Finite Group Databasebeta

← C53×#14725 #27222237

Subgroups — C53×#14725 #27222237

Order 13568.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C53C211yesmaximal, characteristic
2C23×C22⋊C4×C53C211yesmaximal, characteristic, complemented
3C2×C53×#394C212yesmaximal, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#380C211yesmaximal, characteristic, complemented
7C2×C53×#379C211yesmaximal, characteristic, complemented
8C53×#1440C212yesmaximal, complemented
9C53×#1439C212yesmaximal, complemented
10C53×#1438C212yesmaximal, complemented
11C53×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C53C2211yescharacteristic
13C23×D4×C53C2211yescharacteristic
14C23×D4×C53C2212yes—
15C24×C4×C53C2211yescharacteristic
16C24×C4×C53C2211yescharacteristic
17C2×#120×C53—24no—
18C2×#120×C53—24no—
19C2×#120×C53—24no—
20C22×C4⋊C4×C53C2212yescomplemented
21C22×C22⋊C4×C53—24no—
22C22×C22⋊C4×C53—28no—
23C22×C22⋊C4×C53C2211yescharacteristic
24C22×C22⋊C4×C53C2212yes—
25C22×C22⋊C4×C53C2212yes—
26C22×C22⋊C4×C53C2212yes—
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C22⋊C4×C53C2212yes—
30C22×C22⋊C4×C53C2212yes—
31C22×C22⋊C4×C53C2211yescharacteristic, complemented
32C22×C22⋊C4×C53C2212yescomplemented
33C22×C22⋊C4×C53C2211yescharacteristic, complemented
34C53×#394—28no—
35C53×#386—24no—
36C53×#386—24no—
37C53×#380—24no—
38C53×#379—24no—
39C2×#95×C53C2212yescomplemented
40C2×#95×C53C2212yescomplemented
41C2×#95×C53C2211yescharacteristic, complemented
42C2×#95×C53C2212yescomplemented
43C2×#95×C53C2211yescharacteristic, complemented
44C2×#95×C53C2212yescomplemented
45C25×C53—24no—
46C25×C53—22no—
47C25×C53—24no—
48C25×C53—22no—
49C25×C53—22no—
50C25×C53—22no—
51C25×C53—22no—
52C25×C53—22no—
53C25×C53—42no—
54C25×C53—42no—
55C25×C53D414yes—
56C25×C53C2311yescharacteristic
57C25×C53C2312yes—
58C25×C53C2311yescharacteristic
59C22×D4×C53—24no—
60C22×D4×C53—24no—
61C22×D4×C53—22no—
62C22×D4×C53—22no—
63C22×D4×C53—22no—
64C22×D4×C53—22no—
65C22×D4×C53—22no—
66C22×D4×C53—22no—
67C22×D4×C53—24no—
68C22×D4×C53—24no—
69C22×D4×C53—24no—
70C22×D4×C53—42no—
71C22×D4×C53—42no—
72C22×D4×C53D414yes—
73C23×C4×C53—22no—
74C23×C4×C53—22no—
75C23×C4×C53—22no—
76C23×C4×C53—24no—
77C23×C4×C53—24no—
78C23×C4×C53—22no—
79C23×C4×C53—22no—
80C23×C4×C53—42no—
81C23×C4×C53—42no—
82C23×C4×C53D414yescomplemented
83C23×C4×C53C2312yes—
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2312yes—
88C23×C4×C53C2312yes—
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91#120×C53—232no—
92C2×C4⋊C4×C53—24no—
93C2×C4⋊C4×C53—24no—
94C2×C4⋊C4×C53—42no—
95C2×C22⋊C4×C53—232no—
96C2×C22⋊C4×C53—24no—
97C2×C22⋊C4×C53—24no—
98C2×C22⋊C4×C53—22no—
99C2×C22⋊C4×C53—22no—
100C2×C22⋊C4×C53—24no—
101C2×C22⋊C4×C53—24no—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—24no—
109C2×C22⋊C4×C53—24no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—24no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C22⋊C4×C53—24no—
115C2×C22⋊C4×C53—24no—
116C2×C22⋊C4×C53—24no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—24no—
120C2×C22⋊C4×C53—24no—
121C2×C22⋊C4×C53—42no—
122C2×C22⋊C4×C53—42no—
123C2×C22⋊C4×C53—42no—
124C2×C22⋊C4×C53—42no—
125C2×C22⋊C4×C53D414yes—
126C2×C22⋊C4×C53D418yescomplemented
127#95×C53—24no—
128#95×C53—22no—
129#95×C53—22no—
130#95×C53—24no—
131#95×C53—24no—
132#95×C53—42no—
133C24×C53—22no—
134C24×C53—22no—
135C24×C53—22no—
136C24×C53—22no—
137C24×C53—28no—
138C24×C53—28no—
139C24×C53—216no—
140C24×C53—216no—
141C24×C53—28no—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—28no—
155C24×C53—28no—
156C24×C53—21no—
157C24×C53—22no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—22no—
164C24×C53—22no—
165C24×C53—22no—
166C24×C53—48no—
167C24×C53—48no—
168C24×C53—48no—
169C24×C53—48no—
170C24×C53—48no—
171C24×C53—48no—
172C24×C53—48no—
173C24×C53—48no—
174C24×C53—48no—
175C24×C53—44no—
176C24×C53—44no—
177C24×C53—48no—
178C24×C53—44no—
179C24×C53—44no—
180C24×C53—44no—
181C24×C53—44no—
182C24×C53C2×D412yes—
183C24×C53C2×D414yes—
184C24×C53C2×D414yes—
185C24×C53C2×D412yes—
186C24×C53C2×D412yes—
187C24×C53C2×D412yes—
188C24×C53C2×D412yes—
189C24×C53#4114yes—
190C24×C53#4112yes—
191C24×C53#4112yes—
192C24×C53#4112yes—
193C24×C53C2411yescharacteristic
194C2×D4×C53—216no—
195C2×D4×C53—28no—
196C2×D4×C53—28no—
197C2×D4×C53—28no—
198C2×D4×C53—48no—
199C2×D4×C53—48no—
200C2×D4×C53—48no—
201C2×D4×C53—48no—
202C2×D4×C53—48no—
203C2×D4×C53—48no—
204C2×D4×C53—44no—
205C2×D4×C53—44no—
206C2×D4×C53—44no—
207C2×D4×C53—44no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—22no—
211C22×C4×C53—28no—
212C22×C4×C53—28no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—22no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—22no—
223C22×C4×C53—22no—
224C22×C4×C53—21no—
225C22×C4×C53—22no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—22no—
230C22×C4×C53—22no—
231C22×C4×C53—22no—
232C22×C4×C53—22no—
233C22×C4×C53—22no—
234C22×C4×C53—22no—
235C22×C4×C53—28no—
236C22×C4×C53—21no—
237C22×C4×C53—22no—
238C22×C4×C53—22no—
239C22×C4×C53—21no—
240C22×C4×C53—22no—
241C22×C4×C53—22no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—22no—
245C22×C4×C53—21no—
246C22×C4×C53—22no—
247C22×C4×C53—21no—
248C22×C4×C53—22no—
249C22×C4×C53—22no—
250C22×C4×C53—22no—
251C22×C4×C53—22no—
252C22×C4×C53—22no—
253C22×C4×C53—44no—
254C22×C4×C53—48no—
255C22×C4×C53—48no—
256C22×C4×C53—48no—
257C22×C4×C53—48no—
258C22×C4×C53—44no—
259C22×C4×C53—44no—
260C22×C4×C53C2×D412yes—
261C22×C4×C53C2×D412yes—
262C22×C4×C53C2×D414yes—
263C22×C4×C53C2×D414yes—
264C22×C4×C53C2×D412yes—
265C22×C4×C53C2×D414yes—
266C4⋊C4×C53—48no—
267C22⋊C4×C53—216no—
268C22⋊C4×C53—216no—
269C22⋊C4×C53—28no—
270C22⋊C4×C53—216no—
271C22⋊C4×C53—48no—
272C22⋊C4×C53—44no—
273C22⋊C4×C53—48no—
274C22⋊C4×C53—44no—
275C22⋊C4×C53—48no—
276C22⋊C4×C53—44no—
277C22⋊C4×C53—44no—
278C23×C53—22no—
279C23×C53—24no—
280C23×C53—22no—
281C23×C53—24no—
282C23×C53—22no—
283C23×C53—24no—
284C23×C53—22no—
285C23×C53—24no—
286C23×C53—24no—
287C23×C53—24no—
288C23×C53—24no—
289C23×C53—24no—
290C23×C53—24no—
291C23×C53—24no—
292C23×C53—24no—
293C23×C53—24no—
294C23×C53—232no—
295C23×C53—24no—
296C23×C53—24no—
297C23×C53—24no—
298C23×C53—24no—
299C23×C53—24no—
300C23×C53—24no—
301C23×C53—24no—
302C23×C53—24no—
303C23×C53—24no—
304C23×C53—24no—
305C23×C53—24no—
306C23×C53—24no—
307C23×C53—24no—
308C23×C53—24no—
309C23×C53—24no—
310C23×C53—24no—
311C23×C53—24no—
312C23×C53—24no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—24no—
317C23×C53—24no—
318C23×C53—432no—
319C23×C53—432no—
320C23×C53—416no—
321C23×C53—416no—
322C23×C53—416no—
323C23×C53—416no—
324C23×C53—432no—
325C23×C53—432no—
326C23×C53—416no—
327C23×C53—42no—
328C23×C53—42no—
329C23×C53—42no—
330C23×C53—42no—
331C23×C53—42no—
332C23×C53—42no—
333C23×C53—42no—
334C23×C53—42no—
335C23×C53—42no—
336C23×C53—42no—
337C23×C53—42no—
338C23×C53—42no—
339C23×C53—42no—
340C23×C53—42no—
341C23×C53—42no—
342C23×C53—42no—
343C23×C53—416no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—42no—
348C23×C53—41no—
349C23×C53—42no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—42no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—42no—
356C23×C53—42no—
357C23×C53—42no—
358C23×C53—42no—
359C23×C53—42no—
360C23×C53—42no—
361C23×C53—42no—
362C23×C53#12014yes—
363C23×C53#12118yes—
364C23×C53#12114yes—
365C23×C53#12114yes—
366C23×C53#12114yes—
367C23×C53#12314yes—
368C23×C53#12314yes—
369C23×C53#12414yes—
370C23×C53C22×D411yescharacteristic
371C23×C53C22×D411yescharacteristic
372C23×C53C22×D411yescharacteristic
373C23×C53C22×D412yes—
374C23×C53C22×D411yescharacteristic
375C23×C53C2×#4111yescharacteristic
376C23×C53C2×#4111yescharacteristic
377C23×C53C2×#4111yescharacteristic
378C23×C53C2×#4112yes—
379C23×C53H(5,𝔽2)12yes—
380C23×C53H(5,𝔽2)12yes—
381D4×C53—432no—
382D4×C53—416no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—24no—
386C2×C4×C53—24no—
387C2×C4×C53—24no—
388C2×C4×C53—22no—
389C2×C4×C53—22no—
390C2×C4×C53—24no—
391C2×C4×C53—22no—
392C2×C4×C53—22no—
393C2×C4×C53—22no—
394C2×C4×C53—22no—
395C2×C4×C53—24no—
396C2×C4×C53—24no—
397C2×C4×C53—24no—
398C2×C4×C53—24no—
399C2×C4×C53—416no—
400C2×C4×C53—416no—
401C2×C4×C53—42no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—42no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—42no—
408C2×C4×C53—42no—
409C2×C4×C53—42no—
410C2×C4×C53—42no—
411C2×C4×C53—42no—
412C2×C4×C53—42no—
413C2×C4×C53—42no—
414C2×C4×C53—42no—
415C2×C4×C53—41no—
416C2×C4×C53—42no—
417C2×C4×C53—41no—
418C2×C4×C53—42no—
419C2×C4×C53—41no—
420C2×C4×C53—42no—
421C2×C4×C53—41no—
422C2×C4×C53—42no—
423C2×C4×C53—42no—
424C2×C4×C53—41no—
425C2×C4×C53—42no—
426C2×C4×C53—41no—
427C2×C4×C53—42no—
428C2×C4×C53—42no—
429C2×C4×C53—42no—
430C2×C4×C53—42no—
431C2×C4×C53—42no—
432C2×C4×C53#12014yescomplemented
433#14725C5311yesmaximal, characteristic, direct product factor, Sylow
434C22×C53—24no—
435C22×C53—24no—
436C22×C53—24no—
437C22×C53—24no—
438C22×C53—28no—
439C22×C53—24no—
440C22×C53—28no—
441C22×C53—28no—
442C22×C53—28no—
443C22×C53—24no—
444C22×C53—28no—
445C22×C53—28no—
446C22×C53—28no—
447C22×C53—464no—
448C22×C53—44no—
449C22×C53—44no—
450C22×C53—44no—
451C22×C53—44no—
452C22×C53—44no—
453C22×C53—44no—
454C22×C53—44no—
455C22×C53—44no—
456C22×C53—44no—
457C22×C53—44no—
458C22×C53—44no—
459C22×C53—44no—
460C22×C53—42no—
461C22×C53—42no—
462C22×C53—44no—
463C22×C53—44no—
464C22×C53—42no—
465C22×C53—81no—
466C22×C53—81no—
467C22×C53—81no—
468C22×C53—81no—
469C22×C53—82no—
470C22×C53—82no—
471C22×C53#39418yescomplemented
472C22×C53C2×#12011yescharacteristic
473C22×C53C2×#12011yescharacteristic
474C22×C53C2×#12111yescharacteristic
475C22×C53C2×#12112yes—
476C22×C53C2×#12111yescharacteristic
477C22×C53C2×#12111yescharacteristic
478C22×C53C2×#12311yescharacteristic
479C22×C53C2×#12311yescharacteristic
480C22×C53#52511yescharacteristic
481C22×C53#52512yes—
482C22×C53C2×#12411yescharacteristic
483C22×C53#53412yes—
484C22×C53#53411yescharacteristic
485C22×C53#53511yescharacteristic
486C22×C53#53812yes—
487C22×C53D4212yes—
488C22×C53D4212yes—
489C22×C53#54612yes—
490C22×C53#54612yes—
491C22×C53#54612yes—
492C22×C53#54612yes—
493C22×C53#55112yes—
494C22×C53#55112yes—
495C4×C53—24no—
496C4×C53—42no—
497C4×C53—44no—
498C4×C53—42no—
499C4×C53—44no—
500C4×C53—81no—
501C4×C53—81no—
502C4×C53—82no—
503C22×#120C2×C5311yescharacteristic
504C23×C22⋊C4C2×C5311yescharacteristic, complemented
505C2×#394C2×C5312yescomplemented
506C2×#386C2×C5311yescharacteristic, complemented
507C2×#386C2×C5311yescharacteristic, complemented
508C2×#380C2×C5311yescharacteristic, complemented
509C2×#379C2×C5311yescharacteristic, complemented
510#1440C2×C5312yescomplemented
511#1439C2×C5312yescomplemented
512#1438C2×C5312yescomplemented
513C22⋊#95C2×C5311yescharacteristic, complemented
514C2×C53—28no—
515C2×C53—48no—
516C2×C53—82no—
517C2×C53C2×#39411yescharacteristic
518C2×C53#240811yescharacteristic
519C2×C53#241011yescharacteristic
520C2×C53#241012yes—
521C2×C53#241111yescharacteristic
522C2×C53#241212yes—
523C2×C53#241812yes—
524C2×C53#247212yes—
525C2×C53#253411yescharacteristic
526C2×C53#261711yescharacteristic
527C2×C53#284711yescharacteristic
528C26C22×C5311yescharacteristic
529C23×D4C22×C5311yescharacteristic
530C23×D4C22×C5312yes—
531C24×C4C22×C5311yescharacteristic
532C24×C4C22×C5311yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C5312yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C5312yes—
540C22×C22⋊C4C22×C5312yes—
541C22×C22⋊C4C22×C5312yes—
542C22×C22⋊C4C22×C5311yescharacteristic
543C22×C22⋊C4C22×C5311yescharacteristic
544C22×C22⋊C4C22×C5311yescharacteristic
545C22×C22⋊C4C22×C5312yes—
546C22×C22⋊C4C22×C5312yes—
547C22×C22⋊C4C22×C5311yescharacteristic, complemented
548C22×C22⋊C4C22×C5312yescomplemented
549C22×C22⋊C4C22×C5311yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C5312yescomplemented
556C2×#95C22×C5312yescomplemented
557C2×#95C22×C5311yescharacteristic, complemented
558C2×#95C22×C5312yescomplemented
559C2×#95C22×C5311yescharacteristic, complemented
560C2×#95C22×C5312yescomplemented
561C53#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C5314yes—
573C25C23×C5311yescharacteristic
574C25C23×C5312yes—
575C25C23×C5311yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C5314yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C5314yescomplemented
600C23×C4C23×C5312yes—
601C23×C4C23×C5311yescharacteristic
602C23×C4C23×C5311yescharacteristic
603C23×C4C23×C5311yescharacteristic
604C23×C4C23×C5312yes—
605C23×C4C23×C5312yes—
606C23×C4C23×C5311yescharacteristic
607C23×C4C23×C5311yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C5314yes—
643C2×C22⋊C4D4×C5318yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C5312yes—
700C24C2×D4×C5314yes—
701C24C2×D4×C5314yes—
702C24C2×D4×C5312yes—
703C24C2×D4×C5312yes—
704C24C2×D4×C5312yes—
705C24C2×D4×C5312yes—
706C24#41×C5314yes—
707C24#41×C5312yes—
708C24#41×C5312yes—
709C24#41×C5312yes—
710C24C24×C5311yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C5312yes—
778C22×C4C2×D4×C5312yes—
779C22×C4C2×D4×C5314yes—
780C22×C4C2×D4×C5314yes—
781C22×C4C2×D4×C5312yes—
782C22×C4C2×D4×C5314yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—432no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—416no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C5314yes—
880C23#121×C5318yes—
881C23#121×C5314yes—
882C23#121×C5314yes—
883C23#121×C5314yes—
884C23#123×C5314yes—
885C23#123×C5314yes—
886C23#124×C5314yes—
887C23C22×D4×C5311yescharacteristic
888C23C22×D4×C5311yescharacteristic
889C23C22×D4×C5311yescharacteristic
890C23C22×D4×C5312yes—
891C23C22×D4×C5311yescharacteristic
892C23C2×#41×C5311yescharacteristic
893C23C2×#41×C5311yescharacteristic
894C23C2×#41×C5311yescharacteristic
895C23C2×#41×C5312yes—
896C23H(5,𝔽2)×C5312yes—
897C23H(5,𝔽2)×C5312yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C5314yescomplemented
950C22—28no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—28no—
957C22—24no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—82no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22C53×#39418yescomplemented
988C22C2×#120×C5311yescharacteristic
989C22C2×#120×C5311yescharacteristic
990C22C2×#121×C5311yescharacteristic
991C22C2×#121×C5311yescharacteristic
992C22C2×#121×C5312yes—
993C22C2×#121×C5311yescharacteristic
994C22C2×#123×C5311yescharacteristic
995C22C2×#123×C5311yescharacteristic
996C22C53×#52512yes—
997C22C53×#52511yescharacteristic
998C22C2×#124×C5311yescharacteristic
999C22C53×#53411yescharacteristic
1000C22C53×#53412yes—
1001C22C53×#53511yescharacteristic
1002C22C53×#53812yes—
1003C22D42×C5312yes—
1004C22D42×C5312yes—
1005C22C53×#54612yes—
1006C22C53×#54612yes—
1007C22C53×#54612yes—
1008C22C53×#54612yes—
1009C22C53×#55112yes—
1010C22C53×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C53×#39411yescharacteristic
1023C2C53×#240811yescharacteristic
1024C2C53×#241011yescharacteristic
1025C2C53×#241012yes—
1026C2C53×#241111yescharacteristic
1027C2C53×#241212yes—
1028C2C53×#241812yes—
1029C2C53×#247212yes—
1030C2C53×#253411yescharacteristic
1031C2C53×#261711yescharacteristic
1032C2C53×#284711yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC22×#120×C53C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C53C2semidirect
3. C2×C53×#394C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#380C2semidirect
7. C2×C53×#379C2semidirect
8. C53×#1440C2semidirect
9. C53×#1439C2semidirect
10. C53×#1438C2semidirect
11. C53×C22⋊#95C2semidirect
20. C22×C4⋊C4×C53C22semidirect
31. C22×C22⋊C4×C53C22semidirect
32. C22×C22⋊C4×C53C22semidirect
33. C22×C22⋊C4×C53C22semidirect
39. C2×#95×C53C22semidirect
40. C2×#95×C53C22semidirect
41. C2×#95×C53C22semidirect
42. C2×#95×C53C22semidirect
43. C2×#95×C53C22semidirect
44. C2×#95×C53C22semidirect
82. C23×C4×C53D4semidirect
126. C2×C22⋊C4×C53D4semidirect
432. C2×C4×C53#120semidirect
433. #14725C53direct (N × H)
471. C22×C53#394semidirect
504. C23×C22⋊C4C2×C53semidirect
505. C2×#394C2×C53semidirect
506. C2×#386C2×C53semidirect
507. C2×#386C2×C53semidirect
508. C2×#380C2×C53semidirect
509. C2×#379C2×C53semidirect
510. #1440C2×C53semidirect
511. #1439C2×C53semidirect
512. #1438C2×C53semidirect
513. C22⋊#95C2×C53semidirect
536. C22×C4⋊C4C22×C53semidirect
547. C22×C22⋊C4C22×C53semidirect
548. C22×C22⋊C4C22×C53semidirect
549. C22×C22⋊C4C22×C53semidirect
555. C2×#95C22×C53semidirect
556. C2×#95C22×C53semidirect
557. C2×#95C22×C53semidirect
558. C2×#95C22×C53semidirect
559. C2×#95C22×C53semidirect
560. C2×#95C22×C53semidirect
561. C53#14725direct (N × H)
599. C23×C4D4×C53semidirect
643. C2×C22⋊C4D4×C53semidirect
949. C2×C4#120×C53semidirect
987. C22C53×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C532
C23×C22⋊C4×C532
C2×C53×#3942
C2×C53×#3862
C2×C53×#3802
C2×C53×#3792
C53×#14402
C53×#14392
C53×#14382
C53×C22⋊#952
#1472553