Finite Group Databasebeta

← #12305802

Subgroups — #12305802

Order 1280.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2831C211yesmaximal, characteristic, complemented
2#10610138C211yesmaximal, characteristic, complemented
3#10610063C211yesmaximal, characteristic, complemented
4#10610056C211yesmaximal, characteristic, complemented
5#10609864C211yesmaximal, characteristic, complemented
6#10609863C211yesmaximal, characteristic, complemented
7#10609863C211yesmaximal, characteristic, complemented
8#10609746C211yesmaximal, characteristic, complemented
9#10609744C211yesmaximal, characteristic, complemented
10#10609472C211yesmaximal, characteristic, complemented
11#10609471C211yesmaximal, characteristic, complemented
12#10609465C211yesmaximal, characteristic
13#10609396C211yesmaximal, characteristic, complemented
14#10609386C211yesmaximal, characteristic, complemented
15#10609192C211yesmaximal, characteristic, complemented
16#10609191C211yesmaximal, characteristic
17#10609190C211yesmaximal, characteristic
18#10609185C211yesmaximal, characteristic
19#10609180C211yesmaximal, characteristic
20#10609014C211yesmaximal, characteristic, complemented
21#10609013C211yesmaximal, characteristic, complemented
22#10608972C211yesmaximal, characteristic, complemented
23#10608902C211yesmaximal, characteristic, complemented
24#10608615C211yesmaximal, characteristic
25#10608509C211yesmaximal, characteristic, complemented
26#10608336C211yesmaximal, characteristic, complemented
27#10608210C211yesmaximal, characteristic, complemented
28#10607550C211yesmaximal, characteristic, complemented
29#10607184C211yesmaximal, characteristic
30#10607020C211yesmaximal, characteristic, complemented
31#10606672C211yesmaximal, characteristic, complemented
32C2×#4092C2211yescharacteristic
33C2×Q8×Dic5C2211yescharacteristic
34C2×#4042C2211yescharacteristic
35C2×#4033C2211yescharacteristic
36C2×#4033C2211yescharacteristic
37C2×#4029C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4023C2211yescharacteristic
40C2×C42×D5C2211yescharacteristic
41C5×#400C2211yescharacteristic
42C5×#400C2211yescharacteristic
43C5×#400C2211yescharacteristic
44C5×#398C2211yescharacteristic
45C5×#398C2211yescharacteristic
46C5×#397C2211yescharacteristic
47C5×#397C2211yescharacteristic
48C5×#397C2211yescharacteristic
49C5×#396C2211yescharacteristic
50C5×#396C2211yescharacteristic
51C5×#395C2211yescharacteristic
52C5×#393C2211yescharacteristic
53C5×#391C2211yescharacteristic
54C5×#388C2211yescharacteristic
55C5×#387C2211yescharacteristic
56#65518C2211yescharacteristic
57#65518C2211yescharacteristic
58#65283C2211yescharacteristic
59#65283C2211yescharacteristic
60#65282C2211yescharacteristic
61#65282C2211yescharacteristic
62#65282C2211yescharacteristic
63#65281C2211yescharacteristic
64#65278C2211yescharacteristic
65#65278C2211yescharacteristic
66#65276C2211yescharacteristic
67#65275C2211yescharacteristic
68#65275C2211yescharacteristic
69#65275C2211yescharacteristic
70#65275C2211yescharacteristic
71#65273C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65273C2211yescharacteristic
75#65273C2211yescharacteristic
76#65272C2211yescharacteristic
77#65272C2211yescharacteristic
78#65272C2211yescharacteristic
79#65271C2211yescharacteristic
80#65271C2211yescharacteristic
81#65269C2211yescharacteristic
82#65269C2211yescharacteristic
83#65268C2211yescharacteristic
84#65268C2211yescharacteristic
85#65268C2211yescharacteristic
86#65268C2211yescharacteristic
87C4⋊C4×Dic5C2211yescharacteristic
88C4⋊C4×Dic5C2211yescharacteristic
89C4⋊C4×Dic5C2211yescharacteristic
90C4⋊C4×Dic5C2211yescharacteristic
91C4⋊C4×Dic5C2211yescharacteristic
92C4⋊C4×Dic5C2211yescharacteristic
93C4⋊C4×Dic5C2211yescharacteristic
94C4⋊C4×Dic5C2211yescharacteristic
95#65250C2211yescharacteristic
96#65248C2211yescharacteristic
97#65248C2211yescharacteristic
98#65248C2211yescharacteristic
99#65245C2211yescharacteristic
100#65242C2211yescharacteristic
101#65242C2211yescharacteristic
102#65242C2211yescharacteristic
103#65241C2211yescharacteristic
104#65241C2211yescharacteristic
105#65241C2211yescharacteristic
106#65238C2211yescharacteristic
107#65238C2211yescharacteristic
108#65237C2211yescharacteristic
109#65237C2211yescharacteristic
110#65237C2211yescharacteristic
111#65237C2211yescharacteristic
112#65236C2211yescharacteristic
113#65236C2211yescharacteristic
114#65233C2211yescharacteristic
115C22⋊C4×Dic5C2211yescharacteristic
116C22⋊C4×Dic5C2211yescharacteristic
117C22⋊C4×Dic5C2211yescharacteristic
118C22⋊C4×Dic5C2211yescharacteristic
119C22⋊C4×Dic5C2211yescharacteristic
120#65222C2211yescharacteristic
121#65222C2211yescharacteristic
122#65217C2211yescharacteristic
123#64964C2211yescharacteristic
124#64964C2211yescharacteristic
125#64964C2211yescharacteristic
126#64963C2211yescharacteristic
127#64963C2211yescharacteristic
128#64962C2211yescharacteristic
129#64957C2211yescharacteristic
130#64957C2211yescharacteristic
131#64957C2211yescharacteristic
132#64956C2211yescharacteristic
133#64955C2211yescharacteristic
134#64955C2211yescharacteristic
135#64955C2211yescharacteristic
136#64955C2211yescharacteristic
137#64955C2211yescharacteristic
138#64953C2211yescharacteristic
139C5⋊#401C2211yescharacteristic
140C5⋊#401C2211yescharacteristic
141C5⋊#401C2211yescharacteristic
142C5⋊#401C2211yescharacteristic
143#64950C2211yescharacteristic
144#64950C2211yescharacteristic
145#64949C2211yescharacteristic
146#64949C2211yescharacteristic
147#64949C2211yescharacteristic
148#64949C2211yescharacteristic
149#64949C2211yescharacteristic
150#64948C2211yescharacteristic
151#64948C2211yescharacteristic
152#64948C2211yescharacteristic
153#64948C2211yescharacteristic
154#64947C2211yescharacteristic
155#64947C2211yescharacteristic
156#64947C2211yescharacteristic
157#64947C2211yescharacteristic
158#64947C2211yescharacteristic
159#64947C2211yescharacteristic
160#64947C2211yescharacteristic
161#64946C2211yescharacteristic
162#64946C2211yescharacteristic
163#64946C2211yescharacteristic
164#64946C2211yescharacteristic
165#64946C2211yescharacteristic
166#64946C2211yescharacteristic
167#64946C2211yescharacteristic
168#64945C2211yescharacteristic
169#64945C2211yescharacteristic
170#64945C2211yescharacteristic
171#64944C2211yescharacteristic
172#64944C2211yescharacteristic
173#64942C2211yescharacteristic
174#64938C2211yescharacteristic
175#64938C2211yescharacteristic
176#64938C2211yescharacteristic
177#64938C2211yescharacteristic
178#64938C2211yescharacteristic
179#64938C2211yescharacteristic
180#64938C2211yescharacteristic
181#64938C2211yescharacteristic
182#64937C2211yescharacteristic
183#64937C2211yescharacteristic
184#64937C2211yescharacteristic
185#64936C2211yescharacteristic
186#64935C2211yescharacteristic
187#36679—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C23×Dic5C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×Dic10C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C2×C5×C4⋊C4C2311yescharacteristic
197C2×C5×C4⋊C4C2311yescharacteristic
198C2×C5×C4⋊C4C2311yescharacteristic
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×C22⋊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×C42×C5C2311yescharacteristic
214C2×C22⋊Dic5C2311yescharacteristic
215C2×C22⋊Dic5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220#4092—24no—
221Q8×Dic5—42no—
222C2×#685C2311yescharacteristic
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
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×#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×C4×Dic5C2311yescharacteristic
268C2×C4×Dic5C2311yescharacteristic
269C2×C4×Dic5C2311yescharacteristic
270C2×C4×Dic5C2311yescharacteristic
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281#4042—24no—
282#4033—42no—
283#4033—42no—
284#4029—24no—
285#4027—42no—
286#4023—42no—
287C42×D5—42no—
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
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#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#2841—51no—
353#2839—51no—
354#2839—51no—
355#2838—51no—
356#2838—51no—
357#2835—51no—
358#2834—51no—
359#2833—51no—
360#2833—51no—
361#2831—51no—
362#2831D511yescharacteristic, complemented
363#2827—51no—
364#2827—51no—
365#2817—51no—
366#2814—51no—
367#2814—51no—
368#2402—51no—
369#2402—51no—
370#2401—51no—
371#2401—51no—
372#2401—51no—
373#2401—51no—
374#2399—51no—
375#2399—51no—
376#2398—51no—
377#2396—51no—
378#2396—51no—
379#2395—51no—
380C4×C22⋊Q8—51no—
381C4×C22⋊Q8—51no—
382C4×#123—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C22×C4×C5C2411yescharacteristic
389C22×C4×C5C2411yescharacteristic
390C22×C4×C5C2411yescharacteristic
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C2×C22⋊D5—22no—
403C2×C22⋊D5—41no—
404C2×C22⋊D5—41no—
405C22×Dic5—22no—
406C22×Dic5—22no—
407C22×Dic5—22no—
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C2×C4×D5—22no—
424C2×C4×D5—22no—
425C2×C4×D5—22no—
426C2×C4×D5—41no—
427C2×C4×D5—41no—
428C2×C4×D5—41no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5#4114yes—
432C2×Dic10—22no—
433C2×Dic10—41no—
434C2×Dic10—41no—
435C2×Dic10—41no—
436C2×Dic10—41no—
437C2×Dic10—41no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—41no—
440C5×C4⋊C4—41no—
441C5×C4⋊C4—41no—
442C5×C4⋊C4—41no—
443C5×C4⋊C4—41no—
444C5×C4⋊C4—41no—
445C5×C4⋊C4—41no—
446C5×C4⋊C4—41no—
447C5×C4⋊C4—41no—
448C5×C22⋊C4—22no—
449C5×C22⋊C4—41no—
450C5×C22⋊C4—41no—
451C5×C22⋊C4—41no—
452C5×C22⋊C4—41no—
453C5×C22⋊C4—41no—
454C5×C22⋊C4—41no—
455C42×C5—41no—
456C22⋊Dic5—22no—
457C22⋊Dic5—41no—
458C22⋊Dic5—41no—
459C22⋊Dic5—41no—
460C22⋊Dic5—41no—
461C22⋊Dic5—41no—
462#685—22no—
463#685—22no—
464#685—22no—
465#685—22no—
466#685—22no—
467#685—41no—
468#685—41no—
469#685—41no—
470#685—41no—
471#685—41no—
472#685—41no—
473C4⋊Dic5—22no—
474C4⋊Dic5—22no—
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⋊Dic5—41no—
484#683—22no—
485#683—22no—
486#683—22no—
487#683—22no—
488#683—22no—
489#683—41no—
490#683—41no—
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—
507C4×Dic5—22no—
508C4×Dic5—22no—
509C4×Dic5—22no—
510C4×Dic5—22no—
511C4×Dic5—22no—
512C4×Dic5—22no—
513C4×Dic5—22no—
514C4×Dic5—22no—
515C4×Dic5—22no—
516C4×Dic5—22no—
517C4×Dic5—22no—
518C4×Dic5—22no—
519C4×Dic5—22no—
520C4×Dic5—41no—
521C2×#123—51no—
522C2×C22⋊Q8—51no—
523C2×C22⋊Q8—51no—
524C2×C4×Q8—51no—
525C2×C4×Q8—51no—
526C2×C4×Q8—51no—
527C2×C4×D4—51no—
528C2×#117—51no—
529C22×C42—51no—
530#401—51no—
531#401—51no—
532#401—51no—
533#401—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#400—51no—
549#400—51no—
550#400—51no—
551#400—51no—
552#400—51no—
553#400—51no—
554#400—51no—
555#400—51no—
556#400C2×D511yescharacteristic
557#400C2×D511yescharacteristic
558#400C2×D511yescharacteristic
559#399—51no—
560#399—51no—
561#399—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#398—51no—
579#398—51no—
580#398—51no—
581#398C2×D511yescharacteristic
582#398C2×D511yescharacteristic
583#397—51no—
584#397—51no—
585#397—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#397C2×D511yescharacteristic
598#397C2×D511yescharacteristic
599#397C2×D511yescharacteristic
600#396—51no—
601#396—51no—
602#396—51no—
603#396—51no—
604#396—51no—
605#396—51no—
606#396C2×D511yescharacteristic
607#396C2×D511yescharacteristic
608#395—51no—
609#395—51no—
610#395—51no—
611#395—51no—
612#395—51no—
613#395—51no—
614#395—51no—
615#395—51no—
616#395—51no—
617#395C2×D511yescharacteristic
618#394—51no—
619#394—51no—
620#394—51no—
621#394—51no—
622#393—51no—
623#393—51no—
624#393—51no—
625#393C2×D511yescharacteristic
626#391—51no—
627#391C2×D511yescharacteristic
628#389—51no—
629#389—51no—
630#388—51no—
631#388C2×D511yescharacteristic
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387C2×D511yescharacteristic
638#386—51no—
639#385—51no—
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#381—51no—
645#380—51no—
646#380—51no—
647C4×C4⋊C4—51no—
648C4×C4⋊C4—51no—
649C4×C4⋊C4—51no—
650C4×C4⋊C4—51no—
651C4×C4⋊C4—51no—
652C4×C4⋊C4—51no—
653C4×C4⋊C4—51no—
654C4×C4⋊C4—51no—
655C4×C4⋊C4—51no—
656C4×C4⋊C4—51no—
657C4×C4⋊C4—51no—
658C4×C4⋊C4—51no—
659C4×C4⋊C4—51no—
660C4×C4⋊C4—51no—
661C4×C4⋊C4—51no—
662C4×C4⋊C4—51no—
663C4×C22⋊C4—51no—
664C4×C22⋊C4—51no—
665C4×C22⋊C4—51no—
666C4×C22⋊C4—51no—
667C4×C22⋊C4—51no—
668C4×C22⋊C4—51no—
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C4×C22⋊C4—51no—
673#376—51no—
674#376—51no—
675#376—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5—21no—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5C2×#4112yes—
691C5×Q8—44no—
692C2×C4×C5—21no—
693C2×C4×C5—21no—
694C2×C4×C5—21no—
695C2×C4×C5—21no—
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×C5C2×#4112yes—
734C22⋊D5—44no—
735C2×Dic5—21no—
736C2×Dic5—21no—
737C2×Dic5—21no—
738C2×Dic5—21no—
739C2×Dic5—21no—
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—44no—
777C2×Dic5C2×#4112yes—
778C2×Dic5H(5,𝔽2)12yes—
779C2×Dic52−1+412yes—
780C2×Dic52−1+412yes—
781C4×D5—44no—
782C4×D5—44no—
783C4×D5—44no—
784Dic10—44no—
785Dic10—44no—
786C22×Q8—51no—
787C22×Q8—51no—
788C22×Q8C22×D511yescharacteristic
789C22×D4—51no—
790C23×C4—51no—
791C23×C4—51no—
792C23×C4—51no—
793C23×C4—51no—
794#123—104no—
795C22⋊Q8—104no—
796C22⋊Q8—104no—
797C4×Q8—202no—
798C4×Q8—202no—
799C4×Q8—202no—
800C4×D4—202no—
801#117—202no—
802C2×C4⋊C4—51no—
803C2×C4⋊C4—51no—
804C2×C4⋊C4—51no—
805C2×C4⋊C4—51no—
806C2×C4⋊C4—51no—
807C2×C4⋊C4—51no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—51no—
810C2×C4⋊C4—51no—
811C2×C4⋊C4—51no—
812C2×C4⋊C4—51no—
813C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
837C2×C4⋊C4C22×D511yescharacteristic
838C2×C4⋊C4C22×D511yescharacteristic
839C2×C4⋊C4C22×D511yescharacteristic
840C2×C4⋊C4C22×D511yescharacteristic
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
846C2×C22⋊C4—51no—
847C2×C22⋊C4—51no—
848C2×C22⋊C4—51no—
849C2×C22⋊C4—51no—
850C2×C22⋊C4—51no—
851C2×C22⋊C4—51no—
852C2×C22⋊C4—51no—
853C2×C22⋊C4—51no—
854C2×C22⋊C4—51no—
855C2×C22⋊C4—51no—
856C2×C22⋊C4—51no—
857C2×C22⋊C4—51no—
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4C22×D511yescharacteristic
864C2×C22⋊C4C22×D511yescharacteristic
865C2×C22⋊C4C22×D511yescharacteristic
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C42—51no—
871C2×C42—51no—
872C2×C42—51no—
873C2×C42—51no—
874C2×C42—51no—
875C2×C42—51no—
876C2×C42—51no—
877C2×C42—51no—
878C2×C42—51no—
879C2×C42—51no—
880C2×C42—51no—
881C2×C42—51no—
882C2×C42—51no—
883C2×C42—51no—
884C2×C42—202no—
885C2×C42C22×D511yescharacteristic
886#95—51no—
887#95—51no—
888#95—51no—
889#95—51no—
890#95—51no—
891#95—51no—
892#95—51no—
893#95—51no—
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#95C22×D511yescharacteristic
935#95C22×D511yescharacteristic
936#95C22×D511yescharacteristic
937#95C22×D511yescharacteristic
938#95C22×D511yescharacteristic
939#95C22×D511yescharacteristic
940#95C22×D511yescharacteristic
941#95C22×D511yescharacteristic
942#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950C22×C5—41no—
951C22×C5—41no—
952C22×C5—41no—
953C22×C5—41no—
954C22×C5—41no—
955C22×C5—41no—
956C22×C5—41no—
957C22×C5C22×#4111yescharacteristic
958C22×C5C2×H(5,𝔽2)11yescharacteristic
959C22×C5C2×2−1+411yescharacteristic
960C22×C5C2×2−1+411yescharacteristic
961C22×C5#58511yescharacteristic
962C22×C5#58511yescharacteristic
963C22×C5#58511yescharacteristic
964C2×D5—22no—
965C2×D5—22no—
966C2×D5—22no—
967C2×D5—41no—
968C2×D5—41no—
969C2×D5—41no—
970C2×D5—41no—
971C4×C5—22no—
972C4×C5—41no—
973C4×C5—41no—
974C4×C5—41no—
975C4×C5—41no—
976C4×C5—41no—
977C4×C5—41no—
978C4×C5—41no—
979C4×C5—41no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985Dic5—22no—
986Dic5—41no—
987Dic5—41no—
988Dic5—41no—
989Dic5—41no—
990Dic5—41no—
991Dic5—41no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5#56314yes—
1000C24—51no—
1001C24C23×D511yescharacteristic
1002C2×Q8—22no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—102no—
1006C2×Q8—201no—
1007C2×Q8—201no—
1008C2×Q8—201no—
1009C2×Q8—201no—
1010C2×Q8—201no—
1011C2×D4—102no—
1012C2×D4—201no—
1013C2×D4—201no—
1014C22×C4—51no—
1015C22×C4—51no—
1016C22×C4—54no—
1017C22×C4—51no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—51no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—102no—
1031C22×C4—102no—
1032C22×C4—102no—
1033C22×C4—102no—
1034C22×C4—102no—
1035C22×C4—102no—
1036C22×C4—201no—
1037C22×C4—201no—
1038C22×C4—201no—
1039C22×C4—201no—
1040C22×C4—201no—
1041C22×C4C23×D511yescharacteristic
1042C22×C4C23×D511yescharacteristic
1043C22×C4C23×D511yescharacteristic
1044C22×C4C23×D511yescharacteristic
1045C22×C4C23×D511yescharacteristic
1046C22×C4C23×D511yescharacteristic
1047C22×C4C23×D511yescharacteristic
1048C22×C4C23×D511yescharacteristic
1049C22×C4C23×D511yescharacteristic
1050C22×C4C23×D511yescharacteristic
1051C22×C4C23×D511yescharacteristic
1052C22×C4C23×D511yescharacteristic
1053C22×C4C23×D511yescharacteristic
1054C22×C4C23×D511yescharacteristic
1055C4⋊C4—22no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—102no—
1066C4⋊C4—102no—
1067C4⋊C4—102no—
1068C4⋊C4—102no—
1069C4⋊C4—102no—
1070C4⋊C4—102no—
1071C4⋊C4—102no—
1072C4⋊C4—201no—
1073C4⋊C4—201no—
1074C4⋊C4—201no—
1075C4⋊C4—201no—
1076C4⋊C4—201no—
1077C4⋊C4—201no—
1078C4⋊C4—201no—
1079C4⋊C4—201no—
1080C4⋊C4—201no—
1081C4⋊C4—201no—
1082C4⋊C4—201no—
1083C4⋊C4—201no—
1084C4⋊C4—201no—
1085C4⋊C4—201no—
1086C4⋊C4—201no—
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—
1099C22⋊C4—22no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—102no—
1107C22⋊C4—102no—
1108C22⋊C4—102no—
1109C22⋊C4—102no—
1110C22⋊C4—102no—
1111C22⋊C4—102no—
1112C22⋊C4—201no—
1113C22⋊C4—201no—
1114C22⋊C4—201no—
1115C22⋊C4—201no—
1116C22⋊C4—201no—
1117C22⋊C4—201no—
1118C22⋊C4—201no—
1119C22⋊C4—201no—
1120C22⋊C4—201no—
1121C22⋊C4—201no—
1122C22⋊C4—201no—
1123C42—41no—
1124C42—102no—
1125C42—102no—
1126C42—102no—
1127C42—102no—
1128C42—102no—
1129C42—102no—
1130C42—102no—
1131C42—102no—
1132C42—102no—
1133C42—102no—
1134C42—102no—
1135C42—102no—
1136C42—102no—
1137C42—201no—
1138C2×C5—81no—
1139C2×C5#345911yescharacteristic
1140C2×C5#346111yescharacteristic
1141C2×C5#346111yescharacteristic
1142C2×C5C2×#56311yescharacteristic
1143C2×C5#352911yescharacteristic
1144C2×C5#353111yescharacteristic
1145C2×C5#353111yescharacteristic
1146D5—42no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—52no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23—101no—
1160C23—101no—
1161C23C24×D511yescharacteristic
1162Q8—44no—
1163Q8—204no—
1164Q8—204no—
1165D4—204no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
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—52no—
1208C2×C4—52no—
1209C2×C4—52no—
1210C2×C4—52no—
1211C2×C4—101no—
1212C2×C4—101no—
1213C2×C4—101no—
1214C2×C4—101no—
1215C2×C4—101no—
1216C2×C4—101no—
1217C2×C4—101no—
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—204no—
1253C2×C4—204no—
1254C2×C4—204no—
1255C2×C4—204no—
1256C2×C4D5×#4112yes—
1257C5#3667911yescharacteristic, complemented, Sylow
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—102no—
1266C22—102no—
1267C22—102no—
1268C22—201no—
1269C22—201no—
1270C22—201no—
1271C22—201no—
1272C22C2×D5×#4111yescharacteristic
1273C22D5×H(5,𝔽2)11yescharacteristic
1274C22#6628511yescharacteristic
1275C22#6628511yescharacteristic
1276C22D5×2−1+411yescharacteristic
1277C22D5×2−1+411yescharacteristic
1278C22#6628711yescharacteristic
1279C4—22no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—54no—
1294C4—102no—
1295C4—201no—
1296C4—201no—
1297C4—201no—
1298C4—201no—
1299C4—201no—
1300C4—201no—
1301C4—201no—
1302C4—201no—
1303C4—201no—
1304C4—201no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C2—81no—
1309C2—202no—
1310C2#1061828911yescharacteristic
1311C2#1061839711yescharacteristic
1312C2#1061842611yescharacteristic
1313C2#1061899411yescharacteristic
1314C2#1061899511yescharacteristic
1315C2#1061901711yescharacteristic
1316C2D5×#56311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2831C2
prime radicalC22×C22⋊D5C23
hypercenter#2831D5
hypocenterC5#36679
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2831

Complements

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

NH ≅ G/Ntype
1. C5×#2831C2semidirect
2. #10610138C2semidirect
3. #10610063C2semidirect
4. #10610056C2semidirect
5. #10609864C2semidirect
6. #10609863C2semidirect
7. #10609863C2semidirect
8. #10609746C2semidirect
9. #10609744C2semidirect
10. #10609472C2semidirect
11. #10609471C2semidirect
13. #10609396C2semidirect
14. #10609386C2semidirect
15. #10609192C2semidirect
20. #10609014C2semidirect
21. #10609013C2semidirect
22. #10608972C2semidirect
23. #10608902C2semidirect
25. #10608509C2semidirect
26. #10608336C2semidirect
27. #10608210C2semidirect
28. #10607550C2semidirect
30. #10607020C2semidirect
31. #10606672C2semidirect
362. #2831D5semidirect
1257. C5#36679semidirect

Maximal subgroups

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

subgroupindex
C5×#28312
#106101382
#106100632
#106100562
#106098642
#106098632
#106097462
#106097442
#106094722
#106094712
#106094652
#106093962
#106093862
#106091922
#106091912
#106091902
#106091852
#106091802
#106090142
#106090132
#106089722
#106089022
#106086152
#106085092
#106083362
#106082102
#106075502
#106071842
#106070202
#106066722
#366795