Finite Group Databasebeta

← D53×#2898 #28247644

Subgroups — D53×#2898 #28247644

Order 13568.

4882 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D53C211yesmaximal, characteristic
2C2×#131×D53C211yesmaximal, characteristic, complemented
3#520×D53C211yesmaximal, characteristic, complemented
4#20283249C211yesmaximal, characteristic, complemented
5#20283248C211yesmaximal, characteristic, complemented
6#20283247C213yesmaximal, complemented
7#20283246C213yesmaximal, complemented
8#20283245C211yesmaximal, characteristic, complemented
9#20283244C213yesmaximal, complemented
10#20283243C213yesmaximal, complemented
11#417×D53C213yesmaximal, complemented
12#419×D53C213yesmaximal, complemented
13#416×D53C213yesmaximal, complemented
14C2×#103×D53C213yesmaximal, complemented
15C53×#2898C211yesmaximal, characteristic, complemented
16C2×#13133265—21no—
17C2×#13133265C2213yes—
18C2×#13133264—23no—
19C2×#13133264C2211yescharacteristic
20C2×#13133264C2213yes—
212−1+4×D53—28no—
222−1+4×D53C4116yescomplemented
23C2×#41×D53—23no—
24C2×#41×D53C2213yes—
25C2×#41×D53C2211yescharacteristic
26C22×Q8×D53—21no—
27C22×Q8×D53C2213yes—
28C2×#13133225C2213yescomplemented
29C2×#13133224C2211yescharacteristic, complemented
30C2×#13133223C2213yescomplemented
31#131×D53—28no—
32C2×M16×D53C2213yes—
33C22×C8×D53C2213yes—
34#16811106C2211yescharacteristic, complemented
35#16811105—21no—
36#16811104C2213yescomplemented
37#16811103C2213yescomplemented
38#16811102—23no—
39C4×Q8×D53—21no—
40C4×D4×D53—23no—
41#117×D53C2213yes—
42C2×C4⋊C4×D53C2213yes—
43#16810633C2213yescomplemented
44#16810632C2213yescomplemented
45#16810631C2213yescomplemented
46#16810630C2216yescomplemented
47#16810630C2216yescomplemented
48#16810625C2213yescomplemented
49#16810624C2213yescomplemented
50#16810623C2216yescomplemented
51#16810622C2213yescomplemented
52#16810621C2216yescomplemented
53#16810620C2213yescomplemented
54#16810619C2213yescomplemented
55#16810618C2213yescomplemented
56#16810618C2213yescomplemented
57#16810617C2213yescomplemented
58#16810616C2213yescomplemented
59#16810616C2213yescomplemented
60C2×#13133142C2213yescomplemented
61C2×#13133141C2213yescomplemented
62C2×#13133140C2213yescomplemented
63#103×D53C2213yes—
64#103×D53C2216yes—
65#103×D53C2213yes—
66#103×D53C2216yescomplemented
67#103×D53C2216yescomplemented
68#102×D53C2211yescharacteristic
69#102×D53C2213yes—
70C2×2−1+4×C53C2211yescharacteristic
71C2×#131×C53C2211yescharacteristic, complemented
72C53×#520C2211yescharacteristic, complemented
73C53×#419C2213yescomplemented
74C53×#417C2213yescomplemented
75C53×#416C2213yescomplemented
76C2×#103×C53C2213yescomplemented
77#13133265—216no—
78#13133265—212no—
79#13133265C2×C4124yescomplemented
80#13133264—24no—
81#13133264—248no—
82#13133264—212no—
83#13133264C2×C4124yescomplemented
84#13133264C2×C418yescomplemented
85C2×#11719949—23no—
86C2×#11719949D411yescharacteristic
87C2×#11719949C2313yes—
88C2×#11719945—26no—
89C2×#11719945—23no—
90C2×#11719945—23no—
91C2×#11719945C2313yes—
92C2×#11719945C2313yes—
93C2×#11719947—23no—
94C2×#11719947—26no—
95C2×#11719947—23no—
96C2×#11719947D413yes—
97C2×#11719947C2313yes—
98#41×D53—248no—
99#41×D53—212no—
100#41×D53C2×C418yes—
101#41×D53C2×C4124yescomplemented
102#41×D53D418yes—
103C22×Dic106—23no—
104C22×Dic106—23no—
105C22×Dic106C2313yes—
106C2×Q8×D53—21no—
107C2×Q8×D53—216no—
108C2×Q8×D53—23no—
109C2×Q8×D53—212no—
110C2×Q8×D53—23no—
111C2×Q8×D53—23no—
112C2×Q8×D53C2×C4124yescomplemented
113C2×Q8×D53D411yescharacteristic
114C2×Q8×D53C2313yes—
115C2×Q8×D53C2316yes—
116C2×D4×D53—23no—
117C2×D4×D53D413yes—
118C2×D4×D53C2311yescharacteristic
119C22×C4×D53—23no—
120C22×C4×D53—23no—
121C22×C4×D53—23no—
122C22×C4×D53C2313yes—
123#13133225—212no—
124#13133224—24no—
125#13133223—212no—
126C2×#11719917C2313yes—
127C2×#11719912C2316yes—
128M16×D53—212no—
129C22×#88322C2313yes—
130C2×C8×D53—212no—
131C2×C8×D53C2311yescharacteristic
132C2×C8×D53C2313yes—
133C2×C8×D53C2313yes—
134C2×C8×D53C2313yes—
135Q8×Dic53—21no—
136C4×Dic106—23no—
137#13133182—23no—
138C4×D212—23no—
139D4×Dic53—23no—
140#13133179—23no—
141C4×C22⋊D53—26no—
142#13133177—26no—
143#13133176C2313yes—
144#13133175C2313yes—
145#13133175C2313yes—
146#13133174—23no—
147#13133173—23no—
148C2×C4⋊Dic53C2313yes—
149C2×#11719919—23no—
150C4⋊C4×D53—23no—
151C4⋊C4×D53—23no—
152C4⋊C4×D53C2313yes—
153C4⋊C4×D53C2316yes—
154C4⋊C4×D53C2311yescharacteristic
155C22⋊C4×D53—23no—
156C42×D53—23no—
157#13133142C2313yes—
158#13133142C2316yes—
159#13133142C2313yes—
160#13133141C2313yes—
161#13133141C2316yes—
162#13133141C2313yes—
163#13133140C2313yes—
164#13133140C2316yes—
165#13133140C2313yes—
166#13133139C2311yescharacteristic
167#13133139C2313yes—
168#13133138C2311yescharacteristic
169#13133138C2313yes—
170#13133137C2311yescharacteristic
171#13133137C2313yes—
1722−1+4×C53—24no—
1732−1+4×C53C2×C418yescomplemented
174C2×#41×C53—23no—
175C2×#41×C53C2313yes—
176C2×#41×C53C2311yescharacteristic
177C22×Q8×C53—21no—
178C22×Q8×C53C2313yes—
179#131×C53—24no—
180C2×M16×C53C2313yes—
181C22×C8×C53C2313yes—
182C4×Q8×C53—21no—
183C4×D4×C53—23no—
184#117×C53C2313yes—
185C2×C4⋊C4×C53C2313yes—
186#103×C53C2313yes—
187#103×C53C2316yes—
188#103×C53C2313yes—
189#102×C53C2311yescharacteristic
190#102×C53C2313yes—
191C23×D53—21no—
192C23×D53C2×D413yes—
193#41×C53—224no—
194#41×C53—26no—
195#41×C53C22×C414yes—
196#41×C53C22×C4112yescomplemented
197#41×C53C2×D414yes—
198C2×Q8×C53—28no—
199C2×Q8×C53—23no—
200C2×Q8×C53—26no—
201C2×Q8×C53C22×C4112yescomplemented
202C2×Q8×C53C2×D411yescharacteristic
203C2×Q8×C53C2413yes—
204C2×D4×C53—23no—
205C2×D4×C53C2×D413yes—
206C2×D4×C53C2411yescharacteristic
207C22×C4×C53—23no—
208C22×C4×C53—23no—
209C22×C4×C53—23no—
210C22×C4×C53C2413yes—
211C2×C22⋊D53—23no—
212C2×C22⋊D53—23no—
213C2×C22⋊D53—21no—
214C2×C22⋊D53C2×D416yes—
215C22×Dic53—23no—
216C22×Dic53—23no—
217C22×Dic53—23no—
218C22×Dic53C2×D413yes—
219#11719949—224no—
220#11719949—26no—
221#11719949C22⋊C418yes—
222#11719949C22×C4112yescomplemented
223Q8×D53—28no—
224Q8×D53—224no—
225Q8×D53—224no—
226Q8×D53—26no—
227Q8×D53—212no—
228Q8×D53—224no—
229Q8×D53C22⋊C418yes—
230Q8×D53C22×C4112yes—
231Q8×D53C22×C4124yescomplemented
232#11719947—224no—
233#11719947—248no—
234#11719947—224no—
235#11719947—26no—
236#11719947C22⋊C4124yes—
237#11719947C22×C4112yescomplemented
238D4×D53—224no—
239D4×D53—22no—
240D4×D53C22⋊C4124yes—
241D4×D53C22×C414yes—
242#11719945—26no—
243#11719945—248no—
244#11719945—224no—
245#11719945—224no—
246#11719945C22×C4112yes—
247#11719945C22×C4112yescomplemented
248#11719945C2×D4112yes—
249C2×D212—23no—
250C2×D212C2×D413yes—
251C2×D212C2411yescharacteristic
252C2×C4×D53—224no—
253C2×C4×D53—23no—
254C2×C4×D53—26no—
255C2×C4×D53—23no—
256C2×C4×D53—23no—
257C2×C4×D53—224no—
258C2×C4×D53—21no—
259C2×C4×D53—23no—
260C2×C4×D53—26no—
261C2×C4×D53—86no—
262C2×C4×D53C22×C4112yes—
263C2×C4×D53C2×D413yes—
264C2×C4×D53C2×D413yes—
265C2×C4×D53C2×D4112yes—
266C2×C4×D53C2411yescharacteristic
267C2×C4×D53C2413yes—
268C2×Dic106—23no—
269C2×Dic106—26no—
270C2×Dic106—224no—
271C2×Dic106—23no—
272C2×Dic106—26no—
273C2×Dic106—224no—
274C2×Dic106C22×C4112yescomplemented
275C2×Dic106C2×D413yes—
276C2×Dic106C2413yes—
277M16×C53—26no—
278C2×C8×C53—26no—
279C2×C8×C53C2411yescharacteristic
280C2×C8×C53C2413yes—
281C4⋊C4×C53—23no—
282C4⋊C4×C53C2413yes—
283C4⋊C4×C53C2411yescharacteristic
284C22⋊C4×C53—23no—
285C42×C53—23no—
286C22⋊Dic53—23no—
287#11719921—23no—
288#11719921—23no—
289C4⋊Dic53—23no—
290C4⋊Dic53C2413yes—
291C4⋊Dic53C2411yescharacteristic
292#11719919—23no—
293#11719919—26no—
294#11719919—21no—
295C4×Dic53—23no—
296C4×Dic53—23no—
297C4×Dic53—23no—
298#11719917—26no—
299C2×#88322—26no—
300C2×#88322C2411yescharacteristic
301C2×#88322C2413yes—
302#11719912—212no—
303C8×D53—22no—
304C8×D53—26no—
305C8×D53—26no—
306C8×D53—26no—
307C23×C53—21no—
308C23×C53C22×D413yes—
309C22×D53—26no—
310C22×D53—26no—
311C22×D53—21no—
312C22×D53—24no—
313C22×D53—42no—
314C22×D53—42no—
315C22×D53C2×C22⋊C4112yes—
316C22×D53C22×D413yes—
317C22×D53C22×D411yescharacteristic
318Q8×C53—212no—
319Q8×C53—23no—
320Q8×C53C2×C22⋊C414yes—
321Q8×C53C23×C416yes—
322D4×C53—212no—
323D4×C53—21no—
324D4×C53C2×C22⋊C4112yes—
325D4×C53C23×C412yes—
326C2×C4×C53—212no—
327C2×C4×C53—23no—
328C2×C4×C53—212no—
329C2×C4×C53—23no—
330C2×C4×C53—21no—
331C2×C4×C53—83no—
332C2×C4×C53C23×C416yes—
333C2×C4×C53C22×D413yes—
334C2×C4×C53C22×D416yes—
335C2×C4×C53C2511yescharacteristic
336C22⋊D53—212no—
337C22⋊D53—212no—
338C22⋊D53—24no—
339C22⋊D53C2×C22⋊C4124yes—
340C2×Dic53—212no—
341C2×Dic53—23no—
342C2×Dic53—212no—
343C2×Dic53—23no—
344C2×Dic53—21no—
345C2×Dic53—83no—
346C2×Dic53C2×C22⋊C4112yes—
347C2×Dic53C22×D411yescharacteristic
348C2×Dic53C22×D413yes—
349D212—212no—
350D212—21no—
351D212C2×C22⋊C4112yes—
352D212C23×C412yes—
353C4×D53—212no—
354C4×D53—224no—
355C4×D53—212no—
356C4×D53—212no—
357C4×D53—46no—
358C4×D53—42no—
359C4×D53—86no—
360C4×D53C2×C22⋊C4112yes—
361C4×D53C2×C22⋊C4112yes—
362C4×D53C23×C412yes—
363C4×D53C23×C416yes—
364C4×D53C22×D412yes—
365C4×D53C22×D416yes—
366Dic106—212no—
367Dic106—23no—
368Dic106—212no—
369Dic106—224no—
370Dic106C2×C22⋊C4112yes—
371Dic106C23×C416yes—
372C8×C53—21no—
373C8×C53—23no—
374#88322—21no—
375#88322—23no—
376C2×#2898—531nomaximal, Sylow
377C22×C53—23no—
378C22×C53—23no—
379C22×C53—22no—
380C22×C53—41no—
381C22×C53—41no—
382C22×C53C22×C22⋊C416yes—
383C22×C53C23×D411yescharacteristic
384C2×D53—23no—
385C2×D53—23no—
386C2×D53—224no—
387C2×D53—22no—
388C2×D53—41no—
389C2×D53—41no—
390C2×D53—48no—
391C2×D53C22×C22⋊C416yes—
392C2×D53C22×C22⋊C412yes—
393C2×D53#57712yes—
394C2×D53#57812yes—
395C4×C53—26no—
396C4×C53—43no—
397C4×C53—41no—
398C4×C53C22×C22⋊C416yes—
399C4×C53C24×C411yescharacteristic
400C4×C53C23×D411yescharacteristic
401Dic53—26no—
402Dic53—43no—
403Dic53—41no—
404Dic53C22×C22⋊C412yes—
405Dic53C22×C22⋊C416yes—
406C22×2−1+4—531no—
407C22×#131—531no—
408C2×#520—531no—
409#2898—533no—
410#2898—533no—
411#2898—533no—
412#2898—533no—
413#2898—531no—
414#2898—531no—
415#2898—531no—
416#2898D5311yescharacteristic, direct product factor
417C2×#417—533no—
418C2×#419—533no—
419C2×#416—533no—
420C22×#103—533no—
421C2×C53—26no—
422C2×C53—42no—
423C2×C53C23×C22⋊C411yescharacteristic
424C2×C53C2×#57711yescharacteristic
425C2×C53C2×#57811yescharacteristic
426D53—26no—
427D53—42no—
428D53#289814yesdirect product factor
429C2×2−1+4—5316no—
430C2×2−1+4—533no—
431C2×2−1+4—531no—
432C2×2−1+4—533no—
433C2×2−1+4—1061no—
434C2×2−1+4—1063no—
435C2×2−1+4—1068no—
436C2×2−1+4C2×D5311yescharacteristic
437C22×#41—531no—
438C22×#41—533no—
439C22×#41—1063no—
440C23×Q8—533no—
441C23×Q8—1061no—
442C2×#131—531no—
443C2×#131—533no—
444C2×#131—533no—
445C2×#131—1068no—
446C2×#131C2×D5311yescharacteristic, complemented
447C22×M16—533no—
448C23×C8—533no—
449#520—531no—
450#520—533no—
451#520—533no—
452#520—1063no—
453#520—1061no—
454#520C2×D5311yescharacteristic, complemented
455C2×C4×Q8—1061no—
456C2×C4×D4—1063no—
457C2×#117—533no—
458C22×C4⋊C4—533no—
459#419—533no—
460#419—533no—
461#419—533no—
462#419—536no—
463#419—536no—
464#419C2×D5313yescomplemented
465#417—533no—
466#417—533no—
467#417—533no—
468#417—536no—
469#417—536no—
470#417C2×D5313yescomplemented
471#416—533no—
472#416—533no—
473#416—533no—
474#416—533no—
475#416—533no—
476#416—533no—
477#416—533no—
478#416C2×D5313yescomplemented
479C2×#103—533no—
480C2×#103—533no—
481C2×#103—533no—
482C2×#103—533no—
483C2×#103—536no—
484C2×#103—536no—
485C2×#103—536no—
486C2×#103—533no—
487C2×#103C2×D5313yescomplemented
488C2×#102—531no—
489C2×#102—533no—
490C53C2×#289811yescharacteristic, complemented, Sylow
4912−1+4—24no—
4922−1+4—538no—
4932−1+4—5324no—
4942−1+4—5324no—
4952−1+4—10616no—
4962−1+4—10612no—
4972−1+4—10648no—
4982−1+4—10612no—
4992−1+4—1064no—
5002−1+4C4×D5318yescomplemented
501C2×#41—23no—
502C2×#41—538no—
503C2×#41—538no—
504C2×#41—531no—
505C2×#41—533no—
506C2×#41—533no—
507C2×#41—5324no—
508C2×#41—533no—
509C2×#41—533no—
510C2×#41—533no—
511C2×#41—1063no—
512C2×#41—1066no—
513C2×#41—1063no—
514C2×#41—1063no—
515C2×#41—10612no—
516C2×#41—1066no—
517C2×#41—1063no—
518C2×#41—10648no—
519C2×#41—1063no—
520C2×#41C22×D5313yes—
521C2×#41C22×D5311yescharacteristic
522C22×Q8—21no—
523C22×Q8—531no—
524C22×Q8—5324no—
525C22×Q8—533no—
526C22×Q8—536no—
527C22×Q8—533no—
528C22×Q8—1063no—
529C22×Q8—1063no—
530C22×Q8—1063no—
531C22×Q8—1063no—
532C22×Q8—10612no—
533C22×Q8—10616no—
534C22×Q8—1063no—
535C22×Q8—1061no—
536C22×Q8C22×D5313yes—
537C22×D4—533no—
538C22×D4—531no—
539C22×D4—1063no—
540C23×C4—533no—
541C23×C4—1063no—
542C23×C4—1063no—
543C23×C4—1063no—
544#131—24no—
545#131—10612no—
546#131—10612no—
547#131—1064no—
548C2×M16—533no—
549C2×M16—536no—
550C2×M16—10612no—
551C2×M16C22×D5313yes—
552C22×C8—533no—
553C22×C8—531no—
554C22×C8—533no—
555C22×C8—533no—
556C22×C8—533no—
557C22×C8—10612no—
558C22×C8C22×D5313yes—
559C4×Q8—21no—
560C4×Q8—1063no—
561C4×Q8—1063no—
562C4×Q8—1061no—
563C4×D4—23no—
564C4×D4—1063no—
565C4×D4—1066no—
566C4×D4—1063no—
567C4×D4—1066no—
568C4×D4—1063no—
569#117—533no—
570#117—533no—
571#117—533no—
572#117—1063no—
573#117—1063no—
574#117C22×D5313yes—
575C2×C4⋊C4—533no—
576C2×C4⋊C4—533no—
577C2×C4⋊C4—536no—
578C2×C4⋊C4—531no—
579C2×C4⋊C4—1063no—
580C2×C4⋊C4—1063no—
581C2×C4⋊C4—1063no—
582C2×C4⋊C4C22×D5313yes—
583C2×C22⋊C4—1063no—
584C2×C42—1063no—
585#103—533no—
586#103—536no—
587#103—533no—
588#103—533no—
589#103—536no—
590#103—533no—
591#103—533no—
592#103—536no—
593#103—533no—
594#103C22×D5313yes—
595#103C22×D5316yes—
596#103C22×D5313yes—
597#102—531no—
598#102—533no—
599#102—531no—
600#102—533no—
601#102—531no—
602#102—533no—
603#102C22×D5311yescharacteristic
604#102C22×D5313yes—
605C24—533no—
606C24—1061no—
607#41—224no—
608#41—26no—
609#41—538no—
610#41—5324no—
611#41—5312no—
612#41—5312no—
613#41—5312no—
614#41—5312no—
615#41—5312no—
616#41—10624no—
617#41—10648no—
618#41—10624no—
619#41—10624no—
620#41—1066no—
621#41—1066no—
622#41—10648no—
623#41—10624no—
624#41—10624no—
625#41—1066no—
626#41C2×C4×D5314yes—
627#41C2×C4×D53112yescomplemented
628#41D4×D5314yes—
629C2×Q8—28no—
630C2×Q8—23no—
631C2×Q8—26no—
632C2×Q8—538no—
633C2×Q8—533no—
634C2×Q8—5312no—
635C2×Q8—5324no—
636C2×Q8—5312no—
637C2×Q8—533no—
638C2×Q8—1066no—
639C2×Q8—1063no—
640C2×Q8—10624no—
641C2×Q8—10624no—
642C2×Q8—10624no—
643C2×Q8—1066no—
644C2×Q8—10624no—
645C2×Q8—10612no—
646C2×Q8—10624no—
647C2×Q8—1068no—
648C2×Q8—1063no—
649C2×Q8—1066no—
650C2×Q8C2×C4×D53112yescomplemented
651C2×Q8D4×D5311yescharacteristic
652C2×Q8C23×D5313yes—
653C2×D4—23no—
654C2×D4—536no—
655C2×D4—5324no—
656C2×D4—534no—
657C2×D4—533no—
658C2×D4—531no—
659C2×D4—1063no—
660C2×D4—1062no—
661C2×D4—1061no—
662C2×D4—10624no—
663C2×D4—1063no—
664C2×D4—1063no—
665C2×D4D4×D5313yes—
666C2×D4C23×D5311yescharacteristic
667C22×C4—23no—
668C22×C4—23no—
669C22×C4—23no—
670C22×C4—533no—
671C22×C4—5312no—
672C22×C4—533no—
673C22×C4—533no—
674C22×C4—5312no—
675C22×C4—531no—
676C22×C4—533no—
677C22×C4—1063no—
678C22×C4—10624no—
679C22×C4—1063no—
680C22×C4—10624no—
681C22×C4—1066no—
682C22×C4—1066no—
683C22×C4—1061no—
684C22×C4—1063no—
685C22×C4—1063no—
686C22×C4—1063no—
687C22×C4—1063no—
688C22×C4—1063no—
689C22×C4—4246no—
690C22×C4C23×D5313yes—
691M16—26no—
692M16—10612no—
693M16—1066no—
694C2×C8—26no—
695C2×C8—531no—
696C2×C8—533no—
697C2×C8—1062no—
698C2×C8—1066no—
699C2×C8—1066no—
700C2×C8—1066no—
701C2×C8—1066no—
702C2×C8C23×D5311yescharacteristic
703C2×C8C23×D5313yes—
704C4⋊C4—23no—
705C4⋊C4—533no—
706C4⋊C4—531no—
707C4⋊C4—1063no—
708C4⋊C4—1066no—
709C4⋊C4—1061no—
710C4⋊C4—1063no—
711C4⋊C4C23×D5313yes—
712C4⋊C4C23×D5311yescharacteristic
713C22⋊C4—23no—
714C22⋊C4—1063no—
715C22⋊C4—1063no—
716C22⋊C4—1063no—
717C42—23no—
718C42—1063no—
719C42—1063no—
720C42—1063no—
721C23—21no—
722C23—531no—
723C23—5312no—
724C23—533no—
725C23—1066no—
726C23—1066no—
727C23—1064no—
728C23—1061no—
729C23—2122no—
730C23—2122no—
731C23C2×D4×D5313yes—
732Q8—212no—
733Q8—23no—
734Q8—5312no—
735Q8—536no—
736Q8—10612no—
737Q8—10624no—
738Q8—10612no—
739Q8—1063no—
740Q8C22⋊C4×D5314yes—
741Q8C22×C4×D5316yes—
742D4—212no—
743D4—21no—
744D4—5324no—
745D4—5312no—
746D4—532no—
747D4—10612no—
748D4—1064no—
749D4—10612no—
750D4—10612no—
751D4—1061no—
752D4C22⋊C4×D53112yes—
753D4C22×C4×D5312yes—
754C2×C4—212no—
755C2×C4—23no—
756C2×C4—212no—
757C2×C4—21no—
758C2×C4—23no—
759C2×C4—83no—
760C2×C4—5312no—
761C2×C4—533no—
762C2×C4—531no—
763C2×C4—5312no—
764C2×C4—5312no—
765C2×C4—532no—
766C2×C4—536no—
767C2×C4—532no—
768C2×C4—536no—
769C2×C4—10612no—
770C2×C4—10612no—
771C2×C4—10624no—
772C2×C4—10612no—
773C2×C4—10612no—
774C2×C4—1063no—
775C2×C4—10612no—
776C2×C4—1061no—
777C2×C4—1063no—
778C2×C4—4246no—
779C2×C4—4243no—
780C2×C4—2122no—
781C2×C4—2126no—
782C2×C4C22×C4×D5316yes—
783C2×C4C2×D4×D5313yes—
784C2×C4C2×D4×D5316yes—
785C2×C4C24×D5311yescharacteristic
786C8—21no—
787C8—23no—
788C8—1061no—
789C8—1063no—
790C22—23no—
791C22—23no—
792C22—22no—
793C22—41no—
794C22—41no—
795C22—532no—
796C22—532no—
797C22—532no—
798C22—536no—
799C22—10624no—
800C22—1063no—
801C22—1063no—
802C22—1062no—
803C22—2128no—
804C22—2121no—
805C22—2121no—
806C22C2×C22⋊C4×D5316yes—
807C22C22×D4×D5311yescharacteristic
808C4—26no—
809C4—43no—
810C4—41no—
811C4—532no—
812C4—536no—
813C4—1066no—
814C4—2123no—
815C4—2121no—
816C4C2×C22⋊C4×D5316yes—
817C4C23×C4×D5311yescharacteristic
818C4C22×D4×D5311yescharacteristic
819C2—26no—
820C2—42no—
821C2—534no—
822C2—1066no—
823C2—2122no—
824C2C22×C22⋊C4×D5311yescharacteristic
825C2#577×D5311yescharacteristic
826C2#578×D5311yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC53×#2898C2
socleC22×C53C23×D4
prime radicalC2×2−1+4×D53C2
cosocleC2×C4×C53C25
hypercenter#2898D53
hypocenterC53C2×#2898
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#131×D53C2semidirect
3. #520×D53C2semidirect
4. #20283249C2semidirect
5. #20283248C2semidirect
6. #20283247C2semidirect
7. #20283246C2semidirect
8. #20283245C2semidirect
9. #20283244C2semidirect
10. #20283243C2semidirect
11. #417×D53C2semidirect
12. #419×D53C2semidirect
13. #416×D53C2semidirect
14. C2×#103×D53C2semidirect
15. C53×#2898C2semidirect
22. 2−1+4×D53C4semidirect
28. C2×#13133225C22semidirect
29. C2×#13133224C22semidirect
30. C2×#13133223C22semidirect
34. #16811106C22semidirect
36. #16811104C22semidirect
37. #16811103C22semidirect
43. #16810633C22semidirect
44. #16810632C22semidirect
45. #16810631C22semidirect
46. #16810630C22semidirect
47. #16810630C22semidirect
48. #16810625C22semidirect
49. #16810624C22semidirect
50. #16810623C22semidirect
51. #16810622C22semidirect
52. #16810621C22semidirect
53. #16810620C22semidirect
54. #16810619C22semidirect
55. #16810618C22semidirect
56. #16810618C22semidirect
57. #16810617C22semidirect
58. #16810616C22semidirect
59. #16810616C22semidirect
60. C2×#13133142C22semidirect
61. C2×#13133141C22semidirect
62. C2×#13133140C22semidirect
66. #103×D53C22semidirect
67. #103×D53C22semidirect
71. C2×#131×C53C22semidirect
72. C53×#520C22semidirect
73. C53×#419C22semidirect
74. C53×#417C22semidirect
75. C53×#416C22semidirect
76. C2×#103×C53C22semidirect
79. #13133265C2×C4semidirect
83. #13133264C2×C4semidirect
84. #13133264C2×C4semidirect
101. #41×D53C2×C4semidirect
112. C2×Q8×D53C2×C4semidirect
173. 2−1+4×C53C2×C4semidirect
196. #41×C53C22×C4semidirect
201. C2×Q8×C53C22×C4semidirect
222. #11719949C22×C4semidirect
231. Q8×D53C22×C4semidirect
237. #11719947C22×C4semidirect
247. #11719945C22×C4semidirect
274. C2×Dic106C22×C4semidirect
416. #2898D53direct (N × H)
428. D53#2898direct (N × H)
446. C2×#131C2×D53semidirect
454. #520C2×D53semidirect
464. #419C2×D53semidirect
470. #417C2×D53semidirect
478. #416C2×D53semidirect
487. C2×#103C2×D53semidirect
490. C53C2×#2898semidirect
500. 2−1+4C4×D53semidirect
627. #41C2×C4×D53semidirect
650. C2×Q8C2×C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D532
C2×#131×D532
#520×D532
#202832492
#202832482
#202832472
#202832462
#202832452
#202832442
#202832432
#417×D532
#419×D532
#416×D532
C2×#103×D532
C53×#28982
C2×#289853