Finite Group Databasebeta

← #12307088

Subgroups — #12307088

Order 1280.

1512 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2851C211yesmaximal, characteristic, complemented
2#10614782C211yesmaximal, characteristic, complemented
3#10614779C211yesmaximal, characteristic, complemented
4#10613806C211yesmaximal, characteristic, complemented
5#10613796C211yesmaximal, characteristic
6#10608005C211yesmaximal, characteristic, complemented
7#10607913C211yesmaximal, characteristic, complemented
8#10607895C211yesmaximal, characteristic, complemented
9#10607867C211yesmaximal, characteristic, complemented
10#10607092C211yesmaximal, characteristic, complemented
11#10607048C211yesmaximal, characteristic, complemented
12#10606865C211yesmaximal, characteristic, complemented
13#10606862C211yesmaximal, characteristic, complemented
14#10606859C211yesmaximal, characteristic, complemented
15#10606858C211yesmaximal, characteristic, complemented
16#10606809C211yesmaximal, characteristic, complemented
17#10606714C211yesmaximal, characteristic, complemented
18#10606312C211yesmaximal, characteristic
19#10606306C211yesmaximal, characteristic, complemented
20#10606304C211yesmaximal, characteristic, complemented
21#10606300C211yesmaximal, characteristic
22#10606296C211yesmaximal, characteristic
23#10606284C211yesmaximal, characteristic, complemented
24#10606270C211yesmaximal, characteristic, complemented
25#10606247C211yesmaximal, characteristic
26#10605943C211yesmaximal, characteristic, complemented
27#10605935C211yesmaximal, characteristic, complemented
28#10605737C211yesmaximal, characteristic
29#10605689C211yesmaximal, characteristic, complemented
30#10605689C211yesmaximal, characteristic, complemented
31#10605601C211yesmaximal, characteristic
32C2×C5×#125C2211yescharacteristic
33C22×C42×C5C2211yescharacteristic
34C2×C4×C22⋊D5C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C2×#4043C2211yescharacteristic
37C2×#4034C2211yescharacteristic
38C2×#4018C2211yescharacteristic
39C5×#389C2211yescharacteristic
40C5×#389C2211yescharacteristic
41C5×#387C2211yescharacteristic
42C5×#387C2211yescharacteristic
43C5×#387C2211yescharacteristic
44C5×#387C2211yescharacteristic
45C5×#385C2211yescharacteristic
46C5×#385C2211yescharacteristic
47C5×#385C2211yescharacteristic
48C5×#385C2211yescharacteristic
49C5×#382C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C5×#380C2211yescharacteristic
52#65502C2211yescharacteristic
53#65502C2211yescharacteristic
54#65501C2211yescharacteristic
55#65500C2211yescharacteristic
56#65500C2211yescharacteristic
57#65499C2211yescharacteristic
58#65499C2211yescharacteristic
59#65499C2211yescharacteristic
60#65499C2211yescharacteristic
61C4×C22⋊Dic5C2211yescharacteristic
62#65283C2211yescharacteristic
63#65283C2211yescharacteristic
64#65281C2211yescharacteristic
65#65281C2211yescharacteristic
66#65279C2211yescharacteristic
67#65279C2211yescharacteristic
68#65278C2211yescharacteristic
69#65278C2211yescharacteristic
70#65278C2211yescharacteristic
71#65278C2211yescharacteristic
72#65276C2211yescharacteristic
73#65275C2211yescharacteristic
74#65275C2211yescharacteristic
75#65275C2211yescharacteristic
76#65275C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65272C2211yescharacteristic
80#65272C2211yescharacteristic
81#65271C2211yescharacteristic
82#65271C2211yescharacteristic
83#65270C2211yescharacteristic
84#65270C2211yescharacteristic
85#65269C2211yescharacteristic
86#65269C2211yescharacteristic
87#65268C2211yescharacteristic
88#65268C2211yescharacteristic
89#65268C2211yescharacteristic
90#65268C2211yescharacteristic
91#65268C2211yescharacteristic
92#65268C2211yescharacteristic
93#65268C2211yescharacteristic
94#65268C2211yescharacteristic
95#65267C2211yescharacteristic
96#65267C2211yescharacteristic
97#65267C2211yescharacteristic
98#65267C2211yescharacteristic
99#65265C2211yescharacteristic
100#65263C2211yescharacteristic
101#65263C2211yescharacteristic
102#65263C2211yescharacteristic
103#65262C2211yescharacteristic
104#65261C2211yescharacteristic
105#65261C2211yescharacteristic
106#65261C2211yescharacteristic
107#65261C2211yescharacteristic
108#65246C2211yescharacteristic
109#65246C2211yescharacteristic
110#65245C2211yescharacteristic
111#65245C2211yescharacteristic
112#65237C2211yescharacteristic
113#65237C2211yescharacteristic
114#65237C2211yescharacteristic
115#65237C2211yescharacteristic
116#65236C2211yescharacteristic
117#65236C2211yescharacteristic
118#65236C2211yescharacteristic
119#65236C2211yescharacteristic
120#65234C2211yescharacteristic
121#65234C2211yescharacteristic
122#65233C2211yescharacteristic
123#65233C2211yescharacteristic
124#65229C2211yescharacteristic
125#65229C2211yescharacteristic
126C4×#685C2211yescharacteristic
127#65222C2211yescharacteristic
128#65222C2211yescharacteristic
129#65222C2211yescharacteristic
130#65222C2211yescharacteristic
131#65222C2211yescharacteristic
132#65222C2211yescharacteristic
133#65221C2211yescharacteristic
134C4×#683C2211yescharacteristic
135#65218C2211yescharacteristic
136#65218C2211yescharacteristic
137#65217C2211yescharacteristic
138#65217C2211yescharacteristic
139#64962C2211yescharacteristic
140#64962C2211yescharacteristic
141#64962C2211yescharacteristic
142#64962C2211yescharacteristic
143#64957C2211yescharacteristic
144#64957C2211yescharacteristic
145#64956C2211yescharacteristic
146#64956C2211yescharacteristic
147#64956C2211yescharacteristic
148#64955C2211yescharacteristic
149#64953C2211yescharacteristic
150D5×#95C2211yescharacteristic
151#64948C2211yescharacteristic
152#64948C2211yescharacteristic
153#64947C2211yescharacteristic
154#64947C2211yescharacteristic
155#64947C2211yescharacteristic
156#64947C2211yescharacteristic
157#64947C2211yescharacteristic
158#64947C2211yescharacteristic
159#64946C2211yescharacteristic
160#64946C2211yescharacteristic
161#64945C2211yescharacteristic
162#64945C2211yescharacteristic
163#64944C2211yescharacteristic
164#64944C2211yescharacteristic
165#64944C2211yescharacteristic
166#64944C2211yescharacteristic
167#64942C2211yescharacteristic
168#64942C2211yescharacteristic
169#64941C2211yescharacteristic
170#64941C2211yescharacteristic
171#64940C2211yescharacteristic
172#64939C2211yescharacteristic
173#64939C2211yescharacteristic
174#64939C2211yescharacteristic
175#64938C2211yescharacteristic
176#64937C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64935C2211yescharacteristic
180#64935C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36755—51nomaximal, Sylow
188C23×C4×C5C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C22×C22⋊D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C22×Dic10C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C5×#125—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×C4⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C42×C5—42no—
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C4×C22⋊D5Q818yescomplemented
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248#4070—42no—
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×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
283#4043—42no—
284#4034—42no—
285#4018—42no—
286C5×#95C2311yescharacteristic
287C5×#95C2311yescharacteristic
288C5×#95C2311yescharacteristic
289C5×#95C2311yescharacteristic
290C5×#95C2311yescharacteristic
291C5×#95C2311yescharacteristic
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298#3963C2311yescharacteristic
299#3963C2311yescharacteristic
300#3963C2311yescharacteristic
301#3963C2311yescharacteristic
302#3963C2311yescharacteristic
303#3963C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#2855—51no—
351#2851D511yescharacteristic, complemented
352#2805—51no—
353#2804—51no—
354#2790—51no—
355#2788—51no—
356#2788—51no—
357#2784—51no—
358#2780—51no—
359#2774—51no—
360#2763—51no—
361#2763—51no—
362#2755—51no—
363#2742—51no—
364#2729—51no—
365#2720—51no—
366#2713—51no—
367#2692—51no—
368#2665—51no—
369#2665—51no—
370#2612—51no—
371#2607—51no—
372#2605—51no—
373#2605—51no—
374#2570—51no—
375#2569—51no—
376#2439—51no—
377#2438—51no—
378#2319—51no—
379#2318—51no—
380#2290—51no—
381C24×C5C2411yescharacteristic
382C23×D5C2411yescharacteristic
383C22×C4×C5—22no—
384C22×C4×C5—41no—
385C22×C4×C5—41no—
386C22×C4×C5—41no—
387C22×C4×C5—41no—
388C22×C4×C5—41no—
389C22×C4×C5—41no—
390C22×C4×C5—41no—
391C22×C4×C5C2×Q814yes—
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
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C2×C22⋊D5—41no—
407C2×C22⋊D5—41no—
408C2×C22⋊D5C2×Q814yes—
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
423C22×Dic5C2411yescharacteristic
424C2×C4×D5—41no—
425C2×C4×D5—41no—
426C2×C4×D5—41no—
427C2×C4×D5—41no—
428C2×C4×D5—41no—
429C2×C4×D5—41no—
430C2×C4×D5—41no—
431C2×C4×D5—41no—
432C2×C4×D5C2×Q814yes—
433C2×Dic10—22no—
434C2×Dic10—41no—
435C2×Dic10—41no—
436C2×Dic10—41no—
437C2×Dic10—41no—
438C2×Dic10—41no—
439C2×Dic10—41no—
440C2×Dic10—41no—
441C2×Dic10—41no—
442C2×Dic10—41no—
443C2×Dic10—41no—
444C2×Dic10—41no—
445C2×Dic10—41no—
446C2×Dic10—41no—
447C2×Dic10—41no—
448C5×C4⋊C4—22no—
449C5×C4⋊C4—22no—
450C5×C4⋊C4—41no—
451C5×C4⋊C4—41no—
452C5×C4⋊C4—41no—
453C5×C4⋊C4—41no—
454C5×C4⋊C4—41no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C22⋊C4—41no—
461C5×C22⋊C4—41no—
462C5×C22⋊C4—41no—
463C5×C22⋊C4—41no—
464C42×C5—22no—
465C42×C5—22no—
466C42×C5—41no—
467C42×C5—41no—
468C22⋊Dic5—41no—
469C22⋊Dic5—41no—
470C22⋊Dic5—41no—
471C22⋊Dic5—41no—
472C22⋊Dic5—41no—
473C22⋊Dic5—41no—
474C22⋊Dic5C2×Q814yes—
475#685—22no—
476#685—41no—
477#685—41no—
478#685—41no—
479#685—41no—
480#685—41no—
481#685—41no—
482#685—41no—
483#685—41no—
484#685—41no—
485#685C2×Q814yes—
486C4⋊Dic5—22no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489C4⋊Dic5—41no—
490C4⋊Dic5—41no—
491C4⋊Dic5—41no—
492C4⋊Dic5—41no—
493#683—22no—
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#683C2×Q814yes—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C4×Dic5—41no—
522C4×Dic5—41no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5C2×Q814yes—
527C2×C4⋊Q8—51no—
528C2×#125C2×D511yescharacteristic
529C2×C22⋊Q8—51no—
530C2×C22⋊Q8—51no—
531C2×C4×D4—51no—
532C2×#117—51no—
533C22×C42C2×D511yescharacteristic
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#399—51no—
549#399—51no—
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#398—51no—
557#398—51no—
558#396—51no—
559#396—51no—
560#396—51no—
561#396—51no—
562#396—51no—
563#396—51no—
564#395—51no—
565#395—51no—
566#395—51no—
567#395—51no—
568#395—51no—
569#395—51no—
570#395—51no—
571#395—51no—
572#395—51no—
573#395—51no—
574#393—51no—
575#393—51no—
576#393—51no—
577#393—51no—
578#393—51no—
579#393—51no—
580#393—51no—
581#393—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#391—51no—
586#391—51no—
587#391—51no—
588#391—51no—
589#391—51no—
590#391—51no—
591#391—51no—
592#391—51no—
593#391—51no—
594#391—51no—
595#390—51no—
596#390—51no—
597#389—51no—
598#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—51no—
604#389—51no—
605#389—51no—
606#389C2×D511yescharacteristic
607#389C2×D511yescharacteristic
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388—51no—
613#388—51no—
614#388—51no—
615#388—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387C2×D511yescharacteristic
637#387C2×D511yescharacteristic
638#387C2×D511yescharacteristic
639#387C2×D511yescharacteristic
640#386—51no—
641#386—51no—
642#386—51no—
643#386—51no—
644#385—51no—
645#385—51no—
646#385—51no—
647#385—51no—
648#385—51no—
649#385—51no—
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385C2×D511yescharacteristic
655#385C2×D511yescharacteristic
656#385C2×D511yescharacteristic
657#385C2×D511yescharacteristic
658#384—51no—
659#383—51no—
660#382—51no—
661#382—51no—
662#382—51no—
663#382C2×D511yescharacteristic
664#381—51no—
665#381—51no—
666#381—51no—
667#380—51no—
668#380—51no—
669#380—51no—
670#380—51no—
671#380—51no—
672#380C2×D511yescharacteristic
673#380C2×D511yescharacteristic
674C4×C4⋊C4—51no—
675C4×C4⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4—51no—
679#376—51no—
680#376—51no—
681C2×#95—51no—
682C23×C5—21no—
683C23×C5—21no—
684C23×C5—21no—
685C23×C5—21no—
686C23×C5—21no—
687C23×C5—21no—
688C23×C5C22×Q812yes—
689C23×C5C2511yescharacteristic
690C22×D5—21no—
691C22×D5—21no—
692C22×D5—21no—
693C22×D5—21no—
694C22×D5—21no—
695C22×D5—21no—
696C22×D5C22×Q812yes—
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—21no—
736C2×C4×C5—44no—
737C2×C4×C5—44no—
738C2×C4×C5—44no—
739C2×C4×C5C22×Q812yes—
740C2×C4×C5C22×Q812yes—
741C2×C4×C5H(5,𝔽2)12yes—
742C22⋊D5—44no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5C22×Q812yes—
786C2×Dic5C22×Q812yes—
787C2×Dic5C22×Q812yes—
788C4×D5—44no—
789C4×D5—82no—
790C4×D5—82no—
791Dic10—82no—
792Dic10—82no—
793Dic10—82no—
794Dic10—82no—
795Dic10—82no—
796C22×Q8—51no—
797C22×Q8—51no—
798C22×Q8—51no—
799C22×Q8—51no—
800C22×Q8—51no—
801C22×D4—51no—
802C23×C4—51no—
803C23×C4—51no—
804C23×C4—51no—
805C23×C4C22×D511yescharacteristic
806C23×C4C22×D511yescharacteristic
807C23×C4C22×D511yescharacteristic
808C4⋊Q8—202no—
809#125—42no—
810C22⋊Q8—202no—
811C22⋊Q8—202no—
812C4×D4—58no—
813#117—202no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4C22×D511yescharacteristic
847C2×C4⋊C4C22×D511yescharacteristic
848C2×C4⋊C4C22×D511yescharacteristic
849C2×C4⋊C4C22×D511yescharacteristic
850C2×C4⋊C4C22×D511yescharacteristic
851C2×C4⋊C4C22×D511yescharacteristic
852C2×C4⋊C4C22×D511yescharacteristic
853C2×C4⋊C4C22×D511yescharacteristic
854C2×C4⋊C4C22×D511yescharacteristic
855C2×C4⋊C4C22×D511yescharacteristic
856C2×C4⋊C4C22×D511yescharacteristic
857C2×C4⋊C4C22×D511yescharacteristic
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4—51no—
867C2×C22⋊C4—51no—
868C2×C22⋊C4—51no—
869C2×C22⋊C4—51no—
870C2×C22⋊C4—51no—
871C2×C22⋊C4—51no—
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4C22×D511yescharacteristic
877C2×C22⋊C4C22×D511yescharacteristic
878C2×C22⋊C4C22×D511yescharacteristic
879C2×C22⋊C4C22×D511yescharacteristic
880C2×C42—42no—
881C2×C42—51no—
882C2×C42—51no—
883C2×C42—51no—
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42C22×D511yescharacteristic
891C2×C42C22×D511yescharacteristic
892C2×C42C22×D511yescharacteristic
893C2×C42C22×D511yescharacteristic
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954#95C22×D511yescharacteristic
955#95C22×D511yescharacteristic
956#95C22×D511yescharacteristic
957#95C22×D511yescharacteristic
958C22×C5—22no—
959C22×C5—22no—
960C22×C5—22no—
961C22×C5—41no—
962C22×C5—41no—
963C22×C5—41no—
964C22×C5—41no—
965C22×C5C23×Q811yescharacteristic
966C22×C5C2×H(5,𝔽2)11yescharacteristic
967C22×C5#58511yescharacteristic
968C22×C5#58511yescharacteristic
969C22×C5#58511yescharacteristic
970C22×C5#58511yescharacteristic
971C22×C5#58511yescharacteristic
972C2×D5—22no—
973C2×D5—22no—
974C2×D5—22no—
975C2×D5—41no—
976C2×D5—41no—
977C2×D5—41no—
978C2×D5—41no—
979C4×C5—22no—
980C4×C5—22no—
981C4×C5—22no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985C4×C5—41no—
986C4×C5—41no—
987C4×C5—41no—
988C4×C5—41no—
989C4×C5—41no—
990C4×C5—41no—
991C4×C5—41no—
992C4×C5—41no—
993Dic5—22no—
994Dic5—22no—
995Dic5—22no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000Dic5—41no—
1001Dic5—41no—
1002Dic5—41no—
1003Dic5—41no—
1004Dic5—41no—
1005Dic5—41no—
1006Dic5—41no—
1007Dic5—41no—
1008C24—51no—
1009C24C23×D511yescharacteristic
1010C2×Q8—102no—
1011C2×Q8—201no—
1012C2×Q8—201no—
1013C2×Q8—201no—
1014C2×Q8—201no—
1015C2×Q8—201no—
1016C2×Q8—201no—
1017C2×Q8—201no—
1018C2×Q8—201no—
1019C2×Q8—201no—
1020C2×Q8—201no—
1021C2×Q8—201no—
1022C2×Q8—201no—
1023C2×Q8—201no—
1024C2×Q8—201no—
1025C2×D4—54no—
1026C2×D4—201no—
1027C2×D4—201no—
1028C22×C4—22no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—51no—
1039C22×C4—54no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—51no—
1044C22×C4—51no—
1045C22×C4—51no—
1046C22×C4—51no—
1047C22×C4—51no—
1048C22×C4—51no—
1049C22×C4—51no—
1050C22×C4—51no—
1051C22×C4—51no—
1052C22×C4—201no—
1053C22×C4—201no—
1054C22×C4—201no—
1055C22×C4—201no—
1056C22×C4—201no—
1057C22×C4—201no—
1058C22×C4—201no—
1059C22×C4—201no—
1060C22×C4Q8×D514yes—
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
1071C22×C4C23×D511yescharacteristic
1072C22×C4C23×D511yescharacteristic
1073C22×C4C23×D511yescharacteristic
1074C22×C4C23×D511yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—41no—
1078C4⋊C4—41no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—41no—
1083C4⋊C4—41no—
1084C4⋊C4—41no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—54no—
1088C4⋊C4—102no—
1089C4⋊C4—102no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4—201no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—41no—
1122C22⋊C4—41no—
1123C22⋊C4—54no—
1124C22⋊C4—54no—
1125C22⋊C4—102no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C22⋊C4—201no—
1130C22⋊C4—201no—
1131C22⋊C4—201no—
1132C22⋊C4—201no—
1133C22⋊C4—201no—
1134C22⋊C4—201no—
1135C22⋊C4—201no—
1136C22⋊C4—201no—
1137C22⋊C4—201no—
1138C22⋊C4—201no—
1139C22⋊C4—201no—
1140C22⋊C4—201no—
1141C42—22no—
1142C42—22no—
1143C42—41no—
1144C42—41no—
1145C42—54no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C42—201no—
1151C42—201no—
1152C42—201no—
1153C42—201no—
1154C2×C5—42no—
1155C2×C5#345811yescharacteristic
1156C2×C5#350111yescharacteristic
1157C2×C5#350411yescharacteristic
1158C2×C5#353311yescharacteristic
1159C2×C5#354011yescharacteristic
1160C2×C5#356611yescharacteristic
1161C2×C5#356811yescharacteristic
1162D5—42no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—52no—
1170C23—101no—
1171C23—101no—
1172C23—101no—
1173C23—101no—
1174C23—101no—
1175C23—101no—
1176C23C2×Q8×D512yes—
1177C23C24×D511yescharacteristic
1178Q8—402no—
1179Q8—402no—
1180Q8—402no—
1181Q8—402no—
1182Q8—402no—
1183D4—204no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—52no—
1227C2×C4—52no—
1228C2×C4—52no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—101no—
1263C2×C4—101no—
1264C2×C4—101no—
1265C2×C4—101no—
1266C2×C4—101no—
1267C2×C4—101no—
1268C2×C4—101no—
1269C2×C4—101no—
1270C2×C4—101no—
1271C2×C4—204no—
1272C2×C4—402no—
1273C2×C4—402no—
1274C2×C4#414412yes—
1275C2×C4C2×Q8×D512yes—
1276C2×C4C2×Q8×D512yes—
1277C5#3675511yescharacteristic, complemented, Sylow
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—102no—
1286C22—102no—
1287C22—102no—
1288C22—201no—
1289C22—201no—
1290C22—201no—
1291C22—201no—
1292C22C2×#414411yescharacteristic
1293C22C22×Q8×D511yescharacteristic
1294C22#6628311yescharacteristic
1295C22#6628311yescharacteristic
1296C22#6628311yescharacteristic
1297C22#6628311yescharacteristic
1298C22#6628311yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—102no—
1314C4—102no—
1315C4—102no—
1316C4—201no—
1317C4—201no—
1318C4—201no—
1319C4—201no—
1320C4—201no—
1321C4—201no—
1322C4—201no—
1323C4—201no—
1324C4—201no—
1325C4—201no—
1326C4—201no—
1327C4—201no—
1328C2—42no—
1329C2—202no—
1330C2#1061788711yescharacteristic
1331C2#1061795011yescharacteristic
1332C2#1061795611yescharacteristic
1333C2#1061799911yescharacteristic
1334C2#1061804511yescharacteristic
1335C2#1061808611yescharacteristic
1336C2#1061817511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2851C2
prime radicalC22×C22⋊D5C23
hypercenter#2851D5
hypocenterC5#36755
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C5×#2851C2semidirect
2. #10614782C2semidirect
3. #10614779C2semidirect
4. #10613806C2semidirect
6. #10608005C2semidirect
7. #10607913C2semidirect
8. #10607895C2semidirect
9. #10607867C2semidirect
10. #10607092C2semidirect
11. #10607048C2semidirect
12. #10606865C2semidirect
13. #10606862C2semidirect
14. #10606859C2semidirect
15. #10606858C2semidirect
16. #10606809C2semidirect
17. #10606714C2semidirect
19. #10606306C2semidirect
20. #10606304C2semidirect
23. #10606284C2semidirect
24. #10606270C2semidirect
26. #10605943C2semidirect
27. #10605935C2semidirect
29. #10605689C2semidirect
30. #10605689C2semidirect
229. C4×C22⋊D5Q8semidirect
351. #2851D5semidirect
1277. C5#36755semidirect

Maximal subgroups

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

subgroupindex
C5×#28512
#106147822
#106147792
#106138062
#106137962
#106080052
#106079132
#106078952
#106078672
#106070922
#106070482
#106068652
#106068622
#106068592
#106068582
#106068092
#106067142
#106063122
#106063062
#106063042
#106063002
#106062962
#106062842
#106062702
#106062472
#106059432
#106059352
#106057372
#106056892
#106056012
#367555