Finite Group Databasebeta

← D53×#3080 #28251625

Subgroups — D53×#3080 #28251625

Order 13568.

2142 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D53C211yesmaximal, characteristic, complemented
2C4×#41×D53C211yesmaximal, characteristic
3#20284538C211yesmaximal, characteristic, complemented
4#20284537C211yesmaximal, characteristic, complemented
5#20284536C212yesmaximal, complemented
6#20284535C212yesmaximal, complemented
7#20284534C214yesmaximal, complemented
8#20284533C211yesmaximal, characteristic, complemented
9#20284532C214yesmaximal, complemented
10#479×D53C214yesmaximal, complemented
11#478×D53C214yesmaximal, complemented
12#428×D53C212yesmaximal, complemented
13#423×D53C211yesmaximal, characteristic, complemented
14#417×D53C212yesmaximal
15C53×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D53C2211yescharacteristic
17C2×M16×D53C2212yes—
18C2×#13133209C2211yescharacteristic, complemented
19C2×#13133208C2212yescomplemented
20C2×#13133207—22no—
21#125×D53—21no—
22#125×D53—21no—
23#125×D53—21no—
24#125×D53—21no—
25#125×D53C2214yes—
26#125×D53C2214yescomplemented
27#41×Dic53C2211yescharacteristic
28C4×#11719949C2212yes—
29C4×#11719945—21no—
30C4×#11719945C2211yescharacteristic
31#16811091—21no—
32#16811091C2211yescharacteristic
33C4×#11719947—22no—
34C4×#11719947C2212yes—
35C4×Q8×D53C2212yes—
36C4×D4×D53—22no—
37C4×D4×D53C2212yes—
38#117×D53—21no—
39#117×D53C2211yescharacteristic
40C2×C4⋊C4×D53—22no—
41C2×C4⋊C4×D53C2212yes—
42C2×C42×D53—21no—
43C2×C42×D53C2211yescharacteristic
44#16810933C2214yescomplemented
45#16810932C2214yescomplemented
46#16810931C2214yescomplemented
47#16810930C2214yescomplemented
48#16810929C2214yescomplemented
49#16810928C2214yescomplemented
50#16810927C2214yescomplemented
51#16810926C2214yescomplemented
52#16810925C2214yescomplemented
53#16810924C2214yescomplemented
54#16810923C2214yescomplemented
55#16810922C2214yescomplemented
56#16810921C2214yescomplemented
57#16810920C2214yescomplemented
58#16810666C2212yescomplemented
59#16810665C2212yescomplemented
60#16810664C2214yescomplemented
61#16810663C2212yescomplemented
62#16810662C2214yescomplemented
63#107×D53C2214yes—
64#106×D53C2214yes—
65#16810647C2211yescharacteristic, complemented
66#16810646C2212yescomplemented
67#16810645C2214yescomplemented
68C4⋊C8×D53C2214yes—
69#16810625C2212yes—
70#16810624C2212yes—
71#16810623C2214yes—
72#16810622C2212yes—
73#16810621C2214yes—
74#103×D53C2214yes—
75#102×D53C2214yes—
76C2×#125×C53C2211yescharacteristic, complemented
77C4×#41×C53C2211yescharacteristic
78C53×#479C2214yescomplemented
79C53×#478C2214yescomplemented
80C53×#428C2212yescomplemented
81C53×#423C2211yescharacteristic, complemented
82C53×#417C2212yes—
83C2×#11719949C2311yescharacteristic
84C2×#11719945—21no—
85C2×#11719945C2311yescharacteristic
86C2×#11719947—21no—
87C2×#11719947C2311yescharacteristic
88#41×D53—24no—
89#41×D53Q818yes—
90C2×Q8×D53C2311yescharacteristic
91C2×D4×D53—21no—
92C2×D4×D53C2311yescharacteristic
93C22×C4×D53—21no—
94C22×C4×D53—22no—
95C22×C4×D53—22no—
96C22×C4×D53D412yes—
97C22×C4×D53C2311yescharacteristic
98C2×#11719917C2312yes—
99C2×#11719912C2314yes—
100M16×D53—28no—
101C2×C8×D53C2314yes—
102#13133209—21no—
103#13133209—21no—
104#13133209C2314yes—
105#13133208—22no—
106#13133208—22no—
107#13133208C2314yes—
108#13133208C2314yes—
109#13133207—24no—
110#13133207—24no—
111#13133207—24no—
112#13133207—24no—
113Q8×Dic53C2312yes—
114C4×Dic106—22no—
115C4×Dic106C2312yes—
116#13133182—22no—
117#13133182C2312yes—
118C4×D212—22no—
119C4×D212C2312yes—
120D4×Dic53—22no—
121D4×Dic53C2312yes—
122#13133179—22no—
123#13133179C2312yes—
124C4×C22⋊D53—22no—
125C4×C22⋊D53—22no—
126C4×C22⋊D53—22no—
127#13133177—22no—
128#13133177—22no—
129#13133177—22no—
130#13133176—21no—
131#13133176C2311yescharacteristic
132#13133175—22no—
133#13133175C2312yes—
134#13133174—21no—
135#13133174—21no—
136#13133174—21no—
137#13133173—22no—
138#13133173—21no—
139C2×C4⋊Dic53—22no—
140C2×C4⋊Dic53C2312yes—
141C2×#11719919—22no—
142C2×#11719919—22no—
143C2×#11719919—22no—
144C4⋊C4×D53—24no—
145C4⋊C4×D53—24no—
146C4⋊C4×D53—24no—
147C4⋊C4×D53—24no—
148C4⋊C4×D53—22no—
149C4⋊C4×D53—22no—
150C4⋊C4×D53—22no—
151C4⋊C4×D53C2314yes—
152C4⋊C4×D53C2314yes—
153C4⋊C4×D53C2312yes—
154C22⋊C4×D53—21no—
155C22⋊C4×D53—22no—
156C2×C4×Dic53—22no—
157C2×C4×Dic53—21no—
158C2×C4×Dic53D412yes—
159C2×C4×Dic53C2311yescharacteristic
160C42×D53—21no—
161C42×D53—22no—
162C42×D53—21no—
163C42×D53—21no—
164C42×D53—22no—
165C42×D53D411yescharacteristic
166C42×D53D411yescharacteristic
167C42×D53D411yescharacteristic
168C42×D53D411yescharacteristic
169C42×D53C2312yes—
170C42×D53C2312yes—
171#13133151C2314yes—
172#13133150C2314yes—
173#13133150C2314yes—
174#13133149C2314yes—
175#13133148C2314yes—
176#13133148C2314yes—
177C4⋊#88322C2314yes—
178#13133146C2314yes—
179#13133146C2314yes—
180#13133142C2314yes—
181#13133141C2314yes—
182#13133140C2314yes—
183#13133139C2314yes—
184#13133138C2314yes—
185#13133137C2314yes—
186C2×#41×C53C2311yescharacteristic
187C2×M16×C53C2312yes—
188#125×C53—21no—
189#125×C53—21no—
190#125×C53C2314yes—
191C4×Q8×C53C2312yes—
192C4×D4×C53—22no—
193C4×D4×C53C2312yes—
194#117×C53—21no—
195#117×C53C2311yescharacteristic
196C2×C4⋊C4×C53—22no—
197C2×C4⋊C4×C53C2312yes—
198C2×C42×C53—21no—
199C2×C42×C53C2311yescharacteristic
200#107×C53C2314yes—
201#106×C53C2314yes—
202C4⋊C8×C53C2314yes—
203#103×C53C2314yes—
204#102×C53C2314yes—
205C23×D53—21no—
206C23×D53C2×D411yescharacteristic
207#41×C53—22no—
208#41×C53C2×Q814yes—
209C2×Q8×C53C2411yescharacteristic
210C2×D4×C53—21no—
211C2×D4×C53C2411yescharacteristic
212C22×C4×C53—21no—
213C22×C4×C53—22no—
214C22×C4×C53—22no—
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—21no—
218C2×C22⋊D53—21no—
219C2×C22⋊D53—21no—
220C22×Dic53—21no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53C2×D412yes—
224C22×Dic53C2×D411yescharacteristic
225#11719949—22no—
226#11719949C2×Q814yes—
227Q8×D53—22no—
228Q8×D53C2×Q814yes—
229#11719947—28no—
230#11719947—22no—
231#11719947C2×Q814yes—
232D4×D53—28no—
233D4×D53—22no—
234D4×D53C2×Q814yes—
235#11719945—22no—
236#11719945—28no—
237#11719945C2×Q814yes—
238C2×D212—21no—
239C2×D212C2411yescharacteristic
240C2×C4×D53—21no—
241C2×C4×D53—21no—
242C2×C4×D53—21no—
243C2×C4×D53—28no—
244C2×C4×D53—22no—
245C2×C4×D53—24no—
246C2×C4×D53—24no—
247C2×C4×D53—22no—
248C2×C4×D53—22no—
249C2×C4×D53—44no—
250C2×C4×D53—48no—
251C2×C4×D53—48no—
252C2×C4×D53C2×D412yes—
253C2×C4×D53C2×D412yes—
254C2×C4×D53C2×D412yes—
255C2×C4×D53C2×D412yes—
256C2×C4×D53C2×D411yescharacteristic
257C2×C4×D53C2×D411yescharacteristic
258C2×C4×D53C2×Q814yes—
259C2×C4×D53#4114yes—
260C2×C4×D53C2411yescharacteristic
261C2×C4×D53C2411yescharacteristic
262C2×Dic106—21no—
263C2×Dic106C2411yescharacteristic
264M16×C53—24no—
265C2×C8×C53C2414yes—
266C4⋊C4×C53—24no—
267C4⋊C4×C53—24no—
268C4⋊C4×C53—22no—
269C4⋊C4×C53—22no—
270C4⋊C4×C53C2414yes—
271C4⋊C4×C53C2412yes—
272C22⋊C4×C53—21no—
273C22⋊C4×C53—22no—
274C42×C53—21no—
275C42×C53—22no—
276C42×C53C2×D411yescharacteristic
277C42×C53C2×D411yescharacteristic
278C42×C53C2412yes—
279C22⋊Dic53—21no—
280C22⋊Dic53—22no—
281#11719921—22no—
282#11719921—22no—
283#11719921—22no—
284C4⋊Dic53—22no—
285C4⋊Dic53—24no—
286C4⋊Dic53—24no—
287C4⋊Dic53—22no—
288C4⋊Dic53C2414yes—
289C4⋊Dic53C2412yes—
290#11719919—24no—
291#11719919—24no—
292#11719919—22no—
293#11719919—24no—
294#11719919—24no—
295#11719919—24no—
296#11719919—24no—
297#11719919—22no—
298#11719919—22no—
299C4×Dic53—21no—
300C4×Dic53—22no—
301C4×Dic53—22no—
302C4×Dic53—22no—
303C4×Dic53—22no—
304C4×Dic53C2×D411yescharacteristic
305C4×Dic53C2×D412yes—
306C4×Dic53C2×D411yescharacteristic
307C4×Dic53C2×D412yes—
308C4×Dic53C2×D412yes—
309C4×Dic53C2×D412yes—
310C4×Dic53C2412yes—
311#11719917—24no—
312C2×#88322C2414yes—
313#11719912—28no—
314C8×D53—28no—
315C23×C53—21no—
316C23×C53C22×D411yescharacteristic
317C22×D53—24no—
318C22×D53—21no—
319C22×D53—24no—
320C22×D53—44no—
321C22×D53C22⋊Q814yes—
322C22×D53C22×D411yescharacteristic
323C22×D53C22×D411yescharacteristic
324Q8×C53—21no—
325Q8×C53C22×Q812yes—
326D4×C53—24no—
327D4×C53—21no—
328D4×C53C22×Q812yes—
329C2×C4×C53—21no—
330C2×C4×C53—24no—
331C2×C4×C53—22no—
332C2×C4×C53—24no—
333C2×C4×C53—42no—
334C2×C4×C53—44no—
335C2×C4×C53—44no—
336C2×C4×C53C22×D412yes—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C22×Q812yes—
340C2×C4×C53C2×#4112yes—
341C2×C4×C53C2511yescharacteristic
342C22⋊D53—24no—
343C22⋊D53—24no—
344C22⋊D53—24no—
345C2×Dic53—21no—
346C2×Dic53—24no—
347C2×Dic53—22no—
348C2×Dic53—24no—
349C2×Dic53—42no—
350C2×Dic53—44no—
351C2×Dic53—44no—
352C2×Dic53C22⋊Q814yes—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D411yescharacteristic
356C2×Dic53C22×D411yescharacteristic
357D212—24no—
358D212—21no—
359D212C22×Q812yes—
360C4×D53—24no—
361C4×D53—24no—
362C4×D53—24no—
363C4×D53—24no—
364C4×D53—24no—
365C4×D53—42no—
366C4×D53—42no—
367C4×D53—44no—
368C4×D53—44no—
369C4×D53—48no—
370C4×D53—44no—
371C4×D53—48no—
372C4×D53C22⋊Q814yes—
373C4×D53C22⋊Q814yes—
374C4×D53C22×Q812yes—
375C4×D53C22×Q812yes—
376C4×D53C2×#4112yes—
377C4×D53C2×#4112yes—
378Dic106—21no—
379Dic106—24no—
380Dic106C22×Q812yes—
381C8×C53—24no—
382#88322—24no—
383C2×#3080—531nomaximal, Sylow
384C22×C53—22no—
385C22×C53—22no—
386C22×C53—42no—
387C22×C53C2×C22⋊Q812yes—
388C22×C53C23×D411yescharacteristic
389C2×D53—22no—
390C2×D53—28no—
391C2×D53—22no—
392C2×D53—42no—
393C2×D53—48no—
394C2×D53C2×C22⋊Q812yes—
395C2×D53C2×C22⋊Q812yes—
396C2×D53#57514yes—
397C4×C53—22no—
398C4×C53—22no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—44no—
402C4×C53C2×C22⋊Q812yes—
403C4×C53C23×Q811yescharacteristic
404C4×C53C22×#4111yescharacteristic
405Dic53—22no—
406Dic53—22no—
407Dic53—22no—
408Dic53—42no—
409Dic53—44no—
410Dic53C2×C22⋊Q812yes—
411Dic53C2×C22⋊Q812yes—
412C22×#125—531no—
413C2×C4×#41—531no—
414#3080—534no—
415#3080—534no—
416#3080—532no—
417#3080—531no—
418#3080—532no—
419#3080—531no—
420#3080—531no—
421#3080D5311yescharacteristic, direct product factor
422C2×#479—534no—
423C2×#478—534no—
424C2×#428—532no—
425C2×#423—531no—
426C2×#417—532no—
427C2×C53—22no—
428C2×C53—42no—
429C2×C53C22×C22⋊Q811yescharacteristic
430C2×C53C2×#57512yes—
431D53—22no—
432D53—42no—
433D53#308014yesdirect product factor
434C22×#41—531no—
435C22×M16—532no—
436C2×#125—534no—
437C2×#125—534no—
438C2×#125—532no—
439C2×#125—531no—
440C2×#125—1062no—
441C2×#125—1061no—
442C2×#125—1061no—
443C2×#125—1061no—
444C2×#125—1061no—
445C2×#125C2×D5311yescharacteristic, complemented
446C4×#41—531no—
447C4×#41—532no—
448C4×#41—532no—
449C4×#41—531no—
450C4×#41—531no—
451C4×#41—1061no—
452C4×#41—1061no—
453C4×#41—1062no—
454C4×#41C2×D5311yescharacteristic
455C2×C4×Q8—532no—
456C2×C4×D4—532no—
457C2×C4×D4—1062no—
458C2×#117—531no—
459C2×#117—1061no—
460C22×C4⋊C4—532no—
461C22×C4⋊C4—1062no—
462C22×C42—531no—
463C22×C42—1061no—
464#479—534no—
465#479—534no—
466#479—534no—
467#479—534no—
468#479—534no—
469#479—534no—
470#479—534no—
471#479C2×D5314yescomplemented
472#478—534no—
473#478—534no—
474#478—534no—
475#478—534no—
476#478—534no—
477#478—534no—
478#478—534no—
479#478C2×D5314yescomplemented
480#428—532no—
481#428—532no—
482#428—532no—
483#428—534no—
484#428—534no—
485#428C2×D5312yescomplemented
486C2×#107—534no—
487C2×#106—534no—
488#423—532no—
489#423—531no—
490#423—534no—
491#423C2×D5311yescharacteristic, complemented
492C2×C4⋊C8—534no—
493#417—532no—
494#417—532no—
495#417—532no—
496#417—534no—
497#417—534no—
498#417C2×D5312yes—
499C2×#103—534no—
500C2×#102—534no—
501C53C2×#308011yescharacteristic, complemented, Sylow
502C2×#41—538no—
503C2×#41—531no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—1061no—
507C2×#41—1061no—
508C2×#41—1064no—
509C2×#41C22×D5311yescharacteristic
510C22×Q8—531no—
511C22×D4—531no—
512C22×D4—1061no—
513C23×C4—531no—
514C23×C4—532no—
515C23×C4—1061no—
516C23×C4—1062no—
517C23×C4—1062no—
518C2×M16—532no—
519C2×M16—534no—
520C2×M16—1068no—
521C2×M16C22×D5312yes—
522C22×C8—534no—
523#125—21no—
524#125—21no—
525#125—534no—
526#125—534no—
527#125—534no—
528#125—1064no—
529#125—1064no—
530#125—1064no—
531#125—1064no—
532#125—1062no—
533#125—1062no—
534#125—1061no—
535#125—1061no—
536#125C22×D5314yes—
537C4×Q8—532no—
538C4×Q8—532no—
539C4×Q8—532no—
540C4×Q8—1062no—
541C4×Q8—1062no—
542C4×Q8C22×D5312yes—
543C4×D4—22no—
544C4×D4—532no—
545C4×D4—532no—
546C4×D4—532no—
547C4×D4—1062no—
548C4×D4—1062no—
549C4×D4—1062no—
550C4×D4—1062no—
551C4×D4—1062no—
552C4×D4—1062no—
553C4×D4—1062no—
554C4×D4—1062no—
555C4×D4—1062no—
556C4×D4C22×D5312yes—
557#117—21no—
558#117—531no—
559#117—532no—
560#117—1061no—
561#117—1061no—
562#117—1062no—
563#117—1062no—
564#117—1061no—
565#117—1061no—
566#117—1061no—
567#117C22×D5311yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—532no—
570C2×C4⋊C4—534no—
571C2×C4⋊C4—534no—
572C2×C4⋊C4—532no—
573C2×C4⋊C4—1062no—
574C2×C4⋊C4—1062no—
575C2×C4⋊C4—1064no—
576C2×C4⋊C4—1064no—
577C2×C4⋊C4—1064no—
578C2×C4⋊C4—1064no—
579C2×C4⋊C4—1062no—
580C2×C4⋊C4—1062no—
581C2×C4⋊C4—1062no—
582C2×C4⋊C4—1062no—
583C2×C4⋊C4—1062no—
584C2×C4⋊C4C22×D5312yes—
585C2×C22⋊C4—1062no—
586C2×C22⋊C4—1061no—
587C2×C42—21no—
588C2×C42—532no—
589C2×C42—531no—
590C2×C42—531no—
591C2×C42—531no—
592C2×C42—531no—
593C2×C42—531no—
594C2×C42—532no—
595C2×C42—532no—
596C2×C42—1061no—
597C2×C42—1062no—
598C2×C42—1061no—
599C2×C42—1062no—
600C2×C42—1062no—
601C2×C42—1061no—
602C2×C42—1061no—
603C2×C42C22×D5311yescharacteristic
604#107—534no—
605#107—534no—
606#107—534no—
607#107C22×D5314yes—
608#106—534no—
609#106—534no—
610#106—534no—
611#106C22×D5314yes—
612C4⋊C8—534no—
613C4⋊C8—534no—
614C4⋊C8—534no—
615C4⋊C8C22×D5314yes—
616#103—534no—
617#103—534no—
618#103—534no—
619#103C22×D5314yes—
620#102—534no—
621#102—534no—
622#102—534no—
623#102C22×D5314yes—
624C24—531no—
625C24—1061no—
626#41—22no—
627#41—534no—
628#41—534no—
629#41—534no—
630#41—1068no—
631#41—1068no—
632#41—1062no—
633#41—1062no—
634#41—1062no—
635#41Q8×D5314yes—
636C2×Q8—534no—
637C2×Q8—531no—
638C2×Q8—1061no—
639C2×Q8—1062no—
640C2×Q8C23×D5311yescharacteristic
641C2×D4—21no—
642C2×D4—534no—
643C2×D4—531no—
644C2×D4—1061no—
645C2×D4—1062no—
646C2×D4—1061no—
647C2×D4—1068no—
648C2×D4—1061no—
649C2×D4—1061no—
650C2×D4C23×D5311yescharacteristic
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—531no—
657C22×C4—534no—
658C22×C4—534no—
659C22×C4—531no—
660C22×C4—531no—
661C22×C4—532no—
662C22×C4—532no—
663C22×C4—532no—
664C22×C4—532no—
665C22×C4—532no—
666C22×C4—1061no—
667C22×C4—1068no—
668C22×C4—1062no—
669C22×C4—1061no—
670C22×C4—1062no—
671C22×C4—1064no—
672C22×C4—1064no—
673C22×C4—1061no—
674C22×C4—1062no—
675C22×C4—1061no—
676C22×C4—1062no—
677C22×C4—1062no—
678C22×C4—2124no—
679C22×C4—2128no—
680C22×C4—2128no—
681C22×C4D4×D5312yes—
682C22×C4C23×D5311yescharacteristic
683M16—24no—
684M16—1068no—
685M16—1064no—
686C2×C8—534no—
687C2×C8—1068no—
688C2×C8C23×D5314yes—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—534no—
694C4⋊C4—532no—
695C4⋊C4—1064no—
696C4⋊C4—1064no—
697C4⋊C4—1062no—
698C4⋊C4—1064no—
699C4⋊C4—1064no—
700C4⋊C4—1064no—
701C4⋊C4—1064no—
702C4⋊C4—1062no—
703C4⋊C4—1062no—
704C4⋊C4—1062no—
705C4⋊C4—1064no—
706C4⋊C4—1064no—
707C4⋊C4—1062no—
708C4⋊C4C23×D5314yes—
709C4⋊C4C23×D5312yes—
710C22⋊C4—21no—
711C22⋊C4—22no—
712C22⋊C4—1062no—
713C22⋊C4—1062no—
714C22⋊C4—1062no—
715C22⋊C4—1061no—
716C22⋊C4—1062no—
717C42—21no—
718C42—22no—
719C42—532no—
720C42—531no—
721C42—532no—
722C42—531no—
723C42—532no—
724C42—532no—
725C42—532no—
726C42—1062no—
727C42—1062no—
728C42—1062no—
729C42—1061no—
730C42—1062no—
731C42D4×D5311yescharacteristic
732C42D4×D5311yescharacteristic
733C42C23×D5312yes—
734C23—21no—
735C23—531no—
736C23—534no—
737C23—531no—
738C23—1064no—
739C23—1064no—
740C23—1061no—
741C23—2124no—
742C23C2×D4×D5311yescharacteristic
743Q8—21no—
744Q8—532no—
745Q8—1064no—
746Q8—1061no—
747Q8C2×Q8×D5312yes—
748D4—24no—
749D4—21no—
750D4—532no—
751D4—1064no—
752D4—1064no—
753D4—1064no—
754D4—1064no—
755D4—1061no—
756D4C2×Q8×D5312yes—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—534no—
765C2×C4—531no—
766C2×C4—531no—
767C2×C4—534no—
768C2×C4—534no—
769C2×C4—532no—
770C2×C4—532no—
771C2×C4—532no—
772C2×C4—532no—
773C2×C4—532no—
774C2×C4—532no—
775C2×C4—1064no—
776C2×C4—1064no—
777C2×C4—1064no—
778C2×C4—1064no—
779C2×C4—1064no—
780C2×C4—1061no—
781C2×C4—1064no—
782C2×C4—1062no—
783C2×C4—1064no—
784C2×C4—2122no—
785C2×C4—2122no—
786C2×C4—2124no—
787C2×C4—2124no—
788C2×C4—2124no—
789C2×C4—2128no—
790C2×C4—2128no—
791C2×C4—2122no—
792C2×C4—2124no—
793C2×C4—2124no—
794C2×C4C2×D4×D5312yes—
795C2×C4C2×D4×D5312yes—
796C2×C4C2×D4×D5311yescharacteristic
797C2×C4C2×Q8×D5312yes—
798C2×C4#41×D5312yes—
799C2×C4C24×D5311yescharacteristic
800C8—24no—
801C8—1064no—
802C22—22no—
803C22—22no—
804C22—42no—
805C22—534no—
806C22—532no—
807C22—532no—
808C22—1068no—
809C22—1062no—
810C22—1062no—
811C22—2128no—
812C22—2122no—
813C22C22⋊Q8×D5312yes—
814C22C22×D4×D5311yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—44no—
820C4—532no—
821C4—532no—
822C4—1062no—
823C4—1062no—
824C4—1062no—
825C4—2122no—
826C4—2124no—
827C4C22⋊Q8×D5312yes—
828C4C22×Q8×D5311yescharacteristic
829C4C2×#41×D5311yescharacteristic
830C2—22no—
831C2—42no—
832C2—534no—
833C2—1062no—
834C2—2122no—
835C2C2×C22⋊Q8×D5311yescharacteristic
836C2#575×D5312yes—
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3080C2
socleC22×C53C23×D4
prime radicalC2×#41×D53C22
hypercenter#3080D53
hypocenterC53C2×#3080
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#125×D53C2semidirect
3. #20284538C2semidirect
4. #20284537C2semidirect
5. #20284536C2semidirect
6. #20284535C2semidirect
7. #20284534C2semidirect
8. #20284533C2semidirect
9. #20284532C2semidirect
10. #479×D53C2semidirect
11. #478×D53C2semidirect
12. #428×D53C2semidirect
13. #423×D53C2semidirect
15. C53×#3080C2semidirect
18. C2×#13133209C22semidirect
19. C2×#13133208C22semidirect
26. #125×D53C22semidirect
44. #16810933C22semidirect
45. #16810932C22semidirect
46. #16810931C22semidirect
47. #16810930C22semidirect
48. #16810929C22semidirect
49. #16810928C22semidirect
50. #16810927C22semidirect
51. #16810926C22semidirect
52. #16810925C22semidirect
53. #16810924C22semidirect
54. #16810923C22semidirect
55. #16810922C22semidirect
56. #16810921C22semidirect
57. #16810920C22semidirect
58. #16810666C22semidirect
59. #16810665C22semidirect
60. #16810664C22semidirect
61. #16810663C22semidirect
62. #16810662C22semidirect
65. #16810647C22semidirect
66. #16810646C22semidirect
67. #16810645C22semidirect
76. C2×#125×C53C22semidirect
78. C53×#479C22semidirect
79. C53×#478C22semidirect
80. C53×#428C22semidirect
81. C53×#423C22semidirect
421. #3080D53direct (N × H)
433. D53#3080direct (N × H)
445. C2×#125C2×D53semidirect
471. #479C2×D53semidirect
479. #478C2×D53semidirect
485. #428C2×D53semidirect
491. #423C2×D53semidirect
501. C53C2×#3080semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D532
C4×#41×D532
#202845382
#202845372
#202845362
#202845352
#202845342
#202845332
#202845322
#479×D532
#478×D532
#428×D532
#423×D532
#417×D532
C53×#30802
C2×#308053