Finite Group Databasebeta

← #27599383

Subgroups — #27599383

Order 13568.

1668 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283081C212yesmaximal, complemented
2#20282651C212yesmaximal, complemented
3#20282228C212yesmaximal, complemented
4#20281674C212yesmaximal, complemented
5#20281506C212yesmaximal, complemented
6#20281350C212yesmaximal, complemented
7#20281305C212yesmaximal, complemented
8#20281195C212yesmaximal, complemented
9#20281165C212yesmaximal, complemented
10#20280705C212yesmaximal, complemented
11#20280372C211yesmaximal, characteristic, complemented
12#20280281C211yesmaximal, characteristic, complemented
13#20279841C212yesmaximal, complemented
14#20279655C211yesmaximal, characteristic, complemented
15#20279484C212yesmaximal, complemented
16#20277530C211yesmaximal, characteristic, complemented
17#20277359C211yesmaximal, characteristic, complemented
18#20277213C211yesmaximal, characteristic, complemented
19C53×#2610C211yesmaximal, characteristic, complemented
20C2×#13133212C2212yes—
21C2×#13133210C2212yes—
22C2×#13133210C2212yes—
23C2×#13133193C2212yes—
24C2×#13133189C2212yes—
25C2×#13133188C2212yes—
26C2×C4×D212C2211yescharacteristic
27#16810564C2212yes—
28#16810564C2212yes—
29#16810563C2212yes—
30#16810562C2211yescharacteristic
31#16810559C2211yescharacteristic
32#16810559C2212yes—
33#16810557C2212yes—
34#16810555C2212yes—
35#16810552C2212yes—
36#16810551C2212yes—
37#16810549C2212yes—
38#16810546C2212yes—
39#16810546C2212yes—
40#16810540C2211yescharacteristic
41#16810539C2212yes—
42#16810539C2212yes—
43#16810539C2212yes—
44#16810538C2212yes—
45#16810538C2212yes—
46#16810537C2212yes—
47#16810537C2212yes—
48#16810532C2212yes—
49#16810532C2211yescharacteristic
50#16810531C2212yes—
51#16810530C2212yes—
52#16810525C2212yes—
53#16810523C2212yes—
54#16810523C2212yes—
55#16810523C2212yes—
56#16810523C2212yes—
57#16810521C2212yes—
58#16810521C2212yes—
59#16810520C2212yes—
60#16810520C2212yes—
61#16810518C2212yes—
62#16810518C2212yes—
63#16810516C2212yes—
64#16810516C2212yes—
65#16810516C2212yes—
66#16810516C2212yes—
67#16810515C2212yes—
68#16810515C2212yes—
69#16810514C2212yes—
70#16810512C2212yes—
71#16810512C2212yes—
72#16810512C2212yes—
73#16810511C2212yes—
74#16810509C2212yes—
75#16810509C2212yes—
76#16810507C2212yes—
77#16810506C2212yes—
78#16810503C2212yes—
79#16810502C2212yes—
80#16810500C2212yes—
81#16810499C2212yes—
82#16810498C2212yes—
83#16810495C2212yes—
84#16810494C2212yes—
85#16810491C2211yescharacteristic
86#16810485C2212yes—
87#16810484C2212yes—
88#16810482C2212yes—
89C4×C4⋊Dic53C2211yescharacteristic
90C4×C4⋊Dic53C2211yescharacteristic
91C22⋊C4×Dic53C2212yes—
92C4×C22⋊Dic53C2211yescharacteristic
93C4×C22⋊Dic53C2211yescharacteristic
94#16810469C2211yescharacteristic
95C42×Dic53C2211yescharacteristic
96C2×#124×C53C2211yescharacteristic
97C2×#117×C53C2211yescharacteristic
98C53×#395C2211yescharacteristic
99C53×#394C2211yescharacteristic
100C53×#393C2211yescharacteristic
101C53×#392C2211yescharacteristic
102C53×#390C2212yes—
103C53×#388C2212yes—
104C53×#388C2212yes—
105C53×#386C2212yes—
106C53×#376C2211yescharacteristic
107C22×D212C2311yescharacteristic
108C22×C22⋊D53C2312yes—
109C22×C22⋊D53C2312yes—
110C22×C22⋊D53C2312yes—
111C23×Dic53C2312yes—
112C22×C4×D53C2312yes—
113#13133212—44no—
114#13133210—44no—
115#13133210—44no—
116#13133193—44no—
117#13133189—44no—
118#13133188—44no—
119C4×D212—24no—
120C2×C4⋊Dic53C2312yes—
121C2×C4⋊Dic53C2312yes—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2312yes—
124C2×C4⋊Dic53C2312yes—
125C2×C4⋊Dic53C2312yes—
126C2×#11719919C2312yes—
127C2×#11719919C2312yes—
128C2×#11719919C2312yes—
129C2×#11719919C2312yes—
130C2×#11719919C2312yes—
131C2×#11719919C2312yes—
132C2×#11719919C2312yes—
133C2×#11719919C2312yes—
134C2×#11719919C2312yes—
135C2×C22⋊Dic53C2312yes—
136C2×C22⋊Dic53C2312yes—
137C2×C22⋊Dic53C2312yes—
138C2×C22⋊Dic53C2312yes—
139C2×C22⋊Dic53C2312yes—
140C2×C22⋊Dic53C2312yes—
141C2×C22⋊Dic53C2312yes—
142C2×C22⋊Dic53C2312yes—
143C2×#11719921C2312yes—
144C2×#11719921C2312yes—
145C2×#11719921C2312yes—
146C2×#11719921C2312yes—
147C2×#11719921C2312yes—
148C2×#11719921C2312yes—
149C2×#11719921C2312yes—
150C2×#11719921C2312yes—
151C2×#11719921C2312yes—
152C2×#11719921C2312yes—
153C2×C4×Dic53C2312yes—
154C2×C4×Dic53C2311yescharacteristic
155C2×C4×Dic53C2312yes—
156C2×C4×Dic53C2311yescharacteristic
157C2×C4×Dic53C2311yescharacteristic
158C2×C4×Dic53C2312yes—
159C2×C4×Dic53C2311yescharacteristic
160#13133124C2311yescharacteristic
161#13133124C2312yes—
162#13133124C2312yes—
163#13133124C2312yes—
164#13133124C2312yes—
165#13133124C2312yes—
166#13133124C2312yes—
167#13133124C2312yes—
168#13133124C2312yes—
169#13133124C2312yes—
170#13133124C2312yes—
171#13133124C2312yes—
172#13133124C2312yes—
173#13133124C2312yes—
174#13133124C2312yes—
175#13133124C2312yes—
176#13133124C2312yes—
177#13133124C2311yescharacteristic
178C22×Q8×C53C2311yescharacteristic
179C22×D4×C53C2311yescharacteristic
180C22×D4×C53C2312yes—
181C23×C4×C53C2311yescharacteristic
182#124×C53—24no—
183#117×C53—24no—
184C2×C4⋊C4×C53C2311yescharacteristic
185C2×C4⋊C4×C53C2311yescharacteristic
186C2×C4⋊C4×C53C2312yes—
187C2×C22⋊C4×C53C2312yes—
188C2×C22⋊C4×C53C2311yescharacteristic
189C2×C22⋊C4×C53C2311yescharacteristic
190C2×C22⋊C4×C53C2312yes—
191C2×C22⋊C4×C53C2312yes—
192C2×C22⋊C4×C53C2312yes—
193C2×C22⋊C4×C53C2312yes—
194C2×C22⋊C4×C53C2312yes—
195C2×C42×C53C2311yescharacteristic
196C2×C42×C53C2312yes—
197C2×C42×C53C2311yescharacteristic
198#95×C53C2312yes—
199#95×C53C2312yes—
200#95×C53C2312yes—
201#95×C53C2311yescharacteristic
202#95×C53C2311yescharacteristic
203C24×C53C2412yes—
204C24×C53C2411yescharacteristic
205C23×D53C2412yes—
206C2×Q8×C53—22no—
207C2×Q8×C53—42no—
208C2×D4×C53—22no—
209C2×D4×C53—42no—
210C2×D4×C53—42no—
211C2×D4×C53—42no—
212C2×D4×C53—42no—
213C22×C4×C53—22no—
214C22×C4×C53—41no—
215C22×C4×C53—41no—
216C22×C4×C53C2412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C22×C4×C53C2412yes—
220C22×C4×C53C2411yescharacteristic
221C22×C4×C53C2411yescharacteristic
222C22×C4×C53C2411yescharacteristic
223C22×C4×C53C2411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53—42no—
227C2×C22⋊D53—42no—
228C2×C22⋊D53—42no—
229C2×C22⋊D53—42no—
230C2×C22⋊D53—42no—
231C2×C22⋊D53—42no—
232C2×C22⋊D53—42no—
233C2×C22⋊D53—42no—
234C22×Dic53—42no—
235C22×Dic53—42no—
236C22×Dic53—42no—
237C22×Dic53C2412yes—
238C22×Dic53C2412yes—
239C22×Dic53C2412yes—
240C22×Dic53C2412yes—
241C22×Dic53C2412yes—
242C22×Dic53C2412yes—
243C22×Dic53C2412yes—
244C2×D212—22no—
245C2×D212—42no—
246C2×C4×D53—24no—
247C2×C4×D53—42no—
248C2×C4×D53—42no—
249C4⋊C4×C53—22no—
250C4⋊C4×C53—22no—
251C4⋊C4×C53—42no—
252C22⋊C4×C53—22no—
253C22⋊C4×C53—22no—
254C22⋊C4×C53—24no—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—42no—
257C22⋊C4×C53—42no—
258C22⋊C4×C53—42no—
259C22⋊C4×C53—42no—
260C42×C53—22no—
261C42×C53—42no—
262C42×C53#4114yes—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265C22⋊Dic53—42no—
266C22⋊Dic53—42no—
267C22⋊Dic53—42no—
268C22⋊Dic53—42no—
269C22⋊Dic53—42no—
270C22⋊Dic53—42no—
271#11719921—24no—
272#11719921—24no—
273#11719921—42no—
274#11719921—42no—
275#11719921—42no—
276#11719921—42no—
277#11719921—42no—
278#11719921—42no—
279#11719921—42no—
280#11719921—42no—
281C4⋊Dic53—22no—
282C4⋊Dic53—24no—
283C4⋊Dic53—24no—
284C4⋊Dic53—42no—
285C4⋊Dic53—42no—
286C4⋊Dic53—42no—
287#11719919—24no—
288#11719919—24no—
289#11719919—42no—
290#11719919—42no—
291#11719919—42no—
292#11719919—42no—
293#11719919—42no—
294#11719919—42no—
295#11719919—42no—
296C4×Dic53—24no—
297C4×Dic53—41no—
298C4×Dic53—42no—
299C4×Dic53—41no—
300C4×Dic53—41no—
301C4×Dic53—41no—
302C4×Dic53—42no—
303C23×C53—21no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—21no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—21no—
315C23×C53C2511yescharacteristic
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—22no—
323Q8×C53—82no—
324D4×C53—82no—
325D4×C53—84no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—22no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—44no—
347C2×C4×C53C2×#4112yes—
348C2×C4×C53C2×#4112yes—
349C2×C4×C53C2×#4112yes—
350C22⋊D53—84no—
351C22⋊D53—84no—
352C22⋊D53—84no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic53—22no—
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—22no—
363C2×Dic53—22no—
364C2×Dic53—22no—
365C2×Dic53—22no—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—84no—
374C2×Dic53H(5,𝔽2)14yes—
375D212—44no—
376C4×D53—84no—
377#37027—531nomaximal, Sylow
378C22×C53—41no—
379C22×C53—42no—
380C22×C53—41no—
381C22×C53—42no—
382C22×C53—42no—
383C22×C53—41no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—42no—
387C22×C53—42no—
388C22×C53—42no—
389C22×C53—42no—
390C22×C53C22×#4111yescharacteristic
391C22×C53C2×H(5,𝔽2)12yes—
392C22×C53#58512yes—
393C22×C53#58511yescharacteristic
394C22×C53#58511yescharacteristic
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C2×D53—42no—
401C2×D53—42no—
402C4×C53—22no—
403C4×C53—22no—
404C4×C53—22no—
405C4×C53—41no—
406C4×C53—41no—
407C4×C53—41no—
408C4×C53—42no—
409C4×C53—42no—
410C4×C53—42no—
411Dic53—24no—
412Dic53—42no—
413Dic53—42no—
414Dic53—42no—
415Dic53—42no—
416Dic53—42no—
417Dic53—42no—
418#2860—532no—
419#2803—532no—
420#2771—532no—
421#2727—532no—
422#2714—532no—
423#2702—532no—
424#2699—532no—
425#2691—532no—
426#2689—532no—
427#2648—532no—
428#2610D5311yescharacteristic, complemented
429#2606—531no—
430#2598—531no—
431#2559—532no—
432#2540—531no—
433#2526—532no—
434#2337—531no—
435#2319—531no—
436#2298—531no—
437C2×C53—81no—
438C2×C53—82no—
439C2×C53#345511yescharacteristic
440C2×C53#349311yescharacteristic
441C2×C53#350811yescharacteristic
442C2×C53#355112yes—
443C2×C53#356012yes—
444D53—82no—
445C2×#126—532no—
446C2×#126—532no—
447C2×#126—532no—
448C2×#124C2×D5311yescharacteristic
449C2×C22⋊Q8—532no—
450C2×#121—532no—
451C2×#121—532no—
452C2×C4×D4—531no—
453C2×#117C2×D5311yescharacteristic
454#400—531no—
455#400—532no—
456#400—532no—
457#400—532no—
458#399—531no—
459#399—532no—
460#398—532no—
461#398—532no—
462#397—532no—
463#397—532no—
464#397—532no—
465#396—532no—
466#396—532no—
467#395C2×D5311yescharacteristic
468#394—532no—
469#394—532no—
470#394—531no—
471#394—532no—
472#394—532no—
473#394—532no—
474#394—532no—
475#394—532no—
476#394C2×D5311yescharacteristic
477#393C2×D5311yescharacteristic
478#392—532no—
479#392—531no—
480#392—532no—
481#392C2×D5311yescharacteristic
482#391—532no—
483#390—532no—
484#390—532no—
485#390—532no—
486#390—532no—
487#390—532no—
488#390C2×D5312yes—
489#389—532no—
490#389—532no—
491#389—532no—
492#389—532no—
493#389—532no—
494#389—532no—
495#388—532no—
496#388—532no—
497#388—532no—
498#388—532no—
499#388—532no—
500#388—532no—
501#388—532no—
502#388—532no—
503#388—532no—
504#388—532no—
505#388—532no—
506#388C2×D5312yes—
507#388C2×D5312yes—
508#387—532no—
509#387—532no—
510#387—532no—
511#387—532no—
512#386—532no—
513#386—532no—
514#386—532no—
515#386—532no—
516#386C2×D5312yes—
517#385—532no—
518#385—532no—
519#385—532no—
520#383—531no—
521#381—532no—
522#381—532no—
523#380—532no—
524C4×C4⋊C4—531no—
525C4×C4⋊C4—531no—
526C4×C22⋊C4—531no—
527C4×C22⋊C4—531no—
528C4×C22⋊C4—532no—
529#376—531no—
530#376C2×D5311yescharacteristic
531C43—531no—
532C53#3702711yescharacteristic, complemented, Sylow
533C22×Q8C22×D5311yescharacteristic
534C22×D4—532no—
535C22×D4—532no—
536C22×D4—532no—
537C22×D4—531no—
538C22×D4C22×D5311yescharacteristic
539C22×D4C22×D5312yes—
540C23×C4—532no—
541C23×C4—532no—
542C23×C4C22×D5311yescharacteristic
543#126—2124no—
544#126—2124no—
545#126—2124no—
546#124—24no—
547C22⋊Q8—2124no—
548#121—2124no—
549#121—2124no—
550C4×D4—1064no—
551#117—24no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—532no—
554C2×C4⋊C4—532no—
555C2×C4⋊C4—532no—
556C2×C4⋊C4—532no—
557C2×C4⋊C4—532no—
558C2×C4⋊C4—532no—
559C2×C4⋊C4—532no—
560C2×C4⋊C4—532no—
561C2×C4⋊C4—532no—
562C2×C4⋊C4—532no—
563C2×C4⋊C4—532no—
564C2×C4⋊C4—532no—
565C2×C4⋊C4—532no—
566C2×C4⋊C4—532no—
567C2×C4⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C4⋊C4C22×D5312yes—
570C2×C22⋊C4—532no—
571C2×C22⋊C4—532no—
572C2×C22⋊C4—532no—
573C2×C22⋊C4—532no—
574C2×C22⋊C4—532no—
575C2×C22⋊C4—532no—
576C2×C22⋊C4—532no—
577C2×C22⋊C4—532no—
578C2×C22⋊C4—532no—
579C2×C22⋊C4—532no—
580C2×C22⋊C4—532no—
581C2×C22⋊C4—532no—
582C2×C22⋊C4—532no—
583C2×C22⋊C4—532no—
584C2×C22⋊C4—532no—
585C2×C22⋊C4—532no—
586C2×C22⋊C4—532no—
587C2×C22⋊C4—532no—
588C2×C22⋊C4C22×D5311yescharacteristic
589C2×C22⋊C4C22×D5311yescharacteristic
590C2×C22⋊C4C22×D5312yes—
591C2×C22⋊C4C22×D5312yes—
592C2×C22⋊C4C22×D5312yes—
593C2×C22⋊C4C22×D5312yes—
594C2×C22⋊C4C22×D5312yes—
595C2×C22⋊C4C22×D5312yes—
596C2×C42—532no—
597C2×C42—532no—
598C2×C42—531no—
599C2×C42—531no—
600C2×C42—532no—
601C2×C42—531no—
602C2×C42—531no—
603C2×C42C22×D5311yescharacteristic
604C2×C42C22×D5312yes—
605C2×C42C22×D5311yescharacteristic
606#95—532no—
607#95—532no—
608#95—532no—
609#95—532no—
610#95—532no—
611#95—532no—
612#95—532no—
613#95—532no—
614#95—532no—
615#95—532no—
616#95—532no—
617#95—532no—
618#95—531no—
619#95—532no—
620#95—531no—
621#95—532no—
622#95—532no—
623#95—532no—
624#95C22×D5311yescharacteristic
625#95C22×D5311yescharacteristic
626#95C22×D5312yes—
627#95C22×D5312yes—
628#95C22×D5312yes—
629C24—532no—
630C24C23×D5311yescharacteristic
631C24C23×D5312yes—
632C2×Q8—22no—
633C2×Q8—42no—
634C2×D4—22no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—1064no—
640C2×D4—1062no—
641C2×D4—2122no—
642C2×D4—2122no—
643C2×D4—2122no—
644C2×D4—2122no—
645C2×D4—2122no—
646C2×D4—2122no—
647C2×D4—2122no—
648C2×D4—2122no—
649C2×D4—2122no—
650C22×C4—22no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—532no—
654C22×C4—532no—
655C22×C4—532no—
656C22×C4—532no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—532no—
660C22×C4—1064no—
661C22×C4—2122no—
662C22×C4—2122no—
663C22×C4—2122no—
664C22×C4—2122no—
665C22×C4—2122no—
666C22×C4C23×D5311yescharacteristic
667C22×C4C23×D5311yescharacteristic
668C22×C4C23×D5312yes—
669C22×C4C23×D5312yes—
670C22×C4C23×D5311yescharacteristic
671C22×C4C23×D5312yes—
672C22×C4C23×D5311yescharacteristic
673C22×C4C23×D5311yescharacteristic
674C22×C4C23×D5311yescharacteristic
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—42no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1062no—
683C4⋊C4—2122no—
684C4⋊C4—2122no—
685C4⋊C4—2122no—
686C4⋊C4—2122no—
687C4⋊C4—2122no—
688C4⋊C4—2122no—
689C4⋊C4—2122no—
690C4⋊C4—2122no—
691C4⋊C4—2122no—
692C4⋊C4—2122no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—2122no—
706C22⋊C4—2122no—
707C22⋊C4—2122no—
708C22⋊C4—2122no—
709C22⋊C4—2122no—
710C22⋊C4—2122no—
711C22⋊C4—2122no—
712C22⋊C4—2122no—
713C22⋊C4—2122no—
714C22⋊C4—2122no—
715C22⋊C4—2122no—
716C22⋊C4—2122no—
717C22⋊C4—2122no—
718C22⋊C4—2122no—
719C42—22no—
720C42—42no—
721C42—1064no—
722C42—2122no—
723C42—2121no—
724C42—2121no—
725C42—2121no—
726C42—2121no—
727C42—2122no—
728C42#1171994714yes—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—1062no—
742C23—1062no—
743C23—1062no—
744C23—1062no—
745C23—1062no—
746C23—1062no—
747C23—1062no—
748C23C24×D5311yescharacteristic
749Q8—82no—
750D4—82no—
751D4—84no—
752D4—4244no—
753D4—4244no—
754D4—4244no—
755D4—2124no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—44no—
777C2×C4—534no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1062no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1062no—
791C2×C4—1062no—
792C2×C4—1062no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1062no—
796C2×C4—1062no—
797C2×C4—1062no—
798C2×C4—4244no—
799C2×C4—4244no—
800C2×C4C2×#1171994712yes—
801C2×C4C2×#1171994712yes—
802C2×C4C2×#1171994712yes—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—2122no—
816C22—2122no—
817C22—2122no—
818C22—2122no—
819C22—2122no—
820C22—2122no—
821C22—2122no—
822C22C22×#1171994711yescharacteristic
823C22H(5,𝔽2)×D5312yes—
824C22#1681145912yes—
825C22#1681145911yescharacteristic
826C22#1681145911yescharacteristic
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—42no—
836C4—1064no—
837C4—2122no—
838C4—2122no—
839C4—2122no—
840C4—2122no—
841C4—2122no—
842C4—2122no—
843C2—82no—
844C2—81no—
845C2—4242no—
846C2#2028810411yescharacteristic
847C2#2028843211yescharacteristic
848C2#2028859011yescharacteristic
849C2#2028913012yes—
850C2#2028926212yes—
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2610C2
hypercenter#2610D53
hypocenterC53#37027
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #20283081C2semidirect
2. #20282651C2semidirect
3. #20282228C2semidirect
4. #20281674C2semidirect
5. #20281506C2semidirect
6. #20281350C2semidirect
7. #20281305C2semidirect
8. #20281195C2semidirect
9. #20281165C2semidirect
10. #20280705C2semidirect
11. #20280372C2semidirect
12. #20280281C2semidirect
13. #20279841C2semidirect
14. #20279655C2semidirect
15. #20279484C2semidirect
16. #20277530C2semidirect
17. #20277359C2semidirect
18. #20277213C2semidirect
19. C53×#2610C2semidirect
428. #2610D53semidirect
532. C53#37027semidirect

Maximal subgroups

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

subgroupindex
#202830812
#202826512
#202822282
#202816742
#202815062
#202813502
#202813052
#202811952
#202811652
#202807052
#202803722
#202802812
#202798412
#202796552
#202794842
#202775302
#202773592
#202772132
C53×#26102
#3702753