Finite Group Databasebeta

← C53×#14721 #27222233

Subgroups — C53×#14721 #27222233

Order 13568.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C53C211yesmaximal, characteristic, complemented
2C22×C4×D4×C53C211yesmaximal, characteristic, complemented
3C2×C53×#394C211yesmaximal, characteristic, complemented
4C2×C53×#392C211yesmaximal, characteristic
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#385C211yesmaximal, characteristic, complemented
7C53×#1444C211yesmaximal, characteristic, complemented
8C53×#1440C211yesmaximal, characteristic, complemented
9C53×#1439C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1438C211yesmaximal, characteristic, complemented
12C53×#1438C211yesmaximal, characteristic, complemented
13C53×#1437C211yesmaximal, characteristic, complemented
14C53×#1436C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C24×C4×C53C2211yescharacteristic
21C2×#123×C53—24no—
22C2×#123×C53—24no—
23C2×#123×C53—24no—
24C2×C4×D4×C53—24no—
25C2×C4×D4×C53—24no—
26C2×C4×D4×C53—24no—
27C22×C4⋊C4×C53C2211yescharacteristic
28C22×C4⋊C4×C53C2211yescharacteristic
29C22×C4⋊C4×C53C2211yescharacteristic
30C22×C4⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2211yescharacteristic
33C22×C22⋊C4×C53C2211yescharacteristic
34C22×C22⋊C4×C53C2211yescharacteristic
35C22×C22⋊C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C22×C22⋊C4×C53C2211yescharacteristic
43C22×C22⋊C4×C53C2211yescharacteristic
44C22×C42×C53C2211yescharacteristic
45C53×#394—24no—
46C53×#392—24no—
47C53×#386—24no—
48C53×#385—24no—
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C2×#95×C53C2211yescharacteristic
61C25×C53C2311yescharacteristic
62C25×C53C2311yescharacteristic
63C25×C53C2311yescharacteristic
64C22×D4×C53—22no—
65C22×D4×C53—22no—
66C22×D4×C53—22no—
67C22×D4×C53—22no—
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
71C22×D4×C53—22no—
72C22×D4×C53—22no—
73C22×D4×C53—22no—
74C22×D4×C53—22no—
75C22×D4×C53—22no—
76C22×D4×C53—22no—
77C22×D4×C53—22no—
78C22×D4×C53—22no—
79C22×D4×C53—22no—
80C22×D4×C53—41no—
81C22×D4×C53—41no—
82C22×D4×C53—41no—
83C22×D4×C53—41no—
84C22×D4×C53D414yes—
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—22no—
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—41no—
95C23×C4×C53—41no—
96C23×C4×C53—41no—
97C23×C4×C53—41no—
98C23×C4×C53D414yescomplemented
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110C23×C4×C53C2311yescharacteristic
111#123×C53—232no—
112C4×D4×C53—232no—
113C2×C4⋊C4×C53—22no—
114C2×C4⋊C4×C53—22no—
115C2×C4⋊C4×C53—22no—
116C2×C4⋊C4×C53—22no—
117C2×C4⋊C4×C53—22no—
118C2×C4⋊C4×C53—22no—
119C2×C4⋊C4×C53—22no—
120C2×C4⋊C4×C53—22no—
121C2×C4⋊C4×C53—22no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—41no—
124C2×C4⋊C4×C53D414yescomplemented
125C2×C22⋊C4×C53—22no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—22no—
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—22no—
140C2×C22⋊C4×C53—22no—
141C2×C22⋊C4×C53—22no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—22no—
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53—22no—
149C2×C22⋊C4×C53—22no—
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—41no—
157C2×C22⋊C4×C53—41no—
158C2×C22⋊C4×C53—41no—
159C2×C22⋊C4×C53—41no—
160C2×C22⋊C4×C53—41no—
161C2×C22⋊C4×C53—41no—
162C2×C22⋊C4×C53D414yescomplemented
163C2×C22⋊C4×C53D414yescomplemented
164C2×C42×C53—22no—
165C2×C42×C53—22no—
166C2×C42×C53—22no—
167#95×C53—22no—
168#95×C53—22no—
169#95×C53—22no—
170#95×C53—22no—
171#95×C53—22no—
172#95×C53—22no—
173#95×C53—22no—
174#95×C53—22no—
175#95×C53—22no—
176#95×C53—41no—
177#95×C53—41no—
178#95×C53—41no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53—21no—
189C24×C53—21no—
190C24×C53—21no—
191C24×C53—21no—
192C24×C53—21no—
193C24×C53—21no—
194C24×C53—21no—
195C24×C53—21no—
196C24×C53—21no—
197C24×C53—21no—
198C24×C53—21no—
199C24×C53—21no—
200C24×C53—21no—
201C24×C53—21no—
202C24×C53—21no—
203C24×C53—21no—
204C24×C53—21no—
205C24×C53—21no—
206C24×C53—21no—
207C24×C53—21no—
208C24×C53—21no—
209C24×C53—21no—
210C24×C53—21no—
211C24×C53—21no—
212C24×C53—21no—
213C24×C53—21no—
214C24×C53—21no—
215C24×C53—21no—
216C24×C53—21no—
217C24×C53C2×D412yes—
218C24×C53C2×D412yes—
219C24×C53C2×D412yes—
220C24×C53C2×D412yes—
221C24×C53C2×D412yes—
222C24×C53#4112yes—
223C24×C53#4112yes—
224C24×C53C2411yescharacteristic
225C2×D4×C53—28no—
226C2×D4×C53—28no—
227C2×D4×C53—28no—
228C2×D4×C53—28no—
229C2×D4×C53—28no—
230C2×D4×C53—28no—
231C2×D4×C53—28no—
232C2×D4×C53—28no—
233C2×D4×C53—28no—
234C2×D4×C53—44no—
235C2×D4×C53—44no—
236C2×D4×C53—44no—
237C2×D4×C53—44no—
238C2×D4×C53—44no—
239C2×D4×C53—44no—
240C2×D4×C53—44no—
241C2×D4×C53—44no—
242C2×D4×C53—44no—
243C2×D4×C53—44no—
244C2×D4×C53—44no—
245C2×D4×C53—44no—
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—21no—
254C22×C4×C53—28no—
255C22×C4×C53—28no—
256C22×C4×C53—21no—
257C22×C4×C53—21no—
258C22×C4×C53—21no—
259C22×C4×C53—21no—
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—21no—
269C22×C4×C53—21no—
270C22×C4×C53—21no—
271C22×C4×C53—21no—
272C22×C4×C53—21no—
273C22×C4×C53—21no—
274C22×C4×C53—21no—
275C22×C4×C53—21no—
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—21no—
287C22×C4×C53—21no—
288C22×C4×C53—21no—
289C22×C4×C53—21no—
290C22×C4×C53—21no—
291C22×C4×C53—21no—
292C22×C4×C53—21no—
293C22×C4×C53—21no—
294C22×C4×C53—21no—
295C22×C4×C53—21no—
296C22×C4×C53—21no—
297C22×C4×C53—21no—
298C22×C4×C53—21no—
299C22×C4×C53—21no—
300C22×C4×C53—21no—
301C22×C4×C53—21no—
302C22×C4×C53—21no—
303C22×C4×C53—21no—
304C22×C4×C53—28no—
305C22×C4×C53—21no—
306C22×C4×C53—21no—
307C22×C4×C53—21no—
308C22×C4×C53—21no—
309C22×C4×C53—21no—
310C22×C4×C53—21no—
311C22×C4×C53—21no—
312C22×C4×C53—21no—
313C22×C4×C53—21no—
314C22×C4×C53—21no—
315C22×C4×C53—21no—
316C22×C4×C53—21no—
317C22×C4×C53—21no—
318C22×C4×C53—21no—
319C22×C4×C53—44no—
320C22×C4×C53—44no—
321C22×C4×C53—44no—
322C22×C4×C53—44no—
323C22×C4×C53—44no—
324C22×C4×C53—44no—
325C22×C4×C53—44no—
326C22×C4×C53—44no—
327C22×C4×C53—44no—
328C22×C4×C53—44no—
329C22×C4×C53—44no—
330C22×C4×C53C2×D412yes—
331C22×C4×C53C2×D412yes—
332C22×C4×C53C2×D412yes—
333C22×C4×C53C2×D412yes—
334C22×C4×C53C2×D412yes—
335C22×C4×C53C2×D412yes—
336C22×C4×C53C2×D412yes—
337C22×C4×C53C2×D412yes—
338C22×C4×C53C2×D412yes—
339C22×C4×C53C2×D412yes—
340C22×C4×C53#4112yes—
341C22×C4×C53#4112yes—
342C22×C4×C53#4112yes—
343C22×C4×C53#4112yes—
344C4⋊C4×C53—28no—
345C4⋊C4×C53—28no—
346C4⋊C4×C53—28no—
347C4⋊C4×C53—44no—
348C22⋊C4×C53—28no—
349C22⋊C4×C53—28no—
350C22⋊C4×C53—28no—
351C22⋊C4×C53—28no—
352C22⋊C4×C53—28no—
353C22⋊C4×C53—28no—
354C22⋊C4×C53—44no—
355C22⋊C4×C53—44no—
356C22⋊C4×C53—44no—
357C22⋊C4×C53—44no—
358C22⋊C4×C53—44no—
359C22⋊C4×C53—44no—
360C22⋊C4×C53—44no—
361C42×C53—28no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—22no—
387C23×C53—22no—
388C23×C53—22no—
389C23×C53—22no—
390C23×C53—22no—
391C23×C53—22no—
392C23×C53—22no—
393C23×C53—22no—
394C23×C53—22no—
395C23×C53—22no—
396C23×C53—22no—
397C23×C53—22no—
398C23×C53—22no—
399C23×C53—22no—
400C23×C53—22no—
401C23×C53—22no—
402C23×C53—22no—
403C23×C53—22no—
404C23×C53—22no—
405C23×C53—41no—
406C23×C53—41no—
407C23×C53—41no—
408C23×C53—41no—
409C23×C53—41no—
410C23×C53—41no—
411C23×C53—41no—
412C23×C53—41no—
413C23×C53—41no—
414C23×C53—41no—
415C23×C53—41no—
416C23×C53—41no—
417C23×C53—41no—
418C23×C53—41no—
419C23×C53—41no—
420C23×C53—41no—
421C23×C53—41no—
422C23×C53—41no—
423C23×C53—41no—
424C23×C53—41no—
425C23×C53—41no—
426C23×C53—41no—
427C23×C53—41no—
428C23×C53—41no—
429C23×C53—41no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53—41no—
434C23×C53—41no—
435C23×C53—41no—
436C23×C53—41no—
437C23×C53—41no—
438C23×C53—41no—
439C23×C53—41no—
440C23×C53—41no—
441C23×C53—41no—
442C23×C53—41no—
443C23×C53—41no—
444C23×C53—41no—
445C23×C53—41no—
446C23×C53—41no—
447C23×C53—41no—
448C23×C53—41no—
449C23×C53—41no—
450C23×C53—41no—
451C23×C53—41no—
452C23×C53—41no—
453C23×C53—41no—
454C23×C53—41no—
455C23×C53—41no—
456C23×C53—41no—
457C23×C53—41no—
458C23×C53—41no—
459C23×C53—41no—
460C23×C53—41no—
461C23×C53—41no—
462C23×C53—41no—
463C23×C53—41no—
464C23×C53—41no—
465C23×C53#12014yes—
466C23×C53#12314yescomplemented
467C23×C53C22×D411yescharacteristic
468C23×C53C22×D411yescharacteristic
469C23×C53C22×D411yescharacteristic
470C23×C53C22×D411yescharacteristic
471C23×C53C22×D411yescharacteristic
472C23×C53C2×#4111yescharacteristic
473C23×C53C2×#4111yescharacteristic
474C23×C53C2×#4111yescharacteristic
475C23×C53C2×#4111yescharacteristic
476C23×C53C2×#4111yescharacteristic
477C23×C53C2×#4111yescharacteristic
478C23×C53H(5,𝔽2)11yescharacteristic
479C23×C53H(5,𝔽2)11yescharacteristic
480C23×C53H(5,𝔽2)11yescharacteristic
481C23×C532−1+411yescharacteristic
482D4×C53—232no—
483D4×C53—416no—
484D4×C53—416no—
485C2×C4×C53—22no—
486C2×C4×C53—22no—
487C2×C4×C53—22no—
488C2×C4×C53—22no—
489C2×C4×C53—22no—
490C2×C4×C53—22no—
491C2×C4×C53—22no—
492C2×C4×C53—22no—
493C2×C4×C53—22no—
494C2×C4×C53—22no—
495C2×C4×C53—22no—
496C2×C4×C53—22no—
497C2×C4×C53—22no—
498C2×C4×C53—22no—
499C2×C4×C53—22no—
500C2×C4×C53—22no—
501C2×C4×C53—22no—
502C2×C4×C53—22no—
503C2×C4×C53—22no—
504C2×C4×C53—22no—
505C2×C4×C53—22no—
506C2×C4×C53—22no—
507C2×C4×C53—22no—
508C2×C4×C53—22no—
509C2×C4×C53—22no—
510C2×C4×C53—22no—
511C2×C4×C53—22no—
512C2×C4×C53—22no—
513C2×C4×C53—22no—
514C2×C4×C53—22no—
515C2×C4×C53—22no—
516C2×C4×C53—22no—
517C2×C4×C53—22no—
518C2×C4×C53—22no—
519C2×C4×C53—22no—
520C2×C4×C53—22no—
521C2×C4×C53—416no—
522C2×C4×C53—416no—
523C2×C4×C53—41no—
524C2×C4×C53—41no—
525C2×C4×C53—41no—
526C2×C4×C53—41no—
527C2×C4×C53—41no—
528C2×C4×C53—41no—
529C2×C4×C53—41no—
530C2×C4×C53—41no—
531C2×C4×C53—41no—
532C2×C4×C53—41no—
533C2×C4×C53—41no—
534C2×C4×C53—41no—
535C2×C4×C53—41no—
536C2×C4×C53—41no—
537C2×C4×C53—41no—
538C2×C4×C53—41no—
539C2×C4×C53—41no—
540C2×C4×C53—41no—
541C2×C4×C53—41no—
542C2×C4×C53—41no—
543C2×C4×C53—41no—
544C2×C4×C53—41no—
545C2×C4×C53—41no—
546C2×C4×C53—41no—
547C2×C4×C53—41no—
548C2×C4×C53—41no—
549C2×C4×C53—41no—
550C2×C4×C53—41no—
551C2×C4×C53—41no—
552C2×C4×C53—41no—
553C2×C4×C53—41no—
554C2×C4×C53—41no—
555C2×C4×C53—41no—
556C2×C4×C53—41no—
557C2×C4×C53—41no—
558C2×C4×C53—41no—
559C2×C4×C53—41no—
560C2×C4×C53—41no—
561C2×C4×C53—41no—
562C2×C4×C53—41no—
563C2×C4×C53—41no—
564C2×C4×C53—41no—
565C2×C4×C53—41no—
566C2×C4×C53—41no—
567C2×C4×C53—41no—
568C2×C4×C53—41no—
569C2×C4×C53#12014yes—
570C2×C4×C53#12314yescomplemented
571#14721C5311yesmaximal, characteristic, direct product factor, Sylow
572C22×C53—24no—
573C22×C53—24no—
574C22×C53—24no—
575C22×C53—24no—
576C22×C53—24no—
577C22×C53—24no—
578C22×C53—42no—
579C22×C53—42no—
580C22×C53—42no—
581C22×C53—42no—
582C22×C53—42no—
583C22×C53—42no—
584C22×C53—42no—
585C22×C53—42no—
586C22×C53—42no—
587C22×C53—42no—
588C22×C53—42no—
589C22×C53—42no—
590C22×C53—42no—
591C22×C53—42no—
592C22×C53—42no—
593C22×C53—42no—
594C22×C53—42no—
595C22×C53—42no—
596C22×C53—42no—
597C22×C53—42no—
598C22×C53—42no—
599C22×C53—42no—
600C22×C53—42no—
601C22×C53—42no—
602C22×C53—42no—
603C22×C53—42no—
604C22×C53—42no—
605C22×C53—42no—
606C22×C53—42no—
607C22×C53—42no—
608C22×C53—42no—
609C22×C53—81no—
610C22×C53—81no—
611C22×C53—81no—
612C22×C53—81no—
613C22×C53—81no—
614C22×C53—81no—
615C22×C53—81no—
616C22×C53—81no—
617C22×C53C2×#12011yescharacteristic
618C22×C53C2×#12011yescharacteristic
619C22×C53C2×#12311yescharacteristic
620C22×C53C2×#12311yescharacteristic
621C22×C53#52511yescharacteristic
622C22×C53#52511yescharacteristic
623C22×C53#52511yescharacteristic
624C22×C53#52511yescharacteristic
625C22×C53#52511yescharacteristic
626C22×C53#52511yescharacteristic
627C22×C53#53211yescharacteristic
628C22×C53#53211yescharacteristic
629C22×C53#53211yescharacteristic
630C22×C53#53411yescharacteristic
631C22×C53#53711yescharacteristic
632C22×C53#53811yescharacteristic
633C22×C53#53911yescharacteristic
634C22×C53#54011yescharacteristic
635C22×C53#54211yescharacteristic
636C22×C53D4211yescharacteristic
637C22×C53D4211yescharacteristic
638C22×C53D4211yescharacteristic
639C22×C53D4211yescharacteristic
640C22×C53#54611yescharacteristic
641C22×C53#54611yescharacteristic
642C22×C53#54611yescharacteristic
643C22×C53#54711yescharacteristic
644C22×C53#54711yescharacteristic
645C22×C53#54711yescharacteristic
646C22×C53#54811yescharacteristic
647C22×C53#55011yescharacteristic
648C22×C53#55111yescharacteristic
649C22×C53#55311yescharacteristic
650C22×C53#55311yescharacteristic
651C22×C53#55911yescharacteristic
652C4×C53—24no—
653C4×C53—24no—
654C4×C53—42no—
655C4×C53—42no—
656C4×C53—42no—
657C4×C53—42no—
658C4×C53—42no—
659C4×C53—42no—
660C4×C53—42no—
661C4×C53—42no—
662C4×C53—81no—
663C4×C53—81no—
664C22×#123C2×C5311yescharacteristic, complemented
665C22×C4×D4C2×C5311yescharacteristic, complemented
666C2×#394C2×C5311yescharacteristic, complemented
667C2×#392C2×C5311yescharacteristic
668C2×#386C2×C5311yescharacteristic, complemented
669C2×#385C2×C5311yescharacteristic, complemented
670#1444C2×C5311yescharacteristic, complemented
671#1440C2×C5311yescharacteristic, complemented
672#1439C2×C5311yescharacteristic, complemented
673#1439C2×C5311yescharacteristic, complemented
674#1438C2×C5311yescharacteristic, complemented
675#1438C2×C5311yescharacteristic, complemented
676#1437C2×C5311yescharacteristic, complemented
677#1436C2×C5311yescharacteristic, complemented
678C22⋊#95C2×C5311yescharacteristic, complemented
679C2×C53—44no—
680C2×C53—44no—
681C2×C53—82no—
682C2×C53#238811yescharacteristic
683C2×C53#240311yescharacteristic
684C2×C53#240711yescharacteristic
685C2×C53#241811yescharacteristic
686C2×C53#242211yescharacteristic
687C2×C53#243011yescharacteristic
688C2×C53#244311yescharacteristic
689C2×C53#244511yescharacteristic
690C2×C53#245511yescharacteristic
691C2×C53#245611yescharacteristic
692C2×C53#246111yescharacteristic
693C2×C53#246411yescharacteristic
694C2×C53#260211yescharacteristic
695C2×C53#263011yescharacteristic
696C2×C53#284911yescharacteristic
697C23×D4C22×C5311yescharacteristic
698C23×D4C22×C5311yescharacteristic
699C23×D4C22×C5311yescharacteristic
700C24×C4C22×C5311yescharacteristic
701C24×C4C22×C5311yescharacteristic
702C2×#123—24no—
703C2×#123—24no—
704C2×#123—24no—
705C2×C4×D4—24no—
706C2×C4×D4—24no—
707C2×C4×D4—24no—
708C22×C4⋊C4C22×C5311yescharacteristic
709C22×C4⋊C4C22×C5311yescharacteristic
710C22×C4⋊C4C22×C5311yescharacteristic
711C22×C4⋊C4C22×C5311yescharacteristic
712C22×C22⋊C4C22×C5311yescharacteristic
713C22×C22⋊C4C22×C5311yescharacteristic
714C22×C22⋊C4C22×C5311yescharacteristic
715C22×C22⋊C4C22×C5311yescharacteristic
716C22×C22⋊C4C22×C5311yescharacteristic
717C22×C22⋊C4C22×C5311yescharacteristic
718C22×C22⋊C4C22×C5311yescharacteristic
719C22×C22⋊C4C22×C5311yescharacteristic
720C22×C22⋊C4C22×C5311yescharacteristic
721C22×C22⋊C4C22×C5311yescharacteristic
722C22×C22⋊C4C22×C5311yescharacteristic
723C22×C22⋊C4C22×C5311yescharacteristic
724C22×C22⋊C4C22×C5311yescharacteristic
725C22×C42C22×C5311yescharacteristic
726#394—24no—
727#392—24no—
728#386—24no—
729#385—24no—
730C2×#95C22×C5311yescharacteristic
731C2×#95C22×C5311yescharacteristic
732C2×#95C22×C5311yescharacteristic
733C2×#95C22×C5311yescharacteristic
734C2×#95C22×C5311yescharacteristic
735C2×#95C22×C5311yescharacteristic
736C2×#95C22×C5311yescharacteristic
737C2×#95C22×C5311yescharacteristic
738C2×#95C22×C5311yescharacteristic
739C2×#95C22×C5311yescharacteristic
740C2×#95C22×C5311yescharacteristic
741C2×#95C22×C5311yescharacteristic
742C53#1472111yescharacteristic, direct product factor, Sylow
743C25C23×C5311yescharacteristic
744C25C23×C5311yescharacteristic
745C25C23×C5311yescharacteristic
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4—41no—
766C22×D4D4×C5314yes—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—22no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4—41no—
780C23×C4D4×C5314yescomplemented
781C23×C4C23×C5311yescharacteristic
782C23×C4C23×C5311yescharacteristic
783C23×C4C23×C5311yescharacteristic
784C23×C4C23×C5311yescharacteristic
785C23×C4C23×C5311yescharacteristic
786C23×C4C23×C5311yescharacteristic
787C23×C4C23×C5311yescharacteristic
788C23×C4C23×C5311yescharacteristic
789C23×C4C23×C5311yescharacteristic
790C23×C4C23×C5311yescharacteristic
791C23×C4C23×C5311yescharacteristic
792C23×C4C23×C5311yescharacteristic
793#123—232no—
794C4×D4—232no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4—22no—
801C2×C4⋊C4—22no—
802C2×C4⋊C4—22no—
803C2×C4⋊C4—22no—
804C2×C4⋊C4—22no—
805C2×C4⋊C4—41no—
806C2×C4⋊C4D4×C5314yescomplemented
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4—41no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4—41no—
844C2×C22⋊C4D4×C5314yescomplemented
845C2×C22⋊C4D4×C5314yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—41no—
859#95—41no—
860#95—41no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24C2×D4×C5312yes—
900C24C2×D4×C5312yes—
901C24C2×D4×C5312yes—
902C24C2×D4×C5312yes—
903C24C2×D4×C5312yes—
904C24#41×C5312yes—
905C24#41×C5312yes—
906C24C24×C5311yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—28no—
937C22×C4—28no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—28no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—44no—
1012C22×C4C2×D4×C5312yes—
1013C22×C4C2×D4×C5312yes—
1014C22×C4C2×D4×C5312yes—
1015C22×C4C2×D4×C5312yes—
1016C22×C4C2×D4×C5312yes—
1017C22×C4C2×D4×C5312yes—
1018C22×C4C2×D4×C5312yes—
1019C22×C4C2×D4×C5312yes—
1020C22×C4C2×D4×C5312yes—
1021C22×C4C2×D4×C5312yes—
1022C22×C4#41×C5312yes—
1023C22×C4#41×C5312yes—
1024C22×C4#41×C5312yes—
1025C22×C4#41×C5312yes—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—44no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C42—28no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23#120×C5314yes—
1148C23#123×C5314yescomplemented
1149C23C22×D4×C5311yescharacteristic
1150C23C22×D4×C5311yescharacteristic
1151C23C22×D4×C5311yescharacteristic
1152C23C22×D4×C5311yescharacteristic
1153C23C22×D4×C5311yescharacteristic
1154C23C2×#41×C5311yescharacteristic
1155C23C2×#41×C5311yescharacteristic
1156C23C2×#41×C5311yescharacteristic
1157C23C2×#41×C5311yescharacteristic
1158C23C2×#41×C5311yescharacteristic
1159C23C2×#41×C5311yescharacteristic
1160C23H(5,𝔽2)×C5311yescharacteristic
1161C23H(5,𝔽2)×C5311yescharacteristic
1162C23H(5,𝔽2)×C5311yescharacteristic
1163C232−1+4×C5311yescharacteristic
1164D4—232no—
1165D4—416no—
1166D4—416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—416no—
1204C2×C4—416no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4#120×C5314yes—
1252C2×C4#123×C5314yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22C2×#120×C5311yescharacteristic
1299C22C2×#120×C5311yescharacteristic
1300C22C2×#123×C5311yescharacteristic
1301C22C2×#123×C5311yescharacteristic
1302C22C53×#52511yescharacteristic
1303C22C53×#52511yescharacteristic
1304C22C53×#52511yescharacteristic
1305C22C53×#52511yescharacteristic
1306C22C53×#52511yescharacteristic
1307C22C53×#52511yescharacteristic
1308C22C53×#53211yescharacteristic
1309C22C53×#53211yescharacteristic
1310C22C53×#53211yescharacteristic
1311C22C53×#53411yescharacteristic
1312C22C53×#53711yescharacteristic
1313C22C53×#53811yescharacteristic
1314C22C53×#53911yescharacteristic
1315C22C53×#54011yescharacteristic
1316C22C53×#54211yescharacteristic
1317C22D42×C5311yescharacteristic
1318C22D42×C5311yescharacteristic
1319C22D42×C5311yescharacteristic
1320C22D42×C5311yescharacteristic
1321C22C53×#54611yescharacteristic
1322C22C53×#54611yescharacteristic
1323C22C53×#54611yescharacteristic
1324C22C53×#54711yescharacteristic
1325C22C53×#54711yescharacteristic
1326C22C53×#54711yescharacteristic
1327C22C53×#54811yescharacteristic
1328C22C53×#55011yescharacteristic
1329C22C53×#55111yescharacteristic
1330C22C53×#55311yescharacteristic
1331C22C53×#55311yescharacteristic
1332C22C53×#55911yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2C53×#238811yescharacteristic
1349C2C53×#240311yescharacteristic
1350C2C53×#240711yescharacteristic
1351C2C53×#241811yescharacteristic
1352C2C53×#242211yescharacteristic
1353C2C53×#243011yescharacteristic
1354C2C53×#244311yescharacteristic
1355C2C53×#244511yescharacteristic
1356C2C53×#245511yescharacteristic
1357C2C53×#245611yescharacteristic
1358C2C53×#246111yescharacteristic
1359C2C53×#246411yescharacteristic
1360C2C53×#260211yescharacteristic
1361C2C53×#263011yescharacteristic
1362C2C53×#284911yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC2×C53×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C53C2semidirect
2. C22×C4×D4×C53C2semidirect
3. C2×C53×#394C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#385C2semidirect
7. C53×#1444C2semidirect
8. C53×#1440C2semidirect
9. C53×#1439C2semidirect
10. C53×#1439C2semidirect
11. C53×#1438C2semidirect
12. C53×#1438C2semidirect
13. C53×#1437C2semidirect
14. C53×#1436C2semidirect
15. C53×C22⋊#95C2semidirect
98. C23×C4×C53D4semidirect
124. C2×C4⋊C4×C53D4semidirect
162. C2×C22⋊C4×C53D4semidirect
163. C2×C22⋊C4×C53D4semidirect
466. C23×C53#123semidirect
570. C2×C4×C53#123semidirect
571. #14721C53direct (N × H)
664. C22×#123C2×C53semidirect
665. C22×C4×D4C2×C53semidirect
666. C2×#394C2×C53semidirect
668. C2×#386C2×C53semidirect
669. C2×#385C2×C53semidirect
670. #1444C2×C53semidirect
671. #1440C2×C53semidirect
672. #1439C2×C53semidirect
673. #1439C2×C53semidirect
674. #1438C2×C53semidirect
675. #1438C2×C53semidirect
676. #1437C2×C53semidirect
677. #1436C2×C53semidirect
678. C22⋊#95C2×C53semidirect
742. C53#14721direct (N × H)
780. C23×C4D4×C53semidirect
806. C2×C4⋊C4D4×C53semidirect
844. C2×C22⋊C4D4×C53semidirect
845. C2×C22⋊C4D4×C53semidirect
1148. C23#123×C53semidirect
1252. C2×C4#123×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C532
C22×C4×D4×C532
C2×C53×#3942
C2×C53×#3922
C2×C53×#3862
C2×C53×#3852
C53×#14442
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14362
C53×C22⋊#952
#1472153