Finite Group Databasebeta

← D53×#3500 #28292556

Subgroups — D53×#3500 #28292556

Order 13568.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D53C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D53C211yesmaximal, characteristic, complemented
3#20288509C211yesmaximal, characteristic, complemented
4#20288508C211yesmaximal, characteristic, complemented
5#20288507C213yesmaximal, complemented
6#20288506C214yesmaximal, complemented
7#20288505C213yesmaximal, complemented
8#20288504C213yesmaximal, complemented
9#20288503C211yesmaximal, characteristic, complemented
10#20288502C213yesmaximal, complemented
11#20288501C2112yesmaximal, complemented
12#548×D53C214yesmaximal, complemented
13#546×D53C2112yesmaximal, complemented
14#536×D53C213yesmaximal, complemented
15#535×D53C213yesmaximal, complemented
16#532×D53C213yesmaximal, complemented
17C2×#124×D53C213yesmaximal, complemented
18C4×#41×D53C211yesmaximal, characteristic, complemented
19C53×#3500C211yesmaximal, characteristic, complemented
20C2×#13133265C2213yescomplemented
21C2×#13133265C2212yescomplemented
22C2×#13133264C2211yescharacteristic, complemented
23C2×#13133264C2216yescomplemented
24C2×#13133264C2213yescomplemented
252−1+4×D53—216no—
26C2×#13133263C2213yescomplemented
27C2×#13133263C2212yescomplemented
28C2×#13133263C2211yescharacteristic, complemented
29C2×#13133262C2216yescomplemented
30C2×#13133262C2213yescomplemented
31H(5,𝔽2)×D53—216no—
32C2×#41×D53C2213yes—
33C2×#41×D53C2212yes—
34C2×#41×D53C2211yescharacteristic
35C2×#41×D53C2213yescomplemented
36C2×#41×D53C2216yescomplemented
37C22×Q8×D53C2213yescomplemented
38C22×Q8×D53C2212yescomplemented
39C22×D4×D53C2213yes—
40C22×D4×D53C2216yes—
41#16811285C2214yescomplemented
42#16811284C2214yescomplemented
43#16811283C22112yescomplemented
44#16811282C22112yescomplemented
45#16811281C22112yescomplemented
46#16811280C2214yescomplemented
47#16811279C22112yescomplemented
48#16811270C22112yescomplemented
49#16811269C22112yescomplemented
50#16811268C22112yescomplemented
51#16811267C22112yescomplemented
52#16811266C22112yescomplemented
53#16811265C22124yescomplemented
54#16811264C22112yescomplemented
55#16811263C22124yescomplemented
56#16811262C22124yescomplemented
57#16811261C22112yescomplemented
58#16811260C22124yescomplemented
59#16811199C2213yescomplemented
60#16811198C2216yescomplemented
61#16811197C2213yescomplemented
62#16811196C22112yescomplemented
63#16811195C22112yescomplemented
64#16811194C2213yescomplemented
65#16811193C2216yescomplemented
66#16811192C2213yescomplemented
67#16811191C2216yescomplemented
68#16811190C2213yescomplemented
69#16811189C22112yescomplemented
70#16811188C22112yescomplemented
71#16811187C2213yescomplemented
72#16811186C2216yescomplemented
73#16811174C2213yescomplemented
74#16811173C2213yescomplemented
75#16811172C2213yescomplemented
76#16811172C2213yescomplemented
77#16811171C2213yescomplemented
78#16811170C22112yescomplemented
79#16811169C2213yescomplemented
80#16811169C2213yescomplemented
81#16811168C22112yescomplemented
82C4⋊Q8×D53C2213yescomplemented
83#127×D53C2213yescomplemented
84C2×#13133206C2213yescomplemented
85C2×#13133205C2213yescomplemented
86C2×#13133204C2213yescomplemented
87C2×#13133203C22112yescomplemented
88#124×D53C2216yescomplemented
89#124×D53C22112yescomplemented
90#124×D53C2213yescomplemented
91#124×D53C2211yescharacteristic, complemented
92#124×D53C22112yescomplemented
93#124×D53C2216yescomplemented
94#124×D53C2216yescomplemented
95#123×D53C22112yescomplemented
96C22⋊Q8×D53C22112yescomplemented
97#121×D53C22112yescomplemented
98#121×D53C22112yescomplemented
99#120×D53C22112yescomplemented
100#41×Dic53C2211yescharacteristic, complemented
101C4×#11719949C2212yescomplemented
102C4×#11719945C2213yescomplemented
103#16811091C2213yescomplemented
104C4×#11719947C2216yescomplemented
105C4×Q8×D53C2212yescomplemented
106C4×D4×D53C2216yescomplemented
107C4×D4×D53C22112yescomplemented
108#117×D53C2213yescomplemented
109C2×C22⋊C4×D53C22112yescomplemented
110C2×C42×D53C2213yescomplemented
111C2×2−1+4×C53C2211yescharacteristic, complemented
112C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
113C53×#548C2214yescomplemented
114C53×#546C22112yescomplemented
115C53×#536C2213yescomplemented
116C53×#535C2213yescomplemented
117C53×#532C2213yescomplemented
118C2×#124×C53C2213yescomplemented
119C4×#41×C53C2211yescharacteristic, complemented
120C24×D53C2316yes—
121#13133265—216no—
122#13133265—224no—
123#13133264—28no—
124#13133264—248no—
125#13133264—224no—
126#13133263—28no—
127#13133263—216no—
128#13133263—224no—
129#13133262—248no—
130#13133262—224no—
131C2×#11719949C2312yes—
132C2×#11719949C2313yes—
133C2×#11719949C2311yescharacteristic
134C2×#11719949C2316yescomplemented
135C2×#11719949C2313yescomplemented
136C2×#11719945C2316yes—
137C2×#11719945C2313yes—
138C2×#11719945C2316yes—
139C2×#11719945C2313yes—
140C2×#11719945C23112yescomplemented
141C2×#11719945C2316yescomplemented
142C2×#11719945C2313yescomplemented
143C2×#11719945C2316yescomplemented
144C2×#11719947C2316yes—
145C2×#11719947C2316yes—
146C2×#11719947C2313yes—
147C2×#11719947C2313yes—
148C2×#11719947C2316yescomplemented
149C2×#11719947C2316yescomplemented
150C2×#11719947C2313yescomplemented
151C2×#11719947C23112yescomplemented
152#41×D53—216no—
153#41×D53—248no—
154#41×D53—224no—
155#41×D53—224no—
156#41×D53D4116yescomplemented
157C22×Dic106C2316yescomplemented
158C22×Dic106C2316yescomplemented
159C22×Dic106C2313yescomplemented
160C2×Q8×D53—216no—
161C2×Q8×D53—224no—
162C2×Q8×D53C2316yes—
163C2×Q8×D53C2313yes—
164C2×Q8×D53C2311yescharacteristic
165C2×Q8×D53C2311yescharacteristic
166C2×Q8×D53C2312yescomplemented
167C2×Q8×D53C2316yescomplemented
168C2×Q8×D53C2316yescomplemented
169C2×Q8×D53C2316yescomplemented
170C22×D212C2316yes—
171C22×D212C2313yes—
172C22×C22⋊D53C2316yes—
173C22×C22⋊D53C23112yes—
174C2×D4×D53—248no—
175C2×D4×D53—224no—
176C2×D4×D53C23112yes—
177C2×D4×D53C2316yes—
178C2×D4×D53C2316yes—
179C2×D4×D53C2316yes—
180C2×D4×D53C2316yes—
181C2×D4×D53C2316yes—
182C2×D4×D53C2313yes—
183C2×D4×D53C2316yes—
184C2×D4×D53C2316yes—
185C2×D4×D53C2311yescharacteristic
186C2×D4×D53C23112yes—
187C2×D4×D53C2313yes—
188C22×C4×D53C2316yes—
189C22×C4×D53C2316yes—
190C22×C4×D53C2316yes—
191C22×C4×D53C2316yes—
192C22×C4×D53C2313yes—
193#13133217C2313yescomplemented
194#13133216C23112yescomplemented
195#13133215C2313yescomplemented
196#13133215C2313yescomplemented
197#13133214C2313yescomplemented
198#13133213C23112yescomplemented
199#13133213C2313yescomplemented
200#13133213C2313yescomplemented
201#13133206C23112yescomplemented
202#13133206C2313yescomplemented
203#13133206C2316yescomplemented
204#13133206C2311yescharacteristic, complemented
205#13133205C23112yescomplemented
206#13133205C2313yescomplemented
207#13133205C2316yescomplemented
208#13133205C2311yescharacteristic, complemented
209#13133204C23112yescomplemented
210#13133204C2313yescomplemented
211#13133204C2316yescomplemented
212#13133204C2311yescharacteristic, complemented
213#13133203C23124yescomplemented
214#13133203C23124yescomplemented
215#13133203C23112yescomplemented
216#13133203C23124yescomplemented
217#13133203C2314yescomplemented
218#13133202C23124yescomplemented
219#13133201C23112yescomplemented
220#13133200C23112yescomplemented
221#13133199C23124yescomplemented
222#13133198C23112yescomplemented
223#13133197C23112yescomplemented
224#13133196C23112yescomplemented
225#13133195C23124yescomplemented
226#13133194C23124yescomplemented
227#13133193C23112yescomplemented
228#13133192C23112yescomplemented
229#13133192C23112yescomplemented
230#13133191C23112yescomplemented
231#13133191C23112yescomplemented
232#13133190C23124yescomplemented
233#13133190C23112yescomplemented
234#13133190C23112yescomplemented
235#13133189C23112yescomplemented
236#13133189C23124yescomplemented
237#13133189C23112yescomplemented
238#13133188C23112yescomplemented
239#13133188C23112yescomplemented
240#13133187C23124yescomplemented
241#13133187C23112yescomplemented
242#13133186C23112yescomplemented
243#13133185C23124yescomplemented
244#13133185C23112yescomplemented
245Q8×Dic53C2312yescomplemented
246C4×Dic106C2316yescomplemented
247#13133182C2316yescomplemented
248C4×D212C2316yescomplemented
249C4×D212C23112yescomplemented
250D4×Dic53C2316yescomplemented
251D4×Dic53C23112yescomplemented
252#13133179C2316yescomplemented
253#13133179C23112yescomplemented
254C4×C22⋊D53C23112yescomplemented
255C4×C22⋊D53C23112yescomplemented
256C4×C22⋊D53C23112yescomplemented
257#13133177C23112yescomplemented
258#13133177C23112yescomplemented
259#13133177C23112yescomplemented
260#13133176C2313yescomplemented
261#13133175C2316yescomplemented
262#13133174C2316yescomplemented
263#13133173C2316yescomplemented
264C4⋊C4×D53C2316yes—
265C4⋊C4×D53C23112yes—
266C2×C22⋊Dic53C23112yescomplemented
267C2×#11719921C23112yescomplemented
268C2×#11719921C23112yescomplemented
269C22⋊C4×D53C23112yes—
270C22⋊C4×D53C23124yes—
271C22⋊C4×D53C2316yes—
272C22⋊C4×D53C2314yes—
273C22⋊C4×D53C23124yescomplemented
274C22⋊C4×D53C23124yescomplemented
275C2×C4×Dic53C2316yescomplemented
276C2×C4×Dic53C2313yescomplemented
277C42×D53C2311yescharacteristic
278C42×D53C2313yes—
279C42×D53C2316yes—
280C42×D53C2316yescomplemented
281C42×D53C2313yescomplemented
282C42×D53C2313yescomplemented
2832−1+4×C53—28no—
284H(5,𝔽2)×C53—28no—
285C2×#41×C53C2312yes—
286C2×#41×C53C2313yes—
287C2×#41×C53C2311yescharacteristic
288C2×#41×C53C2313yescomplemented
289C2×#41×C53C2316yescomplemented
290C22×Q8×C53C2312yescomplemented
291C22×Q8×C53C2313yescomplemented
292C22×D4×C53C2316yes—
293C22×D4×C53C2313yes—
294C4⋊Q8×C53C2313yescomplemented
295#127×C53C2313yescomplemented
296#124×C53C23112yescomplemented
297#124×C53C2313yescomplemented
298#124×C53C2316yescomplemented
299#124×C53C2311yescharacteristic, complemented
300#123×C53C23112yescomplemented
301C22⋊Q8×C53C23112yescomplemented
302#121×C53C23112yescomplemented
303#121×C53C23112yescomplemented
304#120×C53C23112yescomplemented
305C4×Q8×C53C2312yescomplemented
306C4×D4×C53C2316yescomplemented
307C4×D4×C53C23112yescomplemented
308#117×C53C2313yescomplemented
309C2×C22⋊C4×C53C23112yescomplemented
310C2×C42×C53C2313yescomplemented
311C24×C53C2416yes—
312C23×D53—224no—
313C23×D53—424no—
314C23×D53C2416yes—
315C23×D53C2412yes—
316C23×D53C2413yes—
317C23×D53C24112yes—
318C23×D53C2416yes—
319#41×C53—28no—
320#41×C53—224no—
321#41×C53—212no—
322#41×C53—212no—
323#41×C53C2×D418yescomplemented
324C2×Q8×C53—28no—
325C2×Q8×C53—212no—
326C2×Q8×C53C2416yes—
327C2×Q8×C53C2413yes—
328C2×Q8×C53C2411yescharacteristic
329C2×Q8×C53C2411yescharacteristic
330C2×D4×C53—224no—
331C2×D4×C53—212no—
332C2×D4×C53C2416yes—
333C2×D4×C53C2416yes—
334C2×D4×C53C2416yes—
335C2×D4×C53C2413yes—
336C2×D4×C53C2411yescharacteristic
337C2×D4×C53C24112yes—
338C2×D4×C53C2413yes—
339C22×C4×C53C2416yes—
340C22×C4×C53C2416yes—
341C22×C4×C53C2416yes—
342C22×C4×C53C2416yes—
343C22×C4×C53C2413yes—
344C2×C22⋊D53—248no—
345C2×C22⋊D53—224no—
346C2×C22⋊D53C2416yes—
347C2×C22⋊D53C2416yes—
348C2×C22⋊D53C2416yes—
349C2×C22⋊D53C24112yes—
350C2×C22⋊D53C2416yes—
351C2×C22⋊D53C2416yes—
352C2×C22⋊D53C2412yes—
353C2×C22⋊D53C24112yes—
354C2×C22⋊D53C24112yes—
355C2×C22⋊D53C2416yes—
356C22×Dic53C2416yes—
357C22×Dic53C2416yes—
358C22×Dic53C2416yes—
359C22×Dic53C2416yes—
360C22×Dic53C2413yes—
361#11719949—28no—
362#11719949—224no—
363#11719949—212no—
364#11719949—212no—
365#11719949C2×D418yescomplemented
366Q8×D53—28no—
367Q8×D53—224no—
368Q8×D53—212no—
369Q8×D53—224no—
370Q8×D53—224no—
371Q8×D53—24no—
372Q8×D53—224no—
373Q8×D53C2×D418yes—
374#11719947—224no—
375#11719947—248no—
376#11719947—224no—
377#11719947—224no—
378#11719947—212no—
379#11719947—212no—
380#11719947—224no—
381#11719947C2×D4124yescomplemented
382D4×D53—224no—
383D4×D53—224no—
384D4×D53—224no—
385D4×D53—248no—
386D4×D53—224no—
387D4×D53—224no—
388D4×D53—212no—
389D4×D53—224no—
390D4×D53—224no—
391D4×D53—24no—
392D4×D53—424no—
393D4×D53C2×D4124yes—
394#11719945—212no—
395#11719945—212no—
396#11719945—248no—
397#11719945—224no—
398#11719945—224no—
399#11719945—224no—
400#11719945—224no—
401#11719945C2×D4124yescomplemented
402C2×D212—212no—
403C2×D212—224no—
404C2×D212C2416yes—
405C2×D212C2416yes—
406C2×D212C2416yes—
407C2×D212C2413yes—
408C2×D212C2411yescharacteristic
409C2×D212C24112yes—
410C2×D212C2413yes—
411C2×C4×D53—224no—
412C2×C4×D53—224no—
413C2×C4×D53—224no—
414C2×C4×D53—412no—
415C2×C4×D53C2×D4124yes—
416C2×C4×D53C2412yes—
417C2×C4×D53C2416yes—
418C2×C4×D53C2416yes—
419C2×C4×D53C2412yes—
420C2×C4×D53C24112yes—
421C2×C4×D53C2416yes—
422C2×C4×D53C2416yes—
423C2×C4×D53C2416yes—
424C2×C4×D53C2416yes—
425C2×C4×D53C2416yes—
426C2×C4×D53C2416yes—
427C2×C4×D53C2411yescharacteristic
428C2×C4×D53C2413yes—
429C2×C4×D53C2413yes—
430C2×C4×D53C2413yes—
431C2×Dic106—212no—
432C2×Dic106—224no—
433C2×Dic106—224no—
434C2×Dic106C24112yes—
435C2×Dic106C2416yes—
436C2×Dic106C2416yes—
437C2×Dic106C2412yes—
438C2×Dic106C2413yes—
439C2×Dic106C2411yescharacteristic
440C2×Dic106C2413yes—
441C4⋊C4×C53C2416yes—
442C4⋊C4×C53C24112yes—
443C22⋊C4×C53C24112yes—
444C22⋊C4×C53C24124yes—
445C22⋊C4×C53C2416yes—
446C22⋊C4×C53C2414yes—
447C42×C53C2411yescharacteristic
448C42×C53C2413yes—
449C42×C53C2416yes—
450C22⋊Dic53C24112yes—
451C22⋊Dic53C24124yes—
452C22⋊Dic53C2416yes—
453C22⋊Dic53C2414yes—
454#11719921C24112yes—
455#11719921C24112yes—
456#11719921C24124yes—
457#11719921C24124yes—
458#11719921C24112yes—
459#11719921C2414yes—
460#11719921C2414yes—
461C4⋊Dic53C2416yes—
462C4⋊Dic53C24112yes—
463#11719919C24112yes—
464#11719919C24112yes—
465#11719919C24112yes—
466C4×Dic53C2412yes—
467C4×Dic53C2411yescharacteristic
468C4×Dic53C2416yes—
469C4×Dic53C2413yes—
470C4×Dic53C2416yes—
471C4×Dic53C2416yes—
472C4×Dic53C2416yes—
473C23×C53—212no—
474C23×C53—412no—
475C23×C53C2512yes—
476C23×C53C2516yes—
477C23×C53C2513yes—
478C22×D53—212no—
479C22×D53—212no—
480C22×D53—24no—
481C22×D53—212no—
482C22×D53—28no—
483C22×D53—224no—
484C22×D53—224no—
485C22×D53—424no—
486C22×D53—412no—
487C22×D53—848no—
488C22×D53C22×D4112yes—
489C22×D53C2512yes—
490C22×D53C2516yes—
491C22×D53C2513yes—
492C22×D53C2511yescharacteristic
493Q8×C53—26no—
494Q8×C53—212no—
495Q8×C53—22no—
496Q8×C53C22×D414yes—
497D4×C53—212no—
498D4×C53—212no—
499D4×C53—26no—
500D4×C53—212no—
501D4×C53—22no—
502D4×C53—412no—
503D4×C53C22×D4112yes—
504C2×C4×C53—212no—
505C2×C4×C53—212no—
506C2×C4×C53—212no—
507C2×C4×C53—46no—
508C2×C4×C53C22×D4112yes—
509C2×C4×C53C2516yes—
510C2×C4×C53C2512yes—
511C2×C4×C53C2512yes—
512C2×C4×C53C2516yes—
513C2×C4×C53C2511yescharacteristic
514C2×C4×C53C2513yes—
515C22⋊D53—212no—
516C22⋊D53—212no—
517C22⋊D53—212no—
518C22⋊D53—212no—
519C22⋊D53—24no—
520C22⋊D53—212no—
521C22⋊D53—224no—
522C22⋊D53—412no—
523C22⋊D53—412no—
524C22⋊D53C22×D4124yes—
525C2×Dic53—212no—
526C2×Dic53—212no—
527C2×Dic53—212no—
528C2×Dic53—46no—
529C2×Dic53C22×D4112yes—
530C2×Dic53C2516yes—
531C2×Dic53C2512yes—
532C2×Dic53C2512yes—
533C2×Dic53C2516yes—
534C2×Dic53C2511yescharacteristic
535C2×Dic53C2513yes—
536D212—212no—
537D212—212no—
538D212—26no—
539D212—212no—
540D212—22no—
541D212—412no—
542D212C22×D4112yes—
543C4×D53—24no—
544C4×D53—212no—
545C4×D53—224no—
546C4×D53—24no—
547C4×D53—212no—
548C4×D53—212no—
549C4×D53—212no—
550C4×D53—212no—
551C4×D53—212no—
552C4×D53—46no—
553C4×D53—46no—
554C4×D53C22×D4112yes—
555C4×D53C22×D414yes—
556C4×D53C22×D4112yes—
557C4×D53C22×D4112yes—
558Dic106—26no—
559Dic106—212no—
560Dic106—22no—
561Dic106—212no—
562Dic106—224no—
563Dic106—24no—
564Dic106C22×D4112yes—
565C2×#3500—531nomaximal, Sylow
566C22×C53—26no—
567C22×C53—22no—
568C22×C53—26no—
569C22×C53—24no—
570C22×C53—212no—
571C22×C53—812no—
572C22×C53C23×D416yes—
573C22×C53C2611yescharacteristic
574C2×D53—26no—
575C2×D53—224no—
576C2×D53—22no—
577C2×D53—26no—
578C2×D53—24no—
579C2×D53—212no—
580C2×D53—48no—
581C2×D53—424no—
582C2×D53—824no—
583C2×D53—812no—
584C2×D53C23×D416yes—
585C2×D53C23×D412yes—
586C2×D53#58514yes—
587C4×C53—26no—
588C4×C53—22no—
589C4×C53—22no—
590C4×C53—26no—
591C4×C53C23×D412yes—
592C4×C53C23×D416yes—
593Dic53—26no—
594Dic53—22no—
595Dic53—22no—
596Dic53—26no—
597Dic53C23×D412yes—
598Dic53C23×D416yes—
599C22×2−1+4—531no—
600C22×H(5,𝔽2)—531no—
601#3500—531no—
602#3500—531no—
603#3500—534no—
604#3500—5312no—
605#3500—533no—
606#3500—533no—
607#3500—533no—
608#3500—533no—
609#3500—531no—
610#3500D5311yescharacteristic, direct product factor
611C2×#548—534no—
612C2×#546—5312no—
613C2×#536—533no—
614C2×#535—533no—
615C2×#532—533no—
616C22×#124—533no—
617C2×C4×#41—531no—
618C2×C53—26no—
619C2×C53—46no—
620C2×C53—42no—
621C2×C53C24×D411yescharacteristic
622C2×C53C2×#58512yes—
623D53—26no—
624D53—42no—
625D53—46no—
626D53#350014yesdirect product factor
627C2×2−1+4—531no—
628C2×2−1+4—533no—
629C2×2−1+4—536no—
630C2×2−1+4—532no—
631C2×2−1+4—533no—
632C2×2−1+4—10616no—
633C2×2−1+4C2×D5311yescharacteristic, complemented
634C2×H(5,𝔽2)—532no—
635C2×H(5,𝔽2)—533no—
636C2×H(5,𝔽2)—531no—
637C2×H(5,𝔽2)—536no—
638C2×H(5,𝔽2)—533no—
639C2×H(5,𝔽2)—10616no—
640C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
641C22×#41—531no—
642C22×#41—533no—
643C22×#41—532no—
644C22×#41—533no—
645C22×#41—536no—
646C23×Q8—533no—
647C23×Q8—532no—
648C23×D4—533no—
649C23×D4—536no—
650#548—534no—
651#548—534no—
652#548—5312no—
653#548—5312no—
654#548—5312no—
655#548—534no—
656#548—5312no—
657#548C2×D5314yescomplemented
658#546—5312no—
659#546—5312no—
660#546—5312no—
661#546—5324no—
662#546—5312no—
663#546—5312no—
664#546—5324no—
665#546—5324no—
666#546—5312no—
667#546—5312no—
668#546—5324no—
669#546C2×D53112yescomplemented
670#536—533no—
671#536—533no—
672#536—536no—
673#536—536no—
674#536—5312no—
675#536—5312no—
676#536—533no—
677#536C2×D5313yescomplemented
678#535—533no—
679#535—533no—
680#535—536no—
681#535—536no—
682#535—5312no—
683#535—5312no—
684#535—533no—
685#535C2×D5313yescomplemented
686#532—533no—
687#532—533no—
688#532—533no—
689#532—533no—
690#532—533no—
691#532—533no—
692#532—5312no—
693#532—5312no—
694#532—533no—
695#532C2×D5313yescomplemented
696C2×C4⋊Q8—533no—
697C2×#127—533no—
698C2×#124—533no—
699C2×#124—533no—
700C2×#124—533no—
701C2×#124—536no—
702C2×#124—5312no—
703C2×#124—536no—
704C2×#124—536no—
705C2×#124—5312no—
706C2×#124—531no—
707C2×#124—5312no—
708C2×#124—533no—
709C2×#124C2×D5313yescomplemented
710C2×#123—5312no—
711C2×C22⋊Q8—5312no—
712C2×#121—5312no—
713C2×#121—5312no—
714C2×#120—5312no—
715C4×#41—531no—
716C4×#41—532no—
717C4×#41—536no—
718C4×#41—533no—
719C4×#41—533no—
720C4×#41C2×D5311yescharacteristic, complemented
721C2×C4×Q8—532no—
722C2×C4×D4—536no—
723C2×C4×D4—5312no—
724C2×#117—533no—
725C22×C22⋊C4—5312no—
726C22×C42—533no—
727C53C2×#350011yescharacteristic, complemented, Sylow
728C25—536no—
7292−1+4—28no—
7302−1+4—10616no—
7312−1+4—10624no—
7322−1+4—10648no—
7332−1+4—10624no—
7342−1+4—1068no—
735H(5,𝔽2)—28no—
736H(5,𝔽2)—10648no—
737H(5,𝔽2)—10624no—
738H(5,𝔽2)—10616no—
739H(5,𝔽2)—10624no—
740H(5,𝔽2)—1068no—
741C2×#41—5316no—
742C2×#41—531no—
743C2×#41—533no—
744C2×#41—533no—
745C2×#41—536no—
746C2×#41—532no—
747C2×#41—533no—
748C2×#41—536no—
749C2×#41—533no—
750C2×#41—536no—
751C2×#41—533no—
752C2×#41—536no—
753C2×#41—5312no—
754C2×#41—536no—
755C2×#41—533no—
756C2×#41—536no—
757C2×#41—533no—
758C2×#41—536no—
759C2×#41—533no—
760C2×#41—536no—
761C2×#41—5312no—
762C2×#41—536no—
763C2×#41—10624no—
764C2×#41—10624no—
765C2×#41—10648no—
766C2×#41—10616no—
767C2×#41C22×D5313yes—
768C2×#41C22×D5312yes—
769C2×#41C22×D5311yescharacteristic
770C2×#41C22×D5313yescomplemented
771C2×#41C22×D5316yescomplemented
772C22×Q8—531no—
773C22×Q8—536no—
774C22×Q8—533no—
775C22×Q8—536no—
776C22×Q8—536no—
777C22×Q8—531no—
778C22×Q8—536no—
779C22×Q8—532no—
780C22×Q8—536no—
781C22×Q8—533no—
782C22×Q8—536no—
783C22×Q8—10624no—
784C22×Q8—10616no—
785C22×Q8C22×D5313yescomplemented
786C22×Q8C22×D5312yescomplemented
787C22×D4—533no—
788C22×D4—536no—
789C22×D4—5312no—
790C22×D4—536no—
791C22×D4—536no—
792C22×D4—536no—
793C22×D4—533no—
794C22×D4—536no—
795C22×D4—536no—
796C22×D4—531no—
797C22×D4—5312no—
798C22×D4—536no—
799C22×D4—536no—
800C22×D4—5312no—
801C22×D4—533no—
802C22×D4—536no—
803C22×D4—10624no—
804C22×D4—10648no—
805C22×D4C22×D5313yes—
806C22×D4C22×D5316yes—
807C23×C4—533no—
808C23×C4—536no—
809C23×C4—536no—
810C23×C4—536no—
811C23×C4—536no—
812C4⋊Q8—533no—
813C4⋊Q8—533no—
814C4⋊Q8—5312no—
815C4⋊Q8—533no—
816C4⋊Q8C22×D5313yescomplemented
817#127—5312no—
818#127—533no—
819#127—533no—
820#127—533no—
821#127C22×D5313yescomplemented
822#124—533no—
823#124—536no—
824#124—5312no—
825#124—531no—
826#124—533no—
827#124—536no—
828#124—5312no—
829#124—531no—
830#124—5312no—
831#124—5324no—
832#124—5324no—
833#124—5324no—
834#124—534no—
835#124—533no—
836#124—536no—
837#124—5312no—
838#124—531no—
839#124C22×D5313yescomplemented
840#124C22×D5316yescomplemented
841#124C22×D53112yescomplemented
842#124C22×D5311yescharacteristic, complemented
843#123—5312no—
844#123—5312no—
845#123—5324no—
846#123—5324no—
847#123—5312no—
848#123C22×D53112yescomplemented
849C22⋊Q8—5312no—
850C22⋊Q8—5312no—
851C22⋊Q8—5324no—
852C22⋊Q8—5312no—
853C22⋊Q8—5324no—
854C22⋊Q8C22×D53112yescomplemented
855#121—5312no—
856#121—5312no—
857#121—5312no—
858#121—5312no—
859#121—5324no—
860#121—5312no—
861#121—5312no—
862#121—5312no—
863#121—5312no—
864#121—5312no—
865#121—5312no—
866#121—5324no—
867#121C22×D53112yescomplemented
868#121C22×D53112yescomplemented
869#120—5312no—
870#120—5324no—
871#120—5312no—
872#120—5312no—
873#120—5324no—
874#120C22×D53112yescomplemented
875C4×Q8—532no—
876C4×Q8—536no—
877C4×Q8—536no—
878C4×Q8C22×D5312yescomplemented
879C4×D4—536no—
880C4×D4—5312no—
881C4×D4—5312no—
882C4×D4—5312no—
883C4×D4—5312no—
884C4×D4—536no—
885C4×D4—5312no—
886C4×D4—5312no—
887C4×D4—5312no—
888C4×D4—5312no—
889C4×D4—536no—
890C4×D4—5312no—
891C4×D4C22×D5316yescomplemented
892C4×D4C22×D53112yescomplemented
893#117—533no—
894#117—536no—
895#117—536no—
896#117—536no—
897#117C22×D5313yescomplemented
898C2×C4⋊C4—536no—
899C2×C4⋊C4—5312no—
900C2×C22⋊C4—5312no—
901C2×C22⋊C4—5312no—
902C2×C22⋊C4—5312no—
903C2×C22⋊C4—5312no—
904C2×C22⋊C4—5324no—
905C2×C22⋊C4—5324no—
906C2×C22⋊C4—5324no—
907C2×C22⋊C4—536no—
908C2×C22⋊C4—534no—
909C2×C22⋊C4C22×D53112yescomplemented
910C2×C42—536no—
911C2×C42—533no—
912C2×C42—533no—
913C2×C42—536no—
914C2×C42—536no—
915C2×C42—533no—
916C2×C42—533no—
917C2×C42—531no—
918C2×C42C22×D5313yescomplemented
919C24—533no—
920C24—536no—
921C24—532no—
922C24—5312no—
923C24—536no—
924C24—10624no—
925C24—21224no—
926C24C23×D5316yes—
927#41—28no—
928#41—224no—
929#41—212no—
930#41—212no—
931#41—538no—
932#41—5324no—
933#41—5324no—
934#41—10624no—
935#41—10624no—
936#41—10648no—
937#41—10624no—
938#41—10624no—
939#41—10624no—
940#41—10612no—
941#41—10624no—
942#41—10612no—
943#41—10612no—
944#41—10612no—
945#41—10648no—
946#41—10624no—
947#41—10624no—
948#41—1068no—
949#41—10624no—
950#41—10612no—
951#41—10612no—
952#41D4×D5318yescomplemented
953C2×Q8—28no—
954C2×Q8—212no—
955C2×Q8—538no—
956C2×Q8—533no—
957C2×Q8—5312no—
958C2×Q8—536no—
959C2×Q8—536no—
960C2×Q8—533no—
961C2×Q8—532no—
962C2×Q8—531no—
963C2×Q8—10624no—
964C2×Q8—10624no—
965C2×Q8—10612no—
966C2×Q8—10624no—
967C2×Q8—10624no—
968C2×Q8—10624no—
969C2×Q8—1064no—
970C2×Q8—10624no—
971C2×Q8—1068no—
972C2×Q8—10612no—
973C2×Q8C23×D5316yes—
974C2×Q8C23×D5313yes—
975C2×Q8C23×D5311yescharacteristic
976C2×Q8C23×D5311yescharacteristic
977C2×D4—224no—
978C2×D4—212no—
979C2×D4—536no—
980C2×D4—5324no—
981C2×D4—536no—
982C2×D4—536no—
983C2×D4—536no—
984C2×D4—536no—
985C2×D4—5312no—
986C2×D4—536no—
987C2×D4—532no—
988C2×D4—5312no—
989C2×D4—5312no—
990C2×D4—533no—
991C2×D4—536no—
992C2×D4—536no—
993C2×D4—536no—
994C2×D4—533no—
995C2×D4—531no—
996C2×D4—5312no—
997C2×D4—10624no—
998C2×D4—10612no—
999C2×D4—10624no—
1000C2×D4—10624no—
1001C2×D4—10624no—
1002C2×D4—1064no—
1003C2×D4—10624no—
1004C2×D4—10648no—
1005C2×D4—10624no—
1006C2×D4—10624no—
1007C2×D4—10624no—
1008C2×D4—10648no—
1009C2×D4—10624no—
1010C2×D4—10612no—
1011C2×D4—21224no—
1012C2×D4C23×D5316yes—
1013C2×D4C23×D5316yes—
1014C2×D4C23×D5316yes—
1015C2×D4C23×D5313yes—
1016C2×D4C23×D5311yescharacteristic
1017C2×D4C23×D53112yes—
1018C2×D4C23×D5313yes—
1019C22×C4—533no—
1020C22×C4—5324no—
1021C22×C4—531no—
1022C22×C4—533no—
1023C22×C4—533no—
1024C22×C4—533no—
1025C22×C4—536no—
1026C22×C4—536no—
1027C22×C4—536no—
1028C22×C4—536no—
1029C22×C4—532no—
1030C22×C4—536no—
1031C22×C4—536no—
1032C22×C4—5312no—
1033C22×C4—532no—
1034C22×C4—536no—
1035C22×C4—536no—
1036C22×C4—536no—
1037C22×C4—536no—
1038C22×C4—536no—
1039C22×C4—536no—
1040C22×C4—10624no—
1041C22×C4—10624no—
1042C22×C4—10624no—
1043C22×C4—21212no—
1044C22×C4C23×D5316yes—
1045C22×C4C23×D5316yes—
1046C22×C4C23×D5316yes—
1047C22×C4C23×D5316yes—
1048C22×C4C23×D5313yes—
1049C4⋊C4—5312no—
1050C4⋊C4—536no—
1051C4⋊C4—5312no—
1052C4⋊C4—5312no—
1053C4⋊C4—5312no—
1054C4⋊C4C23×D5316yes—
1055C4⋊C4C23×D53112yes—
1056C22⋊C4—5312no—
1057C22⋊C4—5324no—
1058C22⋊C4—536no—
1059C22⋊C4—534no—
1060C22⋊C4—5312no—
1061C22⋊C4—5312no—
1062C22⋊C4—5324no—
1063C22⋊C4—5324no—
1064C22⋊C4—5312no—
1065C22⋊C4—534no—
1066C22⋊C4—534no—
1067C22⋊C4C23×D53112yes—
1068C22⋊C4C23×D53124yes—
1069C22⋊C4C23×D5316yes—
1070C22⋊C4C23×D5314yes—
1071C42—532no—
1072C42—531no—
1073C42—536no—
1074C42—533no—
1075C42—536no—
1076C42—536no—
1077C42—536no—
1078C42C23×D5311yescharacteristic
1079C42C23×D5313yes—
1080C42C23×D5316yes—
1081C23—212no—
1082C23—412no—
1083C23—531no—
1084C23—5312no—
1085C23—533no—
1086C23—536no—
1087C23—532no—
1088C23—10612no—
1089C23—10624no—
1090C23—1064no—
1091C23—10612no—
1092C23—1068no—
1093C23—10624no—
1094C23—10612no—
1095C23—42448no—
1096C23—21212no—
1097C23—21224no—
1098C23C24×D5316yes—
1099C23C24×D5312yes—
1100C23C24×D5313yes—
1101Q8—212no—
1102Q8—26no—
1103Q8—22no—
1104Q8—5312no—
1105Q8—10612no—
1106Q8—10624no—
1107Q8—1064no—
1108Q8—10612no—
1109Q8—1066no—
1110Q8—1062no—
1111Q8C2×D4×D5314yes—
1112D4—212no—
1113D4—212no—
1114D4—212no—
1115D4—26no—
1116D4—22no—
1117D4—412no—
1118D4—5324no—
1119D4—5312no—
1120D4—10612no—
1121D4—10612no—
1122D4—10612no—
1123D4—10624no—
1124D4—1064no—
1125D4—10612no—
1126D4—10612no—
1127D4—10612no—
1128D4—10612no—
1129D4—10612no—
1130D4—1066no—
1131D4—1062no—
1132D4—21212no—
1133D4—21212no—
1134D4—21212no—
1135D4C2×D4×D53112yes—
1136C2×C4—212no—
1137C2×C4—212no—
1138C2×C4—212no—
1139C2×C4—46no—
1140C2×C4—5312no—
1141C2×C4—531no—
1142C2×C4—533no—
1143C2×C4—534no—
1144C2×C4—5312no—
1145C2×C4—5312no—
1146C2×C4—5312no—
1147C2×C4—532no—
1148C2×C4—536no—
1149C2×C4—536no—
1150C2×C4—532no—
1151C2×C4—10612no—
1152C2×C4—10612no—
1153C2×C4—1064no—
1154C2×C4—10612no—
1155C2×C4—10624no—
1156C2×C4—1064no—
1157C2×C4—10612no—
1158C2×C4—10612no—
1159C2×C4—10612no—
1160C2×C4—10612no—
1161C2×C4—10612no—
1162C2×C4—10612no—
1163C2×C4—2126no—
1164C2×C4—2126no—
1165C2×C4—2126no—
1166C2×C4C2×D4×D53112yes—
1167C2×C4C24×D5312yes—
1168C2×C4C24×D5316yes—
1169C2×C4C24×D5316yes—
1170C2×C4C24×D5312yes—
1171C2×C4C24×D5311yescharacteristic
1172C2×C4C24×D5313yes—
1173C22—26no—
1174C22—22no—
1175C22—26no—
1176C22—24no—
1177C22—212no—
1178C22—812no—
1179C22—532no—
1180C22—534no—
1181C22—536no—
1182C22—10624no—
1183C22—1066no—
1184C22—1062no—
1185C22—1066no—
1186C22—1064no—
1187C22—10612no—
1188C22—42412no—
1189C22—42424no—
1190C22—21224no—
1191C22—2128no—
1192C22C22×D4×D5316yes—
1193C22C25×D5311yescharacteristic
1194C4—22no—
1195C4—26no—
1196C4—22no—
1197C4—26no—
1198C4—532no—
1199C4—536no—
1200C4—1062no—
1201C4—1066no—
1202C4—1062no—
1203C4—1066no—
1204C4C22×D4×D5316yes—
1205C4C22×D4×D5312yes—
1206C2—26no—
1207C2—46no—
1208C2—42no—
1209C2—534no—
1210C2—1066no—
1211C2—2126no—
1212C2—2122no—
1213C2C23×D4×D5311yescharacteristic
1214C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3500C2
hypercenter#3500D53
hypocenterC53C2×#3500
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D53C2semidirect
2. C2×H(5,𝔽2)×D53C2semidirect
3. #20288509C2semidirect
4. #20288508C2semidirect
5. #20288507C2semidirect
6. #20288506C2semidirect
7. #20288505C2semidirect
8. #20288504C2semidirect
9. #20288503C2semidirect
10. #20288502C2semidirect
11. #20288501C2semidirect
12. #548×D53C2semidirect
13. #546×D53C2semidirect
14. #536×D53C2semidirect
15. #535×D53C2semidirect
16. #532×D53C2semidirect
17. C2×#124×D53C2semidirect
18. C4×#41×D53C2semidirect
19. C53×#3500C2semidirect
20. C2×#13133265C22semidirect
21. C2×#13133265C22semidirect
22. C2×#13133264C22semidirect
23. C2×#13133264C22semidirect
24. C2×#13133264C22semidirect
26. C2×#13133263C22semidirect
27. C2×#13133263C22semidirect
28. C2×#13133263C22semidirect
29. C2×#13133262C22semidirect
30. C2×#13133262C22semidirect
35. C2×#41×D53C22semidirect
36. C2×#41×D53C22semidirect
37. C22×Q8×D53C22semidirect
38. C22×Q8×D53C22semidirect
41. #16811285C22semidirect
42. #16811284C22semidirect
43. #16811283C22semidirect
44. #16811282C22semidirect
45. #16811281C22semidirect
46. #16811280C22semidirect
47. #16811279C22semidirect
48. #16811270C22semidirect
49. #16811269C22semidirect
50. #16811268C22semidirect
51. #16811267C22semidirect
52. #16811266C22semidirect
53. #16811265C22semidirect
54. #16811264C22semidirect
55. #16811263C22semidirect
56. #16811262C22semidirect
57. #16811261C22semidirect
58. #16811260C22semidirect
59. #16811199C22semidirect
60. #16811198C22semidirect
61. #16811197C22semidirect
62. #16811196C22semidirect
63. #16811195C22semidirect
64. #16811194C22semidirect
65. #16811193C22semidirect
66. #16811192C22semidirect
67. #16811191C22semidirect
68. #16811190C22semidirect
69. #16811189C22semidirect
70. #16811188C22semidirect
71. #16811187C22semidirect
72. #16811186C22semidirect
73. #16811174C22semidirect
74. #16811173C22semidirect
75. #16811172C22semidirect
76. #16811172C22semidirect
77. #16811171C22semidirect
78. #16811170C22semidirect
79. #16811169C22semidirect
80. #16811169C22semidirect
81. #16811168C22semidirect
82. C4⋊Q8×D53C22semidirect
83. #127×D53C22semidirect
84. C2×#13133206C22semidirect
85. C2×#13133205C22semidirect
86. C2×#13133204C22semidirect
87. C2×#13133203C22semidirect
88. #124×D53C22semidirect
89. #124×D53C22semidirect
90. #124×D53C22semidirect
91. #124×D53C22semidirect
92. #124×D53C22semidirect
93. #124×D53C22semidirect
94. #124×D53C22semidirect
95. #123×D53C22semidirect
96. C22⋊Q8×D53C22semidirect
97. #121×D53C22semidirect
98. #121×D53C22semidirect
99. #120×D53C22semidirect
100. #41×Dic53C22semidirect
101. C4×#11719949C22semidirect
102. C4×#11719945C22semidirect
103. #16811091C22semidirect
104. C4×#11719947C22semidirect
105. C4×Q8×D53C22semidirect
106. C4×D4×D53C22semidirect
107. C4×D4×D53C22semidirect
108. #117×D53C22semidirect
109. C2×C22⋊C4×D53C22semidirect
110. C2×C42×D53C22semidirect
111. C2×2−1+4×C53C22semidirect
112. C2×H(5,𝔽2)×C53C22semidirect
113. C53×#548C22semidirect
114. C53×#546C22semidirect
115. C53×#536C22semidirect
116. C53×#535C22semidirect
117. C53×#532C22semidirect
118. C2×#124×C53C22semidirect
119. C4×#41×C53C22semidirect
134. C2×#11719949C23semidirect
135. C2×#11719949C23semidirect
140. C2×#11719945C23semidirect
141. C2×#11719945C23semidirect
142. C2×#11719945C23semidirect
143. C2×#11719945C23semidirect
148. C2×#11719947C23semidirect
149. C2×#11719947C23semidirect
150. C2×#11719947C23semidirect
151. C2×#11719947C23semidirect
156. #41×D53D4semidirect
157. C22×Dic106C23semidirect
158. C22×Dic106C23semidirect
159. C22×Dic106C23semidirect
166. C2×Q8×D53C23semidirect
167. C2×Q8×D53C23semidirect
168. C2×Q8×D53C23semidirect
169. C2×Q8×D53C23semidirect
193. #13133217C23semidirect
194. #13133216C23semidirect
195. #13133215C23semidirect
196. #13133215C23semidirect
197. #13133214C23semidirect
198. #13133213C23semidirect
199. #13133213C23semidirect
200. #13133213C23semidirect
201. #13133206C23semidirect
202. #13133206C23semidirect
203. #13133206C23semidirect
204. #13133206C23semidirect
205. #13133205C23semidirect
206. #13133205C23semidirect
207. #13133205C23semidirect
208. #13133205C23semidirect
209. #13133204C23semidirect
210. #13133204C23semidirect
211. #13133204C23semidirect
212. #13133204C23semidirect
213. #13133203C23semidirect
214. #13133203C23semidirect
215. #13133203C23semidirect
216. #13133203C23semidirect
217. #13133203C23semidirect
218. #13133202C23semidirect
219. #13133201C23semidirect
220. #13133200C23semidirect
221. #13133199C23semidirect
222. #13133198C23semidirect
223. #13133197C23semidirect
224. #13133196C23semidirect
225. #13133195C23semidirect
226. #13133194C23semidirect
227. #13133193C23semidirect
228. #13133192C23semidirect
229. #13133192C23semidirect
230. #13133191C23semidirect
231. #13133191C23semidirect
232. #13133190C23semidirect
233. #13133190C23semidirect
234. #13133190C23semidirect
235. #13133189C23semidirect
236. #13133189C23semidirect
237. #13133189C23semidirect
238. #13133188C23semidirect
239. #13133188C23semidirect
240. #13133187C23semidirect
241. #13133187C23semidirect
242. #13133186C23semidirect
243. #13133185C23semidirect
244. #13133185C23semidirect
245. Q8×Dic53C23semidirect
246. C4×Dic106C23semidirect
247. #13133182C23semidirect
248. C4×D212C23semidirect
249. C4×D212C23semidirect
250. D4×Dic53C23semidirect
251. D4×Dic53C23semidirect
252. #13133179C23semidirect
253. #13133179C23semidirect
254. C4×C22⋊D53C23semidirect
255. C4×C22⋊D53C23semidirect
256. C4×C22⋊D53C23semidirect
257. #13133177C23semidirect
258. #13133177C23semidirect
259. #13133177C23semidirect
260. #13133176C23semidirect
261. #13133175C23semidirect
262. #13133174C23semidirect
263. #13133173C23semidirect
266. C2×C22⋊Dic53C23semidirect
267. C2×#11719921C23semidirect
268. C2×#11719921C23semidirect
273. C22⋊C4×D53C23semidirect
274. C22⋊C4×D53C23semidirect
275. C2×C4×Dic53C23semidirect
276. C2×C4×Dic53C23semidirect
280. C42×D53C23semidirect
281. C42×D53C23semidirect
282. C42×D53C23semidirect
288. C2×#41×C53C23semidirect
289. C2×#41×C53C23semidirect
290. C22×Q8×C53C23semidirect
291. C22×Q8×C53C23semidirect
294. C4⋊Q8×C53C23semidirect
295. #127×C53C23semidirect
296. #124×C53C23semidirect
297. #124×C53C23semidirect
298. #124×C53C23semidirect
299. #124×C53C23semidirect
300. #123×C53C23semidirect
301. C22⋊Q8×C53C23semidirect
302. #121×C53C23semidirect
303. #121×C53C23semidirect
304. #120×C53C23semidirect
305. C4×Q8×C53C23semidirect
306. C4×D4×C53C23semidirect
307. C4×D4×C53C23semidirect
308. #117×C53C23semidirect
309. C2×C22⋊C4×C53C23semidirect
310. C2×C42×C53C23semidirect
323. #41×C53C2×D4semidirect
365. #11719949C2×D4semidirect
381. #11719947C2×D4semidirect
401. #11719945C2×D4semidirect
610. #3500D53direct (N × H)
626. D53#3500direct (N × H)
633. C2×2−1+4C2×D53semidirect
640. C2×H(5,𝔽2)C2×D53semidirect
657. #548C2×D53semidirect
669. #546C2×D53semidirect
677. #536C2×D53semidirect
685. #535C2×D53semidirect
695. #532C2×D53semidirect
709. C2×#124C2×D53semidirect
720. C4×#41C2×D53semidirect
727. C53C2×#3500semidirect
770. C2×#41C22×D53semidirect
771. C2×#41C22×D53semidirect
785. C22×Q8C22×D53semidirect
786. C22×Q8C22×D53semidirect
816. C4⋊Q8C22×D53semidirect
821. #127C22×D53semidirect
839. #124C22×D53semidirect
840. #124C22×D53semidirect
841. #124C22×D53semidirect
842. #124C22×D53semidirect
848. #123C22×D53semidirect
854. C22⋊Q8C22×D53semidirect
867. #121C22×D53semidirect
868. #121C22×D53semidirect
874. #120C22×D53semidirect
878. C4×Q8C22×D53semidirect
891. C4×D4C22×D53semidirect
892. C4×D4C22×D53semidirect
897. #117C22×D53semidirect
909. C2×C22⋊C4C22×D53semidirect
918. C2×C42C22×D53semidirect
952. #41D4×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×H(5,𝔽2)×D532
#202885092
#202885082
#202885072
#202885062
#202885052
#202885042
#202885032
#202885022
#202885012
#548×D532
#546×D532
#536×D532
#535×D532
#532×D532
C2×#124×D532
C4×#41×D532
C53×#35002
C2×#350053