Finite Group Databasebeta

← C53×#14023 #27221535

Subgroups — C53×#14023 #27221535

Order 13568.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C53C211yesmaximal, characteristic
2C22×C4×D4×C53C211yesmaximal, characteristic, complemented
3C2×C53×#386C211yesmaximal, characteristic, complemented
4C2×C53×#386C211yesmaximal, characteristic, complemented
5C2×C53×#386C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C22×#95×C53C211yesmaximal, characteristic, complemented
8C53×#1441C211yesmaximal, characteristic, complemented
9C53×#1440C211yesmaximal, characteristic, complemented
10C53×#1439C211yesmaximal, characteristic, complemented
11C53×#1438C211yesmaximal, characteristic, complemented
12C53×#1437C211yesmaximal, characteristic, complemented
13C53×#1436C211yesmaximal, characteristic, complemented
14C53×C22⋊#95C211yesmaximal, characteristic, complemented
15C53×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C24×C4×C53C2211yescharacteristic
20C24×C4×C53C2211yescharacteristic
21C24×C4×C53C2211yescharacteristic
22C24×C4×C53C2211yescharacteristic
23C2×#121×C53—24no—
24C2×#121×C53—24no—
25C2×#121×C53C418yescomplemented
26C2×C4×D4×C53—24no—
27C2×C4×D4×C53—24no—
28C2×C4×D4×C53—24no—
29C22×C4⋊C4×C53C2211yescharacteristic
30C22×C4⋊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×C22⋊C4×C53C2211yescharacteristic
41C22×C22⋊C4×C53C2211yescharacteristic
42C22×C42×C53C2211yescharacteristic
43C53×#386—24no—
44C53×#386—24no—
45C53×#386—24no—
46C53×#386—24no—
47C2×#95×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
60C2×#95×C53C2211yescharacteristic
61C2×#95×C53C2211yescharacteristic
62C25×C53C2311yescharacteristic
63C25×C53C2311yescharacteristic
64C25×C53C2311yescharacteristic
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—22no—
76C22×D4×C53—22no—
77C22×D4×C53—22no—
78C22×D4×C53—22no—
79C22×D4×C53—41no—
80C22×D4×C53—41no—
81C22×D4×C53C2×C414yes—
82C22×D4×C53C2×C414yescomplemented
83C22×D4×C53C2×C414yescomplemented
84C22×D4×C53D414yes—
85C22×D4×C53D414yes—
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—22no—
94C23×C4×C53—22no—
95C23×C4×C53—22no—
96C23×C4×C53—22no—
97C23×C4×C53—22no—
98C23×C4×C53—22no—
99C23×C4×C53—22no—
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—22no—
103C23×C4×C53—22no—
104C23×C4×C53—41no—
105C23×C4×C53—41no—
106C23×C4×C53—41no—
107C23×C4×C53—41no—
108C23×C4×C53—41no—
109C23×C4×C53—41no—
110C23×C4×C53—41no—
111C23×C4×C53—41no—
112C23×C4×C53C2×C414yescomplemented
113C23×C4×C53D414yescomplemented
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126#121×C53—232no—
127C4×D4×C53—232no—
128C2×C4⋊C4×C53—22no—
129C2×C4⋊C4×C53—22no—
130C2×C4⋊C4×C53—22no—
131C2×C4⋊C4×C53—22no—
132C2×C4⋊C4×C53—22no—
133C2×C4⋊C4×C53C2×C414yescomplemented
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—22no—
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53—22no—
149C2×C22⋊C4×C53—22no—
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—22no—
154C2×C22⋊C4×C53—22no—
155C2×C22⋊C4×C53—22no—
156C2×C22⋊C4×C53—22no—
157C2×C22⋊C4×C53—22no—
158C2×C22⋊C4×C53—41no—
159C2×C22⋊C4×C53—41no—
160C2×C22⋊C4×C53—41no—
161C2×C22⋊C4×C53—41no—
162C2×C22⋊C4×C53—41no—
163C2×C22⋊C4×C53—41no—
164C2×C22⋊C4×C53C2×C414yescomplemented
165C2×C22⋊C4×C53C2×C414yescomplemented
166C2×C22⋊C4×C53D414yescomplemented
167C2×C42×C53—22no—
168C2×C42×C53—22no—
169C2×C42×C53—22no—
170#95×C53—22no—
171#95×C53—22no—
172#95×C53—22no—
173#95×C53—22no—
174#95×C53—22no—
175#95×C53—22no—
176#95×C53—22no—
177#95×C53—22no—
178#95×C53—22no—
179#95×C53—22no—
180#95×C53—22no—
181#95×C53—41no—
182#95×C53—41no—
183#95×C53D414yescomplemented
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×C53—21no—
216C24×C53—21no—
217C24×C53—21no—
218C24×C53C22×C412yes—
219C24×C53C22×C412yes—
220C24×C53C22×C412yes—
221C24×C53C2×D412yes—
222C24×C53C2×D412yes—
223C24×C53C2×D412yes—
224C24×C53C2×D412yes—
225C24×C53C2×D412yes—
226C24×C53C2×D412yes—
227C24×C53#4112yes—
228C24×C53#4112yes—
229C24×C53C2411yescharacteristic
230C2×D4×C53—28no—
231C2×D4×C53—28no—
232C2×D4×C53—28no—
233C2×D4×C53—28no—
234C2×D4×C53—28no—
235C2×D4×C53—28no—
236C2×D4×C53—28no—
237C2×D4×C53—28no—
238C2×D4×C53—28no—
239C2×D4×C53—28no—
240C2×D4×C53—28no—
241C2×D4×C53—44no—
242C2×D4×C53—44no—
243C2×D4×C53—44no—
244C2×D4×C53—44no—
245C2×D4×C53—44no—
246C2×D4×C53—44no—
247C2×D4×C53—44no—
248C2×D4×C53—44no—
249C2×D4×C53—44no—
250C2×D4×C53C22⋊C4116yescomplemented
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—28no—
264C22×C4×C53—28no—
265C22×C4×C53—28no—
266C22×C4×C53—28no—
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—28no—
310C22×C4×C53—28no—
311C22×C4×C53—21no—
312C22×C4×C53—21no—
313C22×C4×C53—21no—
314C22×C4×C53—21no—
315C22×C4×C53—21no—
316C22×C4×C53—21no—
317C22×C4×C53—21no—
318C22×C4×C53—21no—
319C22×C4×C53—21no—
320C22×C4×C53—21no—
321C22×C4×C53—21no—
322C22×C4×C53—21no—
323C22×C4×C53—21no—
324C22×C4×C53—21no—
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—
337C22×C4×C53—44no—
338C22×C4×C53—44no—
339C22×C4×C53—44no—
340C22×C4×C53—44no—
341C22×C4×C53—44no—
342C22×C4×C53—44no—
343C22×C4×C53—44no—
344C22×C4×C53—44no—
345C22×C4×C53—44no—
346C22×C4×C53—44no—
347C22×C4×C53C22×C412yes—
348C22×C4×C53C22×C412yes—
349C22×C4×C53C22×C412yes—
350C22×C4×C53C22×C412yes—
351C22×C4×C53C2×D412yes—
352C22×C4×C53C2×D412yes—
353C22×C4×C53C2×D412yes—
354C22×C4×C53C2×D412yes—
355C22×C4×C53C2×D412yes—
356C22×C4×C53C2×D412yes—
357C22×C4×C53C2×D412yes—
358C22×C4×C53C2×D412yes—
359C22×C4×C53C2×D412yes—
360C22×C4×C53#4112yes—
361C22×C4×C53#4112yes—
362C22×C4×C53#4112yes—
363C4⋊C4×C53—28no—
364C4⋊C4×C53—28no—
365C22⋊C4×C53—28no—
366C22⋊C4×C53—28no—
367C22⋊C4×C53—28no—
368C22⋊C4×C53—28no—
369C22⋊C4×C53—44no—
370C22⋊C4×C53—44no—
371C22⋊C4×C53—44no—
372C22⋊C4×C53—44no—
373C22⋊C4×C53—44no—
374C22⋊C4×C53—44no—
375C22⋊C4×C53—44no—
376C42×C53—28no—
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—22no—
404C23×C53—22no—
405C23×C53—22no—
406C23×C53—22no—
407C23×C53—22no—
408C23×C53—22no—
409C23×C53—22no—
410C23×C53—22no—
411C23×C53—22no—
412C23×C53—22no—
413C23×C53—22no—
414C23×C53—22no—
415C23×C53—22no—
416C23×C53—22no—
417C23×C53—22no—
418C23×C53—22no—
419C23×C53—22no—
420C23×C53—22no—
421C23×C53—22no—
422C23×C53—22no—
423C23×C53—22no—
424C23×C53—22no—
425C23×C53—22no—
426C23×C53—22no—
427C23×C53—22no—
428C23×C53—22no—
429C23×C53—22no—
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×C53—41no—
464C23×C53—41no—
465C23×C53—41no—
466C23×C53—41no—
467C23×C53—41no—
468C23×C53—41no—
469C23×C53—41no—
470C23×C53—41no—
471C23×C53—41no—
472C23×C53—41no—
473C23×C53—41no—
474C23×C53C2×C22⋊C414yes—
475C23×C53C2×C22⋊C414yes—
476C23×C53C4×D414yes—
477C23×C53C4×D414yes—
478C23×C53#12014yes—
479C23×C53#12114yes—
480C23×C53#12114yes—
481C23×C53#12314yes—
482C23×C53C23×C411yescharacteristic
483C23×C53C22×D411yescharacteristic
484C23×C53C22×D411yescharacteristic
485C23×C53C22×D411yescharacteristic
486C23×C53C22×D411yescharacteristic
487C23×C53C22×D411yescharacteristic
488C23×C53C2×#4111yescharacteristic
489C23×C53C2×#4111yescharacteristic
490C23×C53C2×#4111yescharacteristic
491C23×C53C2×#4111yescharacteristic
492C23×C53C2×#4111yescharacteristic
493C23×C53H(5,𝔽2)11yescharacteristic
494C23×C53H(5,𝔽2)11yescharacteristic
495C23×C53H(5,𝔽2)11yescharacteristic
496C23×C532−1+411yescharacteristic
497D4×C53—232no—
498D4×C53—416no—
499D4×C53—416no—
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—22no—
526C2×C4×C53—22no—
527C2×C4×C53—22no—
528C2×C4×C53—22no—
529C2×C4×C53—22no—
530C2×C4×C53—22no—
531C2×C4×C53—22no—
532C2×C4×C53—22no—
533C2×C4×C53—22no—
534C2×C4×C53—22no—
535C2×C4×C53—22no—
536C2×C4×C53—22no—
537C2×C4×C53—22no—
538C2×C4×C53—22no—
539C2×C4×C53—416no—
540C2×C4×C53—416no—
541C2×C4×C53—416no—
542C2×C4×C53—416no—
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×C53—41no—
566C2×C4×C53—41no—
567C2×C4×C53—41no—
568C2×C4×C53—41no—
569C2×C4×C53—41no—
570C2×C4×C53—41no—
571C2×C4×C53—41no—
572C2×C4×C53—41no—
573C2×C4×C53—41no—
574C2×C4×C53—41no—
575C2×C4×C53—41no—
576C2×C4×C53—41no—
577C2×C4×C53—41no—
578C2×C4×C53—41no—
579C2×C4×C53—41no—
580C2×C4×C53—41no—
581C2×C4×C53—41no—
582C2×C4×C53—41no—
583C2×C4×C53—41no—
584C2×C4×C53—41no—
585C2×C4×C53C2×C22⋊C414yes—
586C2×C4×C53C4×D414yescomplemented
587C2×C4×C53#12114yescomplemented
588#14023C5311yesmaximal, characteristic, direct product factor, Sylow
589C22×C53—24no—
590C22×C53—24no—
591C22×C53—24no—
592C22×C53—24no—
593C22×C53—24no—
594C22×C53—24no—
595C22×C53—24no—
596C22×C53—24no—
597C22×C53—24no—
598C22×C53—24no—
599C22×C53—24no—
600C22×C53—24no—
601C22×C53—24no—
602C22×C53—24no—
603C22×C53—24no—
604C22×C53—24no—
605C22×C53—24no—
606C22×C53—42no—
607C22×C53—42no—
608C22×C53—42no—
609C22×C53—42no—
610C22×C53—42no—
611C22×C53—42no—
612C22×C53—42no—
613C22×C53—42no—
614C22×C53—42no—
615C22×C53—42no—
616C22×C53—42no—
617C22×C53—42no—
618C22×C53—42no—
619C22×C53—42no—
620C22×C53—42no—
621C22×C53—42no—
622C22×C53—42no—
623C22×C53—42no—
624C22×C53—42no—
625C22×C53—81no—
626C22×C53—81no—
627C22×C53—81no—
628C22×C53—81no—
629C22×C53—81no—
630C22×C53—81no—
631C22×C53—81no—
632C22×C53—81no—
633C22×C53#38618yescomplemented
634C22×C53C22×C22⋊C411yescharacteristic
635C22×C53C2×C4×D411yescharacteristic
636C22×C53C2×C4×D411yescharacteristic
637C22×C53C2×C4×D411yescharacteristic
638C22×C53C4×#4111yescharacteristic
639C22×C53#51811yescharacteristic
640C22×C53#52011yescharacteristic
641C22×C53C2×#12011yescharacteristic
642C22×C53C2×#12111yescharacteristic
643C22×C53C2×#12111yescharacteristic
644C22×C53C2×#12111yescharacteristic
645C22×C53C2×#12311yescharacteristic
646C22×C53#52511yescharacteristic
647C22×C53#52911yescharacteristic
648C22×C53#53211yescharacteristic
649C22×C53#53411yescharacteristic
650C22×C53#53711yescharacteristic
651C22×C53#53811yescharacteristic
652C22×C53#53911yescharacteristic
653C22×C53D4211yescharacteristic
654C22×C53D4211yescharacteristic
655C22×C53D4211yescharacteristic
656C22×C53#54611yescharacteristic
657C22×C53#54611yescharacteristic
658C22×C53#54611yescharacteristic
659C22×C53#54611yescharacteristic
660C22×C53#54611yescharacteristic
661C22×C53#54611yescharacteristic
662C22×C53#54711yescharacteristic
663C22×C53#54711yescharacteristic
664C22×C53#54711yescharacteristic
665C22×C53#54811yescharacteristic
666C22×C53#55311yescharacteristic
667C22×C53#55311yescharacteristic
668C22×C53#55311yescharacteristic
669C4×C53—24no—
670C4×C53—24no—
671C4×C53—24no—
672C4×C53—42no—
673C4×C53—42no—
674C4×C53—42no—
675C4×C53—42no—
676C4×C53—42no—
677C4×C53—42no—
678C4×C53—42no—
679C4×C53—81no—
680C4×C53—81no—
681C22×#121C2×C5311yescharacteristic
682C22×C4×D4C2×C5311yescharacteristic, complemented
683C2×#386C2×C5311yescharacteristic, complemented
684C2×#386C2×C5311yescharacteristic, complemented
685C2×#386C2×C5311yescharacteristic, complemented
686C2×#386C2×C5311yescharacteristic, complemented
687C22×#95C2×C5311yescharacteristic, complemented
688#1441C2×C5311yescharacteristic, complemented
689#1440C2×C5311yescharacteristic, complemented
690#1439C2×C5311yescharacteristic, complemented
691#1438C2×C5311yescharacteristic, complemented
692#1437C2×C5311yescharacteristic, complemented
693#1436C2×C5311yescharacteristic, complemented
694C22⋊#95C2×C5311yescharacteristic, complemented
695C22⋊#95C2×C5311yescharacteristic, complemented
696C2×C53—28no—
697C2×C53—44no—
698C2×C53—82no—
699C2×C53C2×#38611yescharacteristic
700C2×C53C4×#12111yescharacteristic
701C2×C53#232511yescharacteristic
702C2×C53D4×C22⋊C411yescharacteristic
703C2×C53#233911yescharacteristic
704C2×C53#236111yescharacteristic
705C2×C53#236411yescharacteristic
706C2×C53#241011yescharacteristic
707C2×C53#241611yescharacteristic
708C2×C53#242411yescharacteristic
709C2×C53#242511yescharacteristic
710C2×C53#243011yescharacteristic
711C2×C53#244311yescharacteristic
712C2×C53#244411yescharacteristic
713C2×C53#254311yescharacteristic
714C23×D4C22×C5311yescharacteristic
715C23×D4C22×C5311yescharacteristic
716C23×D4C22×C5311yescharacteristic
717C24×C4C22×C5311yescharacteristic
718C24×C4C22×C5311yescharacteristic
719C24×C4C22×C5311yescharacteristic
720C24×C4C22×C5311yescharacteristic
721C2×#121—24no—
722C2×#121—24no—
723C2×#121C4×C5318yescomplemented
724C2×C4×D4—24no—
725C2×C4×D4—24no—
726C2×C4×D4—24no—
727C22×C4⋊C4C22×C5311yescharacteristic
728C22×C4⋊C4C22×C5311yescharacteristic
729C22×C22⋊C4C22×C5311yescharacteristic
730C22×C22⋊C4C22×C5311yescharacteristic
731C22×C22⋊C4C22×C5311yescharacteristic
732C22×C22⋊C4C22×C5311yescharacteristic
733C22×C22⋊C4C22×C5311yescharacteristic
734C22×C22⋊C4C22×C5311yescharacteristic
735C22×C22⋊C4C22×C5311yescharacteristic
736C22×C22⋊C4C22×C5311yescharacteristic
737C22×C22⋊C4C22×C5311yescharacteristic
738C22×C22⋊C4C22×C5311yescharacteristic
739C22×C22⋊C4C22×C5311yescharacteristic
740C22×C42C22×C5311yescharacteristic
741#386—24no—
742#386—24no—
743#386—24no—
744#386—24no—
745C2×#95—24no—
746C2×#95C22×C5311yescharacteristic
747C2×#95C22×C5311yescharacteristic
748C2×#95C22×C5311yescharacteristic
749C2×#95C22×C5311yescharacteristic
750C2×#95C22×C5311yescharacteristic
751C2×#95C22×C5311yescharacteristic
752C2×#95C22×C5311yescharacteristic
753C2×#95C22×C5311yescharacteristic
754C2×#95C22×C5311yescharacteristic
755C2×#95C22×C5311yescharacteristic
756C2×#95C22×C5311yescharacteristic
757C2×#95C22×C5311yescharacteristic
758C2×#95C22×C5311yescharacteristic
759C2×#95C22×C5311yescharacteristic
760C53#1402311yescharacteristic, direct product factor, Sylow
761C25C23×C5311yescharacteristic
762C25C23×C5311yescharacteristic
763C25C23×C5311yescharacteristic
764C22×D4—22no—
765C22×D4—22no—
766C22×D4—22no—
767C22×D4—22no—
768C22×D4—22no—
769C22×D4—22no—
770C22×D4—22no—
771C22×D4—22no—
772C22×D4—22no—
773C22×D4—22no—
774C22×D4—22no—
775C22×D4—22no—
776C22×D4—22no—
777C22×D4—22no—
778C22×D4—41no—
779C22×D4—41no—
780C22×D4C2×C4×C5314yes—
781C22×D4C2×C4×C5314yescomplemented
782C22×D4C2×C4×C5314yescomplemented
783C22×D4D4×C5314yes—
784C22×D4D4×C5314yes—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—22no—
790C23×C4—22no—
791C23×C4—22no—
792C23×C4—22no—
793C23×C4—22no—
794C23×C4—22no—
795C23×C4—22no—
796C23×C4—22no—
797C23×C4—22no—
798C23×C4—22no—
799C23×C4—22no—
800C23×C4—22no—
801C23×C4—22no—
802C23×C4—22no—
803C23×C4—41no—
804C23×C4—41no—
805C23×C4—41no—
806C23×C4—41no—
807C23×C4—41no—
808C23×C4—41no—
809C23×C4—41no—
810C23×C4—41no—
811C23×C4C2×C4×C5314yescomplemented
812C23×C4D4×C5314yescomplemented
813C23×C4C23×C5311yescharacteristic
814C23×C4C23×C5311yescharacteristic
815C23×C4C23×C5311yescharacteristic
816C23×C4C23×C5311yescharacteristic
817C23×C4C23×C5311yescharacteristic
818C23×C4C23×C5311yescharacteristic
819C23×C4C23×C5311yescharacteristic
820C23×C4C23×C5311yescharacteristic
821C23×C4C23×C5311yescharacteristic
822C23×C4C23×C5311yescharacteristic
823C23×C4C23×C5311yescharacteristic
824C23×C4C23×C5311yescharacteristic
825#121—232no—
826C4×D4—232no—
827C2×C4⋊C4—22no—
828C2×C4⋊C4—22no—
829C2×C4⋊C4—22no—
830C2×C4⋊C4—22no—
831C2×C4⋊C4—22no—
832C2×C4⋊C4C2×C4×C5314yescomplemented
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—22no—
839C2×C22⋊C4—22no—
840C2×C22⋊C4—22no—
841C2×C22⋊C4—22no—
842C2×C22⋊C4—22no—
843C2×C22⋊C4—22no—
844C2×C22⋊C4—22no—
845C2×C22⋊C4—22no—
846C2×C22⋊C4—22no—
847C2×C22⋊C4—22no—
848C2×C22⋊C4—22no—
849C2×C22⋊C4—22no—
850C2×C22⋊C4—22no—
851C2×C22⋊C4—22no—
852C2×C22⋊C4—22no—
853C2×C22⋊C4—22no—
854C2×C22⋊C4—22no—
855C2×C22⋊C4—22no—
856C2×C22⋊C4—22no—
857C2×C22⋊C4—41no—
858C2×C22⋊C4—41no—
859C2×C22⋊C4—41no—
860C2×C22⋊C4—41no—
861C2×C22⋊C4—41no—
862C2×C22⋊C4—41no—
863C2×C22⋊C4C2×C4×C5314yescomplemented
864C2×C22⋊C4C2×C4×C5314yescomplemented
865C2×C22⋊C4D4×C5314yescomplemented
866C2×C42—22no—
867C2×C42—22no—
868C2×C42—22no—
869#95—22no—
870#95—22no—
871#95—22no—
872#95—22no—
873#95—22no—
874#95—22no—
875#95—22no—
876#95—22no—
877#95—22no—
878#95—22no—
879#95—22no—
880#95—41no—
881#95—41no—
882#95D4×C5314yescomplemented
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24—21no—
900C24—21no—
901C24—21no—
902C24—21no—
903C24—21no—
904C24—21no—
905C24—21no—
906C24—21no—
907C24—21no—
908C24—21no—
909C24—21no—
910C24—21no—
911C24—21no—
912C24—21no—
913C24—21no—
914C24—21no—
915C24—21no—
916C24—21no—
917C24C22×C4×C5312yes—
918C24C22×C4×C5312yes—
919C24C22×C4×C5312yes—
920C24C2×D4×C5312yes—
921C24C2×D4×C5312yes—
922C24C2×D4×C5312yes—
923C24C2×D4×C5312yes—
924C24C2×D4×C5312yes—
925C24C2×D4×C5312yes—
926C24#41×C5312yes—
927C24#41×C5312yes—
928C24C24×C5311yescharacteristic
929C2×D4—28no—
930C2×D4—28no—
931C2×D4—28no—
932C2×D4—28no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—28no—
936C2×D4—28no—
937C2×D4—28no—
938C2×D4—28no—
939C2×D4—28no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4C22⋊C4×C53116yescomplemented
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—28no—
963C22×C4—28no—
964C22×C4—28no—
965C22×C4—28no—
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—21no—
978C22×C4—21no—
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—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
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×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4C22×C4×C5312yes—
1047C22×C4C22×C4×C5312yes—
1048C22×C4C22×C4×C5312yes—
1049C22×C4C22×C4×C5312yes—
1050C22×C4C2×D4×C5312yes—
1051C22×C4C2×D4×C5312yes—
1052C22×C4C2×D4×C5312yes—
1053C22×C4C2×D4×C5312yes—
1054C22×C4C2×D4×C5312yes—
1055C22×C4C2×D4×C5312yes—
1056C22×C4C2×D4×C5312yes—
1057C22×C4C2×D4×C5312yes—
1058C22×C4C2×D4×C5312yes—
1059C22×C4#41×C5312yes—
1060C22×C4#41×C5312yes—
1061C22×C4#41×C5312yes—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C42—28no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
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—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23C2×C22⋊C4×C5314yes—
1174C23C2×C22⋊C4×C5314yes—
1175C23C4×D4×C5314yes—
1176C23C4×D4×C5314yes—
1177C23#120×C5314yes—
1178C23#121×C5314yes—
1179C23#121×C5314yes—
1180C23#123×C5314yes—
1181C23C23×C4×C5311yescharacteristic
1182C23C22×D4×C5311yescharacteristic
1183C23C22×D4×C5311yescharacteristic
1184C23C22×D4×C5311yescharacteristic
1185C23C22×D4×C5311yescharacteristic
1186C23C22×D4×C5311yescharacteristic
1187C23C2×#41×C5311yescharacteristic
1188C23C2×#41×C5311yescharacteristic
1189C23C2×#41×C5311yescharacteristic
1190C23C2×#41×C5311yescharacteristic
1191C23C2×#41×C5311yescharacteristic
1192C23H(5,𝔽2)×C5311yescharacteristic
1193C23H(5,𝔽2)×C5311yescharacteristic
1194C23H(5,𝔽2)×C5311yescharacteristic
1195C232−1+4×C5311yescharacteristic
1196D4—232no—
1197D4—416no—
1198D4—416no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—416no—
1239C2×C4—416no—
1240C2×C4—416no—
1241C2×C4—416no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4C2×C22⋊C4×C5314yes—
1285C2×C4C4×D4×C5314yescomplemented
1286C2×C4#121×C5314yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22C53×#38618yescomplemented
1332C22C22×C22⋊C4×C5311yescharacteristic
1333C22C2×C4×D4×C5311yescharacteristic
1334C22C2×C4×D4×C5311yescharacteristic
1335C22C2×C4×D4×C5311yescharacteristic
1336C22C4×#41×C5311yescharacteristic
1337C22C53×#51811yescharacteristic
1338C22C53×#52011yescharacteristic
1339C22C2×#120×C5311yescharacteristic
1340C22C2×#121×C5311yescharacteristic
1341C22C2×#121×C5311yescharacteristic
1342C22C2×#121×C5311yescharacteristic
1343C22C2×#123×C5311yescharacteristic
1344C22C53×#52511yescharacteristic
1345C22C53×#52911yescharacteristic
1346C22C53×#53211yescharacteristic
1347C22C53×#53411yescharacteristic
1348C22C53×#53711yescharacteristic
1349C22C53×#53811yescharacteristic
1350C22C53×#53911yescharacteristic
1351C22D42×C5311yescharacteristic
1352C22D42×C5311yescharacteristic
1353C22D42×C5311yescharacteristic
1354C22C53×#54611yescharacteristic
1355C22C53×#54611yescharacteristic
1356C22C53×#54611yescharacteristic
1357C22C53×#54611yescharacteristic
1358C22C53×#54611yescharacteristic
1359C22C53×#54611yescharacteristic
1360C22C53×#54711yescharacteristic
1361C22C53×#54711yescharacteristic
1362C22C53×#54711yescharacteristic
1363C22C53×#54811yescharacteristic
1364C22C53×#55311yescharacteristic
1365C22C53×#55311yescharacteristic
1366C22C53×#55311yescharacteristic
1367C4—24no—
1368C4—24no—
1369C4—24no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—81no—
1378C4—81no—
1379C2—28no—
1380C2—44no—
1381C2—82no—
1382C2C2×C53×#38611yescharacteristic
1383C2C4×#121×C5311yescharacteristic
1384C2C53×#232511yescharacteristic
1385C2D4×C22⋊C4×C5311yescharacteristic
1386C2C53×#233911yescharacteristic
1387C2C53×#236111yescharacteristic
1388C2C53×#236411yescharacteristic
1389C2C53×#241011yescharacteristic
1390C2C53×#241611yescharacteristic
1391C2C53×#242411yescharacteristic
1392C2C53×#242511yescharacteristic
1393C2C53×#243011yescharacteristic
1394C2C53×#244311yescharacteristic
1395C2C53×#244411yescharacteristic
1396C2C53×#254311yescharacteristic
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. C22×C4×D4×C53C2semidirect
3. C2×C53×#386C2semidirect
4. C2×C53×#386C2semidirect
5. C2×C53×#386C2semidirect
6. C2×C53×#386C2semidirect
7. C22×#95×C53C2semidirect
8. C53×#1441C2semidirect
9. C53×#1440C2semidirect
10. C53×#1439C2semidirect
11. C53×#1438C2semidirect
12. C53×#1437C2semidirect
13. C53×#1436C2semidirect
14. C53×C22⋊#95C2semidirect
15. C53×C22⋊#95C2semidirect
25. C2×#121×C53C4semidirect
82. C22×D4×C53C2×C4semidirect
83. C22×D4×C53C2×C4semidirect
112. C23×C4×C53C2×C4semidirect
113. C23×C4×C53D4semidirect
133. C2×C4⋊C4×C53C2×C4semidirect
164. C2×C22⋊C4×C53C2×C4semidirect
165. C2×C22⋊C4×C53C2×C4semidirect
166. C2×C22⋊C4×C53D4semidirect
183. #95×C53D4semidirect
250. C2×D4×C53C22⋊C4semidirect
586. C2×C4×C53C4×D4semidirect
587. C2×C4×C53#121semidirect
588. #14023C53direct (N × H)
633. C22×C53#386semidirect
682. C22×C4×D4C2×C53semidirect
683. C2×#386C2×C53semidirect
684. C2×#386C2×C53semidirect
685. C2×#386C2×C53semidirect
686. C2×#386C2×C53semidirect
687. C22×#95C2×C53semidirect
688. #1441C2×C53semidirect
689. #1440C2×C53semidirect
690. #1439C2×C53semidirect
691. #1438C2×C53semidirect
692. #1437C2×C53semidirect
693. #1436C2×C53semidirect
694. C22⋊#95C2×C53semidirect
695. C22⋊#95C2×C53semidirect
723. C2×#121C4×C53semidirect
760. C53#14023direct (N × H)
781. C22×D4C2×C4×C53semidirect
782. C22×D4C2×C4×C53semidirect
811. C23×C4C2×C4×C53semidirect
812. C23×C4D4×C53semidirect
832. C2×C4⋊C4C2×C4×C53semidirect
863. C2×C22⋊C4C2×C4×C53semidirect
864. C2×C22⋊C4C2×C4×C53semidirect
865. C2×C22⋊C4D4×C53semidirect
882. #95D4×C53semidirect
949. C2×D4C22⋊C4×C53semidirect
1285. C2×C4C4×D4×C53semidirect
1286. C2×C4#121×C53semidirect
1331. C22C53×#386semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C532
C22×C4×D4×C532
C2×C53×#3862
C22×#95×C532
C53×#14412
C53×#14402
C53×#14392
C53×#14382
C53×#14372
C53×#14362
C53×C22⋊#952
#1402353