Finite Group Databasebeta

← C53×#16290 #27223802

Subgroups — C53×#16290 #27223802

Order 13568.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#396C211yesmaximal, characteristic, complemented
2C2×C53×#396C211yesmaximal, characteristic, complemented
3C2×C53×#394C211yesmaximal, characteristic, complemented
4C2×C53×#394C211yesmaximal, characteristic, complemented
5C2×C53×#394C211yesmaximal, characteristic, complemented
6C2×C53×#392C211yesmaximal, characteristic
7C2×C53×#390C211yesmaximal, characteristic, complemented
8C2×C53×#388C211yesmaximal, characteristic, complemented
9C53×#1444C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1439C211yesmaximal, characteristic, complemented
12C53×#1439C211yesmaximal, characteristic, complemented
13C53×#1438C211yesmaximal, characteristic, complemented
14C53×#1438C211yesmaximal, characteristic, complemented
15C53×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C22×C4⋊C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C4⋊C4×C53C2211yescharacteristic
22C22×C4⋊C4×C53C2211yescharacteristic
23C22×C4⋊C4×C53C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#396—24no—
42C53×#396—24no—
43C53×#394—24no—
44C53×#394—24no—
45C53×#394—24no—
46C53×#392—24no—
47C53×#390—24no—
48C53×#388—24no—
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—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×C53—41no—
81C22×D4×C53—41no—
82C22×D4×C53—41no—
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2311yescharacteristic
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
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—41no—
108C2×C4⋊C4×C53—41no—
109C2×C4⋊C4×C53—41no—
110C2×C4⋊C4×C53—41no—
111C2×C4⋊C4×C53—41no—
112C2×C4⋊C4×C53—41no—
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—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—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×C53—41no—
153C2×C22⋊C4×C53—41no—
154C2×C22⋊C4×C53—41no—
155C2×C22⋊C4×C53—41no—
156C2×C22⋊C4×C53D414yes—
157C2×C22⋊C4×C53D414yescomplemented
158C2×C42×C53—22no—
159C2×C42×C53—22no—
160C2×C42×C53—41no—
161#95×C53—22no—
162#95×C53—22no—
163#95×C53—22no—
164#95×C53—22no—
165#95×C53—22no—
166#95×C53—41no—
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×C53—21no—
212C24×C53—21no—
213C24×C53C2×D412yes—
214C24×C53C2×D412yes—
215C24×C53#4112yes—
216C24×C53C2411yescharacteristic
217C2×D4×C53—28no—
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—
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—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—21no—
310C22×C4×C53C2×D412yes—
311C22×C4×C53C2×D412yes—
312C22×C4×C53C2×D412yes—
313C22×C4×C53C2×D412yes—
314C22×C4×C53C2×D412yes—
315C22×C4×C53C2×D412yes—
316C22×C4×C53C2×D412yes—
317C22×C4×C53C2×D412yes—
318C22×C4×C53C2×D412yes—
319C22×C4×C53C2×D412yes—
320C22×C4×C53#4112yes—
321C22×C4×C53#4112yes—
322C4⋊C4×C53—44no—
323C4⋊C4×C53—44no—
324C4⋊C4×C53—44no—
325C4⋊C4×C53—44no—
326C4⋊C4×C53—44no—
327C4⋊C4×C53—44no—
328C22⋊C4×C53—28no—
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—
340C22⋊C4×C53—44no—
341C22⋊C4×C53—44no—
342C22⋊C4×C53—44no—
343C42×C53—44no—
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—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
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—41no—
445C23×C53—41no—
446C23×C53—41no—
447C23×C53—41no—
448C23×C53—41no—
449C23×C53C22×D411yescharacteristic
450C23×C53C22×D411yescharacteristic
451C23×C53C22×D411yescharacteristic
452C23×C53C22×D411yescharacteristic
453C23×C53C2×#4111yescharacteristic
454C23×C53C2×#4111yescharacteristic
455C23×C53C2×#4111yescharacteristic
456C23×C53H(5,𝔽2)11yescharacteristic
457C23×C53H(5,𝔽2)11yescharacteristic
458C23×C53H(5,𝔽2)11yescharacteristic
459C23×C53H(5,𝔽2)11yescharacteristic
460C23×C53H(5,𝔽2)11yescharacteristic
461C23×C53H(5,𝔽2)11yescharacteristic
462C23×C532−1+411yescharacteristic
463C23×C532−1+411yescharacteristic
464D4×C53—416no—
465D4×C53—416no—
466D4×C53—416no—
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—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—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—
548C2×C4×C53—41no—
549C2×C4×C53—41no—
550C2×C4×C53#12114yes—
551#16290C5311yesmaximal, characteristic, direct product factor, Sylow
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—81no—
574C22×C53—81no—
575C22×C53—81no—
576C22×C53—81no—
577C22×C53—81no—
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×C53—81no—
595C22×C53—81no—
596C22×C53—81no—
597C22×C53C2×#12111yescharacteristic
598C22×C53#52511yescharacteristic
599C22×C53#53211yescharacteristic
600C22×C53#53411yescharacteristic
601C22×C53#53511yescharacteristic
602C22×C53#53511yescharacteristic
603C22×C53#53611yescharacteristic
604C22×C53#53711yescharacteristic
605C22×C53#53711yescharacteristic
606C22×C53#53711yescharacteristic
607C22×C53#53711yescharacteristic
608C22×C53#53811yescharacteristic
609C22×C53#53811yescharacteristic
610C22×C53#53811yescharacteristic
611C22×C53#53911yescharacteristic
612C22×C53#54011yescharacteristic
613C22×C53#54211yescharacteristic
614C22×C53#54211yescharacteristic
615C22×C53#54211yescharacteristic
616C22×C53D4211yescharacteristic
617C22×C53D4211yescharacteristic
618C22×C53D4211yescharacteristic
619C22×C53D4211yescharacteristic
620C22×C53D4211yescharacteristic
621C22×C53#54611yescharacteristic
622C22×C53#54611yescharacteristic
623C22×C53#54611yescharacteristic
624C22×C53#54711yescharacteristic
625C22×C53#54811yescharacteristic
626C22×C53#55011yescharacteristic
627C22×C53#55111yescharacteristic
628C22×C53#56011yescharacteristic
629C22×C53#56011yescharacteristic
630C22×C53#56211yescharacteristic
631C22×C53#56211yescharacteristic
632C4×C53—24no—
633C4×C53—42no—
634C4×C53—42no—
635C4×C53—42no—
636C4×C53—42no—
637C4×C53—42no—
638C4×C53—42no—
639C4×C53—42no—
640C4×C53—42no—
641C4×C53—42no—
642C4×C53—81no—
643C4×C53—81no—
644C2×#396C2×C5311yescharacteristic, complemented
645C2×#396C2×C5311yescharacteristic, complemented
646C2×#394C2×C5311yescharacteristic, complemented
647C2×#394C2×C5311yescharacteristic, complemented
648C2×#394C2×C5311yescharacteristic, complemented
649C2×#392C2×C5311yescharacteristic
650C2×#390C2×C5311yescharacteristic, complemented
651C2×#388C2×C5311yescharacteristic, complemented
652#1444C2×C5311yescharacteristic, complemented
653#1439C2×C5311yescharacteristic, complemented
654#1439C2×C5311yescharacteristic, complemented
655#1439C2×C5311yescharacteristic, complemented
656#1438C2×C5311yescharacteristic, complemented
657#1438C2×C5311yescharacteristic, complemented
658#1436C2×C5311yescharacteristic, complemented
659C2×C53—82no—
660C2×C53—82no—
661C2×C53—82no—
662C2×C53#242411yescharacteristic
663C2×C53#242811yescharacteristic
664C2×C53#246111yescharacteristic
665C2×C53#262011yescharacteristic
666C2×C53#263011yescharacteristic
667C2×C53#266211yescharacteristic
668C2×C53#266911yescharacteristic
669C2×C53#267211yescharacteristic
670C2×C53#267511yescharacteristic
671C2×C53#267611yescharacteristic
672C2×C53#268111yescharacteristic
673C2×C53#268211yescharacteristic
674C2×C53#268511yescharacteristic
675C2×C53#270511yescharacteristic
676C2×C53#282911yescharacteristic
677C23×D4C22×C5311yescharacteristic
678C23×D4C22×C5311yescharacteristic
679C23×D4C22×C5311yescharacteristic
680C22×C4⋊C4C22×C5311yescharacteristic
681C22×C4⋊C4C22×C5311yescharacteristic
682C22×C4⋊C4C22×C5311yescharacteristic
683C22×C4⋊C4C22×C5311yescharacteristic
684C22×C4⋊C4C22×C5311yescharacteristic
685C22×C4⋊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
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×C42C22×C5311yescharacteristic
702#396—24no—
703#396—24no—
704#394—24no—
705#394—24no—
706#394—24no—
707#392—24no—
708#390—24no—
709#388—24no—
710C2×#95C22×C5311yescharacteristic
711C2×#95C22×C5311yescharacteristic
712C2×#95C22×C5311yescharacteristic
713C2×#95C22×C5311yescharacteristic
714C2×#95C22×C5311yescharacteristic
715C2×#95C22×C5311yescharacteristic
716C2×#95C22×C5311yescharacteristic
717C2×#95C22×C5311yescharacteristic
718C2×#95C22×C5311yescharacteristic
719C2×#95C22×C5311yescharacteristic
720C53#1629011yescharacteristic, direct product factor, Sylow
721C25C23×C5311yescharacteristic
722C25C23×C5311yescharacteristic
723C25C23×C5311yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C23×C4C23×C5311yescharacteristic
746C23×C4C23×C5311yescharacteristic
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
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
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—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—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⋊C4D4×C5314yes—
819C2×C22⋊C4D4×C5314yescomplemented
820C2×C42—22no—
821C2×C42—22no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—41no—
829#95—41no—
830#95—41no—
831#95D4×C5314yescomplemented
832#95D4×C5314yescomplemented
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—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24C2×D4×C5312yes—
876C24C2×D4×C5312yes—
877C24#41×C5312yes—
878C24C24×C5311yescharacteristic
879C2×D4—28no—
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—
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—
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—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4C2×D4×C5312yes—
973C22×C4C2×D4×C5312yes—
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×C4C2×D4×C5312yes—
981C22×C4C2×D4×C5312yes—
982C22×C4#41×C5312yes—
983C22×C4#41×C5312yes—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C22⋊C4—28no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C42—44no—
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—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
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—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C22×D4×C5311yescharacteristic
1112C23C22×D4×C5311yescharacteristic
1113C23C22×D4×C5311yescharacteristic
1114C23C22×D4×C5311yescharacteristic
1115C23C2×#41×C5311yescharacteristic
1116C23C2×#41×C5311yescharacteristic
1117C23C2×#41×C5311yescharacteristic
1118C23H(5,𝔽2)×C5311yescharacteristic
1119C23H(5,𝔽2)×C5311yescharacteristic
1120C23H(5,𝔽2)×C5311yescharacteristic
1121C23H(5,𝔽2)×C5311yescharacteristic
1122C23H(5,𝔽2)×C5311yescharacteristic
1123C23H(5,𝔽2)×C5311yescharacteristic
1124C232−1+4×C5311yescharacteristic
1125C232−1+4×C5311yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
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—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—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—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4#121×C5314yes—
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—81no—
1235C22—81no—
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—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C5311yescharacteristic
1259C22C53×#52511yescharacteristic
1260C22C53×#53211yescharacteristic
1261C22C53×#53411yescharacteristic
1262C22C53×#53511yescharacteristic
1263C22C53×#53511yescharacteristic
1264C22C53×#53611yescharacteristic
1265C22C53×#53711yescharacteristic
1266C22C53×#53711yescharacteristic
1267C22C53×#53711yescharacteristic
1268C22C53×#53711yescharacteristic
1269C22C53×#53811yescharacteristic
1270C22C53×#53811yescharacteristic
1271C22C53×#53811yescharacteristic
1272C22C53×#53911yescharacteristic
1273C22C53×#54011yescharacteristic
1274C22C53×#54211yescharacteristic
1275C22C53×#54211yescharacteristic
1276C22C53×#54211yescharacteristic
1277C22D42×C5311yescharacteristic
1278C22D42×C5311yescharacteristic
1279C22D42×C5311yescharacteristic
1280C22D42×C5311yescharacteristic
1281C22D42×C5311yescharacteristic
1282C22C53×#54611yescharacteristic
1283C22C53×#54611yescharacteristic
1284C22C53×#54611yescharacteristic
1285C22C53×#54711yescharacteristic
1286C22C53×#54811yescharacteristic
1287C22C53×#55011yescharacteristic
1288C22C53×#55111yescharacteristic
1289C22C53×#56011yescharacteristic
1290C22C53×#56011yescharacteristic
1291C22C53×#56211yescharacteristic
1292C22C53×#56211yescharacteristic
1293C4—24no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C53×#242411yescharacteristic
1309C2C53×#242811yescharacteristic
1310C2C53×#246111yescharacteristic
1311C2C53×#262011yescharacteristic
1312C2C53×#263011yescharacteristic
1313C2C53×#266211yescharacteristic
1314C2C53×#266911yescharacteristic
1315C2C53×#267211yescharacteristic
1316C2C53×#267511yescharacteristic
1317C2C53×#267611yescharacteristic
1318C2C53×#268111yescharacteristic
1319C2C53×#268211yescharacteristic
1320C2C53×#268511yescharacteristic
1321C2C53×#270511yescharacteristic
1322C2C53×#282911yescharacteristic
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×#396C2semidirect
2. C2×C53×#396C2semidirect
3. C2×C53×#394C2semidirect
4. C2×C53×#394C2semidirect
5. C2×C53×#394C2semidirect
7. C2×C53×#390C2semidirect
8. C2×C53×#388C2semidirect
9. C53×#1444C2semidirect
10. C53×#1439C2semidirect
11. C53×#1439C2semidirect
12. C53×#1439C2semidirect
13. C53×#1438C2semidirect
14. C53×#1438C2semidirect
15. C53×#1436C2semidirect
157. C2×C22⋊C4×C53D4semidirect
169. #95×C53D4semidirect
170. #95×C53D4semidirect
551. #16290C53direct (N × H)
644. C2×#396C2×C53semidirect
645. C2×#396C2×C53semidirect
646. C2×#394C2×C53semidirect
647. C2×#394C2×C53semidirect
648. C2×#394C2×C53semidirect
650. C2×#390C2×C53semidirect
651. C2×#388C2×C53semidirect
652. #1444C2×C53semidirect
653. #1439C2×C53semidirect
654. #1439C2×C53semidirect
655. #1439C2×C53semidirect
656. #1438C2×C53semidirect
657. #1438C2×C53semidirect
658. #1436C2×C53semidirect
720. C53#16290direct (N × H)
819. C2×C22⋊C4D4×C53semidirect
831. #95D4×C53semidirect
832. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3962
C2×C53×#3942
C2×C53×#3922
C2×C53×#3902
C2×C53×#3882
C53×#14442
C53×#14392
C53×#14382
C53×#14362
#1629053