Finite Group Databasebeta

← C53×#14100 #27221612

Subgroups — C53×#14100 #27221612

Order 13568.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C53C211yesmaximal, characteristic
2C2×C53×#390C211yesmaximal, characteristic, complemented
3C2×C53×#388C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
8C53×#1441C211yesmaximal, characteristic, complemented
9C53×#1438C211yesmaximal, characteristic, complemented
10C53×#1438C211yesmaximal, characteristic, complemented
11C53×#1438C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1437C211yesmaximal, characteristic, complemented
14C53×#1436C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C24×C4×C53C2211yescharacteristic
21C2×#121×C53—24no—
22C2×#121×C53—24no—
23C2×#121×C53C418yescomplemented
24C22×C4⋊C4×C53C2211yescharacteristic
25C22×C4⋊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×C42×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C22×C42×C53C2211yescharacteristic
42C53×#390—24no—
43C53×#388—24no—
44C53×#386—24no—
45C53×#386—24no—
46C4×C22⋊C4×C53—24no—
47C4×C22⋊C4×C53—24no—
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C2×#95×C53C2211yescharacteristic
60C25×C53C2311yescharacteristic
61C25×C53C2311yescharacteristic
62C25×C53C2311yescharacteristic
63C22×D4×C53—22no—
64C22×D4×C53—22no—
65C22×D4×C53—22no—
66C22×D4×C53—22no—
67C22×D4×C53—22no—
68C22×D4×C53—22no—
69C22×D4×C53—22no—
70C22×D4×C53—22no—
71C22×D4×C53—22no—
72C22×D4×C53—22no—
73C22×D4×C53—22no—
74C22×D4×C53—22no—
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×C53C2×C414yes—
82C22×D4×C53C2×C414yes—
83C22×D4×C53C2×C414yescomplemented
84C23×C4×C53—22no—
85C23×C4×C53—22no—
86C23×C4×C53—22no—
87C23×C4×C53—22no—
88C23×C4×C53—22no—
89C23×C4×C53—22no—
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—41no—
94C23×C4×C53—41no—
95C23×C4×C53—41no—
96C23×C4×C53—41no—
97C23×C4×C53C2×C414yescomplemented
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2311yescharacteristic
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2311yescharacteristic
109C23×C4×C53C2311yescharacteristic
110#121×C53—232no—
111C2×C4⋊C4×C53—22no—
112C2×C4⋊C4×C53—22no—
113C2×C4⋊C4×C53—22no—
114C2×C4⋊C4×C53—22no—
115C2×C4⋊C4×C53—41no—
116C2×C4⋊C4×C53C2×C414yescomplemented
117C2×C22⋊C4×C53—22no—
118C2×C22⋊C4×C53—22no—
119C2×C22⋊C4×C53—22no—
120C2×C22⋊C4×C53—22no—
121C2×C22⋊C4×C53—22no—
122C2×C22⋊C4×C53—22no—
123C2×C22⋊C4×C53—22no—
124C2×C22⋊C4×C53—22no—
125C2×C22⋊C4×C53—22no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C22⋊C4×C53—22no—
130C2×C22⋊C4×C53—22no—
131C2×C22⋊C4×C53—22no—
132C2×C22⋊C4×C53—22no—
133C2×C22⋊C4×C53—22no—
134C2×C22⋊C4×C53—22no—
135C2×C22⋊C4×C53—22no—
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—22no—
140C2×C22⋊C4×C53—22no—
141C2×C22⋊C4×C53—22no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—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×C53C2×C414yes—
152C2×C22⋊C4×C53C2×C414yescomplemented
153C2×C22⋊C4×C53D414yes—
154C2×C22⋊C4×C53D414yes—
155C2×C22⋊C4×C53D414yescomplemented
156C2×C42×C53—22no—
157C2×C42×C53—22no—
158C2×C42×C53—22no—
159C2×C42×C53—22no—
160C2×C42×C53—22no—
161C2×C42×C53—22no—
162C2×C42×C53—41no—
163C2×C42×C53—41no—
164C2×C42×C53—41no—
165#95×C53—22no—
166#95×C53—22no—
167#95×C53—22no—
168#95×C53—22no—
169#95×C53—22no—
170#95×C53—22no—
171#95×C53—22no—
172#95×C53—22no—
173#95×C53—22no—
174#95×C53—41no—
175#95×C53—41no—
176#95×C53D414yescomplemented
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×C53—21no—
214C24×C53—21no—
215C24×C53C22×C412yes—
216C24×C53C22×C412yes—
217C24×C53C22×C412yes—
218C24×C53C2×D412yes—
219C24×C53C2×D412yes—
220C24×C53C2×D412yes—
221C24×C53#4112yes—
222C24×C53C2411yescharacteristic
223C2×D4×C53—28no—
224C2×D4×C53—28no—
225C2×D4×C53—28no—
226C2×D4×C53—28no—
227C2×D4×C53—28no—
228C2×D4×C53—28no—
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—
238C2×D4×C53—44no—
239C2×D4×C53—44no—
240C2×D4×C53—44no—
241C2×D4×C53—44no—
242C2×D4×C53—44no—
243C2×D4×C53—44no—
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—28no—
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—28no—
298C22×C4×C53—28no—
299C22×C4×C53—21no—
300C22×C4×C53—21no—
301C22×C4×C53—21no—
302C22×C4×C53—21no—
303C22×C4×C53—21no—
304C22×C4×C53—21no—
305C22×C4×C53—21no—
306C22×C4×C53—21no—
307C22×C4×C53—21no—
308C22×C4×C53—21no—
309C22×C4×C53—21no—
310C22×C4×C53—21no—
311C22×C4×C53—21no—
312C22×C4×C53—21no—
313C22×C4×C53—44no—
314C22×C4×C53—44no—
315C22×C4×C53—44no—
316C22×C4×C53—44no—
317C22×C4×C53—44no—
318C22×C4×C53—44no—
319C22×C4×C53—44no—
320C22×C4×C53—44no—
321C22×C4×C53—44no—
322C22×C4×C53—44no—
323C22×C4×C53—44no—
324C22×C4×C53C22×C412yes—
325C22×C4×C53C22×C412yes—
326C22×C4×C53C22×C412yes—
327C22×C4×C53C22×C412yes—
328C22×C4×C53C2×D412yes—
329C22×C4×C53C2×D412yes—
330C22×C4×C53C2×D412yes—
331C22×C4×C53C2×D412yes—
332C22×C4×C53C2×D412yes—
333C22×C4×C53C2×D412yes—
334C22×C4×C53C2×D412yes—
335C22×C4×C53C2×D412yes—
336C22×C4×C53C2×D412yes—
337C22×C4×C53#4112yes—
338C22×C4×C53#4112yes—
339C22×C4×C53#4112yes—
340C22×C4×C53#4112yes—
341C22×C4×C53#4112yes—
342C4⋊C4×C53—28no—
343C4⋊C4×C53—44no—
344C22⋊C4×C53—28no—
345C22⋊C4×C53—28no—
346C22⋊C4×C53—28no—
347C22⋊C4×C53—28no—
348C22⋊C4×C53—44no—
349C22⋊C4×C53—44no—
350C22⋊C4×C53—44no—
351C22⋊C4×C53—44no—
352C22⋊C4×C53—44no—
353C22⋊C4×C53—44no—
354C22⋊C4×C53—44no—
355C22⋊C4×C53—44no—
356C22⋊C4×C53C22⋊C4116yescomplemented
357C42×C53—44no—
358C42×C53—44no—
359C42×C53—44no—
360C23×C53—22no—
361C23×C53—22no—
362C23×C53—22no—
363C23×C53—22no—
364C23×C53—22no—
365C23×C53—22no—
366C23×C53—22no—
367C23×C53—22no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—22no—
371C23×C53—22no—
372C23×C53—22no—
373C23×C53—22no—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53—22no—
378C23×C53—22no—
379C23×C53—22no—
380C23×C53—22no—
381C23×C53—22no—
382C23×C53—22no—
383C23×C53—22no—
384C23×C53—22no—
385C23×C53—22no—
386C23×C53—22no—
387C23×C53—22no—
388C23×C53—22no—
389C23×C53—22no—
390C23×C53—22no—
391C23×C53—22no—
392C23×C53—22no—
393C23×C53—22no—
394C23×C53—22no—
395C23×C53—22no—
396C23×C53—22no—
397C23×C53—22no—
398C23×C53—22no—
399C23×C53—22no—
400C23×C53—22no—
401C23×C53—22no—
402C23×C53—22no—
403C23×C53—41no—
404C23×C53—41no—
405C23×C53—41no—
406C23×C53—41no—
407C23×C53—41no—
408C23×C53—41no—
409C23×C53—41no—
410C23×C53—41no—
411C23×C53—41no—
412C23×C53—41no—
413C23×C53—41no—
414C23×C53—41no—
415C23×C53—41no—
416C23×C53—41no—
417C23×C53—41no—
418C23×C53—41no—
419C23×C53—41no—
420C23×C53—41no—
421C23×C53—41no—
422C23×C53—41no—
423C23×C53—41no—
424C23×C53—41no—
425C23×C53—41no—
426C23×C53—41no—
427C23×C53—41no—
428C23×C53—41no—
429C23×C53—41no—
430C23×C53—41no—
431C23×C53—41no—
432C23×C53—41no—
433C23×C53—41no—
434C23×C53—41no—
435C23×C53—41no—
436C23×C53—41no—
437C23×C53—41no—
438C23×C53—41no—
439C23×C53—41no—
440C23×C53—41no—
441C23×C53—41no—
442C23×C53—41no—
443C23×C53—41no—
444C23×C53—41no—
445C23×C53—41no—
446C23×C53—41no—
447C23×C53—41no—
448C23×C53—41no—
449C23×C53—41no—
450C23×C53—41no—
451C23×C53—41no—
452C23×C53—41no—
453C23×C53—41no—
454C23×C53—41no—
455C23×C53—41no—
456C23×C53—41no—
457C23×C53—41no—
458C23×C53—41no—
459C23×C53—41no—
460C23×C53—41no—
461C23×C53—41no—
462C23×C53—41no—
463C23×C53C2×C22⋊C414yes—
464C23×C53C4×D414yes—
465C23×C53C23×C411yescharacteristic
466C23×C53C22×D411yescharacteristic
467C23×C53C22×D411yescharacteristic
468C23×C53C22×D411yescharacteristic
469C23×C53C22×D411yescharacteristic
470C23×C53C2×#4111yescharacteristic
471C23×C53C2×#4111yescharacteristic
472C23×C53C2×#4111yescharacteristic
473C23×C53C2×#4111yescharacteristic
474C23×C53C2×#4111yescharacteristic
475C23×C53C2×#4111yescharacteristic
476C23×C53H(5,𝔽2)11yescharacteristic
477C23×C53H(5,𝔽2)11yescharacteristic
478C23×C53H(5,𝔽2)11yescharacteristic
479C23×C53H(5,𝔽2)11yescharacteristic
480D4×C53—416no—
481D4×C53—416no—
482D4×C53—416no—
483C2×C4×C53—22no—
484C2×C4×C53—22no—
485C2×C4×C53—22no—
486C2×C4×C53—22no—
487C2×C4×C53—22no—
488C2×C4×C53—22no—
489C2×C4×C53—22no—
490C2×C4×C53—22no—
491C2×C4×C53—22no—
492C2×C4×C53—22no—
493C2×C4×C53—22no—
494C2×C4×C53—22no—
495C2×C4×C53—22no—
496C2×C4×C53—22no—
497C2×C4×C53—22no—
498C2×C4×C53—22no—
499C2×C4×C53—22no—
500C2×C4×C53—22no—
501C2×C4×C53—22no—
502C2×C4×C53—22no—
503C2×C4×C53—22no—
504C2×C4×C53—22no—
505C2×C4×C53—22no—
506C2×C4×C53—22no—
507C2×C4×C53—22no—
508C2×C4×C53—22no—
509C2×C4×C53—22no—
510C2×C4×C53—22no—
511C2×C4×C53—22no—
512C2×C4×C53—22no—
513C2×C4×C53—22no—
514C2×C4×C53—22no—
515C2×C4×C53—22no—
516C2×C4×C53—22no—
517C2×C4×C53—22no—
518C2×C4×C53—22no—
519C2×C4×C53—22no—
520C2×C4×C53—22no—
521C2×C4×C53—22no—
522C2×C4×C53—22no—
523C2×C4×C53—22no—
524C2×C4×C53—22no—
525C2×C4×C53—416no—
526C2×C4×C53—416no—
527C2×C4×C53—41no—
528C2×C4×C53—41no—
529C2×C4×C53—41no—
530C2×C4×C53—41no—
531C2×C4×C53—41no—
532C2×C4×C53—41no—
533C2×C4×C53—41no—
534C2×C4×C53—41no—
535C2×C4×C53—41no—
536C2×C4×C53—41no—
537C2×C4×C53—41no—
538C2×C4×C53—41no—
539C2×C4×C53—41no—
540C2×C4×C53—41no—
541C2×C4×C53—41no—
542C2×C4×C53—41no—
543C2×C4×C53—41no—
544C2×C4×C53—41no—
545C2×C4×C53—41no—
546C2×C4×C53—41no—
547C2×C4×C53—41no—
548C2×C4×C53—41no—
549C2×C4×C53—41no—
550C2×C4×C53—41no—
551C2×C4×C53—41no—
552C2×C4×C53—41no—
553C2×C4×C53—41no—
554C2×C4×C53—41no—
555C2×C4×C53—41no—
556C2×C4×C53—41no—
557C2×C4×C53—41no—
558C2×C4×C53—41no—
559C2×C4×C53—41no—
560C2×C4×C53—41no—
561C2×C4×C53—41no—
562C2×C4×C53—41no—
563C2×C4×C53—41no—
564C2×C4×C53—41no—
565C2×C4×C53C2×C22⋊C414yes—
566C2×C4×C53C2×C22⋊C414yes—
567C2×C4×C53C4×D414yes—
568C2×C4×C53#12114yescomplemented
569#14100C5311yesmaximal, characteristic, direct product factor, Sylow
570C22×C53—24no—
571C22×C53—24no—
572C22×C53—24no—
573C22×C53—24no—
574C22×C53—24no—
575C22×C53—24no—
576C22×C53—42no—
577C22×C53—42no—
578C22×C53—42no—
579C22×C53—42no—
580C22×C53—42no—
581C22×C53—42no—
582C22×C53—42no—
583C22×C53—42no—
584C22×C53—42no—
585C22×C53—42no—
586C22×C53—42no—
587C22×C53—42no—
588C22×C53—42no—
589C22×C53—42no—
590C22×C53—42no—
591C22×C53—42no—
592C22×C53—42no—
593C22×C53—42no—
594C22×C53—42no—
595C22×C53—42no—
596C22×C53—42no—
597C22×C53—42no—
598C22×C53—42no—
599C22×C53—42no—
600C22×C53—42no—
601C22×C53—42no—
602C22×C53—42no—
603C22×C53—42no—
604C22×C53—42no—
605C22×C53—42no—
606C22×C53—42no—
607C22×C53—81no—
608C22×C53—81no—
609C22×C53—81no—
610C22×C53—81no—
611C22×C53—81no—
612C22×C53—81no—
613C22×C53—81no—
614C22×C53—81no—
615C22×C53C22×C22⋊C411yescharacteristic
616C22×C53C2×C4×D411yescharacteristic
617C22×C53C2×C4×D411yescharacteristic
618C22×C53C4×#4111yescharacteristic
619C22×C53C4×#4111yescharacteristic
620C22×C53#51811yescharacteristic
621C22×C53#51811yescharacteristic
622C22×C53C2×#12111yescharacteristic
623C22×C53#52511yescharacteristic
624C22×C53#52511yescharacteristic
625C22×C53#52511yescharacteristic
626C22×C53#52911yescharacteristic
627C22×C53#53211yescharacteristic
628C22×C53#53211yescharacteristic
629C22×C53#53211yescharacteristic
630C22×C53#53811yescharacteristic
631C22×C53#53811yescharacteristic
632C22×C53#54011yescharacteristic
633C22×C53#54011yescharacteristic
634C22×C53D4211yescharacteristic
635C22×C53D4211yescharacteristic
636C22×C53D4211yescharacteristic
637C22×C53D4211yescharacteristic
638C22×C53#54611yescharacteristic
639C22×C53#54611yescharacteristic
640C22×C53#54611yescharacteristic
641C22×C53#54611yescharacteristic
642C22×C53#54611yescharacteristic
643C22×C53#54611yescharacteristic
644C22×C53#54611yescharacteristic
645C22×C53#55011yescharacteristic
646C22×C53#55311yescharacteristic
647C22×C53#55311yescharacteristic
648C22×C53#55311yescharacteristic
649C22×C53#55511yescharacteristic
650C4×C53—24no—
651C4×C53—24no—
652C4×C53—24no—
653C4×C53—24no—
654C4×C53—42no—
655C4×C53—42no—
656C4×C53—42no—
657C4×C53—42no—
658C4×C53—42no—
659C4×C53—42no—
660C4×C53—81no—
661C4×C53—81no—
662C22×#121C2×C5311yescharacteristic
663C2×#390C2×C5311yescharacteristic, complemented
664C2×#388C2×C5311yescharacteristic, complemented
665C2×#386C2×C5311yescharacteristic, complemented
666C2×#386C2×C5311yescharacteristic, complemented
667C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
668C2×C4×C22⋊C4C2×C5311yescharacteristic, complemented
669#1441C2×C5311yescharacteristic, complemented
670#1438C2×C5311yescharacteristic, complemented
671#1438C2×C5311yescharacteristic, complemented
672#1438C2×C5311yescharacteristic, complemented
673#1437C2×C5311yescharacteristic, complemented
674#1437C2×C5311yescharacteristic, complemented
675#1436C2×C5311yescharacteristic, complemented
676C22⋊#95C2×C5311yescharacteristic, complemented
677C2×C53—44no—
678C2×C53—44no—
679C2×C53—82no—
680C2×C53#229711yescharacteristic
681C2×C53C4×#12111yescharacteristic
682C2×C53#233311yescharacteristic
683C2×C53D4×C22⋊C411yescharacteristic
684C2×C53D4×C22⋊C411yescharacteristic
685C2×C53#236311yescharacteristic
686C2×C53#236411yescharacteristic
687C2×C53#242411yescharacteristic
688C2×C53#242811yescharacteristic
689C2×C53#245611yescharacteristic
690C2×C53#246411yescharacteristic
691C2×C53#246411yescharacteristic
692C2×C53#247611yescharacteristic
693C2×C53#255511yescharacteristic
694C2×C53#255911yescharacteristic
695C23×D4C22×C5311yescharacteristic
696C23×D4C22×C5311yescharacteristic
697C23×D4C22×C5311yescharacteristic
698C24×C4C22×C5311yescharacteristic
699C24×C4C22×C5311yescharacteristic
700C2×#121—24no—
701C2×#121—24no—
702C2×#121C4×C5318yescomplemented
703C22×C4⋊C4C22×C5311yescharacteristic
704C22×C4⋊C4C22×C5311yescharacteristic
705C22×C22⋊C4C22×C5311yescharacteristic
706C22×C22⋊C4C22×C5311yescharacteristic
707C22×C22⋊C4C22×C5311yescharacteristic
708C22×C22⋊C4C22×C5311yescharacteristic
709C22×C22⋊C4C22×C5311yescharacteristic
710C22×C22⋊C4C22×C5311yescharacteristic
711C22×C22⋊C4C22×C5311yescharacteristic
712C22×C22⋊C4C22×C5311yescharacteristic
713C22×C22⋊C4C22×C5311yescharacteristic
714C22×C22⋊C4C22×C5311yescharacteristic
715C22×C22⋊C4C22×C5311yescharacteristic
716C22×C22⋊C4C22×C5311yescharacteristic
717C22×C22⋊C4C22×C5311yescharacteristic
718C22×C42C22×C5311yescharacteristic
719C22×C42C22×C5311yescharacteristic
720C22×C42C22×C5311yescharacteristic
721#390—24no—
722#388—24no—
723#386—24no—
724#386—24no—
725C4×C22⋊C4—24no—
726C4×C22⋊C4—24no—
727C2×#95C22×C5311yescharacteristic
728C2×#95C22×C5311yescharacteristic
729C2×#95C22×C5311yescharacteristic
730C2×#95C22×C5311yescharacteristic
731C2×#95C22×C5311yescharacteristic
732C2×#95C22×C5311yescharacteristic
733C2×#95C22×C5311yescharacteristic
734C2×#95C22×C5311yescharacteristic
735C2×#95C22×C5311yescharacteristic
736C2×#95C22×C5311yescharacteristic
737C2×#95C22×C5311yescharacteristic
738C2×#95C22×C5311yescharacteristic
739C53#1410011yescharacteristic, direct product factor, Sylow
740C25C23×C5311yescharacteristic
741C25C23×C5311yescharacteristic
742C25C23×C5311yescharacteristic
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4—41no—
761C22×D4C2×C4×C5314yes—
762C22×D4C2×C4×C5314yes—
763C22×D4C2×C4×C5314yescomplemented
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4—41no—
777C23×C4C2×C4×C5314yescomplemented
778C23×C4C23×C5311yescharacteristic
779C23×C4C23×C5311yescharacteristic
780C23×C4C23×C5311yescharacteristic
781C23×C4C23×C5311yescharacteristic
782C23×C4C23×C5311yescharacteristic
783C23×C4C23×C5311yescharacteristic
784C23×C4C23×C5311yescharacteristic
785C23×C4C23×C5311yescharacteristic
786C23×C4C23×C5311yescharacteristic
787C23×C4C23×C5311yescharacteristic
788C23×C4C23×C5311yescharacteristic
789C23×C4C23×C5311yescharacteristic
790#121—232no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4C2×C4×C5314yescomplemented
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4C2×C4×C5314yes—
832C2×C22⋊C4C2×C4×C5314yescomplemented
833C2×C22⋊C4D4×C5314yes—
834C2×C22⋊C4D4×C5314yes—
835C2×C22⋊C4D4×C5314yescomplemented
836C2×C42—22no—
837C2×C42—22no—
838C2×C42—22no—
839C2×C42—22no—
840C2×C42—22no—
841C2×C42—22no—
842C2×C42—41no—
843C2×C42—41no—
844C2×C42—41no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—41no—
855#95—41no—
856#95D4×C5314yescomplemented
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C5312yes—
896C24C22×C4×C5312yes—
897C24C22×C4×C5312yes—
898C24C2×D4×C5312yes—
899C24C2×D4×C5312yes—
900C24C2×D4×C5312yes—
901C24#41×C5312yes—
902C24C24×C5311yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
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—28no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
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×C4C22×C4×C5312yes—
1005C22×C4C22×C4×C5312yes—
1006C22×C4C22×C4×C5312yes—
1007C22×C4C22×C4×C5312yes—
1008C22×C4C2×D4×C5312yes—
1009C22×C4C2×D4×C5312yes—
1010C22×C4C2×D4×C5312yes—
1011C22×C4C2×D4×C5312yes—
1012C22×C4C2×D4×C5312yes—
1013C22×C4C2×D4×C5312yes—
1014C22×C4C2×D4×C5312yes—
1015C22×C4C2×D4×C5312yes—
1016C22×C4C2×D4×C5312yes—
1017C22×C4#41×C5312yes—
1018C22×C4#41×C5312yes—
1019C22×C4#41×C5312yes—
1020C22×C4#41×C5312yes—
1021C22×C4#41×C5312yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4C22⋊C4×C53116yescomplemented
1037C42—44no—
1038C42—44no—
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C5314yes—
1144C23C4×D4×C5314yes—
1145C23C23×C4×C5311yescharacteristic
1146C23C22×D4×C5311yescharacteristic
1147C23C22×D4×C5311yescharacteristic
1148C23C22×D4×C5311yescharacteristic
1149C23C22×D4×C5311yescharacteristic
1150C23C2×#41×C5311yescharacteristic
1151C23C2×#41×C5311yescharacteristic
1152C23C2×#41×C5311yescharacteristic
1153C23C2×#41×C5311yescharacteristic
1154C23C2×#41×C5311yescharacteristic
1155C23C2×#41×C5311yescharacteristic
1156C23H(5,𝔽2)×C5311yescharacteristic
1157C23H(5,𝔽2)×C5311yescharacteristic
1158C23H(5,𝔽2)×C5311yescharacteristic
1159C23H(5,𝔽2)×C5311yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—416no—
1206C2×C4—416no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4C2×C22⋊C4×C5314yes—
1246C2×C4C2×C22⋊C4×C5314yes—
1247C2×C4C4×D4×C5314yes—
1248C2×C4#121×C5314yescomplemented
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C5311yescharacteristic
1295C22C2×C4×D4×C5311yescharacteristic
1296C22C2×C4×D4×C5311yescharacteristic
1297C22C4×#41×C5311yescharacteristic
1298C22C4×#41×C5311yescharacteristic
1299C22C53×#51811yescharacteristic
1300C22C53×#51811yescharacteristic
1301C22C2×#121×C5311yescharacteristic
1302C22C53×#52511yescharacteristic
1303C22C53×#52511yescharacteristic
1304C22C53×#52511yescharacteristic
1305C22C53×#52911yescharacteristic
1306C22C53×#53211yescharacteristic
1307C22C53×#53211yescharacteristic
1308C22C53×#53211yescharacteristic
1309C22C53×#53811yescharacteristic
1310C22C53×#53811yescharacteristic
1311C22C53×#54011yescharacteristic
1312C22C53×#54011yescharacteristic
1313C22D42×C5311yescharacteristic
1314C22D42×C5311yescharacteristic
1315C22D42×C5311yescharacteristic
1316C22D42×C5311yescharacteristic
1317C22C53×#54611yescharacteristic
1318C22C53×#54611yescharacteristic
1319C22C53×#54611yescharacteristic
1320C22C53×#54611yescharacteristic
1321C22C53×#54611yescharacteristic
1322C22C53×#54611yescharacteristic
1323C22C53×#54611yescharacteristic
1324C22C53×#55011yescharacteristic
1325C22C53×#55311yescharacteristic
1326C22C53×#55311yescharacteristic
1327C22C53×#55311yescharacteristic
1328C22C53×#55511yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—24no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C53×#229711yescharacteristic
1345C2C4×#121×C5311yescharacteristic
1346C2C53×#233311yescharacteristic
1347C2D4×C22⋊C4×C5311yescharacteristic
1348C2D4×C22⋊C4×C5311yescharacteristic
1349C2C53×#236311yescharacteristic
1350C2C53×#236411yescharacteristic
1351C2C53×#242411yescharacteristic
1352C2C53×#242811yescharacteristic
1353C2C53×#245611yescharacteristic
1354C2C53×#246411yescharacteristic
1355C2C53×#246411yescharacteristic
1356C2C53×#247611yescharacteristic
1357C2C53×#255511yescharacteristic
1358C2C53×#255911yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutatorC23C23×C4×C53
Frattini, cosocleC24C24×C53
prime radicalC22×#121×C53C2
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. C2×C4×C22⋊C4×C53C2semidirect
7. C2×C4×C22⋊C4×C53C2semidirect
8. C53×#1441C2semidirect
9. C53×#1438C2semidirect
10. C53×#1438C2semidirect
11. C53×#1438C2semidirect
12. C53×#1437C2semidirect
13. C53×#1437C2semidirect
14. C53×#1436C2semidirect
15. C53×C22⋊#95C2semidirect
23. C2×#121×C53C4semidirect
83. C22×D4×C53C2×C4semidirect
97. C23×C4×C53C2×C4semidirect
116. C2×C4⋊C4×C53C2×C4semidirect
152. C2×C22⋊C4×C53C2×C4semidirect
155. C2×C22⋊C4×C53D4semidirect
176. #95×C53D4semidirect
356. C22⋊C4×C53C22⋊C4semidirect
568. C2×C4×C53#121semidirect
569. #14100C53direct (N × H)
663. C2×#390C2×C53semidirect
664. C2×#388C2×C53semidirect
665. C2×#386C2×C53semidirect
666. C2×#386C2×C53semidirect
667. C2×C4×C22⋊C4C2×C53semidirect
668. C2×C4×C22⋊C4C2×C53semidirect
669. #1441C2×C53semidirect
670. #1438C2×C53semidirect
671. #1438C2×C53semidirect
672. #1438C2×C53semidirect
673. #1437C2×C53semidirect
674. #1437C2×C53semidirect
675. #1436C2×C53semidirect
676. C22⋊#95C2×C53semidirect
702. C2×#121C4×C53semidirect
739. C53#14100direct (N × H)
763. C22×D4C2×C4×C53semidirect
777. C23×C4C2×C4×C53semidirect
796. C2×C4⋊C4C2×C4×C53semidirect
832. C2×C22⋊C4C2×C4×C53semidirect
835. C2×C22⋊C4D4×C53semidirect
856. #95D4×C53semidirect
1036. C22⋊C4C22⋊C4×C53semidirect
1248. C2×C4#121×C53semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C532
C2×C53×#3902
C2×C53×#3882
C2×C53×#3862
C2×C4×C22⋊C4×C532
C53×#14412
C53×#14382
C53×#14372
C53×#14362
C53×C22⋊#952
#1410053