Finite Group Databasebeta

← C53×#14363 #27221875

Subgroups — C53×#14363 #27221875

Order 13568.

2494 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C53C211yesmaximal, characteristic
2C2×C53×#390C211yesmaximal, characteristic, complemented
3C2×C53×#386C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#381C211yesmaximal, characteristic, complemented
6C53×#1441C211yesmaximal, characteristic, complemented
7C53×#1440C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic, complemented
10C53×#1438C211yesmaximal, characteristic, complemented
11C53×#1438C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1436C211yesmaximal, characteristic, complemented
14C53×C22⋊#95C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C24×C4×C53C2211yescharacteristic
21C2×#121×C53—24no—
22C2×#121×C53—24no—
23C2×#121×C53C418yescomplemented
24C22×C4⋊C4×C53C2211yescharacteristic
25C22×C4⋊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×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#390—24no—
41C53×#386—24no—
42C53×#386—24no—
43C53×#381—24no—
44C2×#95×C53C2211yescharacteristic
45C2×#95×C53C2211yescharacteristic
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—41no—
68C22×D4×C53—41no—
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×C53C2×C414yes—
78C22×D4×C53C2×C414yes—
79C22×D4×C53C2×C414yescomplemented
80C22×D4×C53D414yes—
81C22×D4×C53D414yes—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—22no—
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—41no—
90C23×C4×C53—41no—
91C23×C4×C53—41no—
92C23×C4×C53—41no—
93C23×C4×C53—41no—
94C23×C4×C53—41no—
95C23×C4×C53C2×C414yescomplemented
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
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
108#121×C53—232no—
109C2×C4⋊C4×C53—22no—
110C2×C4⋊C4×C53—22no—
111C2×C4⋊C4×C53—22no—
112C2×C4⋊C4×C53—41no—
113C2×C4⋊C4×C53—41no—
114C2×C4⋊C4×C53C2×C414yescomplemented
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—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—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×C53—41no—
149C2×C22⋊C4×C53—41no—
150C2×C22⋊C4×C53—41no—
151C2×C22⋊C4×C53—41no—
152C2×C22⋊C4×C53C2×C414yes—
153C2×C22⋊C4×C53C2×C414yescomplemented
154C2×C42×C53—22no—
155C2×C42×C53—41no—
156C2×C42×C53—41no—
157#95×C53—22no—
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—41no—
165#95×C53—41no—
166#95×C53—41no—
167#95×C53—41no—
168#95×C53—41no—
169#95×C53—41no—
170#95×C53D414yescomplemented
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×C53C22×C412yes—
210C24×C53C22×C412yes—
211C24×C53C22×C412yes—
212C24×C53C2×D412yes—
213C24×C53C2×D412yes—
214C24×C53C2×D412yes—
215C24×C53C2×D412yes—
216C24×C53C2411yescharacteristic
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—
237C2×D4×C53C22⋊C4116yescomplemented
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—28no—
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—28no—
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—21no—
308C22×C4×C53—21no—
309C22×C4×C53—21no—
310C22×C4×C53—21no—
311C22×C4×C53—21no—
312C22×C4×C53—44no—
313C22×C4×C53—44no—
314C22×C4×C53—44no—
315C22×C4×C53—44no—
316C22×C4×C53—44no—
317C22×C4×C53—44no—
318C22×C4×C53—44no—
319C22×C4×C53—44no—
320C22×C4×C53—44no—
321C22×C4×C53—44no—
322C22×C4×C53—44no—
323C22×C4×C53—44no—
324C22×C4×C53C22×C412yes—
325C22×C4×C53C22×C412yes—
326C22×C4×C53C22×C412yes—
327C22×C4×C53C22×C412yes—
328C22×C4×C53C2×D412yes—
329C22×C4×C53C2×D412yes—
330C22×C4×C53C2×D412yes—
331C22×C4×C53C2×D412yes—
332C22×C4×C53C2×D412yes—
333C22×C4×C53#4112yes—
334C22×C4×C53#4112yes—
335C22×C4×C53#4112yes—
336C4⋊C4×C53—28no—
337C4⋊C4×C53—44no—
338C22⋊C4×C53—28no—
339C22⋊C4×C53—28no—
340C22⋊C4×C53—44no—
341C22⋊C4×C53—44no—
342C22⋊C4×C53—44no—
343C22⋊C4×C53—44no—
344C22⋊C4×C53—44no—
345C22⋊C4×C53—44no—
346C22⋊C4×C53—44no—
347C22⋊C4×C53—44no—
348C22⋊C4×C53—44no—
349C22⋊C4×C53—44no—
350C22⋊C4×C53—44no—
351C42×C53—44no—
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—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—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×C53—41no—
452C23×C53—41no—
453C23×C53—41no—
454C23×C53—41no—
455C23×C53C2×C22⋊C414yes—
456C23×C53C2×C22⋊C414yes—
457C23×C53C23×C411yescharacteristic
458C23×C53C22×D411yescharacteristic
459C23×C53C22×D411yescharacteristic
460C23×C53C22×D411yescharacteristic
461C23×C53C2×#4111yescharacteristic
462C23×C53C2×#4111yescharacteristic
463C23×C53C2×#4111yescharacteristic
464C23×C53H(5,𝔽2)11yescharacteristic
465C23×C53H(5,𝔽2)11yescharacteristic
466C23×C53H(5,𝔽2)11yescharacteristic
467C23×C53H(5,𝔽2)11yescharacteristic
468C23×C53H(5,𝔽2)11yescharacteristic
469C23×C53H(5,𝔽2)11yescharacteristic
470C23×C53H(5,𝔽2)11yescharacteristic
471C23×C532−1+411yescharacteristic
472D4×C53—416no—
473D4×C53—416no—
474D4×C53—416no—
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—416no—
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×C53—41no—
554C2×C4×C53—41no—
555C2×C4×C53—41no—
556C2×C4×C53—41no—
557C2×C4×C53—41no—
558C2×C4×C53—41no—
559C2×C4×C53C2×C22⋊C414yes—
560C2×C4×C53C4×D414yes—
561#14363C5311yesmaximal, characteristic, direct product factor, Sylow
562C22×C53—24no—
563C22×C53—24no—
564C22×C53—24no—
565C22×C53—24no—
566C22×C53—24no—
567C22×C53—24no—
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—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—81no—
600C22×C53—81no—
601C22×C53—81no—
602C22×C53—81no—
603C22×C53—81no—
604C22×C53—81no—
605C22×C53—81no—
606C22×C53—81no—
607C22×C53C22×C22⋊C411yescharacteristic
608C22×C53C2×C4×D411yescharacteristic
609C22×C53C4×#4111yescharacteristic
610C22×C53#51811yescharacteristic
611C22×C53#51811yescharacteristic
612C22×C53#51811yescharacteristic
613C22×C53#52011yescharacteristic
614C22×C53#53411yescharacteristic
615C22×C53#53411yescharacteristic
616C22×C53#53411yescharacteristic
617C22×C53#53411yescharacteristic
618C22×C53#53511yescharacteristic
619C22×C53#53711yescharacteristic
620C22×C53#53811yescharacteristic
621C22×C53#53811yescharacteristic
622C22×C53#54011yescharacteristic
623C22×C53#54011yescharacteristic
624C22×C53#54011yescharacteristic
625C22×C53#54211yescharacteristic
626C22×C53D4211yescharacteristic
627C22×C53D4211yescharacteristic
628C22×C53#54611yescharacteristic
629C22×C53#54611yescharacteristic
630C22×C53#54611yescharacteristic
631C22×C53#54611yescharacteristic
632C22×C53#54611yescharacteristic
633C22×C53#54711yescharacteristic
634C22×C53#54711yescharacteristic
635C22×C53#55011yescharacteristic
636C22×C53#55311yescharacteristic
637C22×C53#55511yescharacteristic
638C22×C53#56011yescharacteristic
639C22×C53#56011yescharacteristic
640C22×C53#56211yescharacteristic
641C22×C53#56211yescharacteristic
642C4×C53—24no—
643C4×C53—24no—
644C4×C53—42no—
645C4×C53—42no—
646C4×C53—42no—
647C4×C53—42no—
648C4×C53—42no—
649C4×C53—42no—
650C4×C53—81no—
651C4×C53—81no—
652C4×C53—81no—
653C4×C53—81no—
654C22×#121C2×C5311yescharacteristic
655C2×#390C2×C5311yescharacteristic, complemented
656C2×#386C2×C5311yescharacteristic, complemented
657C2×#386C2×C5311yescharacteristic, complemented
658C2×#381C2×C5311yescharacteristic, complemented
659#1441C2×C5311yescharacteristic, complemented
660#1440C2×C5311yescharacteristic, complemented
661#1439C2×C5311yescharacteristic, complemented
662#1438C2×C5311yescharacteristic, complemented
663#1438C2×C5311yescharacteristic, complemented
664#1438C2×C5311yescharacteristic, complemented
665#1437C2×C5311yescharacteristic, complemented
666#1436C2×C5311yescharacteristic, complemented
667C22⋊#95C2×C5311yescharacteristic, complemented
668C22⋊#95C2×C5311yescharacteristic, complemented
669C2×C53—44no—
670C2×C53—44no—
671C2×C53—82no—
672C2×C53#230811yescharacteristic
673C2×C53#232411yescharacteristic
674C2×C53#233311yescharacteristic
675C2×C53D4×C22⋊C411yescharacteristic
676C2×C53#233911yescharacteristic
677C2×C53#236311yescharacteristic
678C2×C53#237711yescharacteristic
679C2×C53#267111yescharacteristic
680C2×C53#267311yescharacteristic
681C2×C53#267811yescharacteristic
682C2×C53#268211yescharacteristic
683C2×C53#268611yescharacteristic
684C2×C53#268811yescharacteristic
685C2×C53#269911yescharacteristic
686C2×C53#270111yescharacteristic
687C23×D4C22×C5311yescharacteristic
688C23×D4C22×C5311yescharacteristic
689C23×D4C22×C5311yescharacteristic
690C24×C4C22×C5311yescharacteristic
691C24×C4C22×C5311yescharacteristic
692C2×#121—24no—
693C2×#121—24no—
694C2×#121C4×C5318yescomplemented
695C22×C4⋊C4C22×C5311yescharacteristic
696C22×C4⋊C4C22×C5311yescharacteristic
697C22×C22⋊C4C22×C5311yescharacteristic
698C22×C22⋊C4C22×C5311yescharacteristic
699C22×C22⋊C4C22×C5311yescharacteristic
700C22×C22⋊C4C22×C5311yescharacteristic
701C22×C22⋊C4C22×C5311yescharacteristic
702C22×C22⋊C4C22×C5311yescharacteristic
703C22×C22⋊C4C22×C5311yescharacteristic
704C22×C22⋊C4C22×C5311yescharacteristic
705C22×C22⋊C4C22×C5311yescharacteristic
706C22×C22⋊C4C22×C5311yescharacteristic
707C22×C22⋊C4C22×C5311yescharacteristic
708C22×C22⋊C4C22×C5311yescharacteristic
709C22×C22⋊C4C22×C5311yescharacteristic
710C22×C42C22×C5311yescharacteristic
711#390—24no—
712#386—24no—
713#386—24no—
714#381—24no—
715C2×#95C22×C5311yescharacteristic
716C2×#95C22×C5311yescharacteristic
717C2×#95C22×C5311yescharacteristic
718C2×#95C22×C5311yescharacteristic
719C2×#95C22×C5311yescharacteristic
720C2×#95C22×C5311yescharacteristic
721C2×#95C22×C5311yescharacteristic
722C2×#95C22×C5311yescharacteristic
723C2×#95C22×C5311yescharacteristic
724C2×#95C22×C5311yescharacteristic
725C2×#95C22×C5311yescharacteristic
726C2×#95C22×C5311yescharacteristic
727C2×#95C22×C5311yescharacteristic
728C2×#95C22×C5311yescharacteristic
729C53#1436311yescharacteristic, direct product factor, Sylow
730C25C23×C5311yescharacteristic
731C25C23×C5311yescharacteristic
732C25C23×C5311yescharacteristic
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4C2×C4×C5314yes—
750C22×D4C2×C4×C5314yes—
751C22×D4C2×C4×C5314yescomplemented
752C22×D4D4×C5314yes—
753C22×D4D4×C5314yes—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C2×C4×C5314yescomplemented
768C23×C4C23×C5311yescharacteristic
769C23×C4C23×C5311yescharacteristic
770C23×C4C23×C5311yescharacteristic
771C23×C4C23×C5311yescharacteristic
772C23×C4C23×C5311yescharacteristic
773C23×C4C23×C5311yescharacteristic
774C23×C4C23×C5311yescharacteristic
775C23×C4C23×C5311yescharacteristic
776C23×C4C23×C5311yescharacteristic
777C23×C4C23×C5311yescharacteristic
778C23×C4C23×C5311yescharacteristic
779C23×C4C23×C5311yescharacteristic
780#121—232no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—41no—
785C2×C4⋊C4—41no—
786C2×C4⋊C4C2×C4×C5314yescomplemented
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—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
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⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4C2×C4×C5314yes—
825C2×C22⋊C4C2×C4×C5314yescomplemented
826C2×C42—22no—
827C2×C42—41no—
828C2×C42—41no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95D4×C5314yescomplemented
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24C22×C4×C5312yes—
882C24C22×C4×C5312yes—
883C24C22×C4×C5312yes—
884C24C2×D4×C5312yes—
885C24C2×D4×C5312yes—
886C24C2×D4×C5312yes—
887C24C2×D4×C5312yes—
888C24C24×C5311yescharacteristic
889C2×D4—28no—
890C2×D4—28no—
891C2×D4—28no—
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—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4C22⋊C4×C53116yescomplemented
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—28no—
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—28no—
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—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4C22×C4×C5312yes—
997C22×C4C22×C4×C5312yes—
998C22×C4C22×C4×C5312yes—
999C22×C4C22×C4×C5312yes—
1000C22×C4C2×D4×C5312yes—
1001C22×C4C2×D4×C5312yes—
1002C22×C4C2×D4×C5312yes—
1003C22×C4C2×D4×C5312yes—
1004C22×C4C2×D4×C5312yes—
1005C22×C4#41×C5312yes—
1006C22×C4#41×C5312yes—
1007C22×C4#41×C5312yes—
1008C4⋊C4—28no—
1009C4⋊C4—44no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C42—44no—
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—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—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—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23C2×C22⋊C4×C5314yes—
1128C23C2×C22⋊C4×C5314yes—
1129C23C23×C4×C5311yescharacteristic
1130C23C22×D4×C5311yescharacteristic
1131C23C22×D4×C5311yescharacteristic
1132C23C22×D4×C5311yescharacteristic
1133C23C2×#41×C5311yescharacteristic
1134C23C2×#41×C5311yescharacteristic
1135C23C2×#41×C5311yescharacteristic
1136C23H(5,𝔽2)×C5311yescharacteristic
1137C23H(5,𝔽2)×C5311yescharacteristic
1138C23H(5,𝔽2)×C5311yescharacteristic
1139C23H(5,𝔽2)×C5311yescharacteristic
1140C23H(5,𝔽2)×C5311yescharacteristic
1141C23H(5,𝔽2)×C5311yescharacteristic
1142C23H(5,𝔽2)×C5311yescharacteristic
1143C232−1+4×C5311yescharacteristic
1144D4—416no—
1145D4—416no—
1146D4—416no—
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—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—416no—
1178C2×C4—416no—
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×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×C4C2×C22⋊C4×C5314yes—
1232C2×C4C4×D4×C5314yes—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22C22×C22⋊C4×C5311yescharacteristic
1279C22C2×C4×D4×C5311yescharacteristic
1280C22C4×#41×C5311yescharacteristic
1281C22C53×#51811yescharacteristic
1282C22C53×#51811yescharacteristic
1283C22C53×#51811yescharacteristic
1284C22C53×#52011yescharacteristic
1285C22C53×#53411yescharacteristic
1286C22C53×#53411yescharacteristic
1287C22C53×#53411yescharacteristic
1288C22C53×#53411yescharacteristic
1289C22C53×#53511yescharacteristic
1290C22C53×#53711yescharacteristic
1291C22C53×#53811yescharacteristic
1292C22C53×#53811yescharacteristic
1293C22C53×#54011yescharacteristic
1294C22C53×#54011yescharacteristic
1295C22C53×#54011yescharacteristic
1296C22C53×#54211yescharacteristic
1297C22D42×C5311yescharacteristic
1298C22D42×C5311yescharacteristic
1299C22C53×#54611yescharacteristic
1300C22C53×#54611yescharacteristic
1301C22C53×#54611yescharacteristic
1302C22C53×#54611yescharacteristic
1303C22C53×#54611yescharacteristic
1304C22C53×#54711yescharacteristic
1305C22C53×#54711yescharacteristic
1306C22C53×#55011yescharacteristic
1307C22C53×#55311yescharacteristic
1308C22C53×#55511yescharacteristic
1309C22C53×#56011yescharacteristic
1310C22C53×#56011yescharacteristic
1311C22C53×#56211yescharacteristic
1312C22C53×#56211yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C2—44no—
1326C2—44no—
1327C2—82no—
1328C2C53×#230811yescharacteristic
1329C2C53×#232411yescharacteristic
1330C2C53×#233311yescharacteristic
1331C2D4×C22⋊C4×C5311yescharacteristic
1332C2C53×#233911yescharacteristic
1333C2C53×#236311yescharacteristic
1334C2C53×#237711yescharacteristic
1335C2C53×#267111yescharacteristic
1336C2C53×#267311yescharacteristic
1337C2C53×#267811yescharacteristic
1338C2C53×#268211yescharacteristic
1339C2C53×#268611yescharacteristic
1340C2C53×#268811yescharacteristic
1341C2C53×#269911yescharacteristic
1342C2C53×#270111yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC22×#121×C53C2
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×#386C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#381C2semidirect
6. C53×#1441C2semidirect
7. C53×#1440C2semidirect
8. C53×#1439C2semidirect
9. C53×#1438C2semidirect
10. C53×#1438C2semidirect
11. C53×#1438C2semidirect
12. C53×#1437C2semidirect
13. C53×#1436C2semidirect
14. C53×C22⋊#95C2semidirect
15. C53×C22⋊#95C2semidirect
23. C2×#121×C53C4semidirect
79. C22×D4×C53C2×C4semidirect
95. C23×C4×C53C2×C4semidirect
114. C2×C4⋊C4×C53C2×C4semidirect
153. C2×C22⋊C4×C53C2×C4semidirect
170. #95×C53D4semidirect
237. C2×D4×C53C22⋊C4semidirect
561. #14363C53direct (N × H)
655. C2×#390C2×C53semidirect
656. C2×#386C2×C53semidirect
657. C2×#386C2×C53semidirect
658. C2×#381C2×C53semidirect
659. #1441C2×C53semidirect
660. #1440C2×C53semidirect
661. #1439C2×C53semidirect
662. #1438C2×C53semidirect
663. #1438C2×C53semidirect
664. #1438C2×C53semidirect
665. #1437C2×C53semidirect
666. #1436C2×C53semidirect
667. C22⋊#95C2×C53semidirect
668. C22⋊#95C2×C53semidirect
694. C2×#121C4×C53semidirect
729. C53#14363direct (N × H)
751. C22×D4C2×C4×C53semidirect
767. C23×C4C2×C4×C53semidirect
786. C2×C4⋊C4C2×C4×C53semidirect
825. C2×C22⋊C4C2×C4×C53semidirect
842. #95D4×C53semidirect
909. C2×D4C22⋊C4×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C532
C2×C53×#3902
C2×C53×#3862
C2×C53×#3812
C53×#14412
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14362
C53×C22⋊#952
#1436353