Finite Group Databasebeta

← D53×#3586 #28297935

Subgroups — D53×#3586 #28297935

Order 13568.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#585×D53C211yesmaximal, characteristic, complemented
2C2×2−1+4×D53C211yesmaximal, characteristic, complemented
3#20289503C211yesmaximal, characteristic, complemented
4#20289502C211yesmaximal, characteristic, complemented
5#20289501C211yesmaximal, characteristic, complemented
6#20289500C218yesmaximal, complemented
7#20289499C216yesmaximal, complemented
8#20289498C216yesmaximal, complemented
9#20289497C218yesmaximal, complemented
10#578×D53C218yesmaximal, complemented
11#577×D53C218yesmaximal, complemented
12#575×D53C216yesmaximal, complemented
13C2×#137×D53C216yesmaximal, complemented
14#568×D53C211yesmaximal, characteristic, complemented
15C53×#3586C211yesmaximal, characteristic, complemented
16#16811460—21no—
17#16811460C2214yescomplemented
18#16811459—24no—
19#16811459C2211yescharacteristic, complemented
20#16811459C2216yescomplemented
21#16811458—23no—
22#16811458C2214yescomplemented
23C2×#13133265—21no—
24C2×#13133265C2213yescomplemented
25C2×#13133264—23no—
26C2×#13133264C2211yescharacteristic, complemented
27C2×#13133264C2213yescomplemented
282−1+4×D53—24no—
292−1+4×D53—24no—
302−1+4×D53—21no—
312−1+4×D53C2218yescomplemented
322−1+4×D53C2214yescomplemented
332−1+4×D53C2218yescomplemented
34H(5,𝔽2)×D53—23no—
35H(5,𝔽2)×D53C2214yescomplemented
36C2×#41×D53—24no—
37C2×#41×D53—23no—
38C2×#41×D53C2216yes—
39C2×#41×D53C2211yescharacteristic
40C2×#41×D53C2213yescomplemented
41C22×Q8×D53—21no—
42C22×Q8×D53C2213yescomplemented
43#16811440C2218yescomplemented
44#16811439C22124yescomplemented
45#16811439C22124yescomplemented
46#16811438C2218yescomplemented
47#16811438C2218yescomplemented
48#16811437C22124yescomplemented
49#16811436C22124yescomplemented
50#16811435C2218yescomplemented
51#16811434C2218yescomplemented
52#16811433C22124yescomplemented
53#16811432C22124yescomplemented
54#16811431C2218yescomplemented
55#16811430C22124yescomplemented
56#16811429C22124yescomplemented
57#16811423C2216yescomplemented
58#16811422C22112yescomplemented
59#16811422C22112yescomplemented
60#16811421C2216yescomplemented
61#16811421C2216yescomplemented
62#16811420C22124yescomplemented
63#16811419C22112yescomplemented
64#16811419C22112yescomplemented
65C2×#13133250C2216yescomplemented
66C2×#13133249C22112yescomplemented
67C2×#13133248C2216yescomplemented
68C2×#13133247C2216yescomplemented
69C2×#13133246C22112yescomplemented
70#137×D53C22112yescomplemented
71#137×D53C22124yescomplemented
72#137×D53C22112yescomplemented
73#137×D53C22124yescomplemented
74#137×D53C22124yescomplemented
75AGL(1,ℤ/8)×D53C2214yescomplemented
76AGL(1,ℤ/8)×D53C22112yescomplemented
77#135×D53C22124yescomplemented
78C2×Q16×D53C22112yescomplemented
79C2×SD16×D53C22112yescomplemented
80#16811390C2211yescharacteristic, complemented
81#16811389C2216yescomplemented
82#16811388C2218yescomplemented
83#131×D53C2218yescomplemented
84C2×M16×D53C2216yescomplemented
85C53×#585C2211yescharacteristic, complemented
86C2×2−1+4×C53C2211yescharacteristic, complemented
87C53×#578C2218yescomplemented
88C53×#577C2218yescomplemented
89C53×#575C2216yescomplemented
90C2×#137×C53C2216yescomplemented
91C53×#568C2211yescharacteristic, complemented
92#13133265—21no—
93#13133265—28no—
94#13133265—28no—
95#13133265—24no—
96#13133265—24no—
97#13133265—212no—
98#13133265C23124yescomplemented
99#13133265C23112yescomplemented
100#13133264—24no—
101#13133264—24no—
102#13133264—224no—
103#13133264—224no—
104#13133264—212no—
105#13133264—212no—
106#13133264—26no—
107#13133264C23124yescomplemented
108#13133264C23112yescomplemented
109#13133264C2318yescomplemented
110#13133264C2314yescomplemented
111#13133263—24no—
112#13133263—212no—
113#13133263—26no—
114#13133263C23112yescomplemented
115#13133263C2314yescomplemented
116#13133262—23no—
117#13133262—212no—
118#13133262—212no—
119#13133262—212no—
120#13133262C23112yescomplemented
121C2×#11719949—24no—
122C2×#11719949—23no—
123C2×#11719949D411yescharacteristic
124C2×#11719949C2316yes—
125C2×#11719949C2313yescomplemented
126C2×#11719945—26no—
127C2×#11719945—212no—
128C2×#11719945—23no—
129C2×#11719945—26no—
130C2×#11719945—23no—
131C2×#11719945C2313yes—
132C2×#11719945C2316yes—
133C2×#11719945C2313yescomplemented
134C2×#11719947—23no—
135C2×#11719947—26no—
136C2×#11719947—26no—
137C2×#11719947—23no—
138C2×#11719947—212no—
139C2×#11719947D413yes—
140C2×#11719947C2316yes—
141C2×#11719947C2313yescomplemented
142#41×D53—24no—
143#41×D53—24no—
144#41×D53—24no—
145#41×D53—212no—
146#41×D53—212no—
147#41×D53—224no—
148#41×D53—224no—
149#41×D53—212no—
150#41×D53—26no—
151#41×D53—26no—
152#41×D53—26no—
153#41×D53—26no—
154#41×D53—26no—
155#41×D53—26no—
156#41×D53D414yes—
157#41×D53D414yes—
158#41×D53C23112yes—
159#41×D53C23112yes—
160#41×D53C2314yes—
161#41×D53C23112yes—
162#41×D53C23112yes—
163#41×D53C2314yes—
164#41×D53C2314yes—
165#41×D53C23112yescomplemented
166C22×Dic106—23no—
167C22×Dic106—23no—
168C22×Dic106C2313yescomplemented
169C2×Q8×D53—21no—
170C2×Q8×D53—28no—
171C2×Q8×D53—28no—
172C2×Q8×D53—24no—
173C2×Q8×D53—23no—
174C2×Q8×D53—26no—
175C2×Q8×D53—26no—
176C2×Q8×D53—23no—
177C2×Q8×D53—23no—
178C2×Q8×D53D411yescharacteristic
179C2×Q8×D53C23112yes—
180C2×Q8×D53C2316yes—
181C2×Q8×D53C2313yes—
182C2×Q8×D53C2316yescomplemented
183C2×Q8×D53C23112yescomplemented
184C2×D4×D53—23no—
185C2×D4×D53—26no—
186C2×D4×D53—212no—
187C2×D4×D53D413yes—
188C2×D4×D53C2316yes—
189C2×D4×D53C2311yescharacteristic
190C22×C4×D53—23no—
191C22×C4×D53—23no—
192C22×C4×D53—26no—
193C22×C4×D53C2313yes—
194#13133250C23112yescomplemented
195#13133250C23124yescomplemented
196#13133250C23112yescomplemented
197#13133249C23124yescomplemented
198#13133249C23148yescomplemented
199#13133249C23124yescomplemented
200#13133248C23112yescomplemented
201#13133248C23124yescomplemented
202#13133248C23112yescomplemented
203#13133247C23112yescomplemented
204#13133247C23124yescomplemented
205#13133247C23112yescomplemented
206#13133246C23124yescomplemented
207#13133246C23148yescomplemented
208#13133246C23124yescomplemented
209#13133245C2314yescomplemented
210#13133245C23112yescomplemented
211#13133244C2318yescomplemented
212#13133244C23124yescomplemented
213#13133243C2314yescomplemented
214#13133243C23112yescomplemented
215#13133242C2314yescomplemented
216#13133242C23112yescomplemented
217#13133241C2318yescomplemented
218#13133241C23124yescomplemented
219#13133240C23124yescomplemented
220#13133239C23124yescomplemented
221#13133238C23124yescomplemented
222#13133238C23124yescomplemented
223#13133237C23124yescomplemented
224#13133237C23124yescomplemented
225#13133236C23124yescomplemented
226C2×Dic212C23112yescomplemented
227C2×#11719925C23112yescomplemented
228C2×#11719925C23112yescomplemented
229Q16×D53C23124yes—
230Q16×D53C23148yescomplemented
231C2×#11719913C23112yescomplemented
232C2×#11719923C23112yescomplemented
233C2×#11719924C23112yescomplemented
234SD16×D53C23124yes—
235SD16×D53C2318yes—
236SD16×D53C23148yescomplemented
237D8×D53C2318yes—
238#13133225C23124yescomplemented
239#13133224C2318yescomplemented
240#13133223C23124yescomplemented
241C2×#11719917C2316yescomplemented
242C2×#11719912C23112yescomplemented
243M16×D53C2314yes—
244M16×D53C23112yes—
245M16×D53C23112yescomplemented
246M16×D53C23112yescomplemented
247C2×C8×D53C23112yes—
2482−1+4×C53—24no—
2492−1+4×C53—21no—
2502−1+4×C53C2318yescomplemented
2512−1+4×C53C2314yescomplemented
252H(5,𝔽2)×C53—23no—
253H(5,𝔽2)×C53C2314yescomplemented
254C2×#41×C53—24no—
255C2×#41×C53—23no—
256C2×#41×C53C2316yes—
257C2×#41×C53C2311yescharacteristic
258C2×#41×C53C2313yescomplemented
259C22×Q8×C53—21no—
260C22×Q8×C53C2313yescomplemented
261#137×C53C23112yescomplemented
262#137×C53C23124yescomplemented
263#137×C53C23112yescomplemented
264AGL(1,ℤ/8)×C53C2314yescomplemented
265AGL(1,ℤ/8)×C53C23112yescomplemented
266#135×C53C23124yescomplemented
267C2×Q16×C53C23112yescomplemented
268C2×SD16×C53C23112yescomplemented
269#131×C53C2318yescomplemented
270C2×M16×C53C2316yescomplemented
271C23×D53—21no—
272C23×D53—26no—
273C23×D53C2×D413yes—
274#41×C53—24no—
275#41×C53—212no—
276#41×C53—224no—
277#41×C53—26no—
278#41×C53—26no—
279#41×C53—26no—
280#41×C53C2×D414yes—
281#41×C53C24112yes—
282#41×C53C24112yes—
283#41×C53C2414yes—
284#41×C53C2414yes—
285C2×Q8×C53—28no—
286C2×Q8×C53—24no—
287C2×Q8×C53—23no—
288C2×Q8×C53—26no—
289C2×Q8×C53C2×D411yescharacteristic
290C2×Q8×C53C24112yes—
291C2×Q8×C53C2416yes—
292C2×Q8×C53C2413yes—
293C2×D4×C53—23no—
294C2×D4×C53—26no—
295C2×D4×C53—212no—
296C2×D4×C53C2×D413yes—
297C2×D4×C53C2416yes—
298C2×D4×C53C2411yescharacteristic
299C22×C4×C53—23no—
300C22×C4×C53—23no—
301C22×C4×C53—26no—
302C22×C4×C53C2413yes—
303C2×C22⋊D53—23no—
304C2×C22⋊D53—26no—
305C2×C22⋊D53—23no—
306C2×C22⋊D53—26no—
307C2×C22⋊D53—224no—
308C2×C22⋊D53—21no—
309C2×C22⋊D53—26no—
310C2×C22⋊D53C2×D416yes—
311C22×Dic53—23no—
312C22×Dic53—23no—
313C22×Dic53—26no—
314C22×Dic53C2×D413yes—
315#11719949—24no—
316#11719949—212no—
317#11719949—224no—
318#11719949—26no—
319#11719949—26no—
320#11719949—26no—
321#11719949C2×D414yes—
322#11719949C2×D414yes—
323#11719949C24112yes—
324#11719949C24112yes—
325#11719949C2414yes—
326Q8×D53—28no—
327Q8×D53—24no—
328Q8×D53—23no—
329Q8×D53—212no—
330Q8×D53—23no—
331Q8×D53—212no—
332Q8×D53—26no—
333Q8×D53—212no—
334Q8×D53—212no—
335Q8×D53—212no—
336Q8×D53—26no—
337Q8×D53—224no—
338Q8×D53—212no—
339Q8×D53C2×D414yes—
340Q8×D53C2×D414yes—
341Q8×D53C2416yes—
342Q8×D53C2414yes—
343Q8×D53C24124yes—
344Q8×D53C24112yes—
345Q8×D53C2416yes—
346#11719947—212no—
347#11719947—224no—
348#11719947—224no—
349#11719947—248no—
350#11719947—24no—
351#11719947—212no—
352#11719947—212no—
353#11719947—212no—
354#11719947—212no—
355#11719947—212no—
356#11719947—26no—
357#11719947—26no—
358#11719947—26no—
359#11719947—212no—
360#11719947C2×D4112yes—
361#11719947C2×D4112yes—
362#11719947C24112yes—
363#11719947C24112yes—
364#11719947C2414yes—
365D4×D53—24no—
366D4×D53—212no—
367D4×D53—212no—
368D4×D53—212no—
369D4×D53—212no—
370D4×D53—212no—
371D4×D53—212no—
372D4×D53—224no—
373D4×D53—212no—
374D4×D53—26no—
375D4×D53—21no—
376D4×D53—21no—
377D4×D53—26no—
378D4×D53C2×D4112yes—
379D4×D53C2×D4112yes—
380D4×D53C2412yes—
381D4×D53C2414yes—
382D4×D53C24112yes—
383D4×D53C2412yes—
384#11719945—26no—
385#11719945—26no—
386#11719945—26no—
387#11719945—224no—
388#11719945—248no—
389#11719945—212no—
390#11719945—224no—
391#11719945—212no—
392#11719945—24no—
393#11719945—212no—
394#11719945—212no—
395#11719945—212no—
396#11719945—212no—
397#11719945—212no—
398#11719945C2×D4112yes—
399#11719945C24112yes—
400#11719945C24112yes—
401#11719945C24112yes—
402#11719945C2414yes—
403C2×D212—23no—
404C2×D212—26no—
405C2×D212—212no—
406C2×D212C2×D413yes—
407C2×D212C2416yes—
408C2×D212C2411yescharacteristic
409C2×C4×D53—23no—
410C2×C4×D53—26no—
411C2×C4×D53—212no—
412C2×C4×D53—212no—
413C2×C4×D53—26no—
414C2×C4×D53—23no—
415C2×C4×D53—26no—
416C2×C4×D53—23no—
417C2×C4×D53—26no—
418C2×C4×D53—24no—
419C2×C4×D53—212no—
420C2×C4×D53—212no—
421C2×C4×D53—212no—
422C2×C4×D53—212no—
423C2×C4×D53—212no—
424C2×C4×D53C2×D413yes—
425C2×C4×D53C2×D416yes—
426C2×C4×D53C2×D416yes—
427C2×C4×D53C2×D413yes—
428C2×C4×D53C2416yes—
429C2×C4×D53C2411yescharacteristic
430C2×C4×D53C2413yes—
431C2×C4×D53C2416yes—
432C2×Dic106—23no—
433C2×Dic106—26no—
434C2×Dic106—23no—
435C2×Dic106—26no—
436C2×Dic106—212no—
437C2×Dic106—212no—
438C2×Dic106—26no—
439C2×Dic106—224no—
440C2×Dic106—212no—
441C2×Dic106C2×D413yes—
442C2×Dic106C24112yes—
443C2×Dic106C2416yes—
444C2×Dic106C2413yes—
445Q16×C53C24124yes—
446SD16×C53C24124yes—
447SD16×C53C2418yes—
448D8×C53C2418yes—
449M16×C53C2414yes—
450M16×C53C24112yes—
451C2×C8×C53C24112yes—
452#11719925C24124yes—
453#11719925C24124yes—
454#11719924C24124yes—
455#11719924C2418yes—
456#11719923C24124yes—
457#11719923C2418yes—
458#11719922C2418yes—
459#11719922C2418yes—
460#11719917C2414yes—
461#11719917C24112yes—
462C2×#88322C24112yes—
463Dic212C24124yes—
464D424C2418yes—
465#11719913C24124yes—
466#11719913C2418yes—
467#11719912C2418yes—
468#11719912C24124yes—
469C8×D53C2418yes—
470C8×D53C24124yes—
471C23×C53—21no—
472C23×C53—26no—
473C23×C53C22×D413yes—
474C22×D53—21no—
475C22×D53—26no—
476C22×D53—22no—
477C22×D53—22no—
478C22×D53—24no—
479C22×D53—212no—
480C22×D53—46no—
481C22×D53—44no—
482C22×D53—812no—
483C22×D53C22×D411yescharacteristic
484C22×D53C22×D416yes—
485C22×D53C22×D413yes—
486C22×D53C22×D416yes—
487Q8×C53—212no—
488Q8×C53—23no—
489Q8×C53—26no—
490Q8×C53C22×D414yes—
491Q8×C53C2516yes—
492Q8×C53C2514yes—
493D4×C53—24no—
494D4×C53—212no—
495D4×C53—212no—
496D4×C53—26no—
497D4×C53—21no—
498D4×C53C22×D4112yes—
499D4×C53C2514yes—
500D4×C53C2512yes—
501C2×C4×C53—23no—
502C2×C4×C53—212no—
503C2×C4×C53—26no—
504C2×C4×C53—212no—
505C2×C4×C53—212no—
506C2×C4×C53—24no—
507C2×C4×C53C22×D413yes—
508C2×C4×C53C22×D416yes—
509C2×C4×C53C2511yescharacteristic
510C2×C4×C53C2516yes—
511C22⋊D53—212no—
512C22⋊D53—24no—
513C22⋊D53—212no—
514C22⋊D53—212no—
515C22⋊D53—24no—
516C22⋊D53—212no—
517C22⋊D53—22no—
518C22⋊D53—22no—
519C22⋊D53—24no—
520C22⋊D53—212no—
521C22⋊D53C22×D4124yes—
522C2×Dic53—23no—
523C2×Dic53—212no—
524C2×Dic53—26no—
525C2×Dic53—212no—
526C2×Dic53—212no—
527C2×Dic53—24no—
528C2×Dic53C22×D411yescharacteristic
529C2×Dic53C22×D416yes—
530C2×Dic53C22×D413yes—
531C2×Dic53C22×D416yes—
532D212—24no—
533D212—212no—
534D212—212no—
535D212—26no—
536D212—21no—
537D212C22×D4112yes—
538D212C2514yes—
539D212C2512yes—
540C4×D53—24no—
541C4×D53—26no—
542C4×D53—26no—
543C4×D53—212no—
544C4×D53—224no—
545C4×D53—24no—
546C4×D53—212no—
547C4×D53—212no—
548C4×D53—24no—
549C4×D53—212no—
550C4×D53—212no—
551C4×D53C22×D411yescharacteristic
552C4×D53C22×D416yes—
553C4×D53C22×D416yes—
554C4×D53C22×D416yes—
555C4×D53C22×D416yes—
556C4×D53C22×D411yescharacteristic
557C4×D53C22×D416yes—
558C4×D53C2511yescharacteristic
559C4×D53C2511yescharacteristic
560C4×D53C2516yes—
561Dic106—212no—
562Dic106—23no—
563Dic106—26no—
564Dic106—26no—
565Dic106—224no—
566Dic106—26no—
567Dic106—24no—
568Dic106—212no—
569Dic106C22×D4112yes—
570Dic106C2516yes—
571Dic106C2514yes—
572C8×C53C2518yes—
573#88322C2518yes—
574C2×#3586—531nomaximal, Sylow
575C22×C53—22no—
576C22×C53—24no—
577C22×C53—43no—
578C22×C53—42no—
579C22×C53—86no—
580C22×C53C23×D411yescharacteristic
581C22×C53C23×D416yes—
582C2×D53—22no—
583C2×D53—212no—
584C2×D53—22no—
585C2×D53—24no—
586C2×D53—46no—
587C2×D53—43no—
588C2×D53—44no—
589C2×D53—42no—
590C2×D53—44no—
591C2×D53—48no—
592C2×D53—812no—
593C2×D53—86no—
594C2×D53C23×D411yescharacteristic
595C2×D53C23×D416yes—
596C2×D53C23×D411yescharacteristic
597C4×C53—26no—
598C4×C53—24no—
599C4×C53C23×D416yes—
600C4×C53C23×D411yescharacteristic
601C4×C53C2611yescharacteristic
602Dic53—26no—
603Dic53—24no—
604Dic53C23×D411yescharacteristic
605Dic53C23×D416yes—
606Dic53C23×D411yescharacteristic
607C2×#585—531no—
608C22×2−1+4—531no—
609#3586—531no—
610#3586—531no—
611#3586—538no—
612#3586—538no—
613#3586—536no—
614#3586—536no—
615#3586—531no—
616#3586D5311yescharacteristic, direct product factor
617C2×#578—538no—
618C2×#577—538no—
619C2×#575—536no—
620C22×#137—536no—
621C2×#568—531no—
622C2×C53—21no—
623C2×C53—26no—
624C2×C53—42no—
625C2×C53—44no—
626C2×C53C24×D411yescharacteristic
627D53—21no—
628D53—26no—
629D53—42no—
630D53—44no—
631D53#358612yesdirect product factor
632#585—534no—
633#585—534no—
634#585—536no—
635#585—531no—
636#585—1064no—
637#585—1063no—
638#585—1061no—
639#585C2×D5311yescharacteristic, complemented
640C2×2−1+4—538no—
641C2×2−1+4—538no—
642C2×2−1+4—534no—
643C2×2−1+4—531no—
644C2×2−1+4—533no—
645C2×2−1+4—533no—
646C2×2−1+4—1061no—
647C2×2−1+4—1061no—
648C2×2−1+4—1063no—
649C2×2−1+4—1064no—
650C2×2−1+4—1064no—
651C2×2−1+4C2×D5311yescharacteristic, complemented
652C2×H(5,𝔽2)—534no—
653C2×H(5,𝔽2)—1063no—
654C22×#41—531no—
655C22×#41—536no—
656C22×#41—533no—
657C22×#41—1063no—
658C22×#41—1064no—
659C23×Q8—533no—
660C23×Q8—1061no—
661#578—538no—
662#578—538no—
663#578—5324no—
664#578—5324no—
665#578—5324no—
666#578—5324no—
667#578—538no—
668#578C2×D5318yescomplemented
669#577—538no—
670#577—538no—
671#577—5324no—
672#577—5324no—
673#577—5324no—
674#577—5324no—
675#577—538no—
676#577C2×D5318yescomplemented
677#575—536no—
678#575—536no—
679#575—5312no—
680#575—5312no—
681#575—5312no—
682#575—5312no—
683#575—5324no—
684#575—536no—
685#575C2×D5316yescomplemented
686C2×#137—536no—
687C2×#137—536no—
688C2×#137—5324no—
689C2×#137—5324no—
690C2×#137—5312no—
691C2×#137—5324no—
692C2×#137—5312no—
693C2×#137—5312no—
694C2×#137—5312no—
695C2×#137—536no—
696C2×#137C2×D5316yescomplemented
697C2×AGL(1,ℤ/8)—534no—
698C2×AGL(1,ℤ/8)—5312no—
699C2×#135—5324no—
700C22×Q16—5312no—
701C22×SD16—5312no—
702#568—531no—
703#568—538no—
704#568—536no—
705#568C2×D5311yescharacteristic, complemented
706C2×#131—538no—
707C22×M16—536no—
708C53C2×#358611yescharacteristic, complemented, Sylow
7092−1+4—24no—
7102−1+4—21no—
7112−1+4—5324no—
7122−1+4—538no—
7132−1+4—5312no—
7142−1+4—534no—
7152−1+4—5324no—
7162−1+4—5312no—
7172−1+4—1064no—
7182−1+4—1068no—
7192−1+4—1068no—
7202−1+4—10612no—
7212−1+4—1064no—
7222−1+4—1064no—
7232−1+4—1066no—
7242−1+4—10624no—
7252−1+4—10624no—
7262−1+4—10612no—
7272−1+4—10612no—
7282−1+4—1064no—
7292−1+4—1061no—
7302−1+4C22×D5318yescomplemented
7312−1+4C22×D5314yescomplemented
732H(5,𝔽2)—23no—
733H(5,𝔽2)—5312no—
734H(5,𝔽2)—534no—
735H(5,𝔽2)—5312no—
736H(5,𝔽2)—10612no—
737H(5,𝔽2)—10612no—
738H(5,𝔽2)—10612no—
739H(5,𝔽2)—10612no—
740H(5,𝔽2)—1066no—
741H(5,𝔽2)—1064no—
742H(5,𝔽2)—1063no—
743H(5,𝔽2)C22×D5314yescomplemented
744C2×#41—24no—
745C2×#41—23no—
746C2×#41—534no—
747C2×#41—534no—
748C2×#41—534no—
749C2×#41—534no—
750C2×#41—531no—
751C2×#41—533no—
752C2×#41—533no—
753C2×#41—5312no—
754C2×#41—5312no—
755C2×#41—534no—
756C2×#41—5312no—
757C2×#41—5312no—
758C2×#41—5312no—
759C2×#41—536no—
760C2×#41—533no—
761C2×#41—536no—
762C2×#41—533no—
763C2×#41—536no—
764C2×#41—533no—
765C2×#41—1063no—
766C2×#41—1066no—
767C2×#41—1066no—
768C2×#41—1063no—
769C2×#41—10612no—
770C2×#41—1063no—
771C2×#41—1066no—
772C2×#41—1066no—
773C2×#41—1066no—
774C2×#41—1066no—
775C2×#41—1066no—
776C2×#41—1066no—
777C2×#41—1066no—
778C2×#41—1066no—
779C2×#41—10612no—
780C2×#41—1063no—
781C2×#41—10612no—
782C2×#41—10624no—
783C2×#41—10624no—
784C2×#41—1064no—
785C2×#41—1064no—
786C2×#41—1064no—
787C2×#41—10612no—
788C2×#41—10612no—
789C2×#41—1064no—
790C2×#41—1063no—
791C2×#41C22×D5316yes—
792C2×#41C22×D5311yescharacteristic
793C2×#41C22×D5313yescomplemented
794C22×Q8—21no—
795C22×Q8—531no—
796C22×Q8—5312no—
797C22×Q8—536no—
798C22×Q8—533no—
799C22×Q8—536no—
800C22×Q8—5312no—
801C22×Q8—533no—
802C22×Q8—1063no—
803C22×Q8—1063no—
804C22×Q8—1063no—
805C22×Q8—1066no—
806C22×Q8—1063no—
807C22×Q8—1066no—
808C22×Q8—1068no—
809C22×Q8—1068no—
810C22×Q8—1063no—
811C22×Q8—1064no—
812C22×Q8—1061no—
813C22×Q8C22×D5313yescomplemented
814C22×D4—533no—
815C22×D4—536no—
816C22×D4—531no—
817C22×D4—10612no—
818C22×D4—1063no—
819C22×D4—1066no—
820C23×C4—533no—
821C23×C4—1063no—
822C23×C4—1066no—
823C23×C4—1063no—
824#137—5312no—
825#137—5324no—
826#137—5312no—
827#137—5312no—
828#137—5324no—
829#137—5312no—
830#137—5324no—
831#137—5348no—
832#137—5324no—
833#137—5324no—
834#137—5348no—
835#137—5324no—
836#137—5312no—
837#137—5324no—
838#137—5312no—
839#137C22×D53112yescomplemented
840#137C22×D53124yescomplemented
841#137C22×D53112yescomplemented
842AGL(1,ℤ/8)—534no—
843AGL(1,ℤ/8)—5312no—
844AGL(1,ℤ/8)—534no—
845AGL(1,ℤ/8)—5312no—
846AGL(1,ℤ/8)—538no—
847AGL(1,ℤ/8)—5324no—
848AGL(1,ℤ/8)—538no—
849AGL(1,ℤ/8)—5324no—
850AGL(1,ℤ/8)—534no—
851AGL(1,ℤ/8)—5312no—
852AGL(1,ℤ/8)C22×D5314yescomplemented
853AGL(1,ℤ/8)C22×D53112yescomplemented
854#135—5324no—
855#135—5324no—
856#135—5324no—
857#135—5324no—
858#135—5324no—
859#135—5324no—
860#135—5324no—
861#135C22×D53124yescomplemented
862C2×Q16—5312no—
863C2×Q16—5312no—
864C2×Q16—5324no—
865C2×Q16—5348no—
866C2×Q16—5312no—
867C2×Q16C22×D53112yescomplemented
868C2×SD16—5312no—
869C2×SD16—5312no—
870C2×SD16—5324no—
871C2×SD16—5348no—
872C2×SD16—538no—
873C2×SD16—5312no—
874C2×SD16C22×D53112yescomplemented
875C2×D8—538no—
876#131—538no—
877#131—5324no—
878#131—5324no—
879#131C22×D5318yescomplemented
880C2×M16—536no—
881C2×M16—534no—
882C2×M16—5312no—
883C2×M16—5312no—
884C2×M16—5312no—
885C2×M16—5312no—
886C2×M16C22×D5316yescomplemented
887C22×C8—5312no—
888C24—533no—
889C24—1066no—
890C24—1061no—
891#41—24no—
892#41—212no—
893#41—224no—
894#41—26no—
895#41—26no—
896#41—26no—
897#41—534no—
898#41—534no—
899#41—5312no—
900#41—5312no—
901#41—5312no—
902#41—5312no—
903#41—5312no—
904#41—5312no—
905#41—534no—
906#41—5312no—
907#41—5312no—
908#41—534no—
909#41—5312no—
910#41—5312no—
911#41—534no—
912#41—1064no—
913#41—10612no—
914#41—10612no—
915#41—10612no—
916#41—10612no—
917#41—10612no—
918#41—10624no—
919#41—10612no—
920#41—10648no—
921#41—10624no—
922#41—10612no—
923#41—1064no—
924#41—10612no—
925#41—1066no—
926#41—10612no—
927#41—10612no—
928#41—1066no—
929#41—10612no—
930#41—10612no—
931#41—1066no—
932#41—1066no—
933#41—1066no—
934#41—1066no—
935#41—10624no—
936#41—10648no—
937#41—10612no—
938#41—10612no—
939#41—10624no—
940#41—1064no—
941#41—10612no—
942#41—10624no—
943#41—1066no—
944#41—1066no—
945#41—1066no—
946#41D4×D5314yes—
947#41C23×D53112yes—
948#41C23×D53112yes—
949#41C23×D5314yes—
950#41C23×D5314yes—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—23no—
954C2×Q8—26no—
955C2×Q8—534no—
956C2×Q8—534no—
957C2×Q8—533no—
958C2×Q8—536no—
959C2×Q8—534no—
960C2×Q8—5324no—
961C2×Q8—5312no—
962C2×Q8—536no—
963C2×Q8—5312no—
964C2×Q8—536no—
965C2×Q8—533no—
966C2×Q8—1063no—
967C2×Q8—1066no—
968C2×Q8—10612no—
969C2×Q8—10612no—
970C2×Q8—1066no—
971C2×Q8—10624no—
972C2×Q8—10612no—
973C2×Q8—1063no—
974C2×Q8—1063no—
975C2×Q8—10612no—
976C2×Q8—10612no—
977C2×Q8—1066no—
978C2×Q8—10612no—
979C2×Q8—10612no—
980C2×Q8—10612no—
981C2×Q8—1066no—
982C2×Q8—10624no—
983C2×Q8—10612no—
984C2×Q8—1068no—
985C2×Q8—1064no—
986C2×Q8—1063no—
987C2×Q8—1066no—
988C2×Q8D4×D5311yescharacteristic
989C2×Q8C23×D53112yes—
990C2×Q8C23×D5316yes—
991C2×Q8C23×D5313yes—
992C2×D4—23no—
993C2×D4—26no—
994C2×D4—212no—
995C2×D4—536no—
996C2×D4—5312no—
997C2×D4—5312no—
998C2×D4—532no—
999C2×D4—534no—
1000C2×D4—5312no—
1001C2×D4—532no—
1002C2×D4—533no—
1003C2×D4—536no—
1004C2×D4—531no—
1005C2×D4—10612no—
1006C2×D4—1063no—
1007C2×D4—1066no—
1008C2×D4—1066no—
1009C2×D4—1061no—
1010C2×D4—1061no—
1011C2×D4—1066no—
1012C2×D4—1061no—
1013C2×D4—1066no—
1014C2×D4—10624no—
1015C2×D4—10612no—
1016C2×D4—1064no—
1017C2×D4—10612no—
1018C2×D4—10612no—
1019C2×D4—10612no—
1020C2×D4—10612no—
1021C2×D4—10612no—
1022C2×D4—10624no—
1023C2×D4—1063no—
1024C2×D4—1066no—
1025C2×D4—1063no—
1026C2×D4—1066no—
1027C2×D4—10612no—
1028C2×D4D4×D5313yes—
1029C2×D4C23×D5316yes—
1030C2×D4C23×D5311yescharacteristic
1031C22×C4—23no—
1032C22×C4—23no—
1033C22×C4—26no—
1034C22×C4—533no—
1035C22×C4—533no—
1036C22×C4—536no—
1037C22×C4—533no—
1038C22×C4—536no—
1039C22×C4—536no—
1040C22×C4—531no—
1041C22×C4—533no—
1042C22×C4—536no—
1043C22×C4—1064no—
1044C22×C4—10612no—
1045C22×C4—1063no—
1046C22×C4—10612no—
1047C22×C4—10612no—
1048C22×C4—1066no—
1049C22×C4—10612no—
1050C22×C4—10612no—
1051C22×C4—1063no—
1052C22×C4—1066no—
1053C22×C4—1066no—
1054C22×C4—10612no—
1055C22×C4—10612no—
1056C22×C4—1063no—
1057C22×C4—1066no—
1058C22×C4—1063no—
1059C22×C4—1063no—
1060C22×C4—1066no—
1061C22×C4C23×D5313yes—
1062Q16—5324no—
1063Q16—5324no—
1064Q16—5324no—
1065Q16C23×D53124yes—
1066SD16—5324no—
1067SD16—538no—
1068SD16—5324no—
1069SD16—538no—
1070SD16—5324no—
1071SD16—538no—
1072SD16C23×D53124yes—
1073SD16C23×D5318yes—
1074D8—538no—
1075D8—538no—
1076D8—538no—
1077D8C23×D5318yes—
1078M16—534no—
1079M16—5312no—
1080M16—538no—
1081M16—5324no—
1082M16C23×D5314yes—
1083M16C23×D53112yes—
1084C2×C8—5312no—
1085C2×C8—538no—
1086C2×C8—5324no—
1087C2×C8C23×D53112yes—
1088C23—21no—
1089C23—26no—
1090C23—531no—
1091C23—536no—
1092C23—536no—
1093C23—533no—
1094C23—10612no—
1095C23—1062no—
1096C23—1062no—
1097C23—1064no—
1098C23—1066no—
1099C23—1061no—
1100C23—42412no—
1101C23—2126no—
1102C23—2124no—
1103C23C2×D4×D5313yes—
1104Q8—23no—
1105Q8—212no—
1106Q8—26no—
1107Q8—5312no—
1108Q8—536no—
1109Q8—534no—
1110Q8—1066no—
1111Q8—1066no—
1112Q8—10624no—
1113Q8—1064no—
1114Q8—10612no—
1115Q8—1063no—
1116Q8—10612no—
1117Q8—1066no—
1118Q8C2×D4×D5314yes—
1119Q8C24×D5316yes—
1120Q8C24×D5314yes—
1121D4—24no—
1122D4—212no—
1123D4—212no—
1124D4—26no—
1125D4—21no—
1126D4—5324no—
1127D4—5312no—
1128D4—532no—
1129D4—534no—
1130D4—1064no—
1131D4—10612no—
1132D4—10612no—
1133D4—1064no—
1134D4—10612no—
1135D4—1062no—
1136D4—1062no—
1137D4—1064no—
1138D4—10612no—
1139D4—10612no—
1140D4—1064no—
1141D4—10612no—
1142D4—10612no—
1143D4—1066no—
1144D4—1061no—
1145D4C2×D4×D53112yes—
1146D4C24×D5312yes—
1147D4C24×D5314yes—
1148C2×C4—23no—
1149C2×C4—26no—
1150C2×C4—212no—
1151C2×C4—24no—
1152C2×C4—212no—
1153C2×C4—212no—
1154C2×C4—531no—
1155C2×C4—533no—
1156C2×C4—536no—
1157C2×C4—536no—
1158C2×C4—531no—
1159C2×C4—531no—
1160C2×C4—536no—
1161C2×C4—536no—
1162C2×C4—536no—
1163C2×C4—536no—
1164C2×C4—536no—
1165C2×C4—531no—
1166C2×C4—536no—
1167C2×C4—531no—
1168C2×C4—1064no—
1169C2×C4—10612no—
1170C2×C4—10612no—
1171C2×C4—1064no—
1172C2×C4—1066no—
1173C2×C4—1066no—
1174C2×C4—10612no—
1175C2×C4—10624no—
1176C2×C4—1064no—
1177C2×C4—10612no—
1178C2×C4—10612no—
1179C2×C4—1063no—
1180C2×C4—1066no—
1181C2×C4—10612no—
1182C2×C4—1064no—
1183C2×C4—10612no—
1184C2×C4—10612no—
1185C2×C4C2×D4×D5313yes—
1186C2×C4C2×D4×D5316yes—
1187C2×C4C24×D5316yes—
1188C2×C4C24×D5311yescharacteristic
1189C8—538no—
1190C8C24×D5318yes—
1191C22—22no—
1192C22—24no—
1193C22—43no—
1194C22—42no—
1195C22—86no—
1196C22—531no—
1197C22—531no—
1198C22—536no—
1199C22—10612no—
1200C22—1062no—
1201C22—1062no—
1202C22—1064no—
1203C22—4246no—
1204C22—42412no—
1205C22—2123no—
1206C22—2126no—
1207C22—2122no—
1208C22—2128no—
1209C22—2124no—
1210C22—2124no—
1211C22C22×D4×D5311yescharacteristic
1212C22C22×D4×D5316yes—
1213C4—24no—
1214C4—26no—
1215C4—531no—
1216C4—531no—
1217C4—536no—
1218C4—1064no—
1219C4—1066no—
1220C4C22×D4×D5311yescharacteristic
1221C4C22×D4×D5316yes—
1222C4C25×D5311yescharacteristic
1223C2—21no—
1224C2—26no—
1225C2—42no—
1226C2—44no—
1227C2—532no—
1228C2—1066no—
1229C2—1061no—
1230C2—2124no—
1231C2—2122no—
1232C2C23×D4×D5311yescharacteristic
subgroupG/H
centerC2C23×D4×D53
commutator, cosocleC4×C53C26
FrattiniC4C25×D53
FittingC53×#3586C2
socleC2×C53C24×D4
hypercenter#3586D53
hypocenterC53C2×#3586
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C2×#41 ◁ #3586

Complements

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

NH ≅ G/Ntype
1. #585×D53C2semidirect
2. C2×2−1+4×D53C2semidirect
3. #20289503C2semidirect
4. #20289502C2semidirect
5. #20289501C2semidirect
6. #20289500C2semidirect
7. #20289499C2semidirect
8. #20289498C2semidirect
9. #20289497C2semidirect
10. #578×D53C2semidirect
11. #577×D53C2semidirect
12. #575×D53C2semidirect
13. C2×#137×D53C2semidirect
14. #568×D53C2semidirect
15. C53×#3586C2semidirect
17. #16811460C22semidirect
19. #16811459C22semidirect
20. #16811459C22semidirect
22. #16811458C22semidirect
24. C2×#13133265C22semidirect
26. C2×#13133264C22semidirect
27. C2×#13133264C22semidirect
31. 2−1+4×D53C22semidirect
32. 2−1+4×D53C22semidirect
33. 2−1+4×D53C22semidirect
35. H(5,𝔽2)×D53C22semidirect
40. C2×#41×D53C22semidirect
42. C22×Q8×D53C22semidirect
43. #16811440C22semidirect
44. #16811439C22semidirect
45. #16811439C22semidirect
46. #16811438C22semidirect
47. #16811438C22semidirect
48. #16811437C22semidirect
49. #16811436C22semidirect
50. #16811435C22semidirect
51. #16811434C22semidirect
52. #16811433C22semidirect
53. #16811432C22semidirect
54. #16811431C22semidirect
55. #16811430C22semidirect
56. #16811429C22semidirect
57. #16811423C22semidirect
58. #16811422C22semidirect
59. #16811422C22semidirect
60. #16811421C22semidirect
61. #16811421C22semidirect
62. #16811420C22semidirect
63. #16811419C22semidirect
64. #16811419C22semidirect
65. C2×#13133250C22semidirect
66. C2×#13133249C22semidirect
67. C2×#13133248C22semidirect
68. C2×#13133247C22semidirect
69. C2×#13133246C22semidirect
70. #137×D53C22semidirect
71. #137×D53C22semidirect
72. #137×D53C22semidirect
73. #137×D53C22semidirect
74. #137×D53C22semidirect
75. AGL(1,ℤ/8)×D53C22semidirect
76. AGL(1,ℤ/8)×D53C22semidirect
77. #135×D53C22semidirect
78. C2×Q16×D53C22semidirect
79. C2×SD16×D53C22semidirect
80. #16811390C22semidirect
81. #16811389C22semidirect
82. #16811388C22semidirect
83. #131×D53C22semidirect
84. C2×M16×D53C22semidirect
85. C53×#585C22semidirect
86. C2×2−1+4×C53C22semidirect
87. C53×#578C22semidirect
88. C53×#577C22semidirect
89. C53×#575C22semidirect
90. C2×#137×C53C22semidirect
91. C53×#568C22semidirect
98. #13133265C23semidirect
99. #13133265C23semidirect
107. #13133264C23semidirect
108. #13133264C23semidirect
109. #13133264C23semidirect
110. #13133264C23semidirect
114. #13133263C23semidirect
115. #13133263C23semidirect
120. #13133262C23semidirect
125. C2×#11719949C23semidirect
133. C2×#11719945C23semidirect
141. C2×#11719947C23semidirect
165. #41×D53C23semidirect
168. C22×Dic106C23semidirect
182. C2×Q8×D53C23semidirect
183. C2×Q8×D53C23semidirect
194. #13133250C23semidirect
195. #13133250C23semidirect
196. #13133250C23semidirect
197. #13133249C23semidirect
198. #13133249C23semidirect
199. #13133249C23semidirect
200. #13133248C23semidirect
201. #13133248C23semidirect
202. #13133248C23semidirect
203. #13133247C23semidirect
204. #13133247C23semidirect
205. #13133247C23semidirect
206. #13133246C23semidirect
207. #13133246C23semidirect
208. #13133246C23semidirect
209. #13133245C23semidirect
210. #13133245C23semidirect
211. #13133244C23semidirect
212. #13133244C23semidirect
213. #13133243C23semidirect
214. #13133243C23semidirect
215. #13133242C23semidirect
216. #13133242C23semidirect
217. #13133241C23semidirect
218. #13133241C23semidirect
219. #13133240C23semidirect
220. #13133239C23semidirect
221. #13133238C23semidirect
222. #13133238C23semidirect
223. #13133237C23semidirect
224. #13133237C23semidirect
225. #13133236C23semidirect
226. C2×Dic212C23semidirect
227. C2×#11719925C23semidirect
228. C2×#11719925C23semidirect
230. Q16×D53C23semidirect
231. C2×#11719913C23semidirect
232. C2×#11719923C23semidirect
233. C2×#11719924C23semidirect
236. SD16×D53C23semidirect
238. #13133225C23semidirect
239. #13133224C23semidirect
240. #13133223C23semidirect
241. C2×#11719917C23semidirect
242. C2×#11719912C23semidirect
245. M16×D53C23semidirect
246. M16×D53C23semidirect
250. 2−1+4×C53C23semidirect
251. 2−1+4×C53C23semidirect
253. H(5,𝔽2)×C53C23semidirect
258. C2×#41×C53C23semidirect
260. C22×Q8×C53C23semidirect
261. #137×C53C23semidirect
262. #137×C53C23semidirect
263. #137×C53C23semidirect
264. AGL(1,ℤ/8)×C53C23semidirect
265. AGL(1,ℤ/8)×C53C23semidirect
266. #135×C53C23semidirect
267. C2×Q16×C53C23semidirect
268. C2×SD16×C53C23semidirect
269. #131×C53C23semidirect
270. C2×M16×C53C23semidirect
616. #3586D53direct (N × H)
631. D53#3586direct (N × H)
639. #585C2×D53semidirect
651. C2×2−1+4C2×D53semidirect
668. #578C2×D53semidirect
676. #577C2×D53semidirect
685. #575C2×D53semidirect
696. C2×#137C2×D53semidirect
705. #568C2×D53semidirect
708. C53C2×#3586semidirect
730. 2−1+4C22×D53semidirect
731. 2−1+4C22×D53semidirect
743. H(5,𝔽2)C22×D53semidirect
793. C2×#41C22×D53semidirect
813. C22×Q8C22×D53semidirect
839. #137C22×D53semidirect
840. #137C22×D53semidirect
841. #137C22×D53semidirect
852. AGL(1,ℤ/8)C22×D53semidirect
853. AGL(1,ℤ/8)C22×D53semidirect
861. #135C22×D53semidirect
867. C2×Q16C22×D53semidirect
874. C2×SD16C22×D53semidirect
879. #131C22×D53semidirect
886. C2×M16C22×D53semidirect

Maximal subgroups

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

subgroupindex
#585×D532
C2×2−1+4×D532
#202895032
#202895022
#202895012
#202895002
#202894992
#202894982
#202894972
#578×D532
#577×D532
#575×D532
C2×#137×D532
#568×D532
C53×#35862
C2×#358653