Finite Group Databasebeta

← C53×#23881 #27231393

Subgroups — C53×#23881 #27231393

Order 13568.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#575C211yesmaximal, characteristic, complemented
2C53×#3489C211yesmaximal, characteristic, complemented
3C2×C53×#456C211yesmaximal, characteristic, complemented
4C2×C53×#454C211yesmaximal, characteristic, complemented
5C53×#3005C211yesmaximal, characteristic, complemented
6C53×#2432C211yesmaximal, characteristic, complemented
7C53×#2007C211yesmaximal, characteristic, complemented
8C53×#2006C211yesmaximal, characteristic, complemented
9C53×#2005C211yesmaximal, characteristic, complemented
10C53×#2003C211yesmaximal, characteristic, complemented
11C53×#1901C211yesmaximal, characteristic, complemented
12C53×#1883C211yesmaximal, characteristic, complemented
13C53×#1882C211yesmaximal, characteristic, complemented
14C53×#1871C211yesmaximal, characteristic, complemented
15C53×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C53C2211yescharacteristic
17C22×#41×C53C2211yescharacteristic
18C22×#41×C53C2211yescharacteristic
19C53×#575—24no—
20C53×#575—24no—
21C2×#137×C53—21no—
22C2×#137×C53C2211yescharacteristic
23C2×#137×C53C2211yescharacteristic
24C2×#137×C53C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C53—21no—
26C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C53C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
29C2×#135×C53—21no—
30C2×#135×C53—21no—
31C22×M16×C53C2211yescharacteristic
32D4×Q8×C53—21no—
33C53×#548—21no—
34C53×#547—21no—
35C53×#547—22no—
36C53×#546—21no—
37C53×#546—22no—
38C53×#537—21no—
39C53×#537C2211yescharacteristic
40C53×#536—21no—
41C53×#536C2211yescharacteristic
42C2×C4⋊Q8×C53C2211yescharacteristic, complemented
43C2×#124×C53C2211yescharacteristic, complemented
44C53×#525—21no—
45C53×#525C2211yescharacteristic
46C2×C22⋊Q8×C53—21no—
47C2×C22⋊Q8×C53C2211yescharacteristic
48C53×#520C2211yescharacteristic
49C53×#456—24no—
50C53×#454—24no—
51C53×#452—21no—
52C53×#452—21no—
53C53×#449—21no—
54C53×#449—21no—
55C2×#104×C53C2211yescharacteristic
56C2×#104×C53C2211yescharacteristic
57C2×#104×C53C2211yescharacteristic
58C2×#104×C53C2211yescharacteristic
59C2×#104×C53C2211yescharacteristic, complemented
60C2×#104×C53C2211yescharacteristic, complemented
61C53×#419C2211yescharacteristic, complemented
62C53×#418C2211yescharacteristic, complemented
63C2×#101×C53C2211yescharacteristic, complemented
64C2×#101×C53C2211yescharacteristic, complemented
65C53×#407C2211yescharacteristic
66C53×#394—22no—
67C53×#391C2211yescharacteristic, complemented
68C53×#390C2211yescharacteristic, complemented
69C53×#385—22no—
70C4×C22⋊C4×C53C2211yescharacteristic
71C53×#343C2211yescharacteristic, complemented
72C53×#343C2211yescharacteristic, complemented
73C53×#339C2211yescharacteristic, complemented
74C53×#339C2211yescharacteristic, complemented
752−1+4×C53—22no—
762−1+4×C53—22no—
772−1+4×C53—41no—
782−1+4×C53—41no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—21no—
82C2×#41×C53—22no—
83C2×#41×C53—21no—
84C2×#41×C53—22no—
85C2×#41×C53—22no—
86C2×#41×C53—22no—
87C2×#41×C53—22no—
88C2×#41×C53—21no—
89C2×#41×C53—21no—
90C2×#41×C53—21no—
91C2×#41×C53—21no—
92C2×#41×C53—41no—
93C2×#41×C53—41no—
94C2×#41×C53—41no—
95C2×#41×C53—41no—
96C2×#41×C53D411yescharacteristic
97C2×#41×C53D411yescharacteristic
98C2×#41×C53C2311yescharacteristic
99C2×#41×C53C2311yescharacteristic
100C2×#41×C53C2311yescharacteristic
101C22×Q8×C53—21no—
102C22×Q8×C53—21no—
103C22×Q8×C53D411yescharacteristic
104C22×Q8×C53C2311yescharacteristic
105C22×Q8×C53C2311yescharacteristic
106C22×D4×C53—21no—
107C22×D4×C53—21no—
108C22×D4×C53D411yescharacteristic
109C22×D4×C53C2311yescharacteristic
110C23×C4×C53—21no—
111C23×C4×C53—21no—
112C23×C4×C53C2311yescharacteristic
113#137×C53—28no—
114#137×C53—22no—
115#137×C53—22no—
116#137×C53—22no—
117#137×C53—22no—
118#137×C53—41no—
119#137×C53D414yescomplemented
120AGL(1,ℤ/8)×C53—28no—
121AGL(1,ℤ/8)×C53—22no—
122AGL(1,ℤ/8)×C53—22no—
123AGL(1,ℤ/8)×C53—22no—
124AGL(1,ℤ/8)×C53—22no—
125AGL(1,ℤ/8)×C53—41no—
126AGL(1,ℤ/8)×C53D414yescomplemented
127#135×C53—28no—
128#135×C53—28no—
129C2×Q16×C53—21no—
130C2×Q16×C53—21no—
131C2×Q16×C53—21no—
132C2×SD16×C53—21no—
133C2×SD16×C53—21no—
134C2×SD16×C53—21no—
135C2×SD16×C53—21no—
136C2×SD16×C53—21no—
137C2×SD16×C53—21no—
138C2×D8×C53—21no—
139C2×D8×C53—21no—
140C2×D8×C53—21no—
141C2×M16×C53—22no—
142C2×M16×C53—22no—
143C2×M16×C53—21no—
144C2×M16×C53C2311yescharacteristic
145C2×M16×C53C2311yescharacteristic
146C2×M16×C53C2311yescharacteristic
147C2×M16×C53C2311yescharacteristic
148C22×C8×C53—21no—
149C4⋊Q8×C53—22no—
150C4⋊Q8×C53—21no—
151C4⋊Q8×C53—22no—
152C4⋊Q8×C53—41no—
153#124×C53—22no—
154#124×C53—21no—
155#124×C53—22no—
156#124×C53—41no—
157#123×C53—22no—
158#123×C53—22no—
159#123×C53—22no—
160#123×C53—21no—
161#123×C53—22no—
162C22⋊Q8×C53—22no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53—21no—
166C22⋊Q8×C53—21no—
167C22⋊Q8×C53—21no—
168C22⋊Q8×C53—21no—
169C22⋊Q8×C53—21no—
170C22⋊Q8×C53—21no—
171C22⋊Q8×C53—21no—
172C22⋊Q8×C53—21no—
173C22⋊Q8×C53D411yescharacteristic
174C22⋊Q8×C53D411yescharacteristic
175#121×C53—22no—
176#121×C53—22no—
177#121×C53—22no—
178#121×C53—21no—
179#121×C53—21no—
180#121×C53—22no—
181#121×C53D411yescharacteristic
182#121×C53D411yescharacteristic
183#120×C53—22no—
184#120×C53—21no—
185C4×Q8×C53—21no—
186C4×D4×C53—22no—
187C4×D4×C53—22no—
188C4×D4×C53—21no—
189C4×D4×C53—22no—
190C4×D4×C53—21no—
191C4×D4×C53—21no—
192#117×C53—21no—
193#117×C53C2311yescharacteristic
194C2×C4⋊C4×C53—22no—
195C2×C4⋊C4×C53—21no—
196C2×C4⋊C4×C53—22no—
197C2×C4⋊C4×C53D412yes—
198C2×C4⋊C4×C53C2311yescharacteristic
199C2×C22⋊C4×C53—22no—
200C2×C22⋊C4×C53—21no—
201C2×C22⋊C4×C53—22no—
202C2×C22⋊C4×C53—22no—
203C2×C22⋊C4×C53D412yes—
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206#104×C53—22no—
207#104×C53—22no—
208#104×C53—22no—
209#104×C53—22no—
210#104×C53—41no—
211#104×C53—41no—
212#103×C53—21no—
213#103×C53—21no—
214#102×C53—21no—
215#102×C53—21no—
216#101×C53—22no—
217#101×C53—22no—
218C22⋊C8×C53—21no—
219C22⋊C8×C53—21no—
220#95×C53—21no—
221#95×C53—22no—
222C24×C53—21no—
223C24×C53—21no—
224C24×C53C2×D411yescharacteristic
225#41×C53—21no—
226#41×C53—21no—
227#41×C53—24no—
228#41×C53—24no—
229#41×C53—22no—
230#41×C53—22no—
231#41×C53—21no—
232#41×C53—21no—
233#41×C53—21no—
234#41×C53—21no—
235#41×C53—21no—
236#41×C53—21no—
237#41×C53—21no—
238#41×C53—21no—
239#41×C53—42no—
240#41×C53—42no—
241#41×C53—41no—
242#41×C53—41no—
243#41×C53—42no—
244#41×C53—42no—
245#41×C53—42no—
246#41×C53—42no—
247#41×C53—42no—
248#41×C53—42no—
249#41×C53—44no—
250#41×C53—44no—
251#41×C53—42no—
252#41×C53—42no—
253#41×C53—42no—
254#41×C53—42no—
255#41×C53—42no—
256#41×C53—42no—
257#41×C53C2×D412yes—
258#41×C53C2×D412yes—
259C2×Q8×C53—22no—
260C2×Q8×C53—21no—
261C2×Q8×C53—21no—
262C2×Q8×C53—21no—
263C2×Q8×C53—21no—
264C2×Q8×C53—21no—
265C2×Q8×C53—21no—
266C2×Q8×C53—21no—
267C2×Q8×C53—21no—
268C2×Q8×C53—22no—
269C2×Q8×C53—21no—
270C2×Q8×C53—21no—
271C2×Q8×C53—21no—
272C2×Q8×C53—21no—
273C2×Q8×C53—41no—
274C2×Q8×C53—42no—
275C2×Q8×C53—42no—
276C2×Q8×C53—42no—
277C2×Q8×C53—42no—
278C2×Q8×C53C2×D411yescharacteristic
279C2×Q8×C53C2×D411yescharacteristic
280C2×Q8×C53C2×D412yes—
281C2×Q8×C53C2×D411yescharacteristic
282C2×D4×C53—21no—
283C2×D4×C53—22no—
284C2×D4×C53—22no—
285C2×D4×C53—21no—
286C2×D4×C53—21no—
287C2×D4×C53—21no—
288C2×D4×C53—21no—
289C2×D4×C53—21no—
290C2×D4×C53—22no—
291C2×D4×C53—21no—
292C2×D4×C53—21no—
293C2×D4×C53—21no—
294C2×D4×C53—21no—
295C2×D4×C53—21no—
296C2×D4×C53—21no—
297C2×D4×C53—21no—
298C2×D4×C53—41no—
299C2×D4×C53—42no—
300C2×D4×C53—42no—
301C2×D4×C53—42no—
302C2×D4×C53—42no—
303C2×D4×C53—41no—
304C2×D4×C53—41no—
305C2×D4×C53C2×D411yescharacteristic
306C2×D4×C53C2×D411yescharacteristic
307C2×D4×C53C2×D412yes—
308C2×D4×C53C2×D411yescharacteristic
309C22×C4×C53—21no—
310C22×C4×C53—21no—
311C22×C4×C53—21no—
312C22×C4×C53—21no—
313C22×C4×C53—21no—
314C22×C4×C53—22no—
315C22×C4×C53—22no—
316C22×C4×C53—21no—
317C22×C4×C53—21no—
318C22×C4×C53—21no—
319C22×C4×C53—22no—
320C22×C4×C53—21no—
321C22×C4×C53—21no—
322C22×C4×C53—21no—
323C22×C4×C53—21no—
324C22×C4×C53—21no—
325C22×C4×C53—42no—
326C22×C4×C53—42no—
327C22×C4×C53—42no—
328C22×C4×C53—42no—
329C22×C4×C53—41no—
330C22×C4×C53—41no—
331C22×C4×C53C2×D412yes—
332C22×C4×C53C2×D411yescharacteristic
333C22×C4×C53C2×D411yescharacteristic
334C22×C4×C53C2×D411yescharacteristic
335C22×C4×C53C2×D411yescharacteristic
336C22×C4×C53C2×D411yescharacteristic
337C22×C4×C53C2×D412yes—
338C22×C4×C53C2411yescharacteristic
339Q16×C53—24no—
340Q16×C53—24no—
341Q16×C53—42no—
342SD16×C53—24no—
343SD16×C53—24no—
344SD16×C53—24no—
345SD16×C53—24no—
346SD16×C53—42no—
347SD16×C53—42no—
348D8×C53—24no—
349D8×C53—24no—
350D8×C53—42no—
351M16×C53—24no—
352M16×C53—21no—
353M16×C53—21no—
354M16×C53—21no—
355M16×C53—21no—
356M16×C53—21no—
357M16×C53—21no—
358M16×C53C2×D412yes—
359M16×C53C2×D412yes—
360C2×C8×C53—24no—
361C2×C8×C53—21no—
362C2×C8×C53—21no—
363C2×C8×C53—21no—
364C2×C8×C53—21no—
365C4⋊C4×C53—22no—
366C4⋊C4×C53—22no—
367C4⋊C4×C53—22no—
368C4⋊C4×C53—22no—
369C4⋊C4×C53—21no—
370C4⋊C4×C53—22no—
371C4⋊C4×C53—22no—
372C4⋊C4×C53—21no—
373C4⋊C4×C53—21no—
374C4⋊C4×C53—21no—
375C4⋊C4×C53—44no—
376C4⋊C4×C53C2×D411yescharacteristic
377C4⋊C4×C53C2×D411yescharacteristic
378C22⋊C4×C53—22no—
379C22⋊C4×C53—22no—
380C22⋊C4×C53—22no—
381C22⋊C4×C53—22no—
382C22⋊C4×C53—22no—
383C22⋊C4×C53—21no—
384C22⋊C4×C53—22no—
385C22⋊C4×C53—22no—
386C22⋊C4×C53—21no—
387C22⋊C4×C53—21no—
388C22⋊C4×C53—21no—
389C22⋊C4×C53—21no—
390C22⋊C4×C53—44no—
391C22⋊C4×C53—44no—
392C22⋊C4×C53—42no—
393C42×C53—22no—
394C42×C53—21no—
395C42×C53—21no—
396C42×C53—21no—
397C42×C53—21no—
398C42×C53—21no—
399C23×C53—21no—
400C23×C53—21no—
401C23×C53—21no—
402C23×C53—21no—
403C23×C53—21no—
404C23×C53—22no—
405C23×C53—41no—
406C23×C53—41no—
407C23×C53—42no—
408C23×C53—42no—
409C23×C53—42no—
410C23×C53—42no—
411C23×C53—41no—
412C23×C53—41no—
413C23×C53—81no—
414C23×C53#12011yescharacteristic
415C23×C53#12011yescharacteristic
416C23×C53C22×D411yescharacteristic
417Q8×C53—21no—
418Q8×C53—21no—
419Q8×C53—22no—
420Q8×C53—21no—
421Q8×C53—22no—
422Q8×C53—21no—
423Q8×C53—21no—
424Q8×C53—42no—
425Q8×C53—44no—
426Q8×C53—41no—
427Q8×C53—41no—
428Q8×C53—41no—
429Q8×C53—41no—
430Q8×C53—41no—
431Q8×C53—41no—
432Q8×C53#12012yes—
433D4×C53—22no—
434D4×C53—22no—
435D4×C53—21no—
436D4×C53—22no—
437D4×C53—21no—
438D4×C53—21no—
439D4×C53—22no—
440D4×C53—21no—
441D4×C53—21no—
442D4×C53—42no—
443D4×C53—42no—
444D4×C53—42no—
445D4×C53—42no—
446D4×C53—44no—
447D4×C53—44no—
448D4×C53—44no—
449D4×C53—41no—
450D4×C53—41no—
451D4×C53—41no—
452D4×C53—41no—
453D4×C53—41no—
454D4×C53—41no—
455D4×C53—81no—
456D4×C53—82no—
457D4×C53#12012yes—
458C2×C4×C53—21no—
459C2×C4×C53—21no—
460C2×C4×C53—21no—
461C2×C4×C53—21no—
462C2×C4×C53—21no—
463C2×C4×C53—21no—
464C2×C4×C53—21no—
465C2×C4×C53—21no—
466C2×C4×C53—21no—
467C2×C4×C53—21no—
468C2×C4×C53—21no—
469C2×C4×C53—22no—
470C2×C4×C53—22no—
471C2×C4×C53—22no—
472C2×C4×C53—21no—
473C2×C4×C53—21no—
474C2×C4×C53—22no—
475C2×C4×C53—21no—
476C2×C4×C53—22no—
477C2×C4×C53—21no—
478C2×C4×C53—22no—
479C2×C4×C53—22no—
480C2×C4×C53—22no—
481C2×C4×C53—42no—
482C2×C4×C53—42no—
483C2×C4×C53—42no—
484C2×C4×C53—44no—
485C2×C4×C53—44no—
486C2×C4×C53—44no—
487C2×C4×C53—41no—
488C2×C4×C53—44no—
489C2×C4×C53—41no—
490C2×C4×C53—41no—
491C2×C4×C53—41no—
492C2×C4×C53—41no—
493C2×C4×C53—41no—
494C2×C4×C53—41no—
495C2×C4×C53—41no—
496C2×C4×C53—42no—
497C2×C4×C53—41no—
498C2×C4×C53—41no—
499C2×C4×C53—41no—
500C2×C4×C53—82no—
501C2×C4×C53#12011yescharacteristic
502C2×C4×C53#12011yescharacteristic
503C2×C4×C53C22×D411yescharacteristic
504C2×C4×C53C22×D411yescharacteristic
505C2×C4×C53C22×D411yescharacteristic
506C2×C4×C53C22×D411yescharacteristic
507C2×C4×C53H(5,𝔽2)11yescharacteristic
508C2×C4×C53H(5,𝔽2)11yescharacteristic
509C8×C53—22no—
510C8×C53—22no—
511C8×C53—41no—
512C8×C53—41no—
513#23881C5311yesmaximal, characteristic, direct product factor, Sylow
514C22×C53—21no—
515C22×C53—21no—
516C22×C53—21no—
517C22×C53—21no—
518C22×C53—22no—
519C22×C53—21no—
520C22×C53—21no—
521C22×C53—21no—
522C22×C53—21no—
523C22×C53—44no—
524C22×C53—41no—
525C22×C53—41no—
526C22×C53—41no—
527C22×C53—41no—
528C22×C53—42no—
529C22×C53—41no—
530C22×C53—41no—
531C22×C53—41no—
532C22×C53—41no—
533C22×C53—81no—
534C22×C53—81no—
535C22×C53—82no—
536C22×C53—84no—
537C22×C53—81no—
538C22×C53—81no—
539C22×C53C2×#12011yescharacteristic
540C22×C53D4211yescharacteristic
541C22×C53D4211yescharacteristic
542C4×C53—21no—
543C4×C53—21no—
544C4×C53—22no—
545C4×C53—42no—
546C4×C53—42no—
547C4×C53—41no—
548C4×C53—42no—
549C4×C53—41no—
550C4×C53—42no—
551C4×C53—41no—
552C4×C53—41no—
553C4×C53—81no—
554C4×C53C2×#12011yescharacteristic
555C4×C53#53411yescharacteristic
556C4×C53D4211yescharacteristic
557C4×C53D4211yescharacteristic
558C2×#575C2×C5311yescharacteristic, complemented
559#3489C2×C5311yescharacteristic, complemented
560C2×#456C2×C5311yescharacteristic, complemented
561C2×#454C2×C5311yescharacteristic, complemented
562#3005C2×C5311yescharacteristic, complemented
563#2432C2×C5311yescharacteristic, complemented
564#2007C2×C5311yescharacteristic, complemented
565#2006C2×C5311yescharacteristic, complemented
566#2005C2×C5311yescharacteristic, complemented
567#2003C2×C5311yescharacteristic, complemented
568#1901C2×C5311yescharacteristic, complemented
569#1883C2×C5311yescharacteristic, complemented
570#1882C2×C5311yescharacteristic, complemented
571#1871C2×C5311yescharacteristic, complemented
572#1789C2×C5311yescharacteristic, complemented
573C2×C53—21no—
574C2×C53—21no—
575C2×C53—41no—
576C2×C53—41no—
577C2×C53—42no—
578C2×C53—81no—
579C2×C53—82no—
580C2×C53—81no—
581C2×C53#240311yescharacteristic
582C2×C53#301811yescharacteristic
583C2×C53#302011yescharacteristic
584C2×2−1+4C22×C5311yescharacteristic
585C22×#41C22×C5311yescharacteristic
586C22×#41C22×C5311yescharacteristic
587#575—24no—
588#575—24no—
589C2×#137—21no—
590C2×#137C22×C5311yescharacteristic
591C2×#137C22×C5311yescharacteristic
592C2×#137C22×C5311yescharacteristic, complemented
593C2×AGL(1,ℤ/8)—21no—
594C2×AGL(1,ℤ/8)C22×C5311yescharacteristic
595C2×AGL(1,ℤ/8)C22×C5311yescharacteristic
596C2×AGL(1,ℤ/8)C22×C5311yescharacteristic, complemented
597C2×#135—21no—
598C2×#135—21no—
599C22×M16C22×C5311yescharacteristic
600D4×Q8—21no—
601#548—21no—
602#547—21no—
603#547—22no—
604#546—21no—
605#546—22no—
606#537—21no—
607#537C22×C5311yescharacteristic
608#536—21no—
609#536C22×C5311yescharacteristic
610C2×C4⋊Q8C22×C5311yescharacteristic, complemented
611C2×#124C22×C5311yescharacteristic, complemented
612#525—21no—
613#525C22×C5311yescharacteristic
614C2×C22⋊Q8—21no—
615C2×C22⋊Q8C22×C5311yescharacteristic
616#520C22×C5311yescharacteristic
617#456—24no—
618#454—24no—
619#452—21no—
620#452—21no—
621#449—21no—
622#449—21no—
623C2×#104C22×C5311yescharacteristic
624C2×#104C22×C5311yescharacteristic
625C2×#104C22×C5311yescharacteristic
626C2×#104C22×C5311yescharacteristic
627C2×#104C22×C5311yescharacteristic, complemented
628C2×#104C22×C5311yescharacteristic, complemented
629#419C22×C5311yescharacteristic, complemented
630#418C22×C5311yescharacteristic, complemented
631C2×#101C22×C5311yescharacteristic, complemented
632C2×#101C22×C5311yescharacteristic, complemented
633#407C22×C5311yescharacteristic
634#394—22no—
635#391C22×C5311yescharacteristic, complemented
636#390C22×C5311yescharacteristic, complemented
637#385—22no—
638C4×C22⋊C4C22×C5311yescharacteristic
639#343C22×C5311yescharacteristic, complemented
640#343C22×C5311yescharacteristic, complemented
641#339C22×C5311yescharacteristic, complemented
642#339C22×C5311yescharacteristic, complemented
643C53#2388111yescharacteristic, direct product factor, Sylow
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C5311yescharacteristic
666C2×#41D4×C5311yescharacteristic
667C2×#41C23×C5311yescharacteristic
668C2×#41C23×C5311yescharacteristic
669C2×#41C23×C5311yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C5311yescharacteristic
673C22×Q8C23×C5311yescharacteristic
674C22×Q8C23×C5311yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C5311yescharacteristic
678C22×D4C23×C5311yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C5311yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C5314yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C5314yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C5311yescharacteristic
714C2×M16C23×C5311yescharacteristic
715C2×M16C23×C5311yescharacteristic
716C2×M16C23×C5311yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C5311yescharacteristic
743C22⋊Q8D4×C5311yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C5311yescharacteristic
751#121D4×C5311yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C5311yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C5312yes—
767C2×C4⋊C4C23×C5311yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C5312yes—
773C2×C42C23×C5311yescharacteristic
774C2×C42C23×C5311yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C5311yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C5312yes—
827#41C2×D4×C5312yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C5311yescharacteristic
848C2×Q8C2×D4×C5311yescharacteristic
849C2×Q8C2×D4×C5312yes—
850C2×Q8C2×D4×C5311yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C5311yescharacteristic
875C2×D4C2×D4×C5311yescharacteristic
876C2×D4C2×D4×C5312yes—
877C2×D4C2×D4×C5311yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C5312yes—
901C22×C4C2×D4×C5311yescharacteristic
902C22×C4C2×D4×C5311yescharacteristic
903C22×C4C2×D4×C5311yescharacteristic
904C22×C4C2×D4×C5311yescharacteristic
905C22×C4C2×D4×C5311yescharacteristic
906C22×C4C2×D4×C5312yes—
907C22×C4C24×C5311yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C5312yes—
928M16C2×D4×C5312yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C5311yescharacteristic
946C4⋊C4C2×D4×C5311yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C5311yescharacteristic
984C23#120×C5311yescharacteristic
985C23C22×D4×C5311yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—22no—
989Q8—21no—
990Q8—21no—
991Q8—22no—
992Q8—21no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C5312yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—22no—
1006D4—21no—
1007D4—21no—
1008D4—21no—
1009D4—22no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—42no—
1015D4—44no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C5312yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—41no—
1057C2×C4—44no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C5311yescharacteristic
1071C2×C4#120×C5311yescharacteristic
1072C2×C4C22×D4×C5311yescharacteristic
1073C2×C4C22×D4×C5311yescharacteristic
1074C2×C4C22×D4×C5311yescharacteristic
1075C2×C4C22×D4×C5311yescharacteristic
1076C2×C4H(5,𝔽2)×C5311yescharacteristic
1077C2×C4H(5,𝔽2)×C5311yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—21no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—22no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—42no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C5311yescharacteristic
1108C22D42×C5311yescharacteristic
1109C22D42×C5311yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—41no—
1116C4—41no—
1117C4—42no—
1118C4—41no—
1119C4—42no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C5311yescharacteristic
1123C4C53×#53411yescharacteristic
1124C4D42×C5311yescharacteristic
1125C4D42×C5311yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C53×#240311yescharacteristic
1135C2C53×#301811yescharacteristic
1136C2C53×#302011yescharacteristic
subgroupG/H
center, socleC22×C53C2×#120
commutator, Frattini, cosocleC22×C4C24×C53
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C23×C4×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#575C2semidirect
2. C53×#3489C2semidirect
3. C2×C53×#456C2semidirect
4. C2×C53×#454C2semidirect
5. C53×#3005C2semidirect
6. C53×#2432C2semidirect
7. C53×#2007C2semidirect
8. C53×#2006C2semidirect
9. C53×#2005C2semidirect
10. C53×#2003C2semidirect
11. C53×#1901C2semidirect
12. C53×#1883C2semidirect
13. C53×#1882C2semidirect
14. C53×#1871C2semidirect
15. C53×#1789C2semidirect
24. C2×#137×C53C22semidirect
28. C2×AGL(1,ℤ/8)×C53C22semidirect
42. C2×C4⋊Q8×C53C22semidirect
43. C2×#124×C53C22semidirect
59. C2×#104×C53C22semidirect
60. C2×#104×C53C22semidirect
61. C53×#419C22semidirect
62. C53×#418C22semidirect
63. C2×#101×C53C22semidirect
64. C2×#101×C53C22semidirect
67. C53×#391C22semidirect
68. C53×#390C22semidirect
71. C53×#343C22semidirect
72. C53×#343C22semidirect
73. C53×#339C22semidirect
74. C53×#339C22semidirect
119. #137×C53D4semidirect
126. AGL(1,ℤ/8)×C53D4semidirect
513. #23881C53direct (N × H)
558. C2×#575C2×C53semidirect
559. #3489C2×C53semidirect
560. C2×#456C2×C53semidirect
561. C2×#454C2×C53semidirect
562. #3005C2×C53semidirect
563. #2432C2×C53semidirect
564. #2007C2×C53semidirect
565. #2006C2×C53semidirect
566. #2005C2×C53semidirect
567. #2003C2×C53semidirect
568. #1901C2×C53semidirect
569. #1883C2×C53semidirect
570. #1882C2×C53semidirect
571. #1871C2×C53semidirect
572. #1789C2×C53semidirect
592. C2×#137C22×C53semidirect
596. C2×AGL(1,ℤ/8)C22×C53semidirect
610. C2×C4⋊Q8C22×C53semidirect
611. C2×#124C22×C53semidirect
627. C2×#104C22×C53semidirect
628. C2×#104C22×C53semidirect
629. #419C22×C53semidirect
630. #418C22×C53semidirect
631. C2×#101C22×C53semidirect
632. C2×#101C22×C53semidirect
635. #391C22×C53semidirect
636. #390C22×C53semidirect
639. #343C22×C53semidirect
640. #343C22×C53semidirect
641. #339C22×C53semidirect
642. #339C22×C53semidirect
643. C53#23881direct (N × H)
688. #137D4×C53semidirect
695. AGL(1,ℤ/8)D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#5752
C53×#34892
C2×C53×#4562
C2×C53×#4542
C53×#30052
C53×#24322
C53×#20072
C53×#20062
C53×#20052
C53×#20032
C53×#19012
C53×#18832
C53×#18822
C53×#18712
C53×#17892
#2388153