Finite Group Databasebeta

← C53×#23860 #27231372

Subgroups — C53×#23860 #27231372

Order 13568.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C53C211yesmaximal, characteristic, complemented
2C2×D42×C53C211yesmaximal, characteristic, complemented
3C2×C53×#449C211yesmaximal, characteristic, complemented
4C2×C53×#450C211yesmaximal, characteristic, complemented
5C2×C53×#447C211yesmaximal, characteristic, complemented
6C53×#2407C211yesmaximal, characteristic, complemented
7C53×#2014C211yesmaximal, characteristic, complemented
8C53×#2011C211yesmaximal, characteristic, complemented
9C53×#2000C211yesmaximal, characteristic, complemented
10C53×#1999C211yesmaximal, characteristic, complemented
11C53×#1895C211yesmaximal, characteristic, complemented
12C53×#1879C211yesmaximal, characteristic, complemented
13C53×#1877C211yesmaximal, characteristic, complemented
14C53×#1870C211yesmaximal, characteristic, complemented
15C53×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C53C2211yescharacteristic, complemented
17C23×D4×C53—21no—
18C23×D4×C53C2211yescharacteristic
19C23×D4×C53C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C53—24no—
21C2×AGL(1,ℤ/8)×C53—24no—
22C2×AGL(1,ℤ/8)×C53—24no—
23C22×SD16×C53C2211yescharacteristic
24C22×SD16×C53C2211yescharacteristic, complemented
25C22×SD16×C53C2211yescharacteristic, complemented
26C22×D8×C53C2211yescharacteristic
27C22×D8×C53C2211yescharacteristic, complemented
28C22×D8×C53C2211yescharacteristic, complemented
29C22×M16×C53C2211yescharacteristic, complemented
30D42×C53—24no—
31D42×C53—24no—
32C2×#127×C53C2211yescharacteristic
33C2×C22⋊Q8×C53C2211yescharacteristic, complemented
34C2×#121×C53—21no—
35C2×#121×C53C2211yescharacteristic
36C2×#121×C53C2211yescharacteristic
37C2×#121×C53C2211yescharacteristic, complemented
38C2×#120×C53—21no—
39C2×#120×C53—21no—
40C2×C4×D4×C53C2211yescharacteristic
41C2×C4×D4×C53C2211yescharacteristic
42C53×#450—24no—
43C53×#449—24no—
44C53×#447—24no—
45C2×#103×C53C2211yescharacteristic, complemented
46C2×#102×C53C2211yescharacteristic
47C2×#102×C53C2211yescharacteristic
48C2×#102×C53C2211yescharacteristic, complemented
49C2×#102×C53C2211yescharacteristic, complemented
50C2×#102×C53C2211yescharacteristic, complemented
51C2×#102×C53C2211yescharacteristic, complemented
52C2×#102×C53C2211yescharacteristic, complemented
53C2×C22⋊C8×C53C2211yescharacteristic, complemented
54C2×C22⋊C8×C53C2211yescharacteristic, complemented
55C2×C22⋊C8×C53C2211yescharacteristic, complemented
56C53×#394—21no—
57C53×#392—21no—
58C53×#391C2211yescharacteristic, complemented
59C53×#390C2211yescharacteristic, complemented
60C53×#386—21no—
61C53×#385—21no—
62C53×#380C2211yescharacteristic, complemented
63C53×#340C2211yescharacteristic, complemented
64C53×#340C2211yescharacteristic, complemented
65C53×#336C2211yescharacteristic, complemented
66C53×#336C2211yescharacteristic, complemented
67C25×C53—21no—
68C25×C53—21no—
69C2×#41×C53—22no—
70C2×#41×C53—22no—
71C2×#41×C53—22no—
72C2×#41×C53—22no—
73C2×#41×C53—41no—
74C2×#41×C53—41no—
75C22×Q8×C53C2311yescharacteristic
76C22×D4×C53—22no—
77C22×D4×C53—22no—
78C22×D4×C53—28no—
79C22×D4×C53—21no—
80C22×D4×C53—21no—
81C22×D4×C53—22no—
82C22×D4×C53—22no—
83C22×D4×C53—22no—
84C22×D4×C53—22no—
85C22×D4×C53—21no—
86C22×D4×C53—21no—
87C22×D4×C53—21no—
88C22×D4×C53—21no—
89C22×D4×C53—21no—
90C22×D4×C53—22no—
91C22×D4×C53—21no—
92C22×D4×C53—41no—
93C22×D4×C53—41no—
94C22×D4×C53—41no—
95C22×D4×C53—41no—
96C22×D4×C53—44no—
97C22×D4×C53—44no—
98C22×D4×C53D411yescharacteristic
99C22×D4×C53D414yescomplemented
100C22×D4×C53C2311yescharacteristic
101C22×D4×C53C2311yescharacteristic
102C22×D4×C53C2311yescharacteristic
103C22×D4×C53C2311yescharacteristic
104C23×C4×C53—21no—
105C23×C4×C53—21no—
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108AGL(1,ℤ/8)×C53—232no—
109C2×SD16×C53—22no—
110C2×SD16×C53—22no—
111C2×SD16×C53—22no—
112C2×SD16×C53—22no—
113C2×SD16×C53—22no—
114C2×SD16×C53—22no—
115C2×SD16×C53—22no—
116C2×SD16×C53—41no—
117C2×SD16×C53D414yescomplemented
118C2×D8×C53—22no—
119C2×D8×C53—22no—
120C2×D8×C53—22no—
121C2×D8×C53—22no—
122C2×D8×C53—22no—
123C2×D8×C53—22no—
124C2×D8×C53—22no—
125C2×D8×C53—41no—
126C2×D8×C53D414yescomplemented
127C2×M16×C53—22no—
128C2×M16×C53—22no—
129C2×M16×C53—22no—
130C22×C8×C53C2311yescharacteristic
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134#127×C53—22no—
135#127×C53—22no—
136C22⋊Q8×C53—22no—
137C22⋊Q8×C53—41no—
138#121×C53—28no—
139#121×C53—22no—
140#121×C53—22no—
141#121×C53—22no—
142#121×C53—22no—
143#121×C53—41no—
144#121×C53D414yescomplemented
145#120×C53—28no—
146#120×C53—28no—
147C4×D4×C53—22no—
148C4×D4×C53—22no—
149C4×D4×C53—22no—
150C4×D4×C53—22no—
151C2×C4⋊C4×C53—21no—
152C2×C4⋊C4×C53D411yescharacteristic
153C2×C4⋊C4×C53C2311yescharacteristic
154C2×C4⋊C4×C53C2311yescharacteristic
155C2×C4⋊C4×C53C2311yescharacteristic
156C2×C22⋊C4×C53—21no—
157C2×C22⋊C4×C53—21no—
158C2×C22⋊C4×C53—21no—
159C2×C22⋊C4×C53—21no—
160C2×C22⋊C4×C53—21no—
161C2×C22⋊C4×C53—21no—
162C2×C22⋊C4×C53—21no—
163C2×C22⋊C4×C53—21no—
164C2×C22⋊C4×C53D411yescharacteristic
165C2×C22⋊C4×C53D411yescharacteristic
166C2×C42×C53C2311yescharacteristic
167#103×C53—22no—
168#102×C53—22no—
169#102×C53—22no—
170#102×C53—22no—
171#102×C53—22no—
172#102×C53—22no—
173#102×C53—41no—
174#102×C53—41no—
175C22⋊C8×C53—22no—
176C22⋊C8×C53—22no—
177C22⋊C8×C53—22no—
178#95×C53—21no—
179#95×C53—21no—
180#95×C53—21no—
181C24×C53—21no—
182C24×C53—24no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—24no—
187C24×C53—42no—
188C24×C53—42no—
189C24×C53—42no—
190C24×C53—42no—
191C24×C53—42no—
192C24×C53—42no—
193C24×C53—42no—
194C24×C53—42no—
195C24×C53—81no—
196C24×C53—81no—
197C24×C53—81no—
198C24×C53—81no—
199C24×C53C2×D411yescharacteristic
200C24×C53C2×D411yescharacteristic
201#41×C53—28no—
202#41×C53—44no—
203#41×C53—44no—
204#41×C53—44no—
205C2×Q8×C53—21no—
206C2×Q8×C53—21no—
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53—21no—
210C2×Q8×C53C2×D412yescomplemented
211C2×D4×C53—22no—
212C2×D4×C53—22no—
213C2×D4×C53—28no—
214C2×D4×C53—24no—
215C2×D4×C53—24no—
216C2×D4×C53—24no—
217C2×D4×C53—24no—
218C2×D4×C53—24no—
219C2×D4×C53—24no—
220C2×D4×C53—22no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—21no—
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—21no—
232C2×D4×C53—21no—
233C2×D4×C53—21no—
234C2×D4×C53—21no—
235C2×D4×C53—21no—
236C2×D4×C53—21no—
237C2×D4×C53—21no—
238C2×D4×C53—21no—
239C2×D4×C53—44no—
240C2×D4×C53—44no—
241C2×D4×C53—44no—
242C2×D4×C53—42no—
243C2×D4×C53—42no—
244C2×D4×C53—42no—
245C2×D4×C53—42no—
246C2×D4×C53—42no—
247C2×D4×C53—42no—
248C2×D4×C53—44no—
249C2×D4×C53—44no—
250C2×D4×C53—432no—
251C2×D4×C53—44no—
252C2×D4×C53—42no—
253C2×D4×C53—42no—
254C2×D4×C53—42no—
255C2×D4×C53—42no—
256C2×D4×C53—42no—
257C2×D4×C53—42no—
258C2×D4×C53—44no—
259C2×D4×C53—42no—
260C2×D4×C53—42no—
261C2×D4×C53—42no—
262C2×D4×C53—81no—
263C2×D4×C53—81no—
264C2×D4×C53—81no—
265C2×D4×C53C2×D412yes—
266C2×D4×C53C2×D412yes—
267C2×D4×C53C2×D412yes—
268C2×D4×C53C2×D412yes—
269C2×D4×C53C2×D412yes—
270C2×D4×C53C2×D412yescomplemented
271C22×C4×C53—21no—
272C22×C4×C53—21no—
273C22×C4×C53—21no—
274C22×C4×C53—21no—
275C22×C4×C53—24no—
276C22×C4×C53—21no—
277C22×C4×C53—21no—
278C22×C4×C53—21no—
279C22×C4×C53—21no—
280C22×C4×C53—21no—
281C22×C4×C53—21no—
282C22×C4×C53—21no—
283C22×C4×C53—21no—
284C22×C4×C53—21no—
285C22×C4×C53—21no—
286C22×C4×C53—42no—
287C22×C4×C53—42no—
288C22×C4×C53—42no—
289C22×C4×C53—42no—
290C22×C4×C53—42no—
291C22×C4×C53C2×D411yescharacteristic
292C22×C4×C53C2×D411yescharacteristic
293C22×C4×C53C2×D411yescharacteristic
294C22×C4×C53C2×D412yes—
295C22×C4×C53C2×D412yes—
296C22×C4×C53C2×D411yescharacteristic
297C22×C4×C53C2411yescharacteristic
298SD16×C53—28no—
299SD16×C53—28no—
300SD16×C53—44no—
301D8×C53—28no—
302D8×C53—28no—
303D8×C53—44no—
304M16×C53—28no—
305C2×C8×C53—21no—
306C2×C8×C53—21no—
307C2×C8×C53—21no—
308C2×C8×C53—21no—
309C2×C8×C53—21no—
310C2×C8×C53—21no—
311C2×C8×C53—21no—
312C2×C8×C53—21no—
313C2×C8×C53—21no—
314C2×C8×C53—21no—
315C2×C8×C53C2×D412yescomplemented
316C2×C8×C53C2×D412yescomplemented
317C4⋊C4×C53—22no—
318C4⋊C4×C53—21no—
319C4⋊C4×C53—21no—
320C4⋊C4×C53—21no—
321C4⋊C4×C53—21no—
322C4⋊C4×C53—21no—
323C4⋊C4×C53—42no—
324C4⋊C4×C53C2×D412yes—
325C22⋊C4×C53—24no—
326C22⋊C4×C53—24no—
327C22⋊C4×C53—22no—
328C22⋊C4×C53—24no—
329C22⋊C4×C53—22no—
330C22⋊C4×C53—42no—
331C22⋊C4×C53—42no—
332C22⋊C4×C53—42no—
333C22⋊C4×C53—81no—
334C22⋊C4×C53—81no—
335C42×C53—21no—
336C42×C53—21no—
337C23×C53—21no—
338C23×C53—22no—
339C23×C53—21no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—21no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—21no—
348C23×C53—21no—
349C23×C53—21no—
350C23×C53—21no—
351C23×C53—21no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—48no—
356C23×C53—48no—
357C23×C53—48no—
358C23×C53—48no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—84no—
382C23×C53—84no—
383C23×C53—84no—
384C23×C53—84no—
385C23×C53—84no—
386C23×C53—84no—
387C23×C53—84no—
388C23×C53—84no—
389C23×C53—84no—
390C23×C53—84no—
391C23×C53#12012yes—
392C23×C53AGL(1,ℤ/8)12yescomplemented
393C23×C53C22×D411yescharacteristic
394Q8×C53—22no—
395Q8×C53—22no—
396Q8×C53—41no—
397Q8×C53—41no—
398D4×C53—28no—
399D4×C53—22no—
400D4×C53—22no—
401D4×C53—22no—
402D4×C53—22no—
403D4×C53—22no—
404D4×C53—22no—
405D4×C53—22no—
406D4×C53—22no—
407D4×C53—22no—
408D4×C53—48no—
409D4×C53—48no—
410D4×C53—48no—
411D4×C53—48no—
412D4×C53—48no—
413D4×C53—48no—
414D4×C53—41no—
415D4×C53—41no—
416D4×C53—41no—
417D4×C53—41no—
418D4×C53—41no—
419D4×C53—41no—
420D4×C53—84no—
421D4×C53—84no—
422D4×C53#12014yes—
423C2×C4×C53—21no—
424C2×C4×C53—21no—
425C2×C4×C53—21no—
426C2×C4×C53—21no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—21no—
433C2×C4×C53—21no—
434C2×C4×C53—21no—
435C2×C4×C53—21no—
436C2×C4×C53—22no—
437C2×C4×C53—21no—
438C2×C4×C53—21no—
439C2×C4×C53—48no—
440C2×C4×C53—48no—
441C2×C4×C53—41no—
442C2×C4×C53—41no—
443C2×C4×C53—41no—
444C2×C4×C53—41no—
445C2×C4×C53—41no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53#12012yes—
456C2×C4×C53AGL(1,ℤ/8)12yescomplemented
457C2×C4×C53C22×D411yescharacteristic
458C2×C4×C53C22×D411yescharacteristic
459C2×C4×C53C22×D411yescharacteristic
460C2×C4×C53C22×D411yescharacteristic
461C2×C4×C53H(5,𝔽2)11yescharacteristic
462C2×C4×C53H(5,𝔽2)11yescharacteristic
463C8×C53—22no—
464C8×C53—22no—
465C8×C53—41no—
466C8×C53—41no—
467#23860C5311yesmaximal, characteristic, direct product factor, Sylow
468C22×C53—22no—
469C22×C53—24no—
470C22×C53—22no—
471C22×C53—22no—
472C22×C53—22no—
473C22×C53—22no—
474C22×C53—22no—
475C22×C53—41no—
476C22×C53—42no—
477C22×C53—41no—
478C22×C53—42no—
479C22×C53—41no—
480C22×C53—42no—
481C22×C53—41no—
482C22×C53—42no—
483C22×C53—41no—
484C22×C53—41no—
485C22×C53—42no—
486C22×C53—41no—
487C22×C53—41no—
488C22×C53—42no—
489C22×C53—42no—
490C22×C53—42no—
491C22×C53—42no—
492C22×C53—42no—
493C22×C53—42no—
494C22×C53—42no—
495C22×C53—42no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—816no—
499C22×C53—816no—
500C22×C53—81no—
501C22×C53—81no—
502C22×C53—81no—
503C22×C53—81no—
504C22×C53—81no—
505C22×C53—81no—
506C22×C53—81no—
507C22×C53—81no—
508C22×C53—81no—
509C22×C53—81no—
510C22×C53—81no—
511C22×C53—81no—
512C22×C53C2×#12011yescharacteristic
513C22×C53D4211yescharacteristic
514C22×C53D4211yescharacteristic
515C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
517C22×C53#57611yescharacteristic
518C22×C53#57711yescharacteristic
519C4×C53—22no—
520C4×C53—22no—
521C4×C53—41no—
522C4×C53—42no—
523C4×C53—42no—
524C4×C53—41no—
525C4×C53—81no—
526C4×C53—81no—
527C4×C53C2×#12011yescharacteristic
528C4×C53#53411yescharacteristic
529C4×C53D4211yescharacteristic
530C4×C53D4211yescharacteristic
531C22×AGL(1,ℤ/8)C2×C5311yescharacteristic, complemented
532C2×D42C2×C5311yescharacteristic, complemented
533C2×#449C2×C5311yescharacteristic, complemented
534C2×#450C2×C5311yescharacteristic, complemented
535C2×#447C2×C5311yescharacteristic, complemented
536#2407C2×C5311yescharacteristic, complemented
537#2014C2×C5311yescharacteristic, complemented
538#2011C2×C5311yescharacteristic, complemented
539#2000C2×C5311yescharacteristic, complemented
540#1999C2×C5311yescharacteristic, complemented
541#1895C2×C5311yescharacteristic, complemented
542#1879C2×C5311yescharacteristic, complemented
543#1877C2×C5311yescharacteristic, complemented
544#1870C2×C5311yescharacteristic, complemented
545#1786C2×C5311yescharacteristic, complemented
546C2×C53—42no—
547C2×C53—42no—
548C2×C53—44no—
549C2×C53—82no—
550C2×C53—82no—
551C2×C53—82no—
552C2×C53#240311yescharacteristic
553C2×C53#300311yescharacteristic
554C2×C53#301211yescharacteristic
555C2×C53#326411yescharacteristic
556C2×C53#326511yescharacteristic
557C2×C53#327211yescharacteristic
558C2×C53#327411yescharacteristic
559C22×#41C22×C5311yescharacteristic, complemented
560C23×D4—21no—
561C23×D4C22×C5311yescharacteristic
562C23×D4C22×C5311yescharacteristic
563C2×AGL(1,ℤ/8)—24no—
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C22×SD16C22×C5311yescharacteristic
567C22×SD16C22×C5311yescharacteristic, complemented
568C22×SD16C22×C5311yescharacteristic, complemented
569C22×D8C22×C5311yescharacteristic
570C22×D8C22×C5311yescharacteristic, complemented
571C22×D8C22×C5311yescharacteristic, complemented
572C22×M16C22×C5311yescharacteristic, complemented
573D42—24no—
574D42—24no—
575C2×#127C22×C5311yescharacteristic
576C2×C22⋊Q8C22×C5311yescharacteristic, complemented
577C2×#121—21no—
578C2×#121C22×C5311yescharacteristic
579C2×#121C22×C5311yescharacteristic
580C2×#121C22×C5311yescharacteristic, complemented
581C2×#120—21no—
582C2×#120—21no—
583C2×C4×D4C22×C5311yescharacteristic
584C2×C4×D4C22×C5311yescharacteristic
585#450—24no—
586#449—24no—
587#447—24no—
588C2×#103C22×C5311yescharacteristic, complemented
589C2×#102C22×C5311yescharacteristic
590C2×#102C22×C5311yescharacteristic
591C2×#102C22×C5311yescharacteristic, complemented
592C2×#102C22×C5311yescharacteristic, complemented
593C2×#102C22×C5311yescharacteristic, complemented
594C2×#102C22×C5311yescharacteristic, complemented
595C2×#102C22×C5311yescharacteristic, complemented
596C2×C22⋊C8C22×C5311yescharacteristic, complemented
597C2×C22⋊C8C22×C5311yescharacteristic, complemented
598C2×C22⋊C8C22×C5311yescharacteristic, complemented
599#394—21no—
600#392—21no—
601#391C22×C5311yescharacteristic, complemented
602#390C22×C5311yescharacteristic, complemented
603#386—21no—
604#385—21no—
605#380C22×C5311yescharacteristic, complemented
606#340C22×C5311yescharacteristic, complemented
607#340C22×C5311yescharacteristic, complemented
608#336C22×C5311yescharacteristic, complemented
609#336C22×C5311yescharacteristic, complemented
610C53#2386011yescharacteristic, direct product factor, Sylow
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C5311yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C5311yescharacteristic
643C22×D4D4×C5314yescomplemented
644C22×D4C23×C5311yescharacteristic
645C22×D4C23×C5311yescharacteristic
646C22×D4C23×C5311yescharacteristic
647C22×D4C23×C5311yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C5311yescharacteristic
651C23×C4C23×C5311yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C5314yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C5314yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C5311yescharacteristic
675C22×C8C23×C5311yescharacteristic
676C22×C8C23×C5311yescharacteristic
677C22×C8C23×C5311yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C5314yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C5311yescharacteristic
697C2×C4⋊C4C23×C5311yescharacteristic
698C2×C4⋊C4C23×C5311yescharacteristic
699C2×C4⋊C4C23×C5311yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C5311yescharacteristic
709C2×C22⋊C4D4×C5311yescharacteristic
710C2×C42C23×C5311yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C5311yescharacteristic
744C24C2×D4×C5311yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C5312yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C5312yes—
810C2×D4C2×D4×C5312yes—
811C2×D4C2×D4×C5312yes—
812C2×D4C2×D4×C5312yes—
813C2×D4C2×D4×C5312yes—
814C2×D4C2×D4×C5312yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C5311yescharacteristic
836C22×C4C2×D4×C5311yescharacteristic
837C22×C4C2×D4×C5311yescharacteristic
838C22×C4C2×D4×C5312yes—
839C22×C4C2×D4×C5312yes—
840C22×C4C2×D4×C5311yescharacteristic
841C22×C4C24×C5311yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C5312yescomplemented
860C2×C8C2×D4×C5312yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C5312yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C5312yes—
936C23AGL(1,ℤ/8)×C5312yescomplemented
937C23C22×D4×C5311yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C5314yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C5312yes—
1000C2×C4AGL(1,ℤ/8)×C5312yescomplemented
1001C2×C4C22×D4×C5311yescharacteristic
1002C2×C4C22×D4×C5311yescharacteristic
1003C2×C4C22×D4×C5311yescharacteristic
1004C2×C4C22×D4×C5311yescharacteristic
1005C2×C4H(5,𝔽2)×C5311yescharacteristic
1006C2×C4H(5,𝔽2)×C5311yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—24no—
1018C22—42no—
1019C22—41no—
1020C22—42no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—42no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C5311yescharacteristic
1056C22D42×C5311yescharacteristic
1057C22D42×C5311yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C5311yescharacteristic
1060C22C53×#57611yescharacteristic
1061C22C53×#57711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—42no—
1065C4—41no—
1066C4—41no—
1067C4—42no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C5311yescharacteristic
1071C4C53×#53411yescharacteristic
1072C4D42×C5311yescharacteristic
1073C4D42×C5311yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2C53×#240311yescharacteristic
1081C2C53×#300311yescharacteristic
1082C2C53×#301211yescharacteristic
1083C2C53×#326411yescharacteristic
1084C2C53×#326511yescharacteristic
1085C2C53×#327211yescharacteristic
1086C2C53×#327411yescharacteristic
subgroupG/H
center, socleC23×C53C22×D4
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C53 ◁ C2×C4×D4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C53C2semidirect
2. C2×D42×C53C2semidirect
3. C2×C53×#449C2semidirect
4. C2×C53×#450C2semidirect
5. C2×C53×#447C2semidirect
6. C53×#2407C2semidirect
7. C53×#2014C2semidirect
8. C53×#2011C2semidirect
9. C53×#2000C2semidirect
10. C53×#1999C2semidirect
11. C53×#1895C2semidirect
12. C53×#1879C2semidirect
13. C53×#1877C2semidirect
14. C53×#1870C2semidirect
15. C53×#1786C2semidirect
16. C22×#41×C53C22semidirect
24. C22×SD16×C53C22semidirect
25. C22×SD16×C53C22semidirect
27. C22×D8×C53C22semidirect
28. C22×D8×C53C22semidirect
29. C22×M16×C53C22semidirect
33. C2×C22⋊Q8×C53C22semidirect
37. C2×#121×C53C22semidirect
45. C2×#103×C53C22semidirect
48. C2×#102×C53C22semidirect
49. C2×#102×C53C22semidirect
50. C2×#102×C53C22semidirect
51. C2×#102×C53C22semidirect
52. C2×#102×C53C22semidirect
53. C2×C22⋊C8×C53C22semidirect
54. C2×C22⋊C8×C53C22semidirect
55. C2×C22⋊C8×C53C22semidirect
58. C53×#391C22semidirect
59. C53×#390C22semidirect
62. C53×#380C22semidirect
63. C53×#340C22semidirect
64. C53×#340C22semidirect
65. C53×#336C22semidirect
66. C53×#336C22semidirect
99. C22×D4×C53D4semidirect
117. C2×SD16×C53D4semidirect
126. C2×D8×C53D4semidirect
144. #121×C53D4semidirect
210. C2×Q8×C53C2×D4semidirect
270. C2×D4×C53C2×D4semidirect
315. C2×C8×C53C2×D4semidirect
316. C2×C8×C53C2×D4semidirect
392. C23×C53AGL(1,ℤ/8)semidirect
456. C2×C4×C53AGL(1,ℤ/8)semidirect
467. #23860C53direct (N × H)
531. C22×AGL(1,ℤ/8)C2×C53semidirect
532. C2×D42C2×C53semidirect
533. C2×#449C2×C53semidirect
534. C2×#450C2×C53semidirect
535. C2×#447C2×C53semidirect
536. #2407C2×C53semidirect
537. #2014C2×C53semidirect
538. #2011C2×C53semidirect
539. #2000C2×C53semidirect
540. #1999C2×C53semidirect
541. #1895C2×C53semidirect
542. #1879C2×C53semidirect
543. #1877C2×C53semidirect
544. #1870C2×C53semidirect
545. #1786C2×C53semidirect
559. C22×#41C22×C53semidirect
567. C22×SD16C22×C53semidirect
568. C22×SD16C22×C53semidirect
570. C22×D8C22×C53semidirect
571. C22×D8C22×C53semidirect
572. C22×M16C22×C53semidirect
576. C2×C22⋊Q8C22×C53semidirect
580. C2×#121C22×C53semidirect
588. C2×#103C22×C53semidirect
591. C2×#102C22×C53semidirect
592. C2×#102C22×C53semidirect
593. C2×#102C22×C53semidirect
594. C2×#102C22×C53semidirect
595. C2×#102C22×C53semidirect
596. C2×C22⋊C8C22×C53semidirect
597. C2×C22⋊C8C22×C53semidirect
598. C2×C22⋊C8C22×C53semidirect
601. #391C22×C53semidirect
602. #390C22×C53semidirect
605. #380C22×C53semidirect
606. #340C22×C53semidirect
607. #340C22×C53semidirect
608. #336C22×C53semidirect
609. #336C22×C53semidirect
610. C53#23860direct (N × H)
643. C22×D4D4×C53semidirect
661. C2×SD16D4×C53semidirect
670. C2×D8D4×C53semidirect
688. #121D4×C53semidirect
754. C2×Q8C2×D4×C53semidirect
814. C2×D4C2×D4×C53semidirect
859. C2×C8C2×D4×C53semidirect
860. C2×C8C2×D4×C53semidirect
936. C23AGL(1,ℤ/8)×C53semidirect
1000. C2×C4AGL(1,ℤ/8)×C53semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C532
C2×D42×C532
C2×C53×#4492
C2×C53×#4502
C2×C53×#4472
C53×#24072
C53×#20142
C53×#20112
C53×#20002
C53×#19992
C53×#18952
C53×#18792
C53×#18772
C53×#18702
C53×#17862
#2386053