Finite Group Databasebeta

← C53×#23850 #27231362

Subgroups — C53×#23850 #27231362

Order 13568.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C53C211yesmaximal, characteristic, complemented
2C2×C53×#546C211yesmaximal, characteristic, complemented
3C2×C53×#449C211yesmaximal, characteristic, complemented
4C2×C53×#450C211yesmaximal, characteristic, complemented
5C2×C53×#447C211yesmaximal, characteristic, complemented
6C53×#2407C211yesmaximal, characteristic, complemented
7C53×#2015C211yesmaximal, characteristic, complemented
8C53×#2012C211yesmaximal, characteristic, complemented
9C53×#2001C211yesmaximal, characteristic, complemented
10C53×#2000C211yesmaximal, characteristic, complemented
11C53×#1893C211yesmaximal, characteristic, complemented
12C53×#1879C211yesmaximal, characteristic, complemented
13C53×#1877C211yesmaximal, characteristic, complemented
14C53×#1869C211yesmaximal, characteristic, complemented
15C53×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C53C2211yescharacteristic
17C22×#41×C53C2211yescharacteristic, complemented
18C23×D4×C53C2211yescharacteristic
19C2×#135×C53—24no—
20C2×#135×C53—24no—
21C2×#135×C53—24no—
22C22×Q16×C53C2211yescharacteristic, complemented
23C22×SD16×C53C2211yescharacteristic
24C22×SD16×C53C2211yescharacteristic
25C22×SD16×C53C2211yescharacteristic, complemented
26C22×D8×C53C2211yescharacteristic
27C22×D8×C53C2211yescharacteristic
28C23×C8×C53C2211yescharacteristic, complemented
29C53×#546—24no—
30C53×#546—24no—
31C2×#124×C53C2211yescharacteristic
32C2×#123×C53—21no—
33C2×C22⋊Q8×C53C2211yescharacteristic
34C2×C22⋊Q8×C53C2211yescharacteristic
35C2×#121×C53—21no—
36C2×#121×C53C2211yescharacteristic
37C2×#121×C53C2211yescharacteristic
38C2×#120×C53—21no—
39C2×C4×D4×C53C2211yescharacteristic
40C2×C4×D4×C53C2211yescharacteristic
41C22×C22⋊C4×C53—21no—
42C53×#450—24no—
43C53×#449—24no—
44C53×#447—24no—
45C2×#103×C53C2211yescharacteristic, complemented
46C2×#103×C53C2211yescharacteristic, complemented
47C2×#103×C53C2211yescharacteristic, complemented
48C2×#102×C53C2211yescharacteristic
49C2×#102×C53C2211yescharacteristic
50C2×#102×C53C2211yescharacteristic
51C2×#102×C53C2211yescharacteristic
52C2×#102×C53C2211yescharacteristic, complemented
53C2×C22⋊C8×C53C2211yescharacteristic
54C2×C22⋊C8×C53C2211yescharacteristic
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—
68C2×#41×C53—22no—
69C2×#41×C53—22no—
70C2×#41×C53—22no—
71C2×#41×C53—22no—
72C2×#41×C53—22no—
73C2×#41×C53—22no—
74C2×#41×C53—22no—
75C2×#41×C53—41no—
76C2×#41×C53—41no—
77C2×#41×C53—41no—
78C2×#41×C53—41no—
79C2×#41×C53D414yescomplemented
80C22×Q8×C53C2311yescharacteristic
81C22×Q8×C53C2311yescharacteristic
82C22×D4×C53—21no—
83C22×D4×C53—21no—
84C22×D4×C53—22no—
85C22×D4×C53—22no—
86C22×D4×C53—22no—
87C22×D4×C53—22no—
88C22×D4×C53—21no—
89C22×D4×C53—21no—
90C22×D4×C53—21no—
91C22×D4×C53—41no—
92C22×D4×C53—41no—
93C22×D4×C53D411yescharacteristic
94C22×D4×C53C2311yescharacteristic
95C22×D4×C53C2311yescharacteristic
96C22×D4×C53C2311yescharacteristic
97C23×C4×C53—21no—
98C23×C4×C53—21no—
99C23×C4×C53—21no—
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102#135×C53—232no—
103C2×Q16×C53—22no—
104C2×Q16×C53—22no—
105C2×Q16×C53—22no—
106C2×SD16×C53—22no—
107C2×SD16×C53—22no—
108C2×SD16×C53—22no—
109C2×SD16×C53—22no—
110C2×SD16×C53—22no—
111C2×SD16×C53—22no—
112C2×SD16×C53—22no—
113C2×SD16×C53—41no—
114C2×SD16×C53D414yescomplemented
115C2×D8×C53—22no—
116C2×D8×C53—22no—
117C2×D8×C53—22no—
118C2×D8×C53—22no—
119C2×D8×C53—41no—
120C2×D8×C53D414yescomplemented
121C22×C8×C53—22no—
122C22×C8×C53—22no—
123C22×C8×C53—22no—
124C22×C8×C53C2311yescharacteristic
125C22×C8×C53C2311yescharacteristic
126C22×C8×C53C2311yescharacteristic
127C22×C8×C53C2311yescharacteristic
128#124×C53—22no—
129#124×C53—22no—
130#123×C53—28no—
131C22⋊Q8×C53—22no—
132C22⋊Q8×C53—22no—
133C22⋊Q8×C53—22no—
134C22⋊Q8×C53—41no—
135#121×C53—28no—
136#121×C53—22no—
137#121×C53—22no—
138#121×C53—41no—
139#121×C53D414yescomplemented
140#120×C53—28no—
141C4×D4×C53—22no—
142C4×D4×C53—22no—
143C4×D4×C53—22no—
144C4×D4×C53—22no—
145C2×C4⋊C4×C53—21no—
146C2×C4⋊C4×C53—21no—
147C2×C4⋊C4×C53D411yescharacteristic
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C4⋊C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—28no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53—21no—
154C2×C22⋊C4×C53—21no—
155C2×C22⋊C4×C53—21no—
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×C53D411yescharacteristic
163C2×C22⋊C4×C53D411yescharacteristic
164C2×C42×C53C2311yescharacteristic
165#103×C53—22no—
166#103×C53—41no—
167#103×C53—41no—
168#102×C53—22no—
169#102×C53—22no—
170#102×C53—22no—
171#102×C53—22no—
172#102×C53—22no—
173C22⋊C8×C53—22no—
174C22⋊C8×C53—22no—
175C22⋊C8×C53—22no—
176#95×C53—21no—
177#95×C53—21no—
178#95×C53—21no—
179C24×C53—21no—
180C24×C53—24no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—42no—
184C24×C53—42no—
185C24×C53—42no—
186C24×C53—42no—
187C24×C53—81no—
188C24×C53—81no—
189C24×C53C2×D411yescharacteristic
190C24×C53C2×D411yescharacteristic
191#41×C53—28no—
192#41×C53—28no—
193#41×C53—44no—
194#41×C53—44no—
195#41×C53—44no—
196#41×C53—44no—
197#41×C53—44no—
198#41×C53—44no—
199C2×Q8×C53—21no—
200C2×Q8×C53—21no—
201C2×Q8×C53—21no—
202C2×Q8×C53—21no—
203C2×Q8×C53—21no—
204C2×Q8×C53—21no—
205C2×Q8×C53—21no—
206C2×Q8×C53—21no—
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53C2×D412yes—
210C2×Q8×C53C2×D412yes—
211C2×D4×C53—24no—
212C2×D4×C53—22no—
213C2×D4×C53—24no—
214C2×D4×C53—22no—
215C2×D4×C53—24no—
216C2×D4×C53—21no—
217C2×D4×C53—21no—
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
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—41no—
230C2×D4×C53—42no—
231C2×D4×C53—42no—
232C2×D4×C53—42no—
233C2×D4×C53—44no—
234C2×D4×C53—44no—
235C2×D4×C53—44no—
236C2×D4×C53—42no—
237C2×D4×C53—42no—
238C2×D4×C53—42no—
239C2×D4×C53—42no—
240C2×D4×C53—44no—
241C2×D4×C53—42no—
242C2×D4×C53—42no—
243C2×D4×C53—81no—
244C2×D4×C53—81no—
245C2×D4×C53—81no—
246C2×D4×C53C2×D412yes—
247C2×D4×C53C2×D412yes—
248C2×D4×C53C2×D412yes—
249C2×D4×C53C2×D412yes—
250C2×D4×C53C2×D412yes—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—21no—
255C22×C4×C53—21no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—24no—
259C22×C4×C53—24no—
260C22×C4×C53—21no—
261C22×C4×C53—21no—
262C22×C4×C53—21no—
263C22×C4×C53—21no—
264C22×C4×C53—21no—
265C22×C4×C53—21no—
266C22×C4×C53—21no—
267C22×C4×C53—21no—
268C22×C4×C53—42no—
269C22×C4×C53—42no—
270C22×C4×C53—42no—
271C22×C4×C53—42no—
272C22×C4×C53—42no—
273C22×C4×C53—81no—
274C22×C4×C53—81no—
275C22×C4×C53C2×D411yescharacteristic
276C22×C4×C53C2×D411yescharacteristic
277C22×C4×C53C2×D411yescharacteristic
278C22×C4×C53C2×D411yescharacteristic
279C22×C4×C53C2×D412yes—
280C22×C4×C53C2×D412yes—
281C22×C4×C53C2411yescharacteristic
282Q16×C53—28no—
283SD16×C53—28no—
284SD16×C53—28no—
285SD16×C53—44no—
286D8×C53—28no—
287D8×C53—44no—
288C2×C8×C53—28no—
289C2×C8×C53—21no—
290C2×C8×C53—21no—
291C2×C8×C53—21no—
292C2×C8×C53—21no—
293C2×C8×C53—21no—
294C2×C8×C53—21no—
295C2×C8×C53—21no—
296C2×C8×C53—21no—
297C2×C8×C53—21no—
298C2×C8×C53—21no—
299C2×C8×C53C2×D412yes—
300C2×C8×C53C2×D412yes—
301C4⋊C4×C53—24no—
302C4⋊C4×C53—22no—
303C4⋊C4×C53—21no—
304C4⋊C4×C53—21no—
305C4⋊C4×C53—21no—
306C4⋊C4×C53—21no—
307C4⋊C4×C53—21no—
308C4⋊C4×C53—42no—
309C4⋊C4×C53C2×D412yes—
310C22⋊C4×C53—24no—
311C22⋊C4×C53—24no—
312C22⋊C4×C53—24no—
313C22⋊C4×C53—24no—
314C22⋊C4×C53—22no—
315C22⋊C4×C53—22no—
316C22⋊C4×C53—24no—
317C22⋊C4×C53—42no—
318C22⋊C4×C53—42no—
319C22⋊C4×C53—42no—
320C22⋊C4×C53—81no—
321C22⋊C4×C53—81no—
322C42×C53—21no—
323C42×C53—21no—
324C23×C53—22no—
325C23×C53—21no—
326C23×C53—21no—
327C23×C53—21no—
328C23×C53—21no—
329C23×C53—21no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53—21no—
335C23×C53—21no—
336C23×C53—21no—
337C23×C53—21no—
338C23×C53—21no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53—48no—
342C23×C53—48no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—84no—
360C23×C53—84no—
361C23×C53—84no—
362C23×C53—84no—
363C23×C53—84no—
364C23×C53#12012yes—
365C23×C53#13512yescomplemented
366C23×C53C22×D411yescharacteristic
367Q8×C53—22no—
368Q8×C53—22no—
369Q8×C53—22no—
370Q8×C53—22no—
371Q8×C53—41no—
372Q8×C53—41no—
373Q8×C53—41no—
374Q8×C53—41no—
375D4×C53—22no—
376D4×C53—22no—
377D4×C53—22no—
378D4×C53—22no—
379D4×C53—22no—
380D4×C53—22no—
381D4×C53—22no—
382D4×C53—44no—
383D4×C53—48no—
384D4×C53—48no—
385D4×C53—48no—
386D4×C53—41no—
387D4×C53—41no—
388D4×C53—41no—
389D4×C53—41no—
390D4×C53—84no—
391D4×C53—84no—
392D4×C53#12014yes—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—22no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—22no—
399C2×C4×C53—21no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—21no—
403C2×C4×C53—21no—
404C2×C4×C53—21no—
405C2×C4×C53—21no—
406C2×C4×C53—22no—
407C2×C4×C53—21no—
408C2×C4×C53—21no—
409C2×C4×C53—21no—
410C2×C4×C53—21no—
411C2×C4×C53—48no—
412C2×C4×C53—48no—
413C2×C4×C53—41no—
414C2×C4×C53—41no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—84no—
430C2×C4×C53#12012yes—
431C2×C4×C53C22×D411yescharacteristic
432C2×C4×C53C22×D411yescharacteristic
433C2×C4×C53C22×D411yescharacteristic
434C2×C4×C53C22×D411yescharacteristic
435C2×C4×C53H(5,𝔽2)11yescharacteristic
436C2×C4×C53H(5,𝔽2)11yescharacteristic
437C8×C53—22no—
438C8×C53—22no—
439C8×C53—41no—
440C8×C53—41no—
441#23850C5311yesmaximal, characteristic, direct product factor, Sylow
442C22×C53—22no—
443C22×C53—24no—
444C22×C53—22no—
445C22×C53—22no—
446C22×C53—22no—
447C22×C53—22no—
448C22×C53—22no—
449C22×C53—41no—
450C22×C53—42no—
451C22×C53—41no—
452C22×C53—41no—
453C22×C53—42no—
454C22×C53—42no—
455C22×C53—41no—
456C22×C53—41no—
457C22×C53—41no—
458C22×C53—42no—
459C22×C53—41no—
460C22×C53—42no—
461C22×C53—41no—
462C22×C53—42no—
463C22×C53—42no—
464C22×C53—42no—
465C22×C53—42no—
466C22×C53—42no—
467C22×C53—42no—
468C22×C53—42no—
469C22×C53—816no—
470C22×C53—81no—
471C22×C53—81no—
472C22×C53—81no—
473C22×C53—81no—
474C22×C53—81no—
475C22×C53—81no—
476C22×C53—81no—
477C22×C53—81no—
478C22×C53C2×#12011yescharacteristic
479C22×C53D4211yescharacteristic
480C22×C53D4211yescharacteristic
481C22×C53C2×#13511yescharacteristic
482C22×C53#57511yescharacteristic
483C22×C53#57611yescharacteristic
484C22×C53#57711yescharacteristic
485C4×C53—22no—
486C4×C53—41no—
487C4×C53—42no—
488C4×C53—42no—
489C4×C53—41no—
490C4×C53—41no—
491C4×C53—42no—
492C4×C53—81no—
493C4×C53—81no—
494C4×C53C2×#12011yescharacteristic
495C4×C53#53411yescharacteristic
496C4×C53D4211yescharacteristic
497C4×C53D4211yescharacteristic
498C22×#135C2×C5311yescharacteristic, complemented
499C2×#546C2×C5311yescharacteristic, complemented
500C2×#449C2×C5311yescharacteristic, complemented
501C2×#450C2×C5311yescharacteristic, complemented
502C2×#447C2×C5311yescharacteristic, complemented
503#2407C2×C5311yescharacteristic, complemented
504#2015C2×C5311yescharacteristic, complemented
505#2012C2×C5311yescharacteristic, complemented
506#2001C2×C5311yescharacteristic, complemented
507#2000C2×C5311yescharacteristic, complemented
508#1893C2×C5311yescharacteristic, complemented
509#1879C2×C5311yescharacteristic, complemented
510#1877C2×C5311yescharacteristic, complemented
511#1869C2×C5311yescharacteristic, complemented
512#1788C2×C5311yescharacteristic, complemented
513C2×C53—42no—
514C2×C53—42no—
515C2×C53—44no—
516C2×C53—82no—
517C2×C53—82no—
518C2×C53#240311yescharacteristic
519C2×C53#300211yescharacteristic
520C2×C53#301211yescharacteristic
521C2×C53#326711yescharacteristic
522C2×C53#326811yescharacteristic
523C2×C53#328011yescharacteristic
524C2×C53#328211yescharacteristic
525C22×#41C22×C5311yescharacteristic
526C22×#41C22×C5311yescharacteristic, complemented
527C23×D4C22×C5311yescharacteristic
528C2×#135—24no—
529C2×#135—24no—
530C2×#135—24no—
531C22×Q16C22×C5311yescharacteristic, complemented
532C22×SD16C22×C5311yescharacteristic
533C22×SD16C22×C5311yescharacteristic
534C22×SD16C22×C5311yescharacteristic, complemented
535C22×D8C22×C5311yescharacteristic
536C22×D8C22×C5311yescharacteristic
537C23×C8C22×C5311yescharacteristic, complemented
538#546—24no—
539#546—24no—
540C2×#124C22×C5311yescharacteristic
541C2×#123—21no—
542C2×C22⋊Q8C22×C5311yescharacteristic
543C2×C22⋊Q8C22×C5311yescharacteristic
544C2×#121—21no—
545C2×#121C22×C5311yescharacteristic
546C2×#121C22×C5311yescharacteristic
547C2×#120—21no—
548C2×C4×D4C22×C5311yescharacteristic
549C2×C4×D4C22×C5311yescharacteristic
550C22×C22⋊C4—21no—
551#450—24no—
552#449—24no—
553#447—24no—
554C2×#103C22×C5311yescharacteristic, complemented
555C2×#103C22×C5311yescharacteristic, complemented
556C2×#103C22×C5311yescharacteristic, complemented
557C2×#102C22×C5311yescharacteristic
558C2×#102C22×C5311yescharacteristic
559C2×#102C22×C5311yescharacteristic
560C2×#102C22×C5311yescharacteristic
561C2×#102C22×C5311yescharacteristic, complemented
562C2×C22⋊C8C22×C5311yescharacteristic
563C2×C22⋊C8C22×C5311yescharacteristic
564C2×C22⋊C8C22×C5311yescharacteristic, complemented
565#394—21no—
566#392—21no—
567#391C22×C5311yescharacteristic, complemented
568#390C22×C5311yescharacteristic, complemented
569#386—21no—
570#385—21no—
571#380C22×C5311yescharacteristic, complemented
572#340C22×C5311yescharacteristic, complemented
573#340C22×C5311yescharacteristic, complemented
574#336C22×C5311yescharacteristic, complemented
575#336C22×C5311yescharacteristic, complemented
576C53#2385011yescharacteristic, direct product factor, Sylow
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C5314yescomplemented
590C22×Q8C23×C5311yescharacteristic
591C22×Q8C23×C5311yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C5311yescharacteristic
604C22×D4C23×C5311yescharacteristic
605C22×D4C23×C5311yescharacteristic
606C22×D4C23×C5311yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C5311yescharacteristic
611C23×C4C23×C5311yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C5314yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C5314yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C5311yescharacteristic
635C22×C8C23×C5311yescharacteristic
636C22×C8C23×C5311yescharacteristic
637C22×C8C23×C5311yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C5314yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C5311yescharacteristic
658C2×C4⋊C4C23×C5311yescharacteristic
659C2×C4⋊C4C23×C5311yescharacteristic
660C2×C4⋊C4C23×C5311yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C5311yescharacteristic
673C2×C22⋊C4D4×C5311yescharacteristic
674C2×C42C23×C5311yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C5311yescharacteristic
700C24C2×D4×C5311yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C5312yes—
720C2×Q8C2×D4×C5312yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C5312yes—
757C2×D4C2×D4×C5312yes—
758C2×D4C2×D4×C5312yes—
759C2×D4C2×D4×C5312yes—
760C2×D4C2×D4×C5312yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C5311yescharacteristic
786C22×C4C2×D4×C5311yescharacteristic
787C22×C4C2×D4×C5311yescharacteristic
788C22×C4C2×D4×C5311yescharacteristic
789C22×C4C2×D4×C5312yes—
790C22×C4C2×D4×C5312yes—
791C22×C4C24×C5311yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C5312yes—
810C2×C8C2×D4×C5312yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C5312yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C5312yes—
875C23#135×C5312yescomplemented
876C23C22×D4×C5311yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C5314yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C5312yes—
941C2×C4C22×D4×C5311yescharacteristic
942C2×C4C22×D4×C5311yescharacteristic
943C2×C4C22×D4×C5311yescharacteristic
944C2×C4C22×D4×C5311yescharacteristic
945C2×C4H(5,𝔽2)×C5311yescharacteristic
946C2×C4H(5,𝔽2)×C5311yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—41no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C5311yescharacteristic
988C22D42×C5311yescharacteristic
989C22D42×C5311yescharacteristic
990C22C2×#135×C5311yescharacteristic
991C22C53×#57511yescharacteristic
992C22C53×#57611yescharacteristic
993C22C53×#57711yescharacteristic
994C4—22no—
995C4—41no—
996C4—41no—
997C4—42no—
998C4—41no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C5311yescharacteristic
1004C4C53×#53411yescharacteristic
1005C4D42×C5311yescharacteristic
1006C4D42×C5311yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2C53×#240311yescharacteristic
1013C2C53×#300211yescharacteristic
1014C2C53×#301211yescharacteristic
1015C2C53×#326711yescharacteristic
1016C2C53×#326811yescharacteristic
1017C2C53×#328011yescharacteristic
1018C2C53×#328211yescharacteristic
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×#135×C53C2semidirect
2. C2×C53×#546C2semidirect
3. C2×C53×#449C2semidirect
4. C2×C53×#450C2semidirect
5. C2×C53×#447C2semidirect
6. C53×#2407C2semidirect
7. C53×#2015C2semidirect
8. C53×#2012C2semidirect
9. C53×#2001C2semidirect
10. C53×#2000C2semidirect
11. C53×#1893C2semidirect
12. C53×#1879C2semidirect
13. C53×#1877C2semidirect
14. C53×#1869C2semidirect
15. C53×#1788C2semidirect
17. C22×#41×C53C22semidirect
22. C22×Q16×C53C22semidirect
25. C22×SD16×C53C22semidirect
28. C23×C8×C53C22semidirect
45. C2×#103×C53C22semidirect
46. C2×#103×C53C22semidirect
47. C2×#103×C53C22semidirect
52. C2×#102×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
79. C2×#41×C53D4semidirect
114. C2×SD16×C53D4semidirect
120. C2×D8×C53D4semidirect
139. #121×C53D4semidirect
365. C23×C53#135semidirect
441. #23850C53direct (N × H)
498. C22×#135C2×C53semidirect
499. C2×#546C2×C53semidirect
500. C2×#449C2×C53semidirect
501. C2×#450C2×C53semidirect
502. C2×#447C2×C53semidirect
503. #2407C2×C53semidirect
504. #2015C2×C53semidirect
505. #2012C2×C53semidirect
506. #2001C2×C53semidirect
507. #2000C2×C53semidirect
508. #1893C2×C53semidirect
509. #1879C2×C53semidirect
510. #1877C2×C53semidirect
511. #1869C2×C53semidirect
512. #1788C2×C53semidirect
526. C22×#41C22×C53semidirect
531. C22×Q16C22×C53semidirect
534. C22×SD16C22×C53semidirect
537. C23×C8C22×C53semidirect
554. C2×#103C22×C53semidirect
555. C2×#103C22×C53semidirect
556. C2×#103C22×C53semidirect
561. C2×#102C22×C53semidirect
564. C2×C22⋊C8C22×C53semidirect
567. #391C22×C53semidirect
568. #390C22×C53semidirect
571. #380C22×C53semidirect
572. #340C22×C53semidirect
573. #340C22×C53semidirect
574. #336C22×C53semidirect
575. #336C22×C53semidirect
576. C53#23850direct (N × H)
589. C2×#41D4×C53semidirect
624. C2×SD16D4×C53semidirect
630. C2×D8D4×C53semidirect
649. #121D4×C53semidirect
875. C23#135×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C532
C2×C53×#5462
C2×C53×#4492
C2×C53×#4502
C2×C53×#4472
C53×#24072
C53×#20152
C53×#20122
C53×#20012
C53×#20002
C53×#18932
C53×#18792
C53×#18772
C53×#18692
C53×#17882
#2385053