Finite Group Databasebeta

← C53×#14520 #27222032

Subgroups — C53×#14520 #27222032

Order 13568.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#392C211yesmaximal, characteristic
2C2×C53×#390C211yesmaximal, characteristic, complemented
3C2×C53×#388C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C53×#1442C211yesmaximal, characteristic, complemented
7C53×#1440C211yesmaximal, characteristic, complemented
8C53×#1438C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic, complemented
10C53×#1438C211yesmaximal, characteristic, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1437C211yesmaximal, characteristic, complemented
14C53×#1434C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C22×C4⋊C4×C53C2211yescharacteristic
21C22×C22⋊C4×C53C2211yescharacteristic
22C22×C22⋊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×C42×C53C2211yescharacteristic
36C22×C42×C53C2211yescharacteristic
37C53×#392C418yescomplemented
38C53×#390—24no—
39C53×#388—24no—
40C53×#386—24no—
41C53×#386—24no—
42C2×#95×C53C2211yescharacteristic
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
56C25×C53C2311yescharacteristic
57C25×C53C2311yescharacteristic
58C25×C53C2311yescharacteristic
59C22×D4×C53—22no—
60C22×D4×C53—22no—
61C22×D4×C53—22no—
62C22×D4×C53—22no—
63C22×D4×C53—22no—
64C22×D4×C53—22no—
65C22×D4×C53—41no—
66C22×D4×C53—41no—
67C22×D4×C53—41no—
68C22×D4×C53—41no—
69C22×D4×C53—41no—
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×C53C2×C414yes—
78C22×D4×C53C2×C414yes—
79C22×D4×C53C2×C414yescomplemented
80C23×C4×C53—22no—
81C23×C4×C53—22no—
82C23×C4×C53—22no—
83C23×C4×C53—41no—
84C23×C4×C53—41no—
85C23×C4×C53—41no—
86C23×C4×C53—41no—
87C23×C4×C53C2311yescharacteristic
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
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—41no—
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—41no—
121C2×C22⋊C4×C53—41no—
122C2×C22⋊C4×C53—41no—
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×C53—41no—
130C2×C22⋊C4×C53—41no—
131C2×C22⋊C4×C53—41no—
132C2×C22⋊C4×C53—41no—
133C2×C22⋊C4×C53—41no—
134C2×C22⋊C4×C53—41no—
135C2×C22⋊C4×C53—41no—
136C2×C22⋊C4×C53—41no—
137C2×C22⋊C4×C53—41no—
138C2×C22⋊C4×C53—41no—
139C2×C22⋊C4×C53—41no—
140C2×C22⋊C4×C53C2×C414yes—
141C2×C22⋊C4×C53C2×C414yescomplemented
142C2×C22⋊C4×C53C2×C414yescomplemented
143C2×C22⋊C4×C53D414yescomplemented
144C2×C42×C53—22no—
145C2×C42×C53—22no—
146C2×C42×C53—22no—
147C2×C42×C53—41no—
148C2×C42×C53—41no—
149C2×C42×C53—41no—
150#95×C53—22no—
151#95×C53—22no—
152#95×C53—22no—
153#95×C53—22no—
154#95×C53—41no—
155#95×C53—41no—
156#95×C53—41no—
157#95×C53—41no—
158#95×C53—41no—
159#95×C53—41no—
160#95×C53—41no—
161#95×C53—41no—
162#95×C53C2×C414yescomplemented
163#95×C53D414yescomplemented
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×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×C53C22×C412yes—
205C24×C53C22×C412yes—
206C24×C53C22×C412yes—
207C24×C53C2×D412yes—
208C24×C53#4112yes—
209C24×C53C2411yescharacteristic
210C2×D4×C53—28no—
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—
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—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—44no—
304C22×C4×C53—44no—
305C22×C4×C53—44no—
306C22×C4×C53—44no—
307C22×C4×C53—44no—
308C22×C4×C53—44no—
309C22×C4×C53—44no—
310C22×C4×C53C22×C412yes—
311C22×C4×C53C22×C412yes—
312C22×C4×C53C22×C412yes—
313C22×C4×C53C22×C412yes—
314C22×C4×C53C2×D412yes—
315C22×C4×C53C2×D412yes—
316C22×C4×C53C2×D412yes—
317C22×C4×C53C2×D412yes—
318C22×C4×C53C2×D412yes—
319C22×C4×C53#4112yes—
320C22×C4×C53#4112yes—
321C22×C4×C53#4112yes—
322C4⋊C4×C53—44no—
323C22⋊C4×C53—28no—
324C22⋊C4×C53—44no—
325C22⋊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—
337C42×C53—44no—
338C42×C53—44no—
339C23×C53—22no—
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—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×C53C4×D414yes—
444C23×C53C23×C411yescharacteristic
445C23×C53C22×D411yescharacteristic
446C23×C53C22×D411yescharacteristic
447C23×C53C2×#4111yescharacteristic
448C23×C53C2×#4111yescharacteristic
449C23×C53C2×#4111yescharacteristic
450C23×C53C2×#4111yescharacteristic
451C23×C53H(5,𝔽2)11yescharacteristic
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
459D4×C53—416no—
460D4×C53—416no—
461D4×C53—416no—
462C2×C4×C53—22no—
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—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—416no—
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×C53C4×D414yes—
547#14520C5311yesmaximal, characteristic, direct product factor, Sylow
548C22×C53—24no—
549C22×C53—24no—
550C22×C53—24no—
551C22×C53—42no—
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—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×C53C2×C4×D411yescharacteristic
594C22×C53C2×C4×D411yescharacteristic
595C22×C53C4×#4111yescharacteristic
596C22×C53#51811yescharacteristic
597C22×C53#51811yescharacteristic
598C22×C53#51811yescharacteristic
599C22×C53#51811yescharacteristic
600C22×C53#53411yescharacteristic
601C22×C53#53511yescharacteristic
602C22×C53#53511yescharacteristic
603C22×C53#53511yescharacteristic
604C22×C53#53811yescharacteristic
605C22×C53#53811yescharacteristic
606C22×C53#53811yescharacteristic
607C22×C53#53811yescharacteristic
608C22×C53#54011yescharacteristic
609C22×C53#54011yescharacteristic
610C22×C53#54011yescharacteristic
611C22×C53#54011yescharacteristic
612C22×C53D4211yescharacteristic
613C22×C53#54611yescharacteristic
614C22×C53#54611yescharacteristic
615C22×C53#54611yescharacteristic
616C22×C53#54611yescharacteristic
617C22×C53#54611yescharacteristic
618C22×C53#55011yescharacteristic
619C22×C53#55111yescharacteristic
620C22×C53#55311yescharacteristic
621C22×C53#55311yescharacteristic
622C22×C53#55311yescharacteristic
623C22×C53#55511yescharacteristic
624C22×C53#56011yescharacteristic
625C22×C53#56011yescharacteristic
626C22×C53#56011yescharacteristic
627C22×C53H(3,𝔽4)11yescharacteristic
628C4×C53—24no—
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—42no—
638C4×C53—81no—
639C4×C53—81no—
640C2×#392C2×C5311yescharacteristic
641C2×#390C2×C5311yescharacteristic, complemented
642C2×#388C2×C5311yescharacteristic, complemented
643C2×#386C2×C5311yescharacteristic, complemented
644C2×#386C2×C5311yescharacteristic, complemented
645#1442C2×C5311yescharacteristic, complemented
646#1440C2×C5311yescharacteristic, complemented
647#1438C2×C5311yescharacteristic, complemented
648#1438C2×C5311yescharacteristic, complemented
649#1438C2×C5311yescharacteristic, complemented
650#1437C2×C5311yescharacteristic, complemented
651#1437C2×C5311yescharacteristic, complemented
652#1437C2×C5311yescharacteristic, complemented
653#1434C2×C5311yescharacteristic, complemented
654C22⋊#95C2×C5311yescharacteristic, complemented
655C2×C53—44no—
656C2×C53—82no—
657C2×C53—82no—
658C2×C53#232111yescharacteristic
659C2×C53#232811yescharacteristic
660C2×C53#233311yescharacteristic
661C2×C53#235811yescharacteristic
662C2×C53#236311yescharacteristic
663C2×C53#236411yescharacteristic
664C2×C53#237511yescharacteristic
665C2×C53#267011yescharacteristic
666C2×C53#267311yescharacteristic
667C2×C53#269911yescharacteristic
668C2×C53#270311yescharacteristic
669C2×C53#270311yescharacteristic
670C2×C53#271411yescharacteristic
671C2×C53#275311yescharacteristic
672C2×C53#275611yescharacteristic
673C23×D4C22×C5311yescharacteristic
674C23×D4C22×C5311yescharacteristic
675C23×D4C22×C5311yescharacteristic
676C24×C4C22×C5311yescharacteristic
677C22×C4⋊C4C22×C5311yescharacteristic
678C22×C22⋊C4C22×C5311yescharacteristic
679C22×C22⋊C4C22×C5311yescharacteristic
680C22×C22⋊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×C42C22×C5311yescharacteristic
693C22×C42C22×C5311yescharacteristic
694#392C4×C5318yescomplemented
695#390—24no—
696#388—24no—
697#386—24no—
698#386—24no—
699C2×#95C22×C5311yescharacteristic
700C2×#95C22×C5311yescharacteristic
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
713C53#1452011yescharacteristic, direct product factor, Sylow
714C25C23×C5311yescharacteristic
715C25C23×C5311yescharacteristic
716C25C23×C5311yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×C4×C5314yes—
736C22×D4C2×C4×C5314yes—
737C22×D4C2×C4×C5314yescomplemented
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—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—41no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
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—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
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⋊C4C2×C4×C5314yes—
799C2×C22⋊C4C2×C4×C5314yescomplemented
800C2×C22⋊C4C2×C4×C5314yescomplemented
801C2×C22⋊C4D4×C5314yescomplemented
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807C2×C42—41no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95C2×C4×C5314yescomplemented
821#95D4×C5314yescomplemented
822C24—21no—
823C24—21no—
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—
862C24C22×C4×C5312yes—
863C24C22×C4×C5312yes—
864C24C22×C4×C5312yes—
865C24C2×D4×C5312yes—
866C24#41×C5312yes—
867C24C24×C5311yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
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—
889C22×C4—21no—
890C22×C4—21no—
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—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C5312yes—
969C22×C4C22×C4×C5312yes—
970C22×C4C22×C4×C5312yes—
971C22×C4C22×C4×C5312yes—
972C22×C4C2×D4×C5312yes—
973C22×C4C2×D4×C5312yes—
974C22×C4C2×D4×C5312yes—
975C22×C4C2×D4×C5312yes—
976C22×C4C2×D4×C5312yes—
977C22×C4#41×C5312yes—
978C22×C4#41×C5312yes—
979C22×C4#41×C5312yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C42—44no—
996C42—44no—
997C23—22no—
998C23—22no—
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—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—
1101C23C4×D4×C5314yes—
1102C23C23×C4×C5311yescharacteristic
1103C23C22×D4×C5311yescharacteristic
1104C23C22×D4×C5311yescharacteristic
1105C23C2×#41×C5311yescharacteristic
1106C23C2×#41×C5311yescharacteristic
1107C23C2×#41×C5311yescharacteristic
1108C23C2×#41×C5311yescharacteristic
1109C23H(5,𝔽2)×C5311yescharacteristic
1110C23H(5,𝔽2)×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
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
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—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
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×C4C4×D4×C5314yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
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—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—
1250C22C2×C4×D4×C5311yescharacteristic
1251C22C2×C4×D4×C5311yescharacteristic
1252C22C4×#41×C5311yescharacteristic
1253C22C53×#51811yescharacteristic
1254C22C53×#51811yescharacteristic
1255C22C53×#51811yescharacteristic
1256C22C53×#51811yescharacteristic
1257C22C53×#53411yescharacteristic
1258C22C53×#53511yescharacteristic
1259C22C53×#53511yescharacteristic
1260C22C53×#53511yescharacteristic
1261C22C53×#53811yescharacteristic
1262C22C53×#53811yescharacteristic
1263C22C53×#53811yescharacteristic
1264C22C53×#53811yescharacteristic
1265C22C53×#54011yescharacteristic
1266C22C53×#54011yescharacteristic
1267C22C53×#54011yescharacteristic
1268C22C53×#54011yescharacteristic
1269C22D42×C5311yescharacteristic
1270C22C53×#54611yescharacteristic
1271C22C53×#54611yescharacteristic
1272C22C53×#54611yescharacteristic
1273C22C53×#54611yescharacteristic
1274C22C53×#54611yescharacteristic
1275C22C53×#55011yescharacteristic
1276C22C53×#55111yescharacteristic
1277C22C53×#55311yescharacteristic
1278C22C53×#55311yescharacteristic
1279C22C53×#55311yescharacteristic
1280C22C53×#55511yescharacteristic
1281C22C53×#56011yescharacteristic
1282C22C53×#56011yescharacteristic
1283C22C53×#56011yescharacteristic
1284C22C53×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C53×#232111yescharacteristic
1301C2C53×#232811yescharacteristic
1302C2C53×#233311yescharacteristic
1303C2C53×#235811yescharacteristic
1304C2C53×#236311yescharacteristic
1305C2C53×#236411yescharacteristic
1306C2C53×#237511yescharacteristic
1307C2C53×#267011yescharacteristic
1308C2C53×#267311yescharacteristic
1309C2C53×#269911yescharacteristic
1310C2C53×#270311yescharacteristic
1311C2C53×#270311yescharacteristic
1312C2C53×#271411yescharacteristic
1313C2C53×#275311yescharacteristic
1314C2C53×#275611yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC2×C53×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C53×#390C2semidirect
3. C2×C53×#388C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#386C2semidirect
6. C53×#1442C2semidirect
7. C53×#1440C2semidirect
8. C53×#1438C2semidirect
9. C53×#1438C2semidirect
10. C53×#1438C2semidirect
11. C53×#1437C2semidirect
12. C53×#1437C2semidirect
13. C53×#1437C2semidirect
14. C53×#1434C2semidirect
15. C53×C22⋊#95C2semidirect
37. C53×#392C4semidirect
79. C22×D4×C53C2×C4semidirect
141. C2×C22⋊C4×C53C2×C4semidirect
142. C2×C22⋊C4×C53C2×C4semidirect
143. C2×C22⋊C4×C53D4semidirect
162. #95×C53C2×C4semidirect
163. #95×C53D4semidirect
547. #14520C53direct (N × H)
641. C2×#390C2×C53semidirect
642. C2×#388C2×C53semidirect
643. C2×#386C2×C53semidirect
644. C2×#386C2×C53semidirect
645. #1442C2×C53semidirect
646. #1440C2×C53semidirect
647. #1438C2×C53semidirect
648. #1438C2×C53semidirect
649. #1438C2×C53semidirect
650. #1437C2×C53semidirect
651. #1437C2×C53semidirect
652. #1437C2×C53semidirect
653. #1434C2×C53semidirect
654. C22⋊#95C2×C53semidirect
694. #392C4×C53semidirect
713. C53#14520direct (N × H)
737. C22×D4C2×C4×C53semidirect
799. C2×C22⋊C4C2×C4×C53semidirect
800. C2×C22⋊C4C2×C4×C53semidirect
801. C2×C22⋊C4D4×C53semidirect
820. #95C2×C4×C53semidirect
821. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3922
C2×C53×#3902
C2×C53×#3882
C2×C53×#3862
C53×#14422
C53×#14402
C53×#14382
C53×#14372
C53×#14342
C53×C22⋊#952
#1452053