Finite Group Databasebeta

← #12307095

Subgroups — #12307095

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×#2713C211yesmaximal, characteristic, complemented
2#10614998C211yesmaximal, characteristic, complemented
3#10614987C211yesmaximal, characteristic, complemented
4#10614803C211yesmaximal, characteristic, complemented
5#10614782C211yesmaximal, characteristic, complemented
6#10610088C211yesmaximal, characteristic, complemented
7#10610025C211yesmaximal, characteristic, complemented
8#10609995C211yesmaximal, characteristic, complemented
9#10609965C211yesmaximal, characteristic, complemented
10#10609735C211yesmaximal, characteristic, complemented
11#10609731C211yesmaximal, characteristic
12#10609680C211yesmaximal, characteristic, complemented
13#10609524C211yesmaximal, characteristic, complemented
14#10609001C211yesmaximal, characteristic, complemented
15#10608946C211yesmaximal, characteristic
16#10608942C211yesmaximal, characteristic, complemented
17#10608929C211yesmaximal, characteristic, complemented
18#10608394C211yesmaximal, characteristic, complemented
19#10608390C211yesmaximal, characteristic
20#10608317C211yesmaximal, characteristic, complemented
21#10608287C211yesmaximal, characteristic, complemented
22#10607868C211yesmaximal, characteristic, complemented
23#10607700C211yesmaximal, characteristic
24#10607164C211yesmaximal, characteristic
25#10607011C211yesmaximal, characteristic, complemented
26#10606979C211yesmaximal, characteristic, complemented
27#10606954C211yesmaximal, characteristic, complemented
28#10606864C211yesmaximal, characteristic, complemented
29#10606862C211yesmaximal, characteristic, complemented
30#10606676C211yesmaximal, characteristic
31#10606668C211yesmaximal, characteristic
32C2×C5×C4⋊Q8C2211yescharacteristic
33C2×C5×#125C2211yescharacteristic
34C2×#4092C2211yescharacteristic
35C2×#4043C2211yescharacteristic
36C2×#4039C2211yescharacteristic
37C2×#4038C2211yescharacteristic
38C2×C42×D5C2211yescharacteristic
39C5×#400C2211yescharacteristic
40C5×#400C2211yescharacteristic
41C5×#398C2211yescharacteristic
42C5×#398C2211yescharacteristic
43C5×#395C2211yescharacteristic
44C5×#395C2211yescharacteristic
45C5×#391C2211yescharacteristic
46C5×#391C2211yescharacteristic
47C5×#389C2211yescharacteristic
48C5×#387C2211yescharacteristic
49C5×#387C2211yescharacteristic
50C5×#387C2211yescharacteristic
51C5×#387C2211yescharacteristic
52#65520C2211yescharacteristic
53#65520C2211yescharacteristic
54#65520C2211yescharacteristic
55#65519C2211yescharacteristic
56#65519C2211yescharacteristic
57#65519C2211yescharacteristic
58#65518C2211yescharacteristic
59#65283C2211yescharacteristic
60#65283C2211yescharacteristic
61#65283C2211yescharacteristic
62#65283C2211yescharacteristic
63#65283C2211yescharacteristic
64#65281C2211yescharacteristic
65#65281C2211yescharacteristic
66#65279C2211yescharacteristic
67#65279C2211yescharacteristic
68#65278C2211yescharacteristic
69#65278C2211yescharacteristic
70#65278C2211yescharacteristic
71#65278C2211yescharacteristic
72#65278C2211yescharacteristic
73#65278C2211yescharacteristic
74#65278C2211yescharacteristic
75#65278C2211yescharacteristic
76#65277C2211yescharacteristic
77#65276C2211yescharacteristic
78#65276C2211yescharacteristic
79#65276C2211yescharacteristic
80#65276C2211yescharacteristic
81#65276C2211yescharacteristic
82#65275C2211yescharacteristic
83#65275C2211yescharacteristic
84#65275C2211yescharacteristic
85#65274C2211yescharacteristic
86#65274C2211yescharacteristic
87#65274C2211yescharacteristic
88#65273C2211yescharacteristic
89#65273C2211yescharacteristic
90#65272C2211yescharacteristic
91#65270C2211yescharacteristic
92#65270C2211yescharacteristic
93#65270C2211yescharacteristic
94#65270C2211yescharacteristic
95#65268C2211yescharacteristic
96#65268C2211yescharacteristic
97#65268C2211yescharacteristic
98#65267C2211yescharacteristic
99#65267C2211yescharacteristic
100#65267C2211yescharacteristic
101#65267C2211yescharacteristic
102#65267C2211yescharacteristic
103#65267C2211yescharacteristic
104#65266C2211yescharacteristic
105#65265C2211yescharacteristic
106C4⋊C4×Dic5C2211yescharacteristic
107#65263C2211yescharacteristic
108#65262C2211yescharacteristic
109#65262C2211yescharacteristic
110#65261C2211yescharacteristic
111#65261C2211yescharacteristic
112#65229C2211yescharacteristic
113#65229C2211yescharacteristic
114#65228C2211yescharacteristic
115C4×#685C2211yescharacteristic
116#65225C2211yescharacteristic
117#65222C2211yescharacteristic
118#65222C2211yescharacteristic
119#65221C2211yescharacteristic
120#65218C2211yescharacteristic
121#65217C2211yescharacteristic
122#65217C2211yescharacteristic
123#64965C2211yescharacteristic
124#64962C2211yescharacteristic
125#64962C2211yescharacteristic
126#64962C2211yescharacteristic
127#64962C2211yescharacteristic
128#64962C2211yescharacteristic
129#64959C2211yescharacteristic
130#64959C2211yescharacteristic
131#64958C2211yescharacteristic
132#64958C2211yescharacteristic
133#64957C2211yescharacteristic
134#64957C2211yescharacteristic
135#64957C2211yescharacteristic
136#64957C2211yescharacteristic
137#64957C2211yescharacteristic
138#64957C2211yescharacteristic
139#64956C2211yescharacteristic
140#64956C2211yescharacteristic
141#64955C2211yescharacteristic
142#64955C2211yescharacteristic
143#64954C2211yescharacteristic
144#64954C2211yescharacteristic
145#64954C2211yescharacteristic
146#64954C2211yescharacteristic
147#64953C2211yescharacteristic
148#64953C2211yescharacteristic
149#64953C2211yescharacteristic
150D5×#95C2211yescharacteristic
151#64950C2211yescharacteristic
152#64949C2211yescharacteristic
153#64949C2211yescharacteristic
154#64949C2211yescharacteristic
155#64949C2211yescharacteristic
156#64949C2211yescharacteristic
157#64949C2211yescharacteristic
158#64948C2211yescharacteristic
159#64948C2211yescharacteristic
160#64947C2211yescharacteristic
161#64946C2211yescharacteristic
162#64946C2211yescharacteristic
163#64945C2211yescharacteristic
164#64945C2211yescharacteristic
165#64945C2211yescharacteristic
166#64945C2211yescharacteristic
167#64943C2211yescharacteristic
168#64943C2211yescharacteristic
169#64943C2211yescharacteristic
170#64943C2211yescharacteristic
171#64942C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64940C2211yescharacteristic
176#64939C2211yescharacteristic
177#64939C2211yescharacteristic
178#64938C2211yescharacteristic
179#64937C2211yescharacteristic
180#64936C2211yescharacteristic
181#64935C2211yescharacteristic
182#64935C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36755—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×D20C2311yescharacteristic
191C22×C4×D5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×Dic10C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C22×Dic10C2311yescharacteristic
200C5×C4⋊Q8—42no—
201C5×#125—42no—
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C4⋊C4C2311yescharacteristic
211C2×C5×C4⋊C4C2311yescharacteristic
212C2×C5×C4⋊C4C2311yescharacteristic
213C2×C5×C4⋊C4C2311yescharacteristic
214C2×C5×C4⋊C4C2311yescharacteristic
215C2×C5×C4⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219#4092—42no—
220C2×#685C2311yescharacteristic
221C2×#685C2311yescharacteristic
222C2×#685C2311yescharacteristic
223C2×#685C2311yescharacteristic
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×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
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×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282#4043—42no—
283#4039Q818yescomplemented
284#4038—42no—
285C42×D5—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
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302#3963C2311yescharacteristic
303#3963C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#2855—51no—
351#2851—51no—
352#2805—51no—
353#2804—51no—
354#2790—51no—
355#2788—51no—
356#2788—51no—
357#2784—51no—
358#2780—51no—
359#2774—51no—
360#2763—51no—
361#2763—51no—
362#2755—51no—
363#2742—51no—
364#2729—51no—
365#2720—51no—
366#2713D511yescharacteristic, complemented
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—
381C23×D5C2411yescharacteristic
382C23×D5C2411yescharacteristic
383C2×C5×Q8—22no—
384C2×C5×Q8—41no—
385C2×C5×Q8—41no—
386C2×C5×Q8—41no—
387C2×C5×Q8—41no—
388C2×C5×Q8—41no—
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
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×Dic5C2411yescharacteristic
405C22×Dic5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2411yescharacteristic
409C22×Dic5C2411yescharacteristic
410C22×Dic5C2411yescharacteristic
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C2×D20—41no—
419C2×D20—41no—
420C2×D20C2×Q814yes—
421C2×C4×D5—22no—
422C2×C4×D5—41no—
423C2×C4×D5—41no—
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×D5—41no—
433C2×C4×D5—41no—
434C2×C4×D5—41no—
435C2×C4×D5—41no—
436C2×C4×D5—41no—
437C2×C4×D5C2×Q814yes—
438C2×C4×D5C2×Q814yes—
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—22no—
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×C4⋊C4—41no—
461C5×C4⋊C4C2×Q814yes—
462C42×C5—22no—
463C42×C5—41no—
464C42×C5—41no—
465#685—22no—
466#685—41no—
467#685—41no—
468#685—41no—
469#685—41no—
470#685—41no—
471#685—41no—
472#685—41no—
473#685—41no—
474#685—41no—
475#685—41no—
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—
486#685C2×Q814yes—
487C4⋊Dic5—22no—
488C4⋊Dic5—41no—
489C4⋊Dic5—41no—
490C4⋊Dic5—41no—
491C4⋊Dic5—41no—
492C4⋊Dic5—41no—
493C4⋊Dic5—41no—
494C4⋊Dic5—41no—
495C4⋊Dic5—41no—
496C4⋊Dic5—41no—
497C4⋊Dic5—41no—
498C4⋊Dic5—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—
517C4×Dic5—22no—
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⋊Q8C2×D511yescharacteristic
528C2×#125C2×D511yescharacteristic
529C2×C22⋊Q8—51no—
530C2×C22⋊Q8—51no—
531C2×C4×D4—51no—
532C2×#117—51no—
533C22×C42—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400C2×D511yescharacteristic
547#400C2×D511yescharacteristic
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#398C2×D511yescharacteristic
557#398C2×D511yescharacteristic
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#395C2×D511yescharacteristic
573#395C2×D511yescharacteristic
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#391C2×D511yescharacteristic
594#391C2×D511yescharacteristic
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#389—51no—
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#385—51no—
655#385—51no—
656#385—51no—
657#385—51no—
658#384—51no—
659#383—51no—
660#382—51no—
661#382—51no—
662#382—51no—
663#382—51no—
664#381—51no—
665#381—51no—
666#381—51no—
667#380—51no—
668#380—51no—
669#380—51no—
670#380—51no—
671#380—51no—
672#380—51no—
673#380—51no—
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×C5C2511yescharacteristic
683C22×D5—21no—
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5—21no—
691C22×D5—21no—
692C22×D5—21no—
693C22×D5—21no—
694C22×D5—21no—
695C22×D5C22×Q812yes—
696C22×D5C22×Q812yes—
697C5×Q8—82no—
698C5×Q8—82no—
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—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5C22×Q812yes—
741C2×C4×C5C22×Q812yes—
742C2×C4×C5C22×Q812yes—
743C2×C4×C5H(5,𝔽2)12yes—
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×Dic5C22×Q812yes—
785C2×Dic5C22×Q812yes—
786D20—44no—
787C4×D5—44no—
788C4×D5—44no—
789C4×D5—44no—
790C4×D5—44no—
791C4×D5—82no—
792C4×D5—82no—
793Dic10—82no—
794Dic10—82no—
795Dic10—82no—
796C22×Q8—51no—
797C22×Q8—51no—
798C22×Q8—51no—
799C22×Q8C22×D511yescharacteristic
800C22×Q8C22×D511yescharacteristic
801C22×D4—51no—
802C23×C4—51no—
803C23×C4—51no—
804C23×C4—51no—
805C23×C4—51no—
806C23×C4—51no—
807C23×C4—51no—
808C4⋊Q8—42no—
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⋊C4C22×D511yescharacteristic
845C2×C4⋊C4C22×D511yescharacteristic
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⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C42—51no—
881C2×C42—51no—
882C2×C42—51no—
883C2×C42—51no—
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—202no—
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#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
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×C5C23×Q811yescharacteristic
959C22×C5C2×H(5,𝔽2)11yescharacteristic
960C22×C5#58511yescharacteristic
961C22×C5#58511yescharacteristic
962C22×C5#58511yescharacteristic
963C22×C5#58511yescharacteristic
964C22×C5#58511yescharacteristic
965C2×D5—22no—
966C2×D5—22no—
967C2×D5—22no—
968C2×D5—22no—
969C2×D5—22no—
970C2×D5—22no—
971C2×D5—41no—
972C2×D5—41no—
973C2×D5—41no—
974C2×D5—41no—
975C2×D5—41no—
976C2×D5—41no—
977C2×D5—41no—
978C2×D5—41no—
979C4×C5—22no—
980C4×C5—22no—
981C4×C5—22no—
982C4×C5—22no—
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—
993C4×C5—41no—
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—
1009C24—51no—
1010C2×Q8—22no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—41no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—201no—
1017C2×Q8—201no—
1018C2×Q8—201no—
1019C2×Q8—201no—
1020C2×Q8—201no—
1021C2×Q8—201no—
1022C2×Q8—201no—
1023C2×Q8—201no—
1024C2×Q8—201no—
1025C2×D4—54no—
1026C2×D4—201no—
1027C2×D4—201no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—54no—
1031C22×C4—54no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—51no—
1039C22×C4—51no—
1040C22×C4—51no—
1041C22×C4—51no—
1042C22×C4—51no—
1043C22×C4—51no—
1044C22×C4—102no—
1045C22×C4—201no—
1046C22×C4—201no—
1047C22×C4—201no—
1048C22×C4—201no—
1049C22×C4—201no—
1050C22×C4—201no—
1051C22×C4—201no—
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×C4C23×D511yescharacteristic
1061C22×C4C23×D511yescharacteristic
1062C22×C4C23×D511yescharacteristic
1063C22×C4C23×D511yescharacteristic
1064C22×C4C23×D511yescharacteristic
1065C22×C4C23×D511yescharacteristic
1066C22×C4C23×D511yescharacteristic
1067C22×C4C23×D511yescharacteristic
1068C22×C4C23×D511yescharacteristic
1069C22×C4C23×D511yescharacteristic
1070C22×C4C23×D511yescharacteristic
1071C22×C4C23×D511yescharacteristic
1072C22×C4C23×D511yescharacteristic
1073C22×C4C23×D511yescharacteristic
1074C22×C4C23×D511yescharacteristic
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—22no—
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—41no—
1088C4⋊C4—102no—
1089C4⋊C4—201no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4—201no—
1115C4⋊C4—201no—
1116C4⋊C4—201no—
1117C4⋊C4—201no—
1118C4⋊C4Q8×D514yes—
1119C22⋊C4—54no—
1120C22⋊C4—54no—
1121C22⋊C4—102no—
1122C22⋊C4—201no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
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—41no—
1143C42—41no—
1144C42—54no—
1145C42—102no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42—201no—
1150C42—201no—
1151C42—201no—
1152C42—201no—
1153C42—201no—
1154C2×C5#345811yescharacteristic
1155C2×C5#350111yescharacteristic
1156C2×C5#350411yescharacteristic
1157C2×C5#353311yescharacteristic
1158C2×C5#354011yescharacteristic
1159C2×C5#356611yescharacteristic
1160C2×C5#356811yescharacteristic
1161D5—42no—
1162D5—42no—
1163C23—52no—
1164C23—52no—
1165C23—101no—
1166C23—101no—
1167C23—101no—
1168C23—101no—
1169C23—101no—
1170C23—101no—
1171C23—101no—
1172C23—101no—
1173C23—101no—
1174C23—101no—
1175C23—101no—
1176C23—101no—
1177C23C24×D511yescharacteristic
1178Q8—82no—
1179Q8—82no—
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—21no—
1224C2×C4—21no—
1225C2×C4—52no—
1226C2×C4—52no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—101no—
1263C2×C4—101no—
1264C2×C4—101no—
1265C2×C4—101no—
1266C2×C4—101no—
1267C2×C4—204no—
1268C2×C4—204no—
1269C2×C4—204no—
1270C2×C4—204no—
1271C2×C4—402no—
1272C2×C4—402no—
1273C2×C4#414412yes—
1274C2×C4C2×Q8×D512yes—
1275C2×C4C2×Q8×D512yes—
1276C2×C4C2×Q8×D512yes—
1277C5#3675511yescharacteristic, complemented, Sylow
1278C22—102no—
1279C22—102no—
1280C22—102no—
1281C22—102no—
1282C22—102no—
1283C22—102no—
1284C22—201no—
1285C22—201no—
1286C22—201no—
1287C22—201no—
1288C22—201no—
1289C22—201no—
1290C22—201no—
1291C22—201no—
1292C22C2×#414411yescharacteristic
1293C22C22×Q8×D511yescharacteristic
1294C22#6628311yescharacteristic
1295C22#6628511yescharacteristic
1296C22#6628711yescharacteristic
1297C22#6628711yescharacteristic
1298C22#6628711yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
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—202no—
1329C2—202no—
1330C2#1061824611yescharacteristic
1331C2#1061840811yescharacteristic
1332C2#1061848211yescharacteristic
1333C2#1061856911yescharacteristic
1334C2#1061866211yescharacteristic
1335C2#1061892011yescharacteristic
1336C2#1061902711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2713C2
prime radicalC22×D20C23
hypercenter#2713D5
hypocenterC5#36755
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2713

Complements

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

NH ≅ G/Ntype
1. C5×#2713C2semidirect
2. #10614998C2semidirect
3. #10614987C2semidirect
4. #10614803C2semidirect
5. #10614782C2semidirect
6. #10610088C2semidirect
7. #10610025C2semidirect
8. #10609995C2semidirect
9. #10609965C2semidirect
10. #10609735C2semidirect
12. #10609680C2semidirect
13. #10609524C2semidirect
14. #10609001C2semidirect
16. #10608942C2semidirect
17. #10608929C2semidirect
18. #10608394C2semidirect
20. #10608317C2semidirect
21. #10608287C2semidirect
22. #10607868C2semidirect
25. #10607011C2semidirect
26. #10606979C2semidirect
27. #10606954C2semidirect
28. #10606864C2semidirect
29. #10606862C2semidirect
283. #4039Q8semidirect
366. #2713D5semidirect
1277. C5#36755semidirect

Maximal subgroups

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

subgroupindex
C5×#27132
#106149982
#106149872
#106148032
#106147822
#106100882
#106100252
#106099952
#106099652
#106097352
#106097312
#106096802
#106095242
#106090012
#106089462
#106089422
#106089292
#106083942
#106083902
#106083172
#106082872
#106078682
#106077002
#106071642
#106070112
#106069792
#106069542
#106068642
#106068622
#106066762
#106066682
#367555