Dic5C2211yescharacteristic
86#65261C2211yescharacteristic
87#65261C2211yescharacteristic
88#65261C2211yescharacteristic
89#65250C2211yescharacteristic
90#65250C2211yescharacteristic
91#65250C2211yescharacteristic
92#65248C2211yescharacteristic
93#65246C2211yescharacteristic
94#65246C2211yescharacteristic
95#65246C2211yescharacteristic
96#65246C2211yescharacteristic
97#65245C2211yescharacteristic
98#65242C2211yescharacteristic
99#65241C2211yescharacteristic
100#65241C2211yescharacteristic
101#65241C2211yescharacteristic
102#65240C2211yescharacteristic
103#65238C2211yescharacteristic
104#65237C2211yescharacteristic
105#65237C2211yescharacteristic
106#65236C2211yescharacteristic
107#65234C2211yescharacteristic
108C22⋊C4×Dic5C2211yescharacteristic
109C22⋊C4×Dic5C2211yescharacteristic
110C22⋊C4×Dic5C2211yescharacteristic
111C22⋊C4×Dic5C2211yescharacteristic
112#65229C2211yescharacteristic
113#65229C2211yescharacteristic
114#65229C2211yescharacteristic
115C4×#685C2211yescharacteristic
116C4×#685C2211yescharacteristic
117C4×C4⋊Dic5C2211yescharacteristic
118#65222C2211yescharacteristic
119#65222C2211yescharacteristic
120C42×Dic5C2211yescharacteristic
121C42×Dic5C2211yescharacteristic
122#65218C2211yescharacteristic
123#64966C2211yescharacteristic
124#64964C2211yescharacteristic
125#64964C2211yescharacteristic
126#64964C2211yescharacteristic
127#64964C2211yescharacteristic
128#64964C2211yescharacteristic
129#64964C2211yescharacteristic
130#64963C2211yescharacteristic
131#64963C2211yescharacteristic
132#64963C2211yescharacteristic
133#64962C2211yescharacteristic
134#64962C2211yescharacteristic
135#64961C2211yescharacteristic
136#64961C2211yescharacteristic
137#64961C2211yescharacteristic
138#64958C2211yescharacteristic
139#64957C2211yescharacteristic
140#64956C2211yescharacteristic
141#64956C2211yescharacteristic
142#64955C2211yescharacteristic
143#64955C2211yescharacteristic
144#64955C2211yescharacteristic
145#64955C2211yescharacteristic
146#64955C2211yescharacteristic
147#64955C2211yescharacteristic
148#64955C2211yescharacteristic
149#64955C2211yescharacteristic
150#64954C2211yescharacteristic
151C5⋊#401C2211yescharacteristic
152C5⋊#401C2211yescharacteristic
153#64950C2211yescharacteristic
154#64950C2211yescharacteristic
155#64949C2211yescharacteristic
156#64949C2211yescharacteristic
157#64949C2211yescharacteristic
158#64949C2211yescharacteristic
159#64948C2211yescharacteristic
160#64947C2211yescharacteristic
161#64947C2211yescharacteristic
162#64947C2211yescharacteristic
163#64946C2211yescharacteristic
164#64941C2211yescharacteristic
165#64939C2211yescharacteristic
166#64938C2211yescharacteristic
167#64938C2211yescharacteristic
168#64938C2211yescharacteristic
169#64938C2211yescharacteristic
170#64938C2211yescharacteristic
171#64938C2211yescharacteristic
172#64937C2211yescharacteristic
173#64937C2211yescharacteristic
174#64937C2211yescharacteristic
175#64937C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#34619—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C22×D20C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C42×C5C2311yescharacteristic
215C2×C42×C5C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222Q8×Dic5—42no—
223#4090—24no—
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
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×#685C2311yescharacteristic
245C2×#685C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
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×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290C2×C4×Dic5C2311yescharacteristic
291C2×C4×Dic5C2311yescharacteristic
292C2×C4×Dic5C2311yescharacteristic
293#4042—24no—
294#4039—42no—
295#4038—24no—
296#4038—24no—
297#4038—42no—
298#4033—24no—
299#4033—42no—
300#4031—24no—
301#4030—24no—
302#4027—24no—
303#4027—42no—
304#4023—42no—
305C42×D5—24no—
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312C5×#95C2311yescharacteristic
313C5×#95C2311yescharacteristic
314C5×#95C2311yescharacteristic
315C5×#95C2311yescharacteristic
316C5×#95C2311yescharacteristic
317C5×#95C2311yescharacteristic
318C5×#95C2311yescharacteristic
319C5×#95C2311yescharacteristic
320C5×#95C2311yescharacteristic
321C5×#95C2311yescharacteristic
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#2654—51no—
359#2654—51no—
360#2653—51no—
361#2653—51no—
362#2650—51no—
363#2650D511yescharacteristic, complemented
364#2649—51no—
365#2649—51no—
366#2647—51no—
367#2645—51no—
368#2644—51no—
369#2640—51no—
370#2628—51no—
371#2625—51no—
372#2624—51no—
373#2620—51no—
374#2401—51no—
375#2401—51no—
376#2398—51no—
377#2398—51no—
378#2396—51no—
379#2396—51no—
380#2395—51no—
381#2395—51no—
382C4×C4⋊Q8—51no—
383C4×#124—51no—
384C4×C22⋊Q8—51no—
385C4×#121—51no—
386#2295—51no—
387#2293—51no—
388C4×#117—51no—
389C24×C5C2411yescharacteristic
390C23×D5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C2×C5×Q8—22no—
393C2×C5×Q8—41no—
394C2×C5×Q8—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—41no—
415C22×Dic5—22no—
416C22×Dic5—22no—
417C22×Dic5—22no—
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C2×D20—22no—
433C2×D20—41no—
434C2×D20—41no—
435C2×C4×D5—22no—
436C2×C4×D5—22no—
437C2×C4×D5—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—41no—
445C2×C4×D5—41no—
446C2×C4×D5#4114yes—
447C2×Dic10—22no—
448C2×Dic10—22no—
449C2×Dic10—22no—
450C2×Dic10—22no—
451C2×Dic10—41no—
452C2×Dic10—41no—
453C5×C4⋊C4—22no—
454C5×C4⋊C4—22no—
455C5×C4⋊C4—22no—
456C5×C4⋊C4—22no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C4⋊C4—41no—
461C5×C22⋊C4—22no—
462C5×C22⋊C4—22no—
463C5×C22⋊C4—22no—
464C5×C22⋊C4—41no—
465C5×C22⋊C4—41no—
466C5×C22⋊C4—41no—
467C5×C22⋊C4—41no—
468C42×C5—22no—
469C42×C5—41no—
470C42×C5—41no—
471C22⋊Dic5—22no—
472C22⋊Dic5—41no—
473C22⋊Dic5—41no—
474C22⋊Dic5—41no—
475C22⋊Dic5—41no—
476#685—22no—
477#685—22no—
478#685—22no—
479#685—22no—
480#685—22no—
481#685—22no—
482#685—22no—
483#685—22no—
484#685—22no—
485#685—22no—
486#685—41no—
487#685—41no—
488#685—41no—
489#685—41no—
490#685—41no—
491#685—41no—
492#685—41no—
493#685—41no—
494#685—41no—
495#685—41no—
496#685—41no—
497#685—41no—
498C4⋊Dic5—22no—
499C4⋊Dic5—22no—
500C4⋊Dic5—41no—
501C4⋊Dic5—41no—
502C4⋊Dic5—41no—
503C4⋊Dic5—41no—
504C4⋊Dic5—41no—
505C4⋊Dic5—41no—
506#683—22no—
507#683—22no—
508#683—22no—
509#683—22no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
525#683—41no—
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—41no—
542C4×Dic5—41no—
543C4×Dic5#4114yes—
544C4×Dic5#4114yes—
545C2×C4⋊Q8—51no—
546C2×#124—51no—
547C2×C22⋊Q8—51no—
548C2×#121—51no—
549C2×C4×Q8—51no—
550C2×C4×Q8—51no—
551C2×C4×Q8—51no—
552C2×C4×D4—51no—
553C2×C4×D4—51no—
554C2×C4×D4—51no—
555C2×#117—51no—
556C2×#117—51no—
557C2×#117—51no—
558C2×#117—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#400—51no—
573#400C2×D511yescharacteristic
574#400C2×D511yescharacteristic
575#400C2×D511yescharacteristic
576#399—51no—
577#399—51no—
578#399—51no—
579#399—51no—
580#398—51no—
581#398—51no—
582#398—51no—
583#398—51no—
584#398—51no—
585#398—51no—
586#397—51no—
587#397—51no—
588#397—51no—
589#397—51no—
590#397—51no—
591#397—51no—
592#397—51no—
593#397—51no—
594#397—51no—
595#397—51no—
596#397—51no—
597#397—51no—
598#397—51no—
599#397—51no—
600#397C2×D511yescharacteristic
601#397C2×D511yescharacteristic
602#396—51no—
603#396—51no—
604#396—51no—
605#396—51no—
606#396—51no—
607#396C2×D511yescharacteristic
608#395—51no—
609#395C2×D511yescharacteristic
610#394—51no—
611#394—51no—
612#394—51no—
613#394—51no—
614#394—51no—
615#394—51no—
616#394—51no—
617#394—51no—
618#393—51no—
619#393—51no—
620#393—51no—
621#393—51no—
622#393—51no—
623#393C2×D511yescharacteristic
624#391—51no—
625#391—51no—
626#391—51no—
627#391—51no—
628#391—51no—
629#391C2×D511yescharacteristic
630#390—51no—
631#390—51no—
632#390—51no—
633#390—51no—
634#389—51no—
635#389—51no—
636#389—51no—
637#389—51no—
638#389—51no—
639#389—51no—
640#389—51no—
641#389—51no—
642#389—51no—
643#389—51no—
644#388—51no—
645#388—51no—
646#388—51no—
647#388—51no—
648#388—51no—
649#388—51no—
650#388—51no—
651#388C2×D511yescharacteristic
652#388C2×D511yescharacteristic
653#388C2×D511yescharacteristic
654#387—51no—
655#387—51no—
656#387—51no—
657#387—51no—
658#387C2×D511yescharacteristic
659#387C2×D511yescharacteristic
660#386—51no—
661#386—51no—
662#385—51no—
663#385—51no—
664#384—51no—
665#382—51no—
666#380—51no—
667#380—51no—
668C4×C4⋊C4—51no—
669C4×C4⋊C4—51no—
670C4×C4⋊C4—51no—
671C4×C4⋊C4—51no—
672C4×C4⋊C4—51no—
673C4×C4⋊C4—51no—
674C4×C4⋊C4—51no—
675C4×C4⋊C4—51no—
676C4×C4⋊C4—51no—
677C4×C4⋊C4—51no—
678C4×C4⋊C4—51no—
679C4×C4⋊C4C2×D511yescharacteristic
680C4×C22⋊C4—51no—
681C4×C22⋊C4—51no—
682C4×C22⋊C4—51no—
683C4×C22⋊C4—51no—
684C4×C22⋊C4—51no—
685C4×C22⋊C4—51no—
686C4×C22⋊C4—51no—
687C4×C22⋊C4—51no—
688C4×C22⋊C4—51no—
689C4×C22⋊C4—51no—
690C4×C22⋊C4—51no—
691C4×C22⋊C4—51no—
692C4×C22⋊C4—51no—
693C4×C22⋊C4—51no—
694#376—51no—
695#376—51no—
696#376—51no—
697#376—51no—
698C43—51no—
699C43—51no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5—21no—
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×D5—21no—
720C22×D5—21no—
721C22×D5C2×#4112yes—
722C5×Q8—44no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—21no—
747C2×C4×C5—21no—
748C2×C4×C5—21no—
749C2×C4×C5—21no—
750C2×C4×C5—21no—
751C2×C4×C5—21no—
752C2×C4×C5—21no—
753C2×C4×C5—21no—
754C2×C4×C5—21no—
755C2×C4×C5—21no—
756C2×C4×C5—21no—
757C2×C4×C5—21no—
758C2×C4×C5—21no—
759C2×C4×C5—21no—
760C2×C4×C5—21no—
761C2×C4×C5—21no—
762C2×C4×C5C2×#4112yes—
763C2×C4×C5C2×#4112yes—
764C2×C4×C5C2×#4112yes—
765C22⋊D5—44no—
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×Dic5C2×#4112yes—
804C2×Dic5C2×#4112yes—
805C2×Dic5C2×#4112yes—
806C2×Dic5C2×#4112yes—
807C2×Dic5C2×#4112yes—
808C2×Dic5H(5,𝔽2)12yes—
809C2×Dic52−1+412yes—
810D20—44no—
811C4×D5—28no—
812C4×D5—44no—
813C4×D5—44no—
814C4×D5—44no—
815Dic10—44no—
816Dic10—44no—
817C22×Q8—51no—
818C22×Q8—51no—
819C22×Q8C22×D511yescharacteristic
820C22×D4—51no—
821C22×D4—51no—
822C22×D4—51no—
823C23×C4—51no—
824C23×C4—51no—
825C23×C4—51no—
826C23×C4—51no—
827C23×C4—51no—
828C4⋊Q8—104no—
829#124—104no—
830C22⋊Q8—104no—
831#121—104no—
832C4×Q8—104no—
833C4×Q8—202no—
834C4×Q8—202no—
835C4×D4—104no—
836C4×D4—202no—
837C4×D4—202no—
838#117—104no—
839#117—104no—
840#117—202no—
841#117—202no—
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—51no—
867C2×C4⋊C4—51no—
868C2×C4⋊C4—51no—
869C2×C4⋊C4—51no—
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C4⋊C4C22×D511yescharacteristic
876C2×C4⋊C4C22×D511yescharacteristic
877C2×C4⋊C4C22×D511yescharacteristic
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—51no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4—51no—
886C2×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⋊C4—51no—
898C2×C22⋊C4—51no—
899C2×C22⋊C4—51no—
900C2×C22⋊C4—51no—
901C2×C22⋊C4—51no—
902C2×C22⋊C4—51no—
903C2×C22⋊C4—51no—
904C2×C22⋊C4—51no—
905C2×C22⋊C4C22×D511yescharacteristic
906C2×C22⋊C4C22×D511yescharacteristic
907C2×C22⋊C4C22×D511yescharacteristic
908C2×C22⋊C4C22×D511yescharacteristic
909C2×C22⋊C4C22×D511yescharacteristic
910C2×C22⋊C4C22×D511yescharacteristic
911C2×C22⋊C4C22×D511yescharacteristic
912C2×C42—51no—
913C2×C42—51no—
914C2×C42—51no—
915C2×C42—51no—
916C2×C42—51no—
917C2×C42—51no—
918C2×C42—51no—
919C2×C42—51no—
920C2×C42—51no—
921C2×C42—51no—
922C2×C42—51no—
923C2×C42—51no—
924C2×C42—51no—
925C2×C42—51no—
926C2×C42—51no—
927C2×C42—51no—
928C2×C42—51no—
929C2×C42—51no—
930C2×C42—51no—
931C2×C42—104no—
932C2×C42C22×D511yescharacteristic
933C2×C42C22×D511yescharacteristic
934C2×C42C22×D511yescharacteristic
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#95C22×D511yescharacteristic
972#95C22×D511yescharacteristic
973#95C22×D511yescharacteristic
974#95C22×D511yescharacteristic
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
987C22×C5—41no—
988C22×C5—41no—
989C22×C5—41no—
990C22×C5—41no—
991C22×C5—41no—
992C22×C5—41no—
993C22×C5—41no—
994C22×C5C22×#4111yescharacteristic
995C22×C5C22×#4111yescharacteristic
996C22×C5C22×#4111yescharacteristic
997C22×C5C2×H(5,𝔽2)11yescharacteristic
998C22×C5C2×2−1+411yescharacteristic
999C22×C5#58511yescharacteristic
1000C22×C5#58511yescharacteristic
1001C2×D5—22no—
1002C2×D5—22no—
1003C2×D5—22no—
1004C2×D5—41no—
1005C2×D5—41no—
1006C2×D5—41no—
1007C2×D5—41no—
1008C2×D5—41no—
1009C2×D5—41no—
1010C2×D5—41no—
1011C2×D5—41no—
1012C2×D5—41no—
1013C2×D5—41no—
1014C2×D5—41no—
1015C4×C5—22no—
1016C4×C5—22no—
1017C4×C5—22no—
1018C4×C5—41no—
1019C4×C5—41no—
1020C4×C5—41no—
1021C4×C5—41no—
1022C4×C5—41no—
1023C4×C5—41no—
1024C4×C5—41no—
1025C4×C5—41no—
1026C4×C5—41no—
1027C4×C5—41no—
1028C4×C5—41no—
1029Dic5—22no—
1030Dic5—41no—
1031Dic5—41no—
1032Dic5—41no—
1033Dic5—41no—
1034Dic5—41no—
1035Dic5—41no—
1036Dic5—41no—
1037Dic5—41no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5#52914yes—
1042Dic5#54214yes—
1043C24—51no—
1044C24—51no—
1045C24C23×D511yescharacteristic
1046C2×Q8—22no—
1047C2×Q8—41no—
1048C2×Q8—41no—
1049C2×Q8—102no—
1050C2×Q8—102no—
1051C2×Q8—102no—
1052C2×Q8—102no—
1053C2×Q8—201no—
1054C2×Q8—201no—
1055C2×D4—102no—
1056C2×D4—102no—
1057C2×D4—102no—
1058C2×D4—102no—
1059C2×D4—102no—
1060C2×D4—201no—
1061C2×D4—201no—
1062C2×D4—201no—
1063C2×D4—201no—
1064C22×C4—51no—
1065C22×C4—51no—
1066C22×C4—51no—
1067C22×C4—54no—
1068C22×C4—51no—
1069C22×C4—51no—
1070C22×C4—51no—
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—102no—
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—201no—
1092C22×C4—201no—
1093C22×C4C23×D511yescharacteristic
1094C22×C4C23×D511yescharacteristic
1095C22×C4C23×D511yescharacteristic
1096C22×C4C23×D511yescharacteristic
1097C22×C4C23×D511yescharacteristic
1098C22×C4C23×D511yescharacteristic
1099C22×C4C23×D511yescharacteristic
1100C22×C4C23×D511yescharacteristic
1101C22×C4C23×D511yescharacteristic
1102C22×C4C23×D511yescharacteristic
1103C22×C4C23×D511yescharacteristic
1104C22×C4C23×D511yescharacteristic
1105C22×C4C23×D511yescharacteristic
1106C22×C4C23×D511yescharacteristic
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—22no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—41no—
1114C4⋊C4—41no—
1115C4⋊C4—102no—
1116C4⋊C4—102no—
1117C4⋊C4—102no—
1118C4⋊C4—102no—
1119C4⋊C4—102no—
1120C4⋊C4—102no—
1121C4⋊C4—102no—
1122C4⋊C4—102no—
1123C4⋊C4—102no—
1124C4⋊C4—102no—
1125C4⋊C4—102no—
1126C4⋊C4—102no—
1127C4⋊C4—201no—
1128C4⋊C4—201no—
1129C4⋊C4—201no—
1130C4⋊C4—201no—
1131C4⋊C4—201no—
1132C4⋊C4—201no—
1133C4⋊C4—201no—
1134C4⋊C4—201no—
1135C4⋊C4—201no—
1136C4⋊C4—201no—
1137C4⋊C4—201no—
1138C4⋊C4—201no—
1139C4⋊C4—201no—
1140C4⋊C4—201no—
1141C4⋊C4—201no—
1142C4⋊C4—201no—
1143C22⋊C4—22no—
1144C22⋊C4—22no—
1145C22⋊C4—22no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—102no—
1151C22⋊C4—102no—
1152C22⋊C4—102no—
1153C22⋊C4—102no—
1154C22⋊C4—102no—
1155C22⋊C4—102no—
1156C22⋊C4—102no—
1157C22⋊C4—102no—
1158C22⋊C4—102no—
1159C22⋊C4—102no—
1160C22⋊C4—102no—
1161C22⋊C4—201no—
1162C22⋊C4—201no—
1163C22⋊C4—201no—
1164C22⋊C4—201no—
1165C22⋊C4—201no—
1166C22⋊C4—201no—
1167C22⋊C4—201no—
1168C22⋊C4—201no—
1169C22⋊C4—201no—
1170C22⋊C4—201no—
1171C22⋊C4—201no—
1172C22⋊C4—201no—
1173C22⋊C4—201no—
1174C22⋊C4—201no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
1177C42—22no—
1178C42—41no—
1179C42—41no—
1180C42—54no—
1181C42—54no—
1182C42—102no—
1183C42—102no—
1184C42—102no—
1185C42—102no—
1186C42—102no—
1187C42—102no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—102no—
1195C42—102no—
1196C42—102no—
1197C42—201no—
1198C42—201no—
1199C2×C5—81no—
1200C2×C5C2×#52911yescharacteristic
1201C2×C5C2×#54211yescharacteristic
1202C2×C5#345511yescharacteristic
1203C2×C5#346011yescharacteristic
1204C2×C5#346011yescharacteristic
1205C2×C5#346111yescharacteristic
1206C2×C5#346111yescharacteristic
1207D5—42no—
1208D5—81no—
1209C23—21no—
1210C23—21no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—52no—
1217C23—101no—
1218C23—101no—
1219C23—101no—
1220C23—101no—
1221C23—101no—
1222C23—101no—
1223C23—101no—
1224C23—101no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23—101no—
1230C23C24×D511yescharacteristic
1231Q8—44no—
1232Q8—204no—
1233Q8—204no—
1234D4—204no—
1235D4—204no—
1236D4—204no—
1237C2×C4—21no—
1238C2×C4—21no—
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—52no—
1277C2×C4—52no—
1278C2×C4—52no—
1279C2×C4—52no—
1280C2×C4—52no—
1281C2×C4—52no—
1282C2×C4—52no—
1283C2×C4—108no—
1284C2×C4—101no—
1285C2×C4—101no—
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—204no—
1320C2×C4—204no—
1321C2×C4—204no—
1322C2×C4—204no—
1323C2×C4D5×#4112yes—
1324C2×C4D5×#4112yes—
1325C2×C4D5×#4112yes—
1326C5#3461911yescharacteristic, complemented, Sylow
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—102no—
1335C22—102no—
1336C22—102no—
1337C22—201no—
1338C22—201no—
1339C22—201no—
1340C22—201no—
1341C22—201no—
1342C22—201no—
1343C22—201no—
1344C22—201no—
1345C22—201no—
1346C22—201no—
1347C22—201no—
1348C22C2×D5×#4111yescharacteristic
1349C22C2×D5×#4111yescharacteristic
1350C22C2×D5×#4111yescharacteristic
1351C22D5×H(5,𝔽2)11yescharacteristic
1352C22#6628511yescharacteristic
1353C22D5×2−1+411yescharacteristic
1354C22#6628711yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—54no—
1370C4—54no—
1371C4—102no—
1372C4—201no—
1373C4—201no—
1374C4—201no—
1375C4—201no—
1376C4—201no—
1377C4—201no—
1378C4—201no—
1379C4—201no—
1380C4—201no—
1381C4—201no—
1382C4—201no—
1383C2—81no—
1384C2—202no—
1385C2—401no—
1386C2D5×#52911yescharacteristic
1387C2#1061829011yescharacteristic
1388C2#1061832811yescharacteristic
1389C2#1061839711yescharacteristic
1390C2#1061842511yescharacteristic
1391C2#1061842611yescharacteristic
1392C2D5×#54211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2650C2
prime radicalC2×#4030C22
hypercenter#2650D5
hypocenterC5#34619
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2650

Complements

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

NH ≅ G/Ntype
1. C5×#2650C2semidirect
2. #10609947C2semidirect
3. #10609946C2semidirect
4. #10609939C2semidirect
5. #10609863C2semidirect
6. #10609862C2semidirect
7. #10609860C2semidirect
8. #10609279C2semidirect
10. #10609192C2semidirect
11. #10609190C2semidirect
13. #10609013C2semidirect
14. #10608933C2semidirect
15. #10608901C2semidirect
16. #10608546C2semidirect
17. #10608510C2semidirect
18. #10608292C2semidirect
19. #10608212C2semidirect
20. #10607640C2semidirect
21. #10607636C2semidirect
22. #10607392C2semidirect
23. #10607185C2semidirect
25. #10607181C2semidirect
26. #10607112C2semidirect
27. #10606869C2semidirect
28. #10606672C2semidirect
29. #10606669C2semidirect
30. #10605545C2semidirect
31. C4×#4038C2semidirect
363. #2650D5semidirect
1326. C5#34619semidirect

Maximal subgroups

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

subgroupindex
C5×#26502
#106099472
#106099462
#106099392
#106098632
#106098622
#106098602
#106092792
#106092702
#106091922
#106091902
#106090622
#106090132
#106089332
#106089012
#106085462
#106085102
#106082922
#106082122
#106076402
#106076362
#106073922
#106071852
#106071832
#106071812
#106071122
#106068692
#106066722
#106066692
#106055452
C4×#40382
#346195