Finite Group Databasebeta

← C53×#14519 #27222031

Subgroups — C53×#14519 #27222031

Order 13568.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1342 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×#386C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C2×C53×#385C211yesmaximal, characteristic, complemented
8C53×#1442C211yesmaximal, characteristic, complemented
9C53×#1440C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C53×#1438C211yesmaximal, characteristic, complemented
13C53×#1437C211yesmaximal, characteristic, complemented
14C53×#1434C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C24×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×C42×C53C2211yescharacteristic
37C53×#392C418yescomplemented
38C53×#390—24no—
39C53×#386—24no—
40C53×#386—24no—
41C53×#386—24no—
42C53×#386—24no—
43C53×#385—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—22no—
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
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×C414yescomplemented
81C22×D4×C53C2×C414yescomplemented
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—41no—
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×C53—41no—
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
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—22no—
110C2×C4⋊C4×C53—22no—
111C2×C4⋊C4×C53—41no—
112C2×C4⋊C4×C53—41no—
113C2×C4⋊C4×C53—41no—
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×C414yescomplemented
149C2×C22⋊C4×C53C2×C414yescomplemented
150C2×C22⋊C4×C53C2×C414yescomplemented
151C2×C22⋊C4×C53D414yescomplemented
152C2×C22⋊C4×C53D414yescomplemented
153C2×C42×C53—22no—
154C2×C42×C53—22no—
155C2×C42×C53—41no—
156#95×C53—22no—
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×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×C53C22×C412yes—
209C24×C53C22×C412yes—
210C24×C53C22×C412yes—
211C24×C53C2×D412yes—
212C24×C53C2×D412yes—
213C24×C53#4112yes—
214C24×C53#4112yes—
215C24×C53C2411yescharacteristic
216C2×D4×C53—28no—
217C2×D4×C53—28no—
218C2×D4×C53—28no—
219C2×D4×C53—28no—
220C2×D4×C53—28no—
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—21no—
308C22×C4×C53—21no—
309C22×C4×C53—44no—
310C22×C4×C53—44no—
311C22×C4×C53—44no—
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×C53C22×C412yes—
324C22×C4×C53C22×C412yes—
325C22×C4×C53C22×C412yes—
326C22×C4×C53C22×C412yes—
327C22×C4×C53C2×D412yes—
328C22×C4×C53C2×D412yes—
329C22×C4×C53C2×D412yes—
330C22×C4×C53C2×D412yes—
331C22×C4×C53C2×D412yes—
332C22×C4×C53C2×D412yes—
333C22×C4×C53C2×D412yes—
334C22×C4×C53#4112yes—
335C4⋊C4×C53—44no—
336C4⋊C4×C53—44no—
337C22⋊C4×C53—28no—
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—
345C22⋊C4×C53—44no—
346C22⋊C4×C53—44no—
347C22⋊C4×C53—44no—
348C22⋊C4×C53—44no—
349C22⋊C4×C53—44no—
350C42×C53—44no—
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—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—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×C53—41no—
452C23×C53—41no—
453C23×C53—41no—
454C23×C53C4×D414yes—
455C23×C53C4×D414yes—
456C23×C53C23×C411yescharacteristic
457C23×C53C22×D411yescharacteristic
458C23×C53C22×D411yescharacteristic
459C23×C53C22×D411yescharacteristic
460C23×C53C2×#4111yescharacteristic
461C23×C53C2×#4111yescharacteristic
462C23×C53C2×#4111yescharacteristic
463C23×C53H(5,𝔽2)11yescharacteristic
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×C532−1+411yescharacteristic
471D4×C53—416no—
472D4×C53—416no—
473D4×C53—416no—
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—22no—
507C2×C4×C53—416no—
508C2×C4×C53—416no—
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×C53C4×D414yes—
560#14519C5311yesmaximal, characteristic, direct product factor, Sylow
561C22×C53—24no—
562C22×C53—24no—
563C22×C53—24no—
564C22×C53—24no—
565C22×C53—24no—
566C22×C53—24no—
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—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—81no—
599C22×C53—81no—
600C22×C53—81no—
601C22×C53—81no—
602C22×C53—81no—
603C22×C53—81no—
604C22×C53—81no—
605C22×C53—81no—
606C22×C53C2×C4×D411yescharacteristic
607C22×C53C2×C4×D411yescharacteristic
608C22×C53C2×C4×D411yescharacteristic
609C22×C53#51811yescharacteristic
610C22×C53#51811yescharacteristic
611C22×C53#51811yescharacteristic
612C22×C53#52011yescharacteristic
613C22×C53#53411yescharacteristic
614C22×C53#53411yescharacteristic
615C22×C53#53511yescharacteristic
616C22×C53#53511yescharacteristic
617C22×C53#53511yescharacteristic
618C22×C53#53711yescharacteristic
619C22×C53#53811yescharacteristic
620C22×C53#53811yescharacteristic
621C22×C53#53811yescharacteristic
622C22×C53#53911yescharacteristic
623C22×C53#54011yescharacteristic
624C22×C53#54011yescharacteristic
625C22×C53D4211yescharacteristic
626C22×C53D4211yescharacteristic
627C22×C53D4211yescharacteristic
628C22×C53#54611yescharacteristic
629C22×C53#54611yescharacteristic
630C22×C53#54611yescharacteristic
631C22×C53#54611yescharacteristic
632C22×C53#54711yescharacteristic
633C22×C53#54811yescharacteristic
634C22×C53#55111yescharacteristic
635C22×C53#55111yescharacteristic
636C22×C53#55311yescharacteristic
637C22×C53#56011yescharacteristic
638C22×C53#56011yescharacteristic
639C22×C53#56211yescharacteristic
640C22×C53#56211yescharacteristic
641C4×C53—24no—
642C4×C53—42no—
643C4×C53—42no—
644C4×C53—42no—
645C4×C53—42no—
646C4×C53—42no—
647C4×C53—42no—
648C4×C53—42no—
649C4×C53—42no—
650C4×C53—42no—
651C4×C53—81no—
652C4×C53—81no—
653C2×#392C2×C5311yescharacteristic
654C2×#390C2×C5311yescharacteristic, complemented
655C2×#386C2×C5311yescharacteristic, complemented
656C2×#386C2×C5311yescharacteristic, complemented
657C2×#386C2×C5311yescharacteristic, complemented
658C2×#386C2×C5311yescharacteristic, complemented
659C2×#385C2×C5311yescharacteristic, complemented
660#1442C2×C5311yescharacteristic, complemented
661#1440C2×C5311yescharacteristic, complemented
662#1439C2×C5311yescharacteristic, complemented
663#1439C2×C5311yescharacteristic, complemented
664#1438C2×C5311yescharacteristic, complemented
665#1437C2×C5311yescharacteristic, complemented
666#1434C2×C5311yescharacteristic, complemented
667C22⋊#95C2×C5311yescharacteristic, complemented
668C2×C53—44no—
669C2×C53—44no—
670C2×C53—82no—
671C2×C53#232111yescharacteristic
672C2×C53#232511yescharacteristic
673C2×C53#232811yescharacteristic
674C2×C53#235811yescharacteristic
675C2×C53#235811yescharacteristic
676C2×C53#236111yescharacteristic
677C2×C53#237711yescharacteristic
678C2×C53#266911yescharacteristic
679C2×C53#267111yescharacteristic
680C2×C53#267611yescharacteristic
681C2×C53#267811yescharacteristic
682C2×C53#268811yescharacteristic
683C2×C53#269611yescharacteristic
684C2×C53#270611yescharacteristic
685C2×C53#274911yescharacteristic
686C23×D4C22×C5311yescharacteristic
687C23×D4C22×C5311yescharacteristic
688C23×D4C22×C5311yescharacteristic
689C24×C4C22×C5311yescharacteristic
690C24×C4C22×C5311yescharacteristic
691C22×C4⋊C4C22×C5311yescharacteristic
692C22×C4⋊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×C22⋊C4C22×C5311yescharacteristic
703C22×C22⋊C4C22×C5311yescharacteristic
704C22×C22⋊C4C22×C5311yescharacteristic
705C22×C22⋊C4C22×C5311yescharacteristic
706C22×C42C22×C5311yescharacteristic
707#392C4×C5318yescomplemented
708#390—24no—
709#386—24no—
710#386—24no—
711#386—24no—
712#386—24no—
713#385—24no—
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
723C2×#95C22×C5311yescharacteristic
724C2×#95C22×C5311yescharacteristic
725C2×#95C22×C5311yescharacteristic
726C2×#95C22×C5311yescharacteristic
727C2×#95C22×C5311yescharacteristic
728C53#1451911yescharacteristic, direct product factor, Sylow
729C25C23×C5311yescharacteristic
730C25C23×C5311yescharacteristic
731C25C23×C5311yescharacteristic
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4C2×C4×C5314yes—
751C22×D4C2×C4×C5314yescomplemented
752C22×D4C2×C4×C5314yescomplemented
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—41no—
760C23×C4—41no—
761C23×C4—41no—
762C23×C4—41no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C23×C5311yescharacteristic
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
779C2×C4⋊C4—22no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—41no—
783C2×C4⋊C4—41no—
784C2×C4⋊C4—41no—
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—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
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⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4C2×C4×C5314yescomplemented
820C2×C22⋊C4C2×C4×C5314yescomplemented
821C2×C22⋊C4C2×C4×C5314yescomplemented
822C2×C22⋊C4D4×C5314yescomplemented
823C2×C22⋊C4D4×C5314yescomplemented
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—41no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95C2×C4×C5314yescomplemented
840#95D4×C5314yescomplemented
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—
876C24—21no—
877C24—21no—
878C24—21no—
879C24C22×C4×C5312yes—
880C24C22×C4×C5312yes—
881C24C22×C4×C5312yes—
882C24C2×D4×C5312yes—
883C24C2×D4×C5312yes—
884C24#41×C5312yes—
885C24#41×C5312yes—
886C24C24×C5311yescharacteristic
887C2×D4—28no—
888C2×D4—28no—
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—
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—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
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×C4C22×C4×C5312yes—
995C22×C4C22×C4×C5312yes—
996C22×C4C22×C4×C5312yes—
997C22×C4C22×C4×C5312yes—
998C22×C4C2×D4×C5312yes—
999C22×C4C2×D4×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—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C22⋊C4—28no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
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—
1021C42—44no—
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—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—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—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23C4×D4×C5314yes—
1126C23C4×D4×C5314yes—
1127C23C23×C4×C5311yescharacteristic
1128C23C22×D4×C5311yescharacteristic
1129C23C22×D4×C5311yescharacteristic
1130C23C22×D4×C5311yescharacteristic
1131C23C2×#41×C5311yescharacteristic
1132C23C2×#41×C5311yescharacteristic
1133C23C2×#41×C5311yescharacteristic
1134C23H(5,𝔽2)×C5311yescharacteristic
1135C23H(5,𝔽2)×C5311yescharacteristic
1136C23H(5,𝔽2)×C5311yescharacteristic
1137C23H(5,𝔽2)×C5311yescharacteristic
1138C23H(5,𝔽2)×C5311yescharacteristic
1139C23H(5,𝔽2)×C5311yescharacteristic
1140C23H(5,𝔽2)×C5311yescharacteristic
1141C232−1+4×C5311yescharacteristic
1142D4—416no—
1143D4—416no—
1144D4—416no—
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—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—416no—
1179C2×C4—416no—
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×C4C4×D4×C5314yes—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
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—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—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22C2×C4×D4×C5311yescharacteristic
1277C22C2×C4×D4×C5311yescharacteristic
1278C22C2×C4×D4×C5311yescharacteristic
1279C22C53×#51811yescharacteristic
1280C22C53×#51811yescharacteristic
1281C22C53×#51811yescharacteristic
1282C22C53×#52011yescharacteristic
1283C22C53×#53411yescharacteristic
1284C22C53×#53411yescharacteristic
1285C22C53×#53511yescharacteristic
1286C22C53×#53511yescharacteristic
1287C22C53×#53511yescharacteristic
1288C22C53×#53711yescharacteristic
1289C22C53×#53811yescharacteristic
1290C22C53×#53811yescharacteristic
1291C22C53×#53811yescharacteristic
1292C22C53×#53911yescharacteristic
1293C22C53×#54011yescharacteristic
1294C22C53×#54011yescharacteristic
1295C22D42×C5311yescharacteristic
1296C22D42×C5311yescharacteristic
1297C22D42×C5311yescharacteristic
1298C22C53×#54611yescharacteristic
1299C22C53×#54611yescharacteristic
1300C22C53×#54611yescharacteristic
1301C22C53×#54611yescharacteristic
1302C22C53×#54711yescharacteristic
1303C22C53×#54811yescharacteristic
1304C22C53×#55111yescharacteristic
1305C22C53×#55111yescharacteristic
1306C22C53×#55311yescharacteristic
1307C22C53×#56011yescharacteristic
1308C22C53×#56011yescharacteristic
1309C22C53×#56211yescharacteristic
1310C22C53×#56211yescharacteristic
1311C4—24no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—81no—
1322C4—81no—
1323C2—44no—
1324C2—44no—
1325C2—82no—
1326C2C53×#232111yescharacteristic
1327C2C53×#232511yescharacteristic
1328C2C53×#232811yescharacteristic
1329C2C53×#235811yescharacteristic
1330C2C53×#235811yescharacteristic
1331C2C53×#236111yescharacteristic
1332C2C53×#237711yescharacteristic
1333C2C53×#266911yescharacteristic
1334C2C53×#267111yescharacteristic
1335C2C53×#267611yescharacteristic
1336C2C53×#267811yescharacteristic
1337C2C53×#268811yescharacteristic
1338C2C53×#269611yescharacteristic
1339C2C53×#270611yescharacteristic
1340C2C53×#274911yescharacteristic
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×#386C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#386C2semidirect
7. C2×C53×#385C2semidirect
8. C53×#1442C2semidirect
9. C53×#1440C2semidirect
10. C53×#1439C2semidirect
11. C53×#1439C2semidirect
12. C53×#1438C2semidirect
13. C53×#1437C2semidirect
14. C53×#1434C2semidirect
15. C53×C22⋊#95C2semidirect
37. C53×#392C4semidirect
80. C22×D4×C53C2×C4semidirect
81. C22×D4×C53C2×C4semidirect
148. C2×C22⋊C4×C53C2×C4semidirect
149. C2×C22⋊C4×C53C2×C4semidirect
150. C2×C22⋊C4×C53C2×C4semidirect
151. C2×C22⋊C4×C53D4semidirect
152. C2×C22⋊C4×C53D4semidirect
168. #95×C53C2×C4semidirect
169. #95×C53D4semidirect
560. #14519C53direct (N × H)
654. C2×#390C2×C53semidirect
655. C2×#386C2×C53semidirect
656. C2×#386C2×C53semidirect
657. C2×#386C2×C53semidirect
658. C2×#386C2×C53semidirect
659. C2×#385C2×C53semidirect
660. #1442C2×C53semidirect
661. #1440C2×C53semidirect
662. #1439C2×C53semidirect
663. #1439C2×C53semidirect
664. #1438C2×C53semidirect
665. #1437C2×C53semidirect
666. #1434C2×C53semidirect
667. C22⋊#95C2×C53semidirect
707. #392C4×C53semidirect
728. C53#14519direct (N × H)
751. C22×D4C2×C4×C53semidirect
752. C22×D4C2×C4×C53semidirect
819. C2×C22⋊C4C2×C4×C53semidirect
820. C2×C22⋊C4C2×C4×C53semidirect
821. C2×C22⋊C4C2×C4×C53semidirect
822. C2×C22⋊C4D4×C53semidirect
823. C2×C22⋊C4D4×C53semidirect
839. #95C2×C4×C53semidirect
840. #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×#3862
C2×C53×#3852
C53×#14422
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14342
C53×C22⋊#952
#1451953