Finite Group Databasebeta

← C53×#15493 #27223005

Subgroups — C53×#15493 #27223005

Order 13568.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#399C211yesmaximal, characteristic, complemented
2C2×C53×#397C211yesmaximal, characteristic, complemented
3C2×C53×#394C211yesmaximal, characteristic, complemented
4C2×C53×#392C211yesmaximal, characteristic
5C2×C53×#390C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C2×C53×#386C211yesmaximal, characteristic, complemented
8C2×C53×#380C211yesmaximal, characteristic, complemented
9C53×#1445C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C53×#1438C211yesmaximal, characteristic, complemented
13C53×#1438C211yesmaximal, characteristic, complemented
14C53×#1437C211yesmaximal, 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×C4⋊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×C22⋊C4×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C53×#399—24no—
40C53×#397—24no—
41C53×#394—24no—
42C53×#392—24no—
43C53×#390—24no—
44C53×#386—24no—
45C53×#386—24no—
46C53×#380—24no—
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
58C2×#95×C53C2211yescharacteristic
59C25×C53C2311yescharacteristic
60C25×C53C2311yescharacteristic
61C25×C53C2311yescharacteristic
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—22no—
72C22×D4×C53—22no—
73C22×D4×C53—22no—
74C22×D4×C53—41no—
75C22×D4×C53—41no—
76C22×D4×C53—41no—
77C22×D4×C53—41no—
78C22×D4×C53—41no—
79C22×D4×C53—41no—
80C22×D4×C53—41no—
81C22×D4×C53—41no—
82C22×D4×C53D414yes—
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×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
101C23×C4×C53C2311yescharacteristic
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53—22no—
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—41no—
110C2×C4⋊C4×C53—41no—
111C2×C4⋊C4×C53—41no—
112C2×C4⋊C4×C53—41no—
113C2×C4⋊C4×C53D414yescomplemented
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—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—22no—
140C2×C22⋊C4×C53—22no—
141C2×C22⋊C4×C53—22no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—22no—
144C2×C22⋊C4×C53—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×C53—41no—
153C2×C22⋊C4×C53—41no—
154C2×C22⋊C4×C53—41no—
155C2×C22⋊C4×C53—41no—
156C2×C42×C53—22no—
157C2×C42×C53—41no—
158C2×C42×C53—41no—
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—22no—
166#95×C53—22no—
167#95×C53—41no—
168#95×C53—41no—
169#95×C53D414yescomplemented
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×C53—21no—
210C24×C53—21no—
211C24×C53C2×D412yes—
212C24×C53C2×D412yes—
213C24×C53#4112yes—
214C24×C53#4112yes—
215C24×C53#4112yes—
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×C53—44no—
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—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—21no—
310C22×C4×C53—21no—
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×C53C2×D412yes—
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×C53C2×D412yes—
327C22×C4×C53#4112yes—
328C22×C4×C53#4112yes—
329C4⋊C4×C53—44no—
330C4⋊C4×C53—44no—
331C4⋊C4×C53—44no—
332C4⋊C4×C53—44no—
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—
345C22⋊C4×C53—44no—
346C22⋊C4×C53—44no—
347C42×C53—44no—
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—22no—
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×C53—41no—
452C23×C53#12314yes—
453C23×C53C22×D411yescharacteristic
454C23×C53C22×D411yescharacteristic
455C23×C53C22×D411yescharacteristic
456C23×C53C22×D411yescharacteristic
457C23×C53C2×#4111yescharacteristic
458C23×C53C2×#4111yescharacteristic
459C23×C53C2×#4111yescharacteristic
460C23×C53C2×#4111yescharacteristic
461C23×C53C2×#4111yescharacteristic
462C23×C53H(5,𝔽2)11yescharacteristic
463C23×C53H(5,𝔽2)11yescharacteristic
464C23×C53H(5,𝔽2)11yescharacteristic
465C23×C53H(5,𝔽2)11yescharacteristic
466C23×C53H(5,𝔽2)11yescharacteristic
467C23×C532−1+411yescharacteristic
468D4×C53—416no—
469D4×C53—416no—
470D4×C53—416no—
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—416no—
502C2×C4×C53—41no—
503C2×C4×C53—41no—
504C2×C4×C53—41no—
505C2×C4×C53—41no—
506C2×C4×C53—41no—
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#12114yes—
555C2×C4×C53#12714yes—
556#15493C5311yesmaximal, characteristic, direct product factor, Sylow
557C22×C53—24no—
558C22×C53—24no—
559C22×C53—24no—
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—42no—
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×C53—81no—
602C22×C53C2×#12111yescharacteristic
603C22×C53C2×#12311yescharacteristic
604C22×C53#52511yescharacteristic
605C22×C53#52511yescharacteristic
606C22×C53#52911yescharacteristic
607C22×C53C2×#12711yescharacteristic
608C22×C53#53411yescharacteristic
609C22×C53#53411yescharacteristic
610C22×C53#53511yescharacteristic
611C22×C53#53711yescharacteristic
612C22×C53#53811yescharacteristic
613C22×C53#53811yescharacteristic
614C22×C53#53911yescharacteristic
615C22×C53#54011yescharacteristic
616C22×C53#54211yescharacteristic
617C22×C53D4211yescharacteristic
618C22×C53D4211yescharacteristic
619C22×C53#54611yescharacteristic
620C22×C53#54611yescharacteristic
621C22×C53#54611yescharacteristic
622C22×C53#54611yescharacteristic
623C22×C53#54611yescharacteristic
624C22×C53#54611yescharacteristic
625C22×C53#54611yescharacteristic
626C22×C53#54711yescharacteristic
627C22×C53#54811yescharacteristic
628C22×C53#54811yescharacteristic
629C22×C53#55011yescharacteristic
630C22×C53#55011yescharacteristic
631C22×C53#55111yescharacteristic
632C22×C53#55111yescharacteristic
633C22×C53#55111yescharacteristic
634C22×C53#55311yescharacteristic
635C22×C53#56011yescharacteristic
636C22×C53#56211yescharacteristic
637C4×C53—24no—
638C4×C53—24no—
639C4×C53—42no—
640C4×C53—42no—
641C4×C53—42no—
642C4×C53—42no—
643C4×C53—42no—
644C4×C53—42no—
645C4×C53—81no—
646C4×C53—81no—
647C4×C53—81no—
648C4×C53—81no—
649C2×#399C2×C5311yescharacteristic, complemented
650C2×#397C2×C5311yescharacteristic, complemented
651C2×#394C2×C5311yescharacteristic, complemented
652C2×#392C2×C5311yescharacteristic
653C2×#390C2×C5311yescharacteristic, complemented
654C2×#386C2×C5311yescharacteristic, complemented
655C2×#386C2×C5311yescharacteristic, complemented
656C2×#380C2×C5311yescharacteristic, complemented
657#1445C2×C5311yescharacteristic, complemented
658#1439C2×C5311yescharacteristic, complemented
659#1439C2×C5311yescharacteristic, complemented
660#1438C2×C5311yescharacteristic, complemented
661#1438C2×C5311yescharacteristic, complemented
662#1437C2×C5311yescharacteristic, complemented
663#1436C2×C5311yescharacteristic, complemented
664C2×C53—44no—
665C2×C53—82no—
666C2×C53—82no—
667C2×C53#241211yescharacteristic
668C2×C53#241811yescharacteristic
669C2×C53#242711yescharacteristic
670C2×C53#244311yescharacteristic
671C2×C53#246711yescharacteristic
672C2×C53#247111yescharacteristic
673C2×C53#253911yescharacteristic
674C2×C53#254011yescharacteristic
675C2×C53#254111yescharacteristic
676C2×C53#266811yescharacteristic
677C2×C53#267111yescharacteristic
678C2×C53#269611yescharacteristic
679C2×C53#270311yescharacteristic
680C2×C53#270511yescharacteristic
681C2×C53#273011yescharacteristic
682C23×D4C22×C5311yescharacteristic
683C23×D4C22×C5311yescharacteristic
684C23×D4C22×C5311yescharacteristic
685C24×C4C22×C5311yescharacteristic
686C22×C4⋊C4C22×C5311yescharacteristic
687C22×C4⋊C4C22×C5311yescharacteristic
688C22×C4⋊C4C22×C5311yescharacteristic
689C22×C4⋊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×C22⋊C4C22×C5311yescharacteristic
703C22×C22⋊C4C22×C5311yescharacteristic
704C22×C42C22×C5311yescharacteristic
705#399—24no—
706#397—24no—
707#394—24no—
708#392—24no—
709#390—24no—
710#386—24no—
711#386—24no—
712#380—24no—
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
723C2×#95C22×C5311yescharacteristic
724C2×#95C22×C5311yescharacteristic
725C53#1549311yescharacteristic, direct product factor, Sylow
726C25C23×C5311yescharacteristic
727C25C23×C5311yescharacteristic
728C25C23×C5311yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
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—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4D4×C5314yes—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
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
767C23×C4C23×C5311yescharacteristic
768C23×C4C23×C5311yescharacteristic
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4—41no—
780C2×C4⋊C4D4×C5314yescomplemented
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—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—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
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×C42—22no—
824C2×C42—41no—
825C2×C42—41no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—41no—
835#95—41no—
836#95D4×C5314yescomplemented
837#95D4×C5314yescomplemented
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—
876C24—21no—
877C24—21no—
878C24C2×D4×C5312yes—
879C24C2×D4×C5312yes—
880C24#41×C5312yes—
881C24#41×C5312yes—
882C24#41×C5312yes—
883C24C24×C5311yescharacteristic
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—28no—
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—
903C2×D4—44no—
904C2×D4—44no—
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—28no—
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—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
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×C4C2×D4×C5312yes—
993C22×C4C2×D4×C5312yes—
994C22×C4#41×C5312yes—
995C22×C4#41×C5312yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊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—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C42—44no—
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—22no—
1046C23—22no—
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—
1117C23—41no—
1118C23—41no—
1119C23#123×C5314yes—
1120C23C22×D4×C5311yescharacteristic
1121C23C22×D4×C5311yescharacteristic
1122C23C22×D4×C5311yescharacteristic
1123C23C22×D4×C5311yescharacteristic
1124C23C2×#41×C5311yescharacteristic
1125C23C2×#41×C5311yescharacteristic
1126C23C2×#41×C5311yescharacteristic
1127C23C2×#41×C5311yescharacteristic
1128C23C2×#41×C5311yescharacteristic
1129C23H(5,𝔽2)×C5311yescharacteristic
1130C23H(5,𝔽2)×C5311yescharacteristic
1131C23H(5,𝔽2)×C5311yescharacteristic
1132C23H(5,𝔽2)×C5311yescharacteristic
1133C23H(5,𝔽2)×C5311yescharacteristic
1134C232−1+4×C5311yescharacteristic
1135D4—416no—
1136D4—416no—
1137D4—416no—
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—416no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
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×C4—41no—
1220C2×C4—41no—
1221C2×C4#121×C5314yes—
1222C2×C4#127×C5314yes—
1223C22—24no—
1224C22—24no—
1225C22—24no—
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—42no—
1251C22—42no—
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—
1266C22—81no—
1267C22—81no—
1268C22C2×#121×C5311yescharacteristic
1269C22C2×#123×C5311yescharacteristic
1270C22C53×#52511yescharacteristic
1271C22C53×#52511yescharacteristic
1272C22C53×#52911yescharacteristic
1273C22C2×#127×C5311yescharacteristic
1274C22C53×#53411yescharacteristic
1275C22C53×#53411yescharacteristic
1276C22C53×#53511yescharacteristic
1277C22C53×#53711yescharacteristic
1278C22C53×#53811yescharacteristic
1279C22C53×#53811yescharacteristic
1280C22C53×#53911yescharacteristic
1281C22C53×#54011yescharacteristic
1282C22C53×#54211yescharacteristic
1283C22D42×C5311yescharacteristic
1284C22D42×C5311yescharacteristic
1285C22C53×#54611yescharacteristic
1286C22C53×#54611yescharacteristic
1287C22C53×#54611yescharacteristic
1288C22C53×#54611yescharacteristic
1289C22C53×#54611yescharacteristic
1290C22C53×#54611yescharacteristic
1291C22C53×#54611yescharacteristic
1292C22C53×#54711yescharacteristic
1293C22C53×#54811yescharacteristic
1294C22C53×#54811yescharacteristic
1295C22C53×#55011yescharacteristic
1296C22C53×#55011yescharacteristic
1297C22C53×#55111yescharacteristic
1298C22C53×#55111yescharacteristic
1299C22C53×#55111yescharacteristic
1300C22C53×#55311yescharacteristic
1301C22C53×#56011yescharacteristic
1302C22C53×#56211yescharacteristic
1303C4—24no—
1304C4—24no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—44no—
1316C2—82no—
1317C2—82no—
1318C2C53×#241211yescharacteristic
1319C2C53×#241811yescharacteristic
1320C2C53×#242711yescharacteristic
1321C2C53×#244311yescharacteristic
1322C2C53×#246711yescharacteristic
1323C2C53×#247111yescharacteristic
1324C2C53×#253911yescharacteristic
1325C2C53×#254011yescharacteristic
1326C2C53×#254111yescharacteristic
1327C2C53×#266811yescharacteristic
1328C2C53×#267111yescharacteristic
1329C2C53×#269611yescharacteristic
1330C2C53×#270311yescharacteristic
1331C2C53×#270511yescharacteristic
1332C2C53×#273011yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
prime radicalC2×C53×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#399C2semidirect
2. C2×C53×#397C2semidirect
3. C2×C53×#394C2semidirect
5. C2×C53×#390C2semidirect
6. C2×C53×#386C2semidirect
7. C2×C53×#386C2semidirect
8. C2×C53×#380C2semidirect
9. C53×#1445C2semidirect
10. C53×#1439C2semidirect
11. C53×#1439C2semidirect
12. C53×#1438C2semidirect
13. C53×#1438C2semidirect
14. C53×#1437C2semidirect
15. C53×#1436C2semidirect
113. C2×C4⋊C4×C53D4semidirect
169. #95×C53D4semidirect
170. #95×C53D4semidirect
556. #15493C53direct (N × H)
649. C2×#399C2×C53semidirect
650. C2×#397C2×C53semidirect
651. C2×#394C2×C53semidirect
653. C2×#390C2×C53semidirect
654. C2×#386C2×C53semidirect
655. C2×#386C2×C53semidirect
656. C2×#380C2×C53semidirect
657. #1445C2×C53semidirect
658. #1439C2×C53semidirect
659. #1439C2×C53semidirect
660. #1438C2×C53semidirect
661. #1438C2×C53semidirect
662. #1437C2×C53semidirect
663. #1436C2×C53semidirect
725. C53#15493direct (N × H)
780. C2×C4⋊C4D4×C53semidirect
836. #95D4×C53semidirect
837. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3992
C2×C53×#3972
C2×C53×#3942
C2×C53×#3922
C2×C53×#3902
C2×C53×#3862
C2×C53×#3802
C53×#14452
C53×#14392
C53×#14382
C53×#14372
C53×#14362
#1549353