Finite Group Databasebeta

← C53×#14534 #27222046

Subgroups — C53×#14534 #27222046

Order 13568.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#392C211yesmaximal, characteristic
2C2×C53×#390C211yesmaximal, characteristic, complemented
3C2×C53×#390C211yesmaximal, characteristic, complemented
4C2×C53×#388C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C2×C53×#385C211yesmaximal, 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×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C4⋊C4×C53C2211yescharacteristic
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2211yescharacteristic
24C22×C22⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C22⋊C4×C53C2211yescharacteristic
30C22×C22⋊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×C42×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C53×#392C418yescomplemented
40C53×#390—24no—
41C53×#390—24no—
42C53×#388—24no—
43C53×#386—24no—
44C53×#386—24no—
45C53×#385—24no—
46C2×#95×C53C2211yescharacteristic
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
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
58C25×C53C2311yescharacteristic
59C25×C53C2311yescharacteristic
60C25×C53C2311yescharacteristic
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—22no—
68C22×D4×C53—22no—
69C22×D4×C53—41no—
70C22×D4×C53—41no—
71C22×D4×C53—41no—
72C22×D4×C53—41no—
73C22×D4×C53—41no—
74C22×D4×C53—41no—
75C22×D4×C53—41no—
76C22×D4×C53—41no—
77C22×D4×C53—41no—
78C22×D4×C53—41no—
79C22×D4×C53C2×C414yes—
80C22×D4×C53C2×C414yes—
81C22×D4×C53C2×C414yescomplemented
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—22no—
85C23×C4×C53—41no—
86C23×C4×C53—41no—
87C23×C4×C53—41no—
88C23×C4×C53—41no—
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2311yescharacteristic
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—41no—
106C2×C4⋊C4×C53—41no—
107C2×C4⋊C4×C53—41no—
108C2×C4⋊C4×C53—41no—
109C2×C4⋊C4×C53D414yescomplemented
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—22no—
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—22no—
124C2×C22⋊C4×C53—22no—
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—41no—
131C2×C22⋊C4×C53—41no—
132C2×C22⋊C4×C53—41no—
133C2×C22⋊C4×C53—41no—
134C2×C22⋊C4×C53—41no—
135C2×C22⋊C4×C53—41no—
136C2×C22⋊C4×C53—41no—
137C2×C22⋊C4×C53—41no—
138C2×C22⋊C4×C53—41no—
139C2×C22⋊C4×C53—41no—
140C2×C22⋊C4×C53—41no—
141C2×C22⋊C4×C53—41no—
142C2×C22⋊C4×C53—41no—
143C2×C22⋊C4×C53—41no—
144C2×C22⋊C4×C53—41no—
145C2×C22⋊C4×C53—41no—
146C2×C22⋊C4×C53—41no—
147C2×C22⋊C4×C53—41no—
148C2×C22⋊C4×C53C2×C414yes—
149C2×C22⋊C4×C53C2×C414yescomplemented
150C2×C22⋊C4×C53C2×C414yescomplemented
151C2×C22⋊C4×C53D414yescomplemented
152C2×C42×C53—22no—
153C2×C42×C53—22no—
154C2×C42×C53—22no—
155C2×C42×C53—41no—
156C2×C42×C53—41no—
157C2×C42×C53—41no—
158#95×C53—22no—
159#95×C53—22no—
160#95×C53—22no—
161#95×C53—22no—
162#95×C53—22no—
163#95×C53—22no—
164#95×C53—22no—
165#95×C53—41no—
166#95×C53—41no—
167#95×C53—41no—
168#95×C53C2×C414yescomplemented
169#95×C53D414yescomplemented
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
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×C53C22×C412yes—
211C24×C53C22×C412yes—
212C24×C53C22×C412yes—
213C24×C53C2×D412yes—
214C24×C53#4112yes—
215C24×C53C2411yescharacteristic
216C2×D4×C53—28no—
217C2×D4×C53—28no—
218C2×D4×C53—28no—
219C2×D4×C53—28no—
220C2×D4×C53—44no—
221C2×D4×C53—44no—
222C2×D4×C53—44no—
223C2×D4×C53—44no—
224C2×D4×C53—44no—
225C2×D4×C53—44no—
226C2×D4×C53—44no—
227C2×D4×C53—44no—
228C2×D4×C53—44no—
229C2×D4×C53—44no—
230C2×D4×C53—44no—
231C2×D4×C53—44no—
232C2×D4×C53—44no—
233C2×D4×C53—44no—
234C2×D4×C53—44no—
235C2×D4×C53—44no—
236C2×D4×C53—44no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
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—21no—
255C22×C4×C53—21no—
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—21no—
305C22×C4×C53—21no—
306C22×C4×C53—21no—
307C22×C4×C53—44no—
308C22×C4×C53—44no—
309C22×C4×C53—44no—
310C22×C4×C53—44no—
311C22×C4×C53—44no—
312C22×C4×C53—44no—
313C22×C4×C53—44no—
314C22×C4×C53C22×C412yes—
315C22×C4×C53C22×C412yes—
316C22×C4×C53C22×C412yes—
317C22×C4×C53C22×C412yes—
318C22×C4×C53C2×D412yes—
319C22×C4×C53C2×D412yes—
320C22×C4×C53C2×D412yes—
321C22×C4×C53C2×D412yes—
322C22×C4×C53C2×D412yes—
323C22×C4×C53C2×D412yes—
324C22×C4×C53C2×D412yes—
325C22×C4×C53C2×D412yes—
326C22×C4×C53#4112yes—
327C22×C4×C53#4112yes—
328C4⋊C4×C53—44no—
329C4⋊C4×C53—44no—
330C4⋊C4×C53—44no—
331C22⋊C4×C53—28no—
332C22⋊C4×C53—28no—
333C22⋊C4×C53—44no—
334C22⋊C4×C53—44no—
335C22⋊C4×C53—44no—
336C22⋊C4×C53—44no—
337C22⋊C4×C53—44no—
338C22⋊C4×C53—44no—
339C22⋊C4×C53—44no—
340C22⋊C4×C53—44no—
341C22⋊C4×C53—44no—
342C22⋊C4×C53—44no—
343C22⋊C4×C53—44no—
344C22⋊C4×C53—44no—
345C42×C53—44no—
346C42×C53—44no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
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—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53—41no—
395C23×C53—41no—
396C23×C53—41no—
397C23×C53—41no—
398C23×C53—41no—
399C23×C53—41no—
400C23×C53—41no—
401C23×C53—41no—
402C23×C53—41no—
403C23×C53—41no—
404C23×C53—41no—
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×C53C4×D414yes—
452C23×C53C23×C411yescharacteristic
453C23×C53C22×D411yescharacteristic
454C23×C53C22×D411yescharacteristic
455C23×C53C22×D411yescharacteristic
456C23×C53C2×#4111yescharacteristic
457C23×C53C2×#4111yescharacteristic
458C23×C53C2×#4111yescharacteristic
459C23×C53H(5,𝔽2)11yescharacteristic
460C23×C53H(5,𝔽2)11yescharacteristic
461C23×C53H(5,𝔽2)11yescharacteristic
462C23×C53H(5,𝔽2)11yescharacteristic
463C23×C53H(5,𝔽2)11yescharacteristic
464C23×C53H(5,𝔽2)11yescharacteristic
465C23×C53H(5,𝔽2)11yescharacteristic
466C23×C532−1+411yescharacteristic
467D4×C53—416no—
468D4×C53—416no—
469D4×C53—416no—
470C2×C4×C53—22no—
471C2×C4×C53—22no—
472C2×C4×C53—22no—
473C2×C4×C53—22no—
474C2×C4×C53—22no—
475C2×C4×C53—22no—
476C2×C4×C53—22no—
477C2×C4×C53—22no—
478C2×C4×C53—22no—
479C2×C4×C53—22no—
480C2×C4×C53—22no—
481C2×C4×C53—22no—
482C2×C4×C53—22no—
483C2×C4×C53—22no—
484C2×C4×C53—22no—
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—416no—
507C2×C4×C53—41no—
508C2×C4×C53—41no—
509C2×C4×C53—41no—
510C2×C4×C53—41no—
511C2×C4×C53—41no—
512C2×C4×C53—41no—
513C2×C4×C53—41no—
514C2×C4×C53—41no—
515C2×C4×C53—41no—
516C2×C4×C53—41no—
517C2×C4×C53—41no—
518C2×C4×C53—41no—
519C2×C4×C53—41no—
520C2×C4×C53—41no—
521C2×C4×C53—41no—
522C2×C4×C53—41no—
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×C53C4×D414yes—
554C2×C4×C53C4×D414yes—
555#14534C5311yesmaximal, characteristic, direct product factor, Sylow
556C22×C53—24no—
557C22×C53—24no—
558C22×C53—24no—
559C22×C53—42no—
560C22×C53—42no—
561C22×C53—42no—
562C22×C53—42no—
563C22×C53—42no—
564C22×C53—42no—
565C22×C53—42no—
566C22×C53—42no—
567C22×C53—42no—
568C22×C53—42no—
569C22×C53—42no—
570C22×C53—42no—
571C22×C53—42no—
572C22×C53—42no—
573C22×C53—42no—
574C22×C53—42no—
575C22×C53—42no—
576C22×C53—42no—
577C22×C53—42no—
578C22×C53—42no—
579C22×C53—42no—
580C22×C53—42no—
581C22×C53—42no—
582C22×C53—42no—
583C22×C53—42no—
584C22×C53—42no—
585C22×C53—81no—
586C22×C53—81no—
587C22×C53—81no—
588C22×C53—81no—
589C22×C53—81no—
590C22×C53—81no—
591C22×C53—81no—
592C22×C53—81no—
593C22×C53—81no—
594C22×C53—81no—
595C22×C53—81no—
596C22×C53—81no—
597C22×C53—81no—
598C22×C53—81no—
599C22×C53—81no—
600C22×C53—81no—
601C22×C53C2×C4×D411yescharacteristic
602C22×C53C2×C4×D411yescharacteristic
603C22×C53C2×C4×D411yescharacteristic
604C22×C53#51811yescharacteristic
605C22×C53#51811yescharacteristic
606C22×C53#51811yescharacteristic
607C22×C53#52011yescharacteristic
608C22×C53#53411yescharacteristic
609C22×C53#53411yescharacteristic
610C22×C53#53511yescharacteristic
611C22×C53#53511yescharacteristic
612C22×C53#53511yescharacteristic
613C22×C53#53711yescharacteristic
614C22×C53#53811yescharacteristic
615C22×C53#53811yescharacteristic
616C22×C53#53811yescharacteristic
617C22×C53#53811yescharacteristic
618C22×C53#54011yescharacteristic
619C22×C53#54211yescharacteristic
620C22×C53D4211yescharacteristic
621C22×C53D4211yescharacteristic
622C22×C53D4211yescharacteristic
623C22×C53#54611yescharacteristic
624C22×C53#54611yescharacteristic
625C22×C53#54711yescharacteristic
626C22×C53#54811yescharacteristic
627C22×C53#55011yescharacteristic
628C22×C53#55011yescharacteristic
629C22×C53#55111yescharacteristic
630C22×C53#55311yescharacteristic
631C22×C53#55911yescharacteristic
632C22×C53#56011yescharacteristic
633C22×C53#56011yescharacteristic
634C22×C53#56211yescharacteristic
635C22×C53#56211yescharacteristic
636C4×C53—24no—
637C4×C53—24no—
638C4×C53—42no—
639C4×C53—42no—
640C4×C53—42no—
641C4×C53—42no—
642C4×C53—42no—
643C4×C53—42no—
644C4×C53—42no—
645C4×C53—42no—
646C4×C53—81no—
647C4×C53—81no—
648C2×#392C2×C5311yescharacteristic
649C2×#390C2×C5311yescharacteristic, complemented
650C2×#390C2×C5311yescharacteristic, complemented
651C2×#388C2×C5311yescharacteristic, complemented
652C2×#386C2×C5311yescharacteristic, complemented
653C2×#386C2×C5311yescharacteristic, complemented
654C2×#385C2×C5311yescharacteristic, complemented
655#1440C2×C5311yescharacteristic, complemented
656#1439C2×C5311yescharacteristic, complemented
657#1439C2×C5311yescharacteristic, complemented
658#1438C2×C5311yescharacteristic, complemented
659#1438C2×C5311yescharacteristic, complemented
660#1437C2×C5311yescharacteristic, complemented
661#1436C2×C5311yescharacteristic, complemented
662#1436C2×C5311yescharacteristic, complemented
663C2×C53—44no—
664C2×C53—82no—
665C2×C53—82no—
666C2×C53#232111yescharacteristic
667C2×C53#232111yescharacteristic
668C2×C53#232411yescharacteristic
669C2×C53#235811yescharacteristic
670C2×C53#236111yescharacteristic
671C2×C53#236611yescharacteristic
672C2×C53#237711yescharacteristic
673C2×C53#266911yescharacteristic
674C2×C53#267311yescharacteristic
675C2×C53#267611yescharacteristic
676C2×C53#268211yescharacteristic
677C2×C53#271011yescharacteristic
678C2×C53#271411yescharacteristic
679C2×C53#273011yescharacteristic
680C2×C53#279711yescharacteristic
681C23×D4C22×C5311yescharacteristic
682C23×D4C22×C5311yescharacteristic
683C23×D4C22×C5311yescharacteristic
684C24×C4C22×C5311yescharacteristic
685C22×C4⋊C4C22×C5311yescharacteristic
686C22×C4⋊C4C22×C5311yescharacteristic
687C22×C4⋊C4C22×C5311yescharacteristic
688C22×C22⋊C4C22×C5311yescharacteristic
689C22×C22⋊C4C22×C5311yescharacteristic
690C22×C22⋊C4C22×C5311yescharacteristic
691C22×C22⋊C4C22×C5311yescharacteristic
692C22×C22⋊C4C22×C5311yescharacteristic
693C22×C22⋊C4C22×C5311yescharacteristic
694C22×C22⋊C4C22×C5311yescharacteristic
695C22×C22⋊C4C22×C5311yescharacteristic
696C22×C22⋊C4C22×C5311yescharacteristic
697C22×C22⋊C4C22×C5311yescharacteristic
698C22×C22⋊C4C22×C5311yescharacteristic
699C22×C22⋊C4C22×C5311yescharacteristic
700C22×C22⋊C4C22×C5311yescharacteristic
701C22×C22⋊C4C22×C5311yescharacteristic
702C22×C42C22×C5311yescharacteristic
703C22×C42C22×C5311yescharacteristic
704#392C4×C5318yescomplemented
705#390—24no—
706#390—24no—
707#388—24no—
708#386—24no—
709#386—24no—
710#385—24no—
711C2×#95C22×C5311yescharacteristic
712C2×#95C22×C5311yescharacteristic
713C2×#95C22×C5311yescharacteristic
714C2×#95C22×C5311yescharacteristic
715C2×#95C22×C5311yescharacteristic
716C2×#95C22×C5311yescharacteristic
717C2×#95C22×C5311yescharacteristic
718C2×#95C22×C5311yescharacteristic
719C2×#95C22×C5311yescharacteristic
720C2×#95C22×C5311yescharacteristic
721C2×#95C22×C5311yescharacteristic
722C2×#95C22×C5311yescharacteristic
723C53#1453411yescharacteristic, direct product factor, Sylow
724C25C23×C5311yescharacteristic
725C25C23×C5311yescharacteristic
726C25C23×C5311yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4C2×C4×C5314yes—
746C22×D4C2×C4×C5314yes—
747C22×D4C2×C4×C5314yescomplemented
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4C23×C5311yescharacteristic
756C23×C4C23×C5311yescharacteristic
757C23×C4C23×C5311yescharacteristic
758C23×C4C23×C5311yescharacteristic
759C23×C4C23×C5311yescharacteristic
760C23×C4C23×C5311yescharacteristic
761C23×C4C23×C5311yescharacteristic
762C23×C4C23×C5311yescharacteristic
763C23×C4C23×C5311yescharacteristic
764C23×C4C23×C5311yescharacteristic
765C23×C4C23×C5311yescharacteristic
766C23×C4C23×C5311yescharacteristic
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4D4×C5314yescomplemented
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4C2×C4×C5314yes—
815C2×C22⋊C4C2×C4×C5314yescomplemented
816C2×C22⋊C4C2×C4×C5314yescomplemented
817C2×C22⋊C4D4×C5314yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823C2×C42—41no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—41no—
832#95—41no—
833#95—41no—
834#95C2×C4×C5314yescomplemented
835#95D4×C5314yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
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—
876C24C22×C4×C5312yes—
877C24C22×C4×C5312yes—
878C24C22×C4×C5312yes—
879C24C2×D4×C5312yes—
880C24#41×C5312yes—
881C24C24×C5311yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
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—21no—
937C22×C4—21no—
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—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C5312yes—
981C22×C4C22×C4×C5312yes—
982C22×C4C22×C4×C5312yes—
983C22×C4C22×C4×C5312yes—
984C22×C4C2×D4×C5312yes—
985C22×C4C2×D4×C5312yes—
986C22×C4C2×D4×C5312yes—
987C22×C4C2×D4×C5312yes—
988C22×C4C2×D4×C5312yes—
989C22×C4C2×D4×C5312yes—
990C22×C4C2×D4×C5312yes—
991C22×C4C2×D4×C5312yes—
992C22×C4#41×C5312yes—
993C22×C4#41×C5312yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
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—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
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—
1117C23C4×D4×C5314yes—
1118C23C23×C4×C5311yescharacteristic
1119C23C22×D4×C5311yescharacteristic
1120C23C22×D4×C5311yescharacteristic
1121C23C22×D4×C5311yescharacteristic
1122C23C2×#41×C5311yescharacteristic
1123C23C2×#41×C5311yescharacteristic
1124C23C2×#41×C5311yescharacteristic
1125C23H(5,𝔽2)×C5311yescharacteristic
1126C23H(5,𝔽2)×C5311yescharacteristic
1127C23H(5,𝔽2)×C5311yescharacteristic
1128C23H(5,𝔽2)×C5311yescharacteristic
1129C23H(5,𝔽2)×C5311yescharacteristic
1130C23H(5,𝔽2)×C5311yescharacteristic
1131C23H(5,𝔽2)×C5311yescharacteristic
1132C232−1+4×C5311yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
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×C4C4×D4×C5314yes—
1220C2×C4C4×D4×C5314yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22C2×C4×D4×C5311yescharacteristic
1267C22C2×C4×D4×C5311yescharacteristic
1268C22C2×C4×D4×C5311yescharacteristic
1269C22C53×#51811yescharacteristic
1270C22C53×#51811yescharacteristic
1271C22C53×#51811yescharacteristic
1272C22C53×#52011yescharacteristic
1273C22C53×#53411yescharacteristic
1274C22C53×#53411yescharacteristic
1275C22C53×#53511yescharacteristic
1276C22C53×#53511yescharacteristic
1277C22C53×#53511yescharacteristic
1278C22C53×#53711yescharacteristic
1279C22C53×#53811yescharacteristic
1280C22C53×#53811yescharacteristic
1281C22C53×#53811yescharacteristic
1282C22C53×#53811yescharacteristic
1283C22C53×#54011yescharacteristic
1284C22C53×#54211yescharacteristic
1285C22D42×C5311yescharacteristic
1286C22D42×C5311yescharacteristic
1287C22D42×C5311yescharacteristic
1288C22C53×#54611yescharacteristic
1289C22C53×#54611yescharacteristic
1290C22C53×#54711yescharacteristic
1291C22C53×#54811yescharacteristic
1292C22C53×#55011yescharacteristic
1293C22C53×#55011yescharacteristic
1294C22C53×#55111yescharacteristic
1295C22C53×#55311yescharacteristic
1296C22C53×#55911yescharacteristic
1297C22C53×#56011yescharacteristic
1298C22C53×#56011yescharacteristic
1299C22C53×#56211yescharacteristic
1300C22C53×#56211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C53×#232111yescharacteristic
1317C2C53×#232111yescharacteristic
1318C2C53×#232411yescharacteristic
1319C2C53×#235811yescharacteristic
1320C2C53×#236111yescharacteristic
1321C2C53×#236611yescharacteristic
1322C2C53×#237711yescharacteristic
1323C2C53×#266911yescharacteristic
1324C2C53×#267311yescharacteristic
1325C2C53×#267611yescharacteristic
1326C2C53×#268211yescharacteristic
1327C2C53×#271011yescharacteristic
1328C2C53×#271411yescharacteristic
1329C2C53×#273011yescharacteristic
1330C2C53×#279711yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC2×C53×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C53×#390C2semidirect
3. C2×C53×#390C2semidirect
4. C2×C53×#388C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#386C2semidirect
7. C2×C53×#385C2semidirect
8. C53×#1440C2semidirect
9. C53×#1439C2semidirect
10. C53×#1439C2semidirect
11. C53×#1438C2semidirect
12. C53×#1438C2semidirect
13. C53×#1437C2semidirect
14. C53×#1436C2semidirect
15. C53×#1436C2semidirect
39. C53×#392C4semidirect
81. C22×D4×C53C2×C4semidirect
109. C2×C4⋊C4×C53D4semidirect
149. C2×C22⋊C4×C53C2×C4semidirect
150. C2×C22⋊C4×C53C2×C4semidirect
151. C2×C22⋊C4×C53D4semidirect
168. #95×C53C2×C4semidirect
169. #95×C53D4semidirect
555. #14534C53direct (N × H)
649. C2×#390C2×C53semidirect
650. C2×#390C2×C53semidirect
651. C2×#388C2×C53semidirect
652. C2×#386C2×C53semidirect
653. C2×#386C2×C53semidirect
654. C2×#385C2×C53semidirect
655. #1440C2×C53semidirect
656. #1439C2×C53semidirect
657. #1439C2×C53semidirect
658. #1438C2×C53semidirect
659. #1438C2×C53semidirect
660. #1437C2×C53semidirect
661. #1436C2×C53semidirect
662. #1436C2×C53semidirect
704. #392C4×C53semidirect
723. C53#14534direct (N × H)
747. C22×D4C2×C4×C53semidirect
775. C2×C4⋊C4D4×C53semidirect
815. C2×C22⋊C4C2×C4×C53semidirect
816. C2×C22⋊C4C2×C4×C53semidirect
817. C2×C22⋊C4D4×C53semidirect
834. #95C2×C4×C53semidirect
835. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3922
C2×C53×#3902
C2×C53×#3882
C2×C53×#3862
C2×C53×#3852
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14362
#1453453