Finite Group Databasebeta

← C53×#16287 #27223799

Subgroups — C53×#16287 #27223799

Order 13568.

2114 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#397C211yesmaximal, characteristic, complemented
2C2×C53×#394C211yesmaximal, characteristic, complemented
3C2×C53×#394C211yesmaximal, characteristic, complemented
4C2×C53×#392C211yesmaximal, characteristic
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C53×#1442C211yesmaximal, characteristic, complemented
8C53×#1442C211yesmaximal, characteristic, complemented
9C53×#1439C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C53×#1439C211yesmaximal, characteristic, complemented
13C53×#1438C211yesmaximal, characteristic, complemented
14C53×#1438C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C4⋊C4×C53C2211yescharacteristic
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C22⋊C4×C53C2211yescharacteristic
24C22×C22⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C22×C22⋊C4×C53C2211yescharacteristic
28C22×C22⋊C4×C53C2211yescharacteristic
29C22×C22⋊C4×C53C2211yescharacteristic
30C22×C22⋊C4×C53C2211yescharacteristic
31C22×C22⋊C4×C53C2211yescharacteristic
32C22×C22⋊C4×C53C2211yescharacteristic
33C22×C22⋊C4×C53C2211yescharacteristic
34C22×C22⋊C4×C53C2211yescharacteristic
35C22×C22⋊C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2211yescharacteristic
37C53×#397—24no—
38C53×#394—24no—
39C53×#394—24no—
40C53×#392—24no—
41C53×#386—24no—
42C53×#386—24no—
43C2×#95×C53C2211yescharacteristic
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
57C25×C53C2311yescharacteristic
58C25×C53C2311yescharacteristic
59C25×C53C2311yescharacteristic
60C22×D4×C53—22no—
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—41no—
71C22×D4×C53—41no—
72C22×D4×C53—41no—
73C22×D4×C53—41no—
74C22×D4×C53—41no—
75C22×D4×C53—41no—
76C22×D4×C53—41no—
77C22×D4×C53—41no—
78C22×D4×C53—41no—
79C22×D4×C53—41no—
80C22×D4×C53D414yes—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—22no—
84C23×C4×C53—41no—
85C23×C4×C53—41no—
86C23×C4×C53—41no—
87C23×C4×C53—41no—
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2311yescharacteristic
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—41no—
104C2×C4⋊C4×C53—41no—
105C2×C4⋊C4×C53—41no—
106C2×C4⋊C4×C53—41no—
107C2×C4⋊C4×C53—41no—
108C2×C4⋊C4×C53—41no—
109C2×C22⋊C4×C53—22no—
110C2×C22⋊C4×C53—22no—
111C2×C22⋊C4×C53—22no—
112C2×C22⋊C4×C53—22no—
113C2×C22⋊C4×C53—22no—
114C2×C22⋊C4×C53—22no—
115C2×C22⋊C4×C53—22no—
116C2×C22⋊C4×C53—22no—
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—22no—
124C2×C22⋊C4×C53—22no—
125C2×C22⋊C4×C53—22no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—22no—
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
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×C53—41no—
149C2×C22⋊C4×C53—41no—
150C2×C22⋊C4×C53D414yescomplemented
151#95×C53—22no—
152#95×C53—22no—
153#95×C53—22no—
154#95×C53—22no—
155#95×C53—22no—
156#95×C53—22no—
157#95×C53—22no—
158#95×C53—22no—
159#95×C53—22no—
160#95×C53—41no—
161#95×C53—41no—
162#95×C53—41no—
163#95×C53—41no—
164#95×C53D414yescomplemented
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
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×C53C2×D412yes—
206C24×C53C2×D412yes—
207C24×C53C2×D412yes—
208C24×C53#4112yes—
209C24×C53#4112yes—
210C24×C53C2411yescharacteristic
211C2×D4×C53—28no—
212C2×D4×C53—28no—
213C2×D4×C53—44no—
214C2×D4×C53—44no—
215C2×D4×C53—44no—
216C2×D4×C53—44no—
217C2×D4×C53—44no—
218C2×D4×C53—44no—
219C2×D4×C53—44no—
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—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53—21no—
236C22×C4×C53—21no—
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—44no—
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×C53C2×D412yes—
316C22×C4×C53C2×D412yes—
317C22×C4×C53C2×D412yes—
318C22×C4×C53C2×D412yes—
319C22×C4×C53C2×D412yes—
320C22×C4×C53C2×D412yes—
321C22×C4×C53#4112yes—
322C22×C4×C53#4112yes—
323C4⋊C4×C53—44no—
324C4⋊C4×C53—44no—
325C4⋊C4×C53—44no—
326C22⋊C4×C53—44no—
327C22⋊C4×C53—44no—
328C22⋊C4×C53—44no—
329C22⋊C4×C53—44no—
330C22⋊C4×C53—44no—
331C22⋊C4×C53—44no—
332C22⋊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—
340C23×C53—22no—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—22no—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—22no—
359C23×C53—22no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53—41no—
384C23×C53—41no—
385C23×C53—41no—
386C23×C53—41no—
387C23×C53—41no—
388C23×C53—41no—
389C23×C53—41no—
390C23×C53—41no—
391C23×C53—41no—
392C23×C53—41no—
393C23×C53—41no—
394C23×C53—41no—
395C23×C53—41no—
396C23×C53—41no—
397C23×C53—41no—
398C23×C53—41no—
399C23×C53—41no—
400C23×C53—41no—
401C23×C53—41no—
402C23×C53—41no—
403C23×C53—41no—
404C23×C53—41no—
405C23×C53—41no—
406C23×C53—41no—
407C23×C53—41no—
408C23×C53—41no—
409C23×C53—41no—
410C23×C53—41no—
411C23×C53—41no—
412C23×C53—41no—
413C23×C53—41no—
414C23×C53—41no—
415C23×C53—41no—
416C23×C53—41no—
417C23×C53—41no—
418C23×C53—41no—
419C23×C53—41no—
420C23×C53—41no—
421C23×C53—41no—
422C23×C53—41no—
423C23×C53—41no—
424C23×C53—41no—
425C23×C53—41no—
426C23×C53—41no—
427C23×C53—41no—
428C23×C53—41no—
429C23×C53—41no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53—41no—
434C23×C53—41no—
435C23×C53—41no—
436C23×C53—41no—
437C23×C53—41no—
438C23×C53—41no—
439C23×C53—41no—
440C23×C53—41no—
441C23×C53—41no—
442C23×C53—41no—
443C23×C53—41no—
444C23×C53#12114yes—
445C23×C53C22×D411yescharacteristic
446C23×C53C22×D411yescharacteristic
447C23×C53C22×D411yescharacteristic
448C23×C53C2×#4111yescharacteristic
449C23×C53C2×#4111yescharacteristic
450C23×C53C2×#4111yescharacteristic
451C23×C53C2×#4111yescharacteristic
452C23×C53H(5,𝔽2)11yescharacteristic
453C23×C53H(5,𝔽2)11yescharacteristic
454C23×C53H(5,𝔽2)11yescharacteristic
455C23×C53H(5,𝔽2)11yescharacteristic
456C23×C53H(5,𝔽2)11yescharacteristic
457C23×C53H(5,𝔽2)11yescharacteristic
458C23×C53H(5,𝔽2)11yescharacteristic
459C23×C532−1+411yescharacteristic
460D4×C53—416no—
461D4×C53—416no—
462D4×C53—416no—
463C2×C4×C53—22no—
464C2×C4×C53—22no—
465C2×C4×C53—22no—
466C2×C4×C53—22no—
467C2×C4×C53—22no—
468C2×C4×C53—22no—
469C2×C4×C53—22no—
470C2×C4×C53—22no—
471C2×C4×C53—22no—
472C2×C4×C53—22no—
473C2×C4×C53—22no—
474C2×C4×C53—22no—
475C2×C4×C53—22no—
476C2×C4×C53—22no—
477C2×C4×C53—22no—
478C2×C4×C53—22no—
479C2×C4×C53—22no—
480C2×C4×C53—22no—
481C2×C4×C53—22no—
482C2×C4×C53—22no—
483C2×C4×C53—22no—
484C2×C4×C53—22no—
485C2×C4×C53—22no—
486C2×C4×C53—22no—
487C2×C4×C53—416no—
488C2×C4×C53—41no—
489C2×C4×C53—41no—
490C2×C4×C53—41no—
491C2×C4×C53—41no—
492C2×C4×C53—41no—
493C2×C4×C53—41no—
494C2×C4×C53—41no—
495C2×C4×C53—41no—
496C2×C4×C53—41no—
497C2×C4×C53—41no—
498C2×C4×C53—41no—
499C2×C4×C53—41no—
500C2×C4×C53—41no—
501C2×C4×C53—41no—
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—
548#16287C5311yesmaximal, characteristic, direct product factor, Sylow
549C22×C53—24no—
550C22×C53—24no—
551C22×C53—24no—
552C22×C53—42no—
553C22×C53—42no—
554C22×C53—42no—
555C22×C53—42no—
556C22×C53—42no—
557C22×C53—42no—
558C22×C53—42no—
559C22×C53—42no—
560C22×C53—42no—
561C22×C53—42no—
562C22×C53—42no—
563C22×C53—42no—
564C22×C53—42no—
565C22×C53—42no—
566C22×C53—42no—
567C22×C53—42no—
568C22×C53—42no—
569C22×C53—42no—
570C22×C53—42no—
571C22×C53—42no—
572C22×C53—42no—
573C22×C53—42no—
574C22×C53—42no—
575C22×C53—42no—
576C22×C53—42no—
577C22×C53—42no—
578C22×C53—81no—
579C22×C53—81no—
580C22×C53—81no—
581C22×C53—81no—
582C22×C53—81no—
583C22×C53—81no—
584C22×C53—81no—
585C22×C53—81no—
586C22×C53—81no—
587C22×C53—81no—
588C22×C53—81no—
589C22×C53—81no—
590C22×C53—81no—
591C22×C53—81no—
592C22×C53—81no—
593C22×C53—81no—
594C22×C53C2×#12111yescharacteristic
595C22×C53#52511yescharacteristic
596C22×C53#52911yescharacteristic
597C22×C53#53411yescharacteristic
598C22×C53#53411yescharacteristic
599C22×C53#53411yescharacteristic
600C22×C53#53511yescharacteristic
601C22×C53#53511yescharacteristic
602C22×C53#53711yescharacteristic
603C22×C53#53811yescharacteristic
604C22×C53#53811yescharacteristic
605C22×C53#53811yescharacteristic
606C22×C53#53811yescharacteristic
607C22×C53#53811yescharacteristic
608C22×C53#53811yescharacteristic
609C22×C53#53911yescharacteristic
610C22×C53#53911yescharacteristic
611C22×C53#54011yescharacteristic
612C22×C53#54011yescharacteristic
613C22×C53D4211yescharacteristic
614C22×C53D4211yescharacteristic
615C22×C53#54611yescharacteristic
616C22×C53#54611yescharacteristic
617C22×C53#54611yescharacteristic
618C22×C53#54611yescharacteristic
619C22×C53#54611yescharacteristic
620C22×C53#54711yescharacteristic
621C22×C53#54711yescharacteristic
622C22×C53#55011yescharacteristic
623C22×C53#55111yescharacteristic
624C22×C53#55311yescharacteristic
625C22×C53#56011yescharacteristic
626C22×C53H(3,𝔽4)11yescharacteristic
627C22×C53#56211yescharacteristic
628C22×C53#56211yescharacteristic
629C4×C53—42no—
630C4×C53—42no—
631C4×C53—42no—
632C4×C53—42no—
633C4×C53—42no—
634C4×C53—42no—
635C4×C53—42no—
636C4×C53—42no—
637C4×C53—81no—
638C4×C53—81no—
639C4×C53—81no—
640C4×C53—81no—
641C2×#397C2×C5311yescharacteristic, complemented
642C2×#394C2×C5311yescharacteristic, complemented
643C2×#394C2×C5311yescharacteristic, complemented
644C2×#392C2×C5311yescharacteristic
645C2×#386C2×C5311yescharacteristic, complemented
646C2×#386C2×C5311yescharacteristic, complemented
647#1442C2×C5311yescharacteristic, complemented
648#1442C2×C5311yescharacteristic, complemented
649#1439C2×C5311yescharacteristic, complemented
650#1439C2×C5311yescharacteristic, complemented
651#1439C2×C5311yescharacteristic, complemented
652#1439C2×C5311yescharacteristic, complemented
653#1438C2×C5311yescharacteristic, complemented
654#1438C2×C5311yescharacteristic, complemented
655C22⋊#95C2×C5311yescharacteristic, complemented
656C2×C53—44no—
657C2×C53—82no—
658C2×C53—82no—
659C2×C53#242411yescharacteristic
660C2×C53#242511yescharacteristic
661C2×C53#246711yescharacteristic
662C2×C53#261711yescharacteristic
663C2×C53#263611yescharacteristic
664C2×C53#264811yescharacteristic
665C2×C53#267011yescharacteristic
666C2×C53#267111yescharacteristic
667C2×C53#267311yescharacteristic
668C2×C53#268211yescharacteristic
669C2×C53#268411yescharacteristic
670C2×C53#268811yescharacteristic
671C2×C53#270611yescharacteristic
672C2×C53#270811yescharacteristic
673C2×C53#282411yescharacteristic
674C23×D4C22×C5311yescharacteristic
675C23×D4C22×C5311yescharacteristic
676C23×D4C22×C5311yescharacteristic
677C24×C4C22×C5311yescharacteristic
678C22×C4⋊C4C22×C5311yescharacteristic
679C22×C4⋊C4C22×C5311yescharacteristic
680C22×C4⋊C4C22×C5311yescharacteristic
681C22×C22⋊C4C22×C5311yescharacteristic
682C22×C22⋊C4C22×C5311yescharacteristic
683C22×C22⋊C4C22×C5311yescharacteristic
684C22×C22⋊C4C22×C5311yescharacteristic
685C22×C22⋊C4C22×C5311yescharacteristic
686C22×C22⋊C4C22×C5311yescharacteristic
687C22×C22⋊C4C22×C5311yescharacteristic
688C22×C22⋊C4C22×C5311yescharacteristic
689C22×C22⋊C4C22×C5311yescharacteristic
690C22×C22⋊C4C22×C5311yescharacteristic
691C22×C22⋊C4C22×C5311yescharacteristic
692C22×C22⋊C4C22×C5311yescharacteristic
693C22×C22⋊C4C22×C5311yescharacteristic
694C22×C22⋊C4C22×C5311yescharacteristic
695#397—24no—
696#394—24no—
697#394—24no—
698#392—24no—
699#386—24no—
700#386—24no—
701C2×#95C22×C5311yescharacteristic
702C2×#95C22×C5311yescharacteristic
703C2×#95C22×C5311yescharacteristic
704C2×#95C22×C5311yescharacteristic
705C2×#95C22×C5311yescharacteristic
706C2×#95C22×C5311yescharacteristic
707C2×#95C22×C5311yescharacteristic
708C2×#95C22×C5311yescharacteristic
709C2×#95C22×C5311yescharacteristic
710C2×#95C22×C5311yescharacteristic
711C2×#95C22×C5311yescharacteristic
712C2×#95C22×C5311yescharacteristic
713C2×#95C22×C5311yescharacteristic
714C2×#95C22×C5311yescharacteristic
715C53#1628711yescharacteristic, direct product factor, Sylow
716C25C23×C5311yescharacteristic
717C25C23×C5311yescharacteristic
718C25C23×C5311yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C5314yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4C23×C5311yescharacteristic
748C23×C4C23×C5311yescharacteristic
749C23×C4C23×C5311yescharacteristic
750C23×C4C23×C5311yescharacteristic
751C23×C4C23×C5311yescharacteristic
752C23×C4C23×C5311yescharacteristic
753C23×C4C23×C5311yescharacteristic
754C23×C4C23×C5311yescharacteristic
755C23×C4C23×C5311yescharacteristic
756C23×C4C23×C5311yescharacteristic
757C23×C4C23×C5311yescharacteristic
758C23×C4C23×C5311yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4—41no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4D4×C5314yescomplemented
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95D4×C5314yescomplemented
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C5312yes—
865C24C2×D4×C5312yes—
866C24C2×D4×C5312yes—
867C24#41×C5312yes—
868C24#41×C5312yes—
869C24C24×C5311yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C5312yes—
975C22×C4C2×D4×C5312yes—
976C22×C4C2×D4×C5312yes—
977C22×C4C2×D4×C5312yes—
978C22×C4C2×D4×C5312yes—
979C22×C4C2×D4×C5312yes—
980C22×C4#41×C5312yes—
981C22×C4#41×C5312yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊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⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23#121×C5314yes—
1104C23C22×D4×C5311yescharacteristic
1105C23C22×D4×C5311yescharacteristic
1106C23C22×D4×C5311yescharacteristic
1107C23C2×#41×C5311yescharacteristic
1108C23C2×#41×C5311yescharacteristic
1109C23C2×#41×C5311yescharacteristic
1110C23C2×#41×C5311yescharacteristic
1111C23H(5,𝔽2)×C5311yescharacteristic
1112C23H(5,𝔽2)×C5311yescharacteristic
1113C23H(5,𝔽2)×C5311yescharacteristic
1114C23H(5,𝔽2)×C5311yescharacteristic
1115C23H(5,𝔽2)×C5311yescharacteristic
1116C23H(5,𝔽2)×C5311yescharacteristic
1117C23H(5,𝔽2)×C5311yescharacteristic
1118C232−1+4×C5311yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—416no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
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—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C5311yescharacteristic
1253C22C53×#52511yescharacteristic
1254C22C53×#52911yescharacteristic
1255C22C53×#53411yescharacteristic
1256C22C53×#53411yescharacteristic
1257C22C53×#53411yescharacteristic
1258C22C53×#53511yescharacteristic
1259C22C53×#53511yescharacteristic
1260C22C53×#53711yescharacteristic
1261C22C53×#53811yescharacteristic
1262C22C53×#53811yescharacteristic
1263C22C53×#53811yescharacteristic
1264C22C53×#53811yescharacteristic
1265C22C53×#53811yescharacteristic
1266C22C53×#53811yescharacteristic
1267C22C53×#53911yescharacteristic
1268C22C53×#53911yescharacteristic
1269C22C53×#54011yescharacteristic
1270C22C53×#54011yescharacteristic
1271C22D42×C5311yescharacteristic
1272C22D42×C5311yescharacteristic
1273C22C53×#54611yescharacteristic
1274C22C53×#54611yescharacteristic
1275C22C53×#54611yescharacteristic
1276C22C53×#54611yescharacteristic
1277C22C53×#54611yescharacteristic
1278C22C53×#54711yescharacteristic
1279C22C53×#54711yescharacteristic
1280C22C53×#55011yescharacteristic
1281C22C53×#55111yescharacteristic
1282C22C53×#55311yescharacteristic
1283C22C53×#56011yescharacteristic
1284C22C53×H(3,𝔽4)11yescharacteristic
1285C22C53×#56211yescharacteristic
1286C22C53×#56211yescharacteristic
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C53×#242411yescharacteristic
1303C2C53×#242511yescharacteristic
1304C2C53×#246711yescharacteristic
1305C2C53×#261711yescharacteristic
1306C2C53×#263611yescharacteristic
1307C2C53×#264811yescharacteristic
1308C2C53×#267011yescharacteristic
1309C2C53×#267111yescharacteristic
1310C2C53×#267311yescharacteristic
1311C2C53×#268211yescharacteristic
1312C2C53×#268411yescharacteristic
1313C2C53×#268811yescharacteristic
1314C2C53×#270611yescharacteristic
1315C2C53×#270811yescharacteristic
1316C2C53×#282411yescharacteristic
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×#397C2semidirect
2. C2×C53×#394C2semidirect
3. C2×C53×#394C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#386C2semidirect
7. C53×#1442C2semidirect
8. C53×#1442C2semidirect
9. C53×#1439C2semidirect
10. C53×#1439C2semidirect
11. C53×#1439C2semidirect
12. C53×#1439C2semidirect
13. C53×#1438C2semidirect
14. C53×#1438C2semidirect
15. C53×C22⋊#95C2semidirect
150. C2×C22⋊C4×C53D4semidirect
164. #95×C53D4semidirect
548. #16287C53direct (N × H)
641. C2×#397C2×C53semidirect
642. C2×#394C2×C53semidirect
643. C2×#394C2×C53semidirect
645. C2×#386C2×C53semidirect
646. C2×#386C2×C53semidirect
647. #1442C2×C53semidirect
648. #1442C2×C53semidirect
649. #1439C2×C53semidirect
650. #1439C2×C53semidirect
651. #1439C2×C53semidirect
652. #1439C2×C53semidirect
653. #1438C2×C53semidirect
654. #1438C2×C53semidirect
655. C22⋊#95C2×C53semidirect
715. C53#16287direct (N × H)
809. C2×C22⋊C4D4×C53semidirect
823. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3972
C2×C53×#3942
C2×C53×#3922
C2×C53×#3862
C53×#14422
C53×#14392
C53×#14382
C53×C22⋊#952
#1628753