Finite Group Databasebeta

← C53×#24140 #27231652

Subgroups — C53×#24140 #27231652

Order 13568.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#3505C211yesmaximal, characteristic, complemented
2C53×#2848C211yesmaximal, characteristic, complemented
3C53×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C53C211yesmaximal, characteristic, complemented
5C53×#2044C212yesmaximal, complemented
6C53×#2021C212yesmaximal, complemented
7C53×#1996C211yesmaximal, characteristic, complemented
8C53×#1964C211yesmaximal, characteristic, complemented
9C53×#1889C212yesmaximal, complemented
10C53×#1867C212yesmaximal, complemented
11C53×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C53C2211yescharacteristic
13C53×#553—21no—
14C53×#553—22no—
15C53×#552—21no—
16C53×#551—22no—
17C53×#548—21no—
18C53×#546—21no—
19C53×#539—21no—
20C53×#538—21no—
21C53×#534C2212yes—
22C53×#529—21no—
23C53×#525—21no—
24C2×C22⋊Q8×C53—21no—
25C2×C22⋊Q8×C53C2211yescharacteristic
26C2×#121×C53—21no—
27C2×#121×C53C2211yescharacteristic
28C2×#120×C53C2211yescharacteristic
29C2×#120×C53C2212yes—
30C53×#518C2212yes—
31C2×C4×D4×C53—21no—
32C2×C4×D4×C53C2211yescharacteristic
33C2×#99×C53C2212yes—
34C2×#99×C53C2212yes—
35C2×#99×C53C2212yes—
36C53×#386—21no—
37C53×#386—22no—
38C53×#386C2211yescharacteristic
39C53×#386C2212yes—
40C53×#385—21no—
41C53×#385—22no—
42C53×#385C2211yescharacteristic
43C53×#385C2212yes—
44C53×#380—21no—
45C53×#380—21no—
46C53×#380C2211yescharacteristic
47C53×#380C2211yescharacteristic
48C53×#379C2212yes—
49C53×#379C2211yescharacteristic
50C4×C22⋊C4×C53—21no—
51C4×C22⋊C4×C53C2211yescharacteristic
52C53×#342C2212yes—
53C53×#342C2212yes—
54C53×#342C2212yes—
55C25×C53C2311yescharacteristic
56C2×#41×C53—21no—
57C22×Q8×C53D411yescharacteristic, complemented
58C22×D4×C53—21no—
59C22×D4×C53—22no—
60C22×D4×C53D411yescharacteristic, complemented
61C22×D4×C53C2311yescharacteristic
62C22×D4×C53C2312yes—
63C23×C4×C53—21no—
64C23×C4×C53—21no—
65C23×C4×C53—21no—
66C23×C4×C53—21no—
67C23×C4×C53—21no—
68C23×C4×C53—21no—
69C23×C4×C53—44no—
70C23×C4×C53D411yescharacteristic, complemented
71C23×C4×C53C2311yescharacteristic
72C23×C4×C53C2311yescharacteristic
73#126×C53—22no—
74#126×C53—22no—
75#126×C53—22no—
76#125×C53—21no—
77#125×C53—22no—
78#124×C53—21no—
79#124×C53—22no—
80#123×C53—22no—
81#123×C53—22no—
82#123×C53—22no—
83#123×C53—22no—
84#123×C53—22no—
85C22⋊Q8×C53—21no—
86C22⋊Q8×C53—22no—
87C22⋊Q8×C53—21no—
88C22⋊Q8×C53—21no—
89C22⋊Q8×C53—21no—
90C22⋊Q8×C53—21no—
91C22⋊Q8×C53—44no—
92#121×C53—21no—
93#121×C53—22no—
94#121×C53—21no—
95#121×C53—21no—
96#121×C53—21no—
97#121×C53—21no—
98#121×C53—22no—
99#121×C53—22no—
100#121×C53—44no—
101#120×C53—22no—
102#120×C53—22no—
103#120×C53—22no—
104#120×C53—22no—
105#120×C53—24no—
106#120×C53—42no—
107C4×Q8×C53—21no—
108C4×D4×C53—22no—
109C4×D4×C53—21no—
110C4×D4×C53—21no—
111C4×D4×C53—21no—
112C4×D4×C53—21no—
113C4×D4×C53—21no—
114C4×D4×C53—22no—
115C4×D4×C53—22no—
116C4×D4×C53—22no—
117C4×D4×C53—22no—
118C4×D4×C53—44no—
119#117×C53—21no—
120#117×C53—22no—
121#117×C53—22no—
122C2×C4⋊C4×C53—21no—
123C2×C4⋊C4×C53—21no—
124C2×C4⋊C4×C53—21no—
125C2×C4⋊C4×C53—22no—
126C2×C4⋊C4×C53D411yescharacteristic, complemented
127C2×C4⋊C4×C53D411yescharacteristic, complemented
128C2×C4⋊C4×C53D411yescharacteristic, complemented
129C2×C4⋊C4×C53D412yescomplemented
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—21no—
134C2×C22⋊C4×C53—21no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—21no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53D411yescharacteristic, complemented
140C2×C22⋊C4×C53D412yescomplemented
141C2×C22⋊C4×C53C2312yes—
142C2×C22⋊C4×C53C2311yescharacteristic
143C2×C22⋊C4×C53C2312yes—
144C2×C22⋊C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53C2311yescharacteristic
146C2×C22⋊C4×C53C2312yes—
147C2×C42×C53—21no—
148C2×C42×C53D411yescharacteristic, complemented
149#99×C53—24no—
150#99×C53—42no—
151#99×C53—42no—
152#95×C53—21no—
153#95×C53—21no—
154#95×C53—21no—
155#95×C53—22no—
156#95×C53—22no—
157#95×C53—21no—
158#95×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—42no—
166C24×C53—42no—
167C24×C53C2×D412yes—
168C24×C53C2×D411yescharacteristic
169C24×C53#4112yescomplemented
170C24×C53C2411yescharacteristic
171#41×C53—82no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53—42no—
175C2×D4×C53—24no—
176C2×D4×C53—21no—
177C2×D4×C53—22no—
178C2×D4×C53—21no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—22no—
184C2×D4×C53—21no—
185C2×D4×C53—22no—
186C2×D4×C53—21no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—22no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—42no—
193C2×D4×C53—42no—
194C2×D4×C53—42no—
195C2×D4×C53—44no—
196C2×D4×C53—44no—
197C2×D4×C53—44no—
198C22×C4×C53—24no—
199C22×C4×C53—24no—
200C22×C4×C53—24no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—42no—
213C22×C4×C53—42no—
214C22×C4×C53—42no—
215C22×C4×C53—42no—
216C22×C4×C53—42no—
217C22×C4×C53—42no—
218C22×C4×C53—42no—
219C22×C4×C53—42no—
220C22×C4×C53—42no—
221C22×C4×C53—42no—
222C22×C4×C53—42no—
223C22×C4×C53—42no—
224C22×C4×C53—41no—
225C22×C4×C53—41no—
226C22×C4×C53—41no—
227C22×C4×C53—41no—
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D412yes—
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2×D411yescharacteristic
236C22×C4×C53C2×D412yes—
237C22×C4×C53C2×D411yescharacteristic
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D411yescharacteristic
240C4⋊C4×C53—22no—
241C4⋊C4×C53—22no—
242C4⋊C4×C53—22no—
243C4⋊C4×C53—22no—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—22no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—22no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—42no—
253C4⋊C4×C53—42no—
254C4⋊C4×C53—42no—
255C4⋊C4×C53—44no—
256C22⋊C4×C53—22no—
257C22⋊C4×C53—22no—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—22no—
260C22⋊C4×C53—22no—
261C22⋊C4×C53—22no—
262C22⋊C4×C53—22no—
263C22⋊C4×C53—21no—
264C22⋊C4×C53—22no—
265C22⋊C4×C53—21no—
266C22⋊C4×C53—22no—
267C22⋊C4×C53—21no—
268C22⋊C4×C53—22no—
269C22⋊C4×C53—21no—
270C22⋊C4×C53—21no—
271C22⋊C4×C53—22no—
272C22⋊C4×C53—22no—
273C22⋊C4×C53—22no—
274C22⋊C4×C53—21no—
275C22⋊C4×C53—22no—
276C22⋊C4×C53—22no—
277C22⋊C4×C53—21no—
278C22⋊C4×C53—44no—
279C22⋊C4×C53—42no—
280C22⋊C4×C53—44no—
281C22⋊C4×C53—42no—
282C22⋊C4×C53—44no—
283C22⋊C4×C53—42no—
284C22⋊C4×C53—44no—
285C22⋊C4×C53#4112yescomplemented
286C42×C53—22no—
287C42×C53—22no—
288C42×C53—21no—
289C42×C53—21no—
290C42×C53—42no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—21no—
301C23×C53—22no—
302C23×C53—21no—
303C23×C53—21no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—41no—
307C23×C53—44no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—44no—
316C23×C53—44no—
317C23×C53—44no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—42no—
321C23×C53—42no—
322C23×C53—41no—
323C23×C53—41no—
324C23×C53—41no—
325C23×C53—41no—
326C23×C53C22×D411yescharacteristic
327C23×C53C22×D411yescharacteristic
328C23×C53C22×D411yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53C2×#4111yescharacteristic
331C23×C53H(5,𝔽2)11yescharacteristic
332C23×C532−1+411yescharacteristic
333Q8×C53—42no—
334Q8×C53—81no—
335D4×C53—48no—
336D4×C53—42no—
337D4×C53—42no—
338D4×C53—41no—
339D4×C53—41no—
340D4×C53—41no—
341D4×C53—42no—
342D4×C53—42no—
343D4×C53—41no—
344D4×C53—42no—
345D4×C53—81no—
346D4×C53—82no—
347D4×C53—82no—
348D4×C53—88no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—21no—
356C2×C4×C53—21no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—21no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—21no—
363C2×C4×C53—21no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—44no—
370C2×C4×C53—44no—
371C2×C4×C53—44no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—44no—
379C2×C4×C53—42no—
380C2×C4×C53—41no—
381C2×C4×C53—42no—
382C2×C4×C53—41no—
383C2×C4×C53—42no—
384C2×C4×C53—42no—
385C2×C4×C53—42no—
386C2×C4×C53—41no—
387C2×C4×C53—42no—
388C2×C4×C53—41no—
389C2×C4×C53—42no—
390C2×C4×C53—41no—
391C2×C4×C53—42no—
392C2×C4×C53—42no—
393C2×C4×C53—81no—
394C2×C4×C53—82no—
395C2×C4×C53—82no—
396C2×C4×C53#12011yescharacteristic
397C2×C4×C53#12011yescharacteristic
398C2×C4×C53#12011yescharacteristic
399C2×C4×C53#12011yescharacteristic
400#24140C5311yesmaximal, characteristic, direct product factor, Sylow
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—24no—
408C22×C53—24no—
409C22×C53—24no—
410C22×C53—41no—
411C22×C53—41no—
412C22×C53—41no—
413C22×C53—41no—
414C22×C53—42no—
415C22×C53—42no—
416C22×C53—42no—
417C22×C53—42no—
418C22×C53—42no—
419C22×C53—42no—
420C22×C53—42no—
421C22×C53—42no—
422C22×C53—42no—
423C22×C53—42no—
424C22×C53—42no—
425C22×C53—42no—
426C22×C53—42no—
427C22×C53—41no—
428C22×C53—42no—
429C22×C53—41no—
430C22×C53—42no—
431C22×C53—42no—
432C22×C53—41no—
433C22×C53—82no—
434C22×C53—81no—
435C22×C53—82no—
436C22×C53C2×#12011yescharacteristic
437C22×C53#52511yescharacteristic
438C22×C53#53711yescharacteristic
439C22×C53#54611yescharacteristic
440C22×C53#54711yescharacteristic
441C22×C53#54811yescharacteristic
442C22×C53#55011yescharacteristic
443C4×C53—21no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—42no—
447C4×C53—41no—
448C4×C53—42no—
449C4×C53—42no—
450C4×C53—41no—
451C4×C53—42no—
452C4×C53—41no—
453C4×C53—42no—
454C4×C53—82no—
455C4×C53—81no—
456C4×C53—82no—
457C4×C53B(4,𝔽2)12yes—
458#3505C2×C5311yescharacteristic, complemented
459#2848C2×C5311yescharacteristic, complemented
460#2847C2×C5311yescharacteristic, complemented
461C4×#120C2×C5311yescharacteristic, complemented
462#2044C2×C5312yescomplemented
463#2021C2×C5312yescomplemented
464#1996C2×C5311yescharacteristic, complemented
465#1964C2×C5311yescharacteristic, complemented
466#1889C2×C5312yescomplemented
467#1867C2×C5312yescomplemented
468#1799C2×C5311yescharacteristic, complemented
469C2×C53—21no—
470C2×C53—21no—
471C2×C53—21no—
472C2×C53—21no—
473C2×C53—21no—
474C2×C53—21no—
475C2×C53—44no—
476C2×C53—81no—
477C2×C53—82no—
478C2×C53#240711yescharacteristic
479C2×C53C2×B(4,𝔽2)11yescharacteristic
480C2×C53#302511yescharacteristic
481C24×C4C22×C5311yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C5312yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C5311yescharacteristic
495C2×#121—21no—
496C2×#121C22×C5311yescharacteristic
497C2×#120C22×C5311yescharacteristic
498C2×#120C22×C5312yes—
499#518C22×C5312yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C5311yescharacteristic
502C2×#99C22×C5312yes—
503C2×#99C22×C5312yes—
504C2×#99C22×C5312yes—
505#386—22no—
506#386—21no—
507#386C22×C5312yes—
508#386C22×C5311yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C5312yes—
512#385C22×C5311yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C5311yescharacteristic
516#380C22×C5311yescharacteristic
517#379C22×C5312yes—
518#379C22×C5311yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C5311yescharacteristic
521#342C22×C5312yes—
522#342C22×C5312yes—
523#342C22×C5312yes—
524C53#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C5311yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C5311yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C5311yescharacteristic, complemented
531C22×D4C23×C5311yescharacteristic
532C22×D4C23×C5312yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C5311yescharacteristic, complemented
541C23×C4C23×C5311yescharacteristic
542C23×C4C23×C5311yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C5311yescharacteristic, complemented
597C2×C4⋊C4D4×C5311yescharacteristic, complemented
598C2×C4⋊C4D4×C5311yescharacteristic, complemented
599C2×C4⋊C4D4×C5312yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C5311yescharacteristic, complemented
610C2×C22⋊C4D4×C5312yescomplemented
611C2×C22⋊C4C23×C5312yes—
612C2×C22⋊C4C23×C5311yescharacteristic
613C2×C22⋊C4C23×C5312yes—
614C2×C22⋊C4C23×C5311yescharacteristic
615C2×C22⋊C4C23×C5312yes—
616C2×C22⋊C4C23×C5311yescharacteristic
617C2×C42—21no—
618C2×C42D4×C5311yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C5312yes—
638C24C2×D4×C5311yescharacteristic
639C24#41×C5312yescomplemented
640C24C24×C5311yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C5311yescharacteristic
699C22×C4C2×D4×C5312yes—
700C22×C4C2×D4×C5311yescharacteristic
701C22×C4C2×D4×C5311yescharacteristic
702C22×C4C2×D4×C5311yescharacteristic
703C22×C4C2×D4×C5311yescharacteristic
704C22×C4C2×D4×C5312yes—
705C22×C4C2×D4×C5311yescharacteristic
706C22×C4C2×D4×C5312yes—
707C22×C4C2×D4×C5311yescharacteristic
708C22×C4C2×D4×C5311yescharacteristic
709C22×C4C2×D4×C5311yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C5312yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C5311yescharacteristic
797C23C22×D4×C5311yescharacteristic
798C23C22×D4×C5311yescharacteristic
799C23C2×#41×C5311yescharacteristic
800C23C2×#41×C5311yescharacteristic
801C23H(5,𝔽2)×C5311yescharacteristic
802C232−1+4×C5311yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C5311yescharacteristic
867C2×C4#120×C5311yescharacteristic
868C2×C4#120×C5311yescharacteristic
869C2×C4#120×C5311yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C5311yescharacteristic
906C22C53×#52511yescharacteristic
907C22C53×#53711yescharacteristic
908C22C53×#54611yescharacteristic
909C22C53×#54711yescharacteristic
910C22C53×#54811yescharacteristic
911C22C53×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C53×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C53×#240711yescharacteristic
937C2C2×C53×B(4,𝔽2)11yescharacteristic
938C2C53×#302511yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC24C24×C53
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#3505C2semidirect
2. C53×#2848C2semidirect
3. C53×#2847C2semidirect
4. C4×#120×C53C2semidirect
5. C53×#2044C2semidirect
6. C53×#2021C2semidirect
7. C53×#1996C2semidirect
8. C53×#1964C2semidirect
9. C53×#1889C2semidirect
10. C53×#1867C2semidirect
11. C53×#1799C2semidirect
57. C22×Q8×C53D4semidirect
60. C22×D4×C53D4semidirect
70. C23×C4×C53D4semidirect
126. C2×C4⋊C4×C53D4semidirect
127. C2×C4⋊C4×C53D4semidirect
128. C2×C4⋊C4×C53D4semidirect
129. C2×C4⋊C4×C53D4semidirect
139. C2×C22⋊C4×C53D4semidirect
140. C2×C22⋊C4×C53D4semidirect
148. C2×C42×C53D4semidirect
169. C24×C53#41semidirect
285. C22⋊C4×C53#41semidirect
400. #24140C53direct (N × H)
458. #3505C2×C53semidirect
459. #2848C2×C53semidirect
460. #2847C2×C53semidirect
461. C4×#120C2×C53semidirect
462. #2044C2×C53semidirect
463. #2021C2×C53semidirect
464. #1996C2×C53semidirect
465. #1964C2×C53semidirect
466. #1889C2×C53semidirect
467. #1867C2×C53semidirect
468. #1799C2×C53semidirect
524. C53#24140direct (N × H)
527. C22×Q8D4×C53semidirect
530. C22×D4D4×C53semidirect
540. C23×C4D4×C53semidirect
596. C2×C4⋊C4D4×C53semidirect
597. C2×C4⋊C4D4×C53semidirect
598. C2×C4⋊C4D4×C53semidirect
599. C2×C4⋊C4D4×C53semidirect
609. C2×C22⋊C4D4×C53semidirect
610. C2×C22⋊C4D4×C53semidirect
618. C2×C42D4×C53semidirect
639. C24#41×C53semidirect
755. C22⋊C4#41×C53semidirect

Maximal subgroups

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

subgroupindex
C53×#35052
C53×#28482
C53×#28472
C4×#120×C532
C53×#20442
C53×#20212
C53×#19962
C53×#19642
C53×#18892
C53×#18672
C53×#17992
#2414053