Finite Group Databasebeta

← C53×#14095 #27221607

Subgroups — C53×#14095 #27221607

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C53C211yesmaximal, characteristic
2C2×C53×#390C211yesmaximal, characteristic
3C2×C53×#387C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
6C53×#1441C211yesmaximal, characteristic, complemented
7C53×#1439C211yesmaximal, characteristic, complemented
8C53×#1439C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic
10C53×#1437C211yesmaximal, characteristic, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1437C211yesmaximal, characteristic, complemented
14C53×#1436C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C24×C4×C53C2211yescharacteristic
18C2×#123×C53—24no—
19C2×#123×C53—24no—
20C2×#123×C53C418yescomplemented
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×C42×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#390—24no—
41C53×#387—24no—
42C4×C4⋊C4×C53—24no—
43C4×C22⋊C4×C53—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
60C22×D4×C53—22no—
61C22×D4×C53—22no—
62C22×D4×C53—22no—
63C22×D4×C53—22no—
64C22×D4×C53—41no—
65C22×D4×C53—41no—
66C22×D4×C53C2×C414yes—
67C23×C4×C53—22no—
68C23×C4×C53—22no—
69C23×C4×C53—22no—
70C23×C4×C53—22no—
71C23×C4×C53—41no—
72C23×C4×C53—41no—
73C23×C4×C53C2×C414yes—
74C23×C4×C53C2311yescharacteristic
75C23×C4×C53C2311yescharacteristic
76C23×C4×C53C2311yescharacteristic
77C23×C4×C53C2311yescharacteristic
78C23×C4×C53C2311yescharacteristic
79C23×C4×C53C2311yescharacteristic
80C23×C4×C53C2311yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C23×C4×C53C2311yescharacteristic
86C23×C4×C53C2311yescharacteristic
87#123×C53—232no—
88C2×C4⋊C4×C53—22no—
89C2×C4⋊C4×C53—22no—
90C2×C4⋊C4×C53—22no—
91C2×C4⋊C4×C53—22no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—41no—
96C2×C4⋊C4×C53C2×C414yes—
97C2×C4⋊C4×C53C2×C414yes—
98C2×C4⋊C4×C53D414yes—
99C2×C4⋊C4×C53D414yes—
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53—22no—
102C2×C22⋊C4×C53—22no—
103C2×C22⋊C4×C53—22no—
104C2×C22⋊C4×C53—22no—
105C2×C22⋊C4×C53—22no—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—22no—
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—41no—
124C2×C22⋊C4×C53—41no—
125C2×C22⋊C4×C53—41no—
126C2×C22⋊C4×C53—41no—
127C2×C22⋊C4×C53—41no—
128C2×C22⋊C4×C53—41no—
129C2×C22⋊C4×C53C2×C414yes—
130C2×C22⋊C4×C53C2×C414yes—
131C2×C22⋊C4×C53C2×C414yes—
132C2×C22⋊C4×C53D414yes—
133C2×C42×C53—22no—
134C2×C42×C53—22no—
135C2×C42×C53—22no—
136C2×C42×C53—22no—
137C2×C42×C53—22no—
138C2×C42×C53—22no—
139C2×C42×C53—22no—
140C2×C42×C53—22no—
141C2×C42×C53—22no—
142C2×C42×C53—41no—
143C2×C42×C53—41no—
144C2×C42×C53—41no—
145#95×C53—22no—
146#95×C53—22no—
147#95×C53—22no—
148#95×C53—22no—
149#95×C53—22no—
150#95×C53—22no—
151#95×C53—22no—
152#95×C53—22no—
153#95×C53—22no—
154#95×C53—22no—
155#95×C53—41no—
156#95×C53—41no—
157#95×C53—41no—
158#95×C53—41no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
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×C53C22×C412yes—
186C24×C53C22×C412yes—
187C24×C53C2×D412yes—
188C24×C53#4112yes—
189C24×C53C2411yescharacteristic
190C2×D4×C53—28no—
191C2×D4×C53—28no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—44no—
196C2×D4×C53—44no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—28no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53—21no—
227C22×C4×C53—21no—
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
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—28no—
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—44no—
272C22×C4×C53—44no—
273C22×C4×C53—44no—
274C22×C4×C53—44no—
275C22×C4×C53—44no—
276C22×C4×C53C22×C412yes—
277C22×C4×C53C22×C412yes—
278C22×C4×C53C22×C412yes—
279C22×C4×C53C22×C412yes—
280C22×C4×C53C22×C412yes—
281C22×C4×C53C2×D412yes—
282C22×C4×C53C2×D412yes—
283C22×C4×C53C2×D412yes—
284C22×C4×C53C2×D412yes—
285C22×C4×C53C2×D412yes—
286C22×C4×C53C2×D412yes—
287C22×C4×C53C2×D412yes—
288C22×C4×C53C2×D412yes—
289C22×C4×C53#4112yes—
290C22×C4×C53#4112yes—
291C22×C4×C53#4112yes—
292C22×C4×C53#4112yes—
293C22×C4×C53#4112yes—
294C22×C4×C53#4112yes—
295C4⋊C4×C53—28no—
296C4⋊C4×C53—28no—
297C4⋊C4×C53—44no—
298C4⋊C4×C53C22⋊C4116yescomplemented
299C22⋊C4×C53—28no—
300C22⋊C4×C53—28no—
301C22⋊C4×C53—28no—
302C22⋊C4×C53—28no—
303C22⋊C4×C53—28no—
304C22⋊C4×C53—44no—
305C22⋊C4×C53—44no—
306C22⋊C4×C53—44no—
307C22⋊C4×C53—44no—
308C22⋊C4×C53—44no—
309C22⋊C4×C53—44no—
310C42×C53—28no—
311C42×C53—44no—
312C42×C53—44no—
313C42×C53—44no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
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×C53C4×D414yes—
384C23×C53C23×C411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C2×#4111yescharacteristic
389C23×C53C2×#4111yescharacteristic
390C23×C53C2×#4111yescharacteristic
391C23×C53C2×#4111yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53H(5,𝔽2)11yescharacteristic
396C23×C53H(5,𝔽2)11yescharacteristic
397C23×C53H(5,𝔽2)11yescharacteristic
398C23×C532−1+411yescharacteristic
399D4×C53—416no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—22no—
416C2×C4×C53—22no—
417C2×C4×C53—22no—
418C2×C4×C53—22no—
419C2×C4×C53—22no—
420C2×C4×C53—22no—
421C2×C4×C53—22no—
422C2×C4×C53—22no—
423C2×C4×C53—22no—
424C2×C4×C53—22no—
425C2×C4×C53—22no—
426C2×C4×C53—22no—
427C2×C4×C53—22no—
428C2×C4×C53—22no—
429C2×C4×C53—22no—
430C2×C4×C53—22no—
431C2×C4×C53—22no—
432C2×C4×C53—22no—
433C2×C4×C53—22no—
434C2×C4×C53—22no—
435C2×C4×C53—22no—
436C2×C4×C53—22no—
437C2×C4×C53—22no—
438C2×C4×C53—22no—
439C2×C4×C53—22no—
440C2×C4×C53—22no—
441C2×C4×C53—22no—
442C2×C4×C53—22no—
443C2×C4×C53—22no—
444C2×C4×C53—22no—
445C2×C4×C53—416no—
446C2×C4×C53—41no—
447C2×C4×C53—41no—
448C2×C4×C53—41no—
449C2×C4×C53—41no—
450C2×C4×C53—41no—
451C2×C4×C53—41no—
452C2×C4×C53—41no—
453C2×C4×C53—41no—
454C2×C4×C53—41no—
455C2×C4×C53—41no—
456C2×C4×C53—41no—
457C2×C4×C53—41no—
458C2×C4×C53—41no—
459C2×C4×C53—41no—
460C2×C4×C53—41no—
461C2×C4×C53—41no—
462C2×C4×C53—41no—
463C2×C4×C53—41no—
464C2×C4×C53—41no—
465C2×C4×C53—41no—
466C2×C4×C53—41no—
467C2×C4×C53—41no—
468C2×C4×C53—41no—
469C2×C4×C53—41no—
470C2×C4×C53—41no—
471C2×C4×C53—41no—
472C2×C4×C53—41no—
473C2×C4×C53—41no—
474C2×C4×C53—41no—
475C2×C4×C53—41no—
476C2×C4×C53—41no—
477C2×C4×C53—41no—
478C2×C4×C53—41no—
479C2×C4×C53—41no—
480C2×C4×C53—41no—
481C2×C4×C53—41no—
482C2×C4×C53—41no—
483C2×C4×C53—41no—
484C2×C4×C53—41no—
485C2×C4×C53—41no—
486C2×C4×C53—41no—
487C2×C4×C53—41no—
488C2×C4×C53C2×C22⋊C414yes—
489C2×C4×C53C2×C22⋊C414yes—
490C2×C4×C53C2×C22⋊C414yes—
491C2×C4×C53#12314yescomplemented
492#14095C5311yesmaximal, characteristic, direct product factor, Sylow
493C22×C53—24no—
494C22×C53—24no—
495C22×C53—24no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—42no—
499C22×C53—42no—
500C22×C53—42no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—81no—
516C22×C53—81no—
517C22×C53—81no—
518C22×C53—81no—
519C22×C53—81no—
520C22×C53—81no—
521C22×C53—81no—
522C22×C53—81no—
523C22×C53C22×C22⋊C411yescharacteristic
524C22×C53C2×C4×D411yescharacteristic
525C22×C53C4×#4111yescharacteristic
526C22×C53C4×#4111yescharacteristic
527C22×C53C4×#4111yescharacteristic
528C22×C53#51811yescharacteristic
529C22×C53#52011yescharacteristic
530C22×C53C2×#12311yescharacteristic
531C22×C53#52511yescharacteristic
532C22×C53#52511yescharacteristic
533C22×C53#52511yescharacteristic
534C22×C53#52911yescharacteristic
535C22×C53#52911yescharacteristic
536C22×C53#53211yescharacteristic
537C22×C53#53211yescharacteristic
538C22×C53#53811yescharacteristic
539C22×C53#53911yescharacteristic
540C22×C53#54011yescharacteristic
541C22×C53#54211yescharacteristic
542C22×C53D4211yescharacteristic
543C22×C53D4211yescharacteristic
544C22×C53#54611yescharacteristic
545C22×C53#54611yescharacteristic
546C22×C53#54611yescharacteristic
547C22×C53#54711yescharacteristic
548C22×C53#54811yescharacteristic
549C22×C53#54811yescharacteristic
550C22×C53#55011yescharacteristic
551C22×C53#55011yescharacteristic
552C22×C53#55111yescharacteristic
553C22×C53#55111yescharacteristic
554C22×C53#55211yescharacteristic
555C22×C53#55311yescharacteristic
556C22×C53#55311yescharacteristic
557C22×C53#55911yescharacteristic
558C4×C53—24no—
559C4×C53—24no—
560C4×C53—24no—
561C4×C53—24no—
562C4×C53—42no—
563C4×C53—42no—
564C4×C53—42no—
565C4×C53—42no—
566C4×C53—42no—
567C4×C53—42no—
568C4×C53—42no—
569C4×C53—81no—
570C4×C53—81no—
571C22×#123C2×C5311yescharacteristic
572C2×#390C2×C5311yescharacteristic
573C2×#387C2×C5311yescharacteristic, complemented
574C2×C4×C4⋊C4C2×C5311yescharacteristic, complemented
575C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
576#1441C2×C5311yescharacteristic, complemented
577#1439C2×C5311yescharacteristic, complemented
578#1439C2×C5311yescharacteristic, complemented
579#1438C2×C5311yescharacteristic
580#1437C2×C5311yescharacteristic, complemented
581#1437C2×C5311yescharacteristic, complemented
582#1437C2×C5311yescharacteristic, complemented
583#1437C2×C5311yescharacteristic, complemented
584#1436C2×C5311yescharacteristic, complemented
585C22⋊#95C2×C5311yescharacteristic, complemented
586C2×C53—44no—
587C2×C53—82no—
588C2×C53#229711yescharacteristic
589C2×C53C4×#12311yescharacteristic
590C2×C53#233511yescharacteristic
591C2×C53D4×C22⋊C411yescharacteristic
592C2×C53#234111yescharacteristic
593C2×C53#235911yescharacteristic
594C2×C53#237411yescharacteristic
595C2×C53#244311yescharacteristic
596C2×C53#244511yescharacteristic
597C2×C53#245611yescharacteristic
598C2×C53#245811yescharacteristic
599C2×C53#246111yescharacteristic
600C2×C53#247111yescharacteristic
601C2×C53#255411yescharacteristic
602C2×C53#255811yescharacteristic
603C23×D4C22×C5311yescharacteristic
604C24×C4C22×C5311yescharacteristic
605C2×#123—24no—
606C2×#123—24no—
607C2×#123C4×C5318yescomplemented
608C22×C4⋊C4C22×C5311yescharacteristic
609C22×C4⋊C4C22×C5311yescharacteristic
610C22×C4⋊C4C22×C5311yescharacteristic
611C22×C4⋊C4C22×C5311yescharacteristic
612C22×C22⋊C4C22×C5311yescharacteristic
613C22×C22⋊C4C22×C5311yescharacteristic
614C22×C22⋊C4C22×C5311yescharacteristic
615C22×C22⋊C4C22×C5311yescharacteristic
616C22×C22⋊C4C22×C5311yescharacteristic
617C22×C22⋊C4C22×C5311yescharacteristic
618C22×C22⋊C4C22×C5311yescharacteristic
619C22×C22⋊C4C22×C5311yescharacteristic
620C22×C22⋊C4C22×C5311yescharacteristic
621C22×C22⋊C4C22×C5311yescharacteristic
622C22×C22⋊C4C22×C5311yescharacteristic
623C22×C42C22×C5311yescharacteristic
624C22×C42C22×C5311yescharacteristic
625C22×C42C22×C5311yescharacteristic
626C22×C42C22×C5311yescharacteristic
627#390—24no—
628#387—24no—
629C4×C4⋊C4—24no—
630C4×C22⋊C4—24no—
631C2×#95C22×C5311yescharacteristic
632C2×#95C22×C5311yescharacteristic
633C2×#95C22×C5311yescharacteristic
634C2×#95C22×C5311yescharacteristic
635C2×#95C22×C5311yescharacteristic
636C2×#95C22×C5311yescharacteristic
637C2×#95C22×C5311yescharacteristic
638C2×#95C22×C5311yescharacteristic
639C2×#95C22×C5311yescharacteristic
640C2×#95C22×C5311yescharacteristic
641C2×#95C22×C5311yescharacteristic
642C2×#95C22×C5311yescharacteristic
643C2×#95C22×C5311yescharacteristic
644C2×#95C22×C5311yescharacteristic
645C53#1409511yescharacteristic, direct product factor, Sylow
646C25C23×C5311yescharacteristic
647C25C23×C5311yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C5314yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C5314yes—
662C23×C4C23×C5311yescharacteristic
663C23×C4C23×C5311yescharacteristic
664C23×C4C23×C5311yescharacteristic
665C23×C4C23×C5311yescharacteristic
666C23×C4C23×C5311yescharacteristic
667C23×C4C23×C5311yescharacteristic
668C23×C4C23×C5311yescharacteristic
669C23×C4C23×C5311yescharacteristic
670C23×C4C23×C5311yescharacteristic
671C23×C4C23×C5311yescharacteristic
672C23×C4C23×C5311yescharacteristic
673C23×C4C23×C5311yescharacteristic
674C23×C4C23×C5311yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C5314yes—
685C2×C4⋊C4C2×C4×C5314yes—
686C2×C4⋊C4D4×C5314yes—
687C2×C4⋊C4D4×C5314yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C5314yes—
718C2×C22⋊C4C2×C4×C5314yes—
719C2×C22⋊C4C2×C4×C5314yes—
720C2×C22⋊C4D4×C5314yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C5312yes—
774C24C22×C4×C5312yes—
775C24C2×D4×C5312yes—
776C24#41×C5312yes—
777C24C24×C5311yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C5312yes—
865C22×C4C22×C4×C5312yes—
866C22×C4C22×C4×C5312yes—
867C22×C4C22×C4×C5312yes—
868C22×C4C22×C4×C5312yes—
869C22×C4C2×D4×C5312yes—
870C22×C4C2×D4×C5312yes—
871C22×C4C2×D4×C5312yes—
872C22×C4C2×D4×C5312yes—
873C22×C4C2×D4×C5312yes—
874C22×C4C2×D4×C5312yes—
875C22×C4C2×D4×C5312yes—
876C22×C4C2×D4×C5312yes—
877C22×C4#41×C5312yes—
878C22×C4#41×C5312yes—
879C22×C4#41×C5312yes—
880C22×C4#41×C5312yes—
881C22×C4#41×C5312yes—
882C22×C4#41×C5312yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C53116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C5314yes—
972C23C23×C4×C5311yescharacteristic
973C23C22×D4×C5311yescharacteristic
974C23C22×D4×C5311yescharacteristic
975C23C22×D4×C5311yescharacteristic
976C23C2×#41×C5311yescharacteristic
977C23C2×#41×C5311yescharacteristic
978C23C2×#41×C5311yescharacteristic
979C23C2×#41×C5311yescharacteristic
980C23C2×#41×C5311yescharacteristic
981C23C2×#41×C5311yescharacteristic
982C23C2×#41×C5311yescharacteristic
983C23H(5,𝔽2)×C5311yescharacteristic
984C23H(5,𝔽2)×C5311yescharacteristic
985C23H(5,𝔽2)×C5311yescharacteristic
986C232−1+4×C5311yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C5314yes—
1077C2×C4C2×C22⋊C4×C5314yes—
1078C2×C4C2×C22⋊C4×C5314yes—
1079C2×C4#123×C5314yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C5311yescharacteristic
1111C22C2×C4×D4×C5311yescharacteristic
1112C22C4×#41×C5311yescharacteristic
1113C22C4×#41×C5311yescharacteristic
1114C22C4×#41×C5311yescharacteristic
1115C22C53×#51811yescharacteristic
1116C22C53×#52011yescharacteristic
1117C22C2×#123×C5311yescharacteristic
1118C22C53×#52511yescharacteristic
1119C22C53×#52511yescharacteristic
1120C22C53×#52511yescharacteristic
1121C22C53×#52911yescharacteristic
1122C22C53×#52911yescharacteristic
1123C22C53×#53211yescharacteristic
1124C22C53×#53211yescharacteristic
1125C22C53×#53811yescharacteristic
1126C22C53×#53911yescharacteristic
1127C22C53×#54011yescharacteristic
1128C22C53×#54211yescharacteristic
1129C22D42×C5311yescharacteristic
1130C22D42×C5311yescharacteristic
1131C22C53×#54611yescharacteristic
1132C22C53×#54611yescharacteristic
1133C22C53×#54611yescharacteristic
1134C22C53×#54711yescharacteristic
1135C22C53×#54811yescharacteristic
1136C22C53×#54811yescharacteristic
1137C22C53×#55011yescharacteristic
1138C22C53×#55011yescharacteristic
1139C22C53×#55111yescharacteristic
1140C22C53×#55111yescharacteristic
1141C22C53×#55211yescharacteristic
1142C22C53×#55311yescharacteristic
1143C22C53×#55311yescharacteristic
1144C22C53×#55911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C53×#229711yescharacteristic
1161C2C4×#123×C5311yescharacteristic
1162C2C53×#233511yescharacteristic
1163C2D4×C22⋊C4×C5311yescharacteristic
1164C2C53×#234111yescharacteristic
1165C2C53×#235911yescharacteristic
1166C2C53×#237411yescharacteristic
1167C2C53×#244311yescharacteristic
1168C2C53×#244511yescharacteristic
1169C2C53×#245611yescharacteristic
1170C2C53×#245811yescharacteristic
1171C2C53×#246111yescharacteristic
1172C2C53×#247111yescharacteristic
1173C2C53×#255411yescharacteristic
1174C2C53×#255811yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC23×D4×C53C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C53×#387C2semidirect
4. C2×C4×C4⋊C4×C53C2semidirect
5. C2×C4×C22⋊C4×C53C2semidirect
6. C53×#1441C2semidirect
7. C53×#1439C2semidirect
8. C53×#1439C2semidirect
10. C53×#1437C2semidirect
11. C53×#1437C2semidirect
12. C53×#1437C2semidirect
13. C53×#1437C2semidirect
14. C53×#1436C2semidirect
15. C53×C22⋊#95C2semidirect
20. C2×#123×C53C4semidirect
298. C4⋊C4×C53C22⋊C4semidirect
491. C2×C4×C53#123semidirect
492. #14095C53direct (N × H)
573. C2×#387C2×C53semidirect
574. C2×C4×C4⋊C4C2×C53semidirect
575. C2×C4×C22⋊C4C2×C53semidirect
576. #1441C2×C53semidirect
577. #1439C2×C53semidirect
578. #1439C2×C53semidirect
580. #1437C2×C53semidirect
581. #1437C2×C53semidirect
582. #1437C2×C53semidirect
583. #1437C2×C53semidirect
584. #1436C2×C53semidirect
585. C22⋊#95C2×C53semidirect
607. C2×#123C4×C53semidirect
645. C53#14095direct (N × H)
886. C4⋊C4C22⋊C4×C53semidirect
1079. C2×C4#123×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C532
C2×C53×#3902
C2×C53×#3872
C2×C4×C4⋊C4×C532
C2×C4×C22⋊C4×C532
C53×#14412
C53×#14392
C53×#14382
C53×#14372
C53×#14362
C53×C22⋊#952
#1409553