Finite Group Databasebeta

← C53×#16284 #27223796

Subgroups — C53×#16284 #27223796

Order 13568.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C53×#394C211yesmaximal, characteristic, complemented
2C2×C53×#392C211yesmaximal, characteristic, complemented
3C2×C53×#392C211yesmaximal, characteristic, complemented
4C2×C53×#392C211yesmaximal, characteristic, complemented
5C2×C53×#392C211yesmaximal, characteristic, complemented
6C2×C53×#386C211yesmaximal, characteristic, complemented
7C2×C53×#386C211yesmaximal, characteristic, complemented
8C2×C53×#386C211yesmaximal, characteristic, complemented
9C53×#1443C211yesmaximal, characteristic, complemented
10C53×#1440C211yesmaximal, characteristic, complemented
11C53×#1440C211yesmaximal, characteristic, complemented
12C53×#1439C211yesmaximal, characteristic, complemented
13C53×#1439C211yesmaximal, characteristic, complemented
14C53×#1438C211yesmaximal, characteristic, complemented
15C53×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C53C2211yescharacteristic
17C23×D4×C53C2211yescharacteristic
18C23×D4×C53C2211yescharacteristic
19C23×D4×C53C2211yescharacteristic
20C23×D4×C53C2211yescharacteristic
21C23×D4×C53C2211yescharacteristic
22C24×C4×C53C2211yescharacteristic
23C22×C4⋊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×C22⋊C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C53×#394—24no—
40C53×#392—24no—
41C53×#392—24no—
42C53×#392—24no—
43C53×#392—24no—
44C53×#386—24no—
45C53×#386—24no—
46C53×#386—24no—
47C2×#95×C53C2211yescharacteristic
48C2×#95×C53C2211yescharacteristic
49C2×#95×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C2×#95×C53C2211yescharacteristic
59C25×C53C2311yescharacteristic
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—22no—
76C22×D4×C53—22no—
77C22×D4×C53—22no—
78C22×D4×C53—22no—
79C22×D4×C53—22no—
80C22×D4×C53—22no—
81C22×D4×C53—22no—
82C22×D4×C53—22no—
83C22×D4×C53—22no—
84C22×D4×C53—41no—
85C22×D4×C53—41no—
86C22×D4×C53—41no—
87C22×D4×C53—41no—
88C22×D4×C53—41no—
89C22×D4×C53—41no—
90C22×D4×C53—41no—
91C22×D4×C53—41no—
92C22×D4×C53—41no—
93C22×D4×C53—41no—
94C22×D4×C53—41no—
95C22×D4×C53—41no—
96C22×D4×C53—41no—
97C22×D4×C53—41no—
98C22×D4×C53—41no—
99C22×D4×C53—41no—
100C22×D4×C53—41no—
101C22×D4×C53—41no—
102C22×D4×C53—41no—
103C22×D4×C53—41no—
104C22×D4×C53D414yescomplemented
105C23×C4×C53—22no—
106C23×C4×C53—22no—
107C23×C4×C53—22no—
108C23×C4×C53—41no—
109C23×C4×C53—41no—
110C23×C4×C53—41no—
111C23×C4×C53—41no—
112C23×C4×C53C2311yescharacteristic
113C23×C4×C53C2311yescharacteristic
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
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—41no—
125C2×C4⋊C4×C53—41no—
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—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—41no—
150C2×C22⋊C4×C53—41no—
151C2×C22⋊C4×C53—41no—
152C2×C22⋊C4×C53—41no—
153C2×C22⋊C4×C53—41no—
154C2×C22⋊C4×C53—41no—
155C2×C22⋊C4×C53—41no—
156C2×C22⋊C4×C53—41no—
157C2×C22⋊C4×C53—41no—
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×C53—41no—
165C2×C22⋊C4×C53—41no—
166C2×C22⋊C4×C53—41no—
167C2×C22⋊C4×C53—41no—
168C2×C22⋊C4×C53—41no—
169C2×C22⋊C4×C53D414yescomplemented
170C2×C22⋊C4×C53D414yescomplemented
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—41no—
181#95×C53—41no—
182#95×C53D414yescomplemented
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×C53—21no—
216C24×C53—21no—
217C24×C53—21no—
218C24×C53—21no—
219C24×C53—21no—
220C24×C53—21no—
221C24×C53—21no—
222C24×C53—21no—
223C24×C53—21no—
224C24×C53—21no—
225C24×C53—21no—
226C24×C53—21no—
227C24×C53—21no—
228C24×C53—21no—
229C24×C53—21no—
230C24×C53—21no—
231C24×C53—21no—
232C24×C53—21no—
233C24×C53—21no—
234C24×C53—21no—
235C24×C53—21no—
236C24×C53—21no—
237C24×C53C2×D412yes—
238C24×C53C2×D412yes—
239C24×C53C2×D412yes—
240C24×C53C2×D412yes—
241C24×C53#4112yes—
242C24×C53#4112yes—
243C24×C53C2411yescharacteristic
244C2×D4×C53—28no—
245C2×D4×C53—28no—
246C2×D4×C53—28no—
247C2×D4×C53—44no—
248C2×D4×C53—44no—
249C2×D4×C53—44no—
250C2×D4×C53—44no—
251C2×D4×C53—44no—
252C2×D4×C53—44no—
253C2×D4×C53—44no—
254C2×D4×C53—44no—
255C2×D4×C53—44no—
256C2×D4×C53—44no—
257C2×D4×C53—44no—
258C2×D4×C53—44no—
259C2×D4×C53—44no—
260C2×D4×C53—44no—
261C2×D4×C53—44no—
262C2×D4×C53—44no—
263C2×D4×C53—44no—
264C2×D4×C53—44no—
265C2×D4×C53—44no—
266C2×D4×C53—44no—
267C2×D4×C53—44no—
268C2×D4×C53—44no—
269C2×D4×C53—44no—
270C2×D4×C53—44no—
271C2×D4×C53—44no—
272C2×D4×C53—44no—
273C2×D4×C53—44no—
274C2×D4×C53—44no—
275C2×D4×C53—44no—
276C2×D4×C53—44no—
277C2×D4×C53—44no—
278C2×D4×C53—44no—
279C2×D4×C53—44no—
280C2×D4×C53—44no—
281C2×D4×C53—44no—
282C2×D4×C53—44no—
283C2×D4×C53—44no—
284C2×D4×C53—44no—
285C2×D4×C53—44no—
286C22×C4×C53—21no—
287C22×C4×C53—21no—
288C22×C4×C53—21no—
289C22×C4×C53—21no—
290C22×C4×C53—21no—
291C22×C4×C53—21no—
292C22×C4×C53—21no—
293C22×C4×C53—21no—
294C22×C4×C53—21no—
295C22×C4×C53—21no—
296C22×C4×C53—21no—
297C22×C4×C53—21no—
298C22×C4×C53—21no—
299C22×C4×C53—21no—
300C22×C4×C53—21no—
301C22×C4×C53—21no—
302C22×C4×C53—21no—
303C22×C4×C53—21no—
304C22×C4×C53—21no—
305C22×C4×C53—21no—
306C22×C4×C53—21no—
307C22×C4×C53—21no—
308C22×C4×C53—21no—
309C22×C4×C53—21no—
310C22×C4×C53—21no—
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—21no—
326C22×C4×C53—21no—
327C22×C4×C53—21no—
328C22×C4×C53—21no—
329C22×C4×C53—21no—
330C22×C4×C53—21no—
331C22×C4×C53—21no—
332C22×C4×C53—21no—
333C22×C4×C53—21no—
334C22×C4×C53—21no—
335C22×C4×C53—21no—
336C22×C4×C53—21no—
337C22×C4×C53—21no—
338C22×C4×C53—21no—
339C22×C4×C53—21no—
340C22×C4×C53—21no—
341C22×C4×C53—21no—
342C22×C4×C53—21no—
343C22×C4×C53—21no—
344C22×C4×C53—21no—
345C22×C4×C53—21no—
346C22×C4×C53—21no—
347C22×C4×C53—21no—
348C22×C4×C53—21no—
349C22×C4×C53—21no—
350C22×C4×C53—21no—
351C22×C4×C53—21no—
352C22×C4×C53—21no—
353C22×C4×C53—21no—
354C22×C4×C53—44no—
355C22×C4×C53—44no—
356C22×C4×C53—44no—
357C22×C4×C53—44no—
358C22×C4×C53—44no—
359C22×C4×C53—44no—
360C22×C4×C53—44no—
361C22×C4×C53C2×D412yes—
362C22×C4×C53C2×D412yes—
363C22×C4×C53C2×D412yes—
364C22×C4×C53C2×D412yes—
365C22×C4×C53C2×D412yes—
366C22×C4×C53C2×D412yes—
367C22×C4×C53C2×D412yes—
368C22×C4×C53C2×D412yes—
369C22×C4×C53#4112yes—
370C4⋊C4×C53—44no—
371C22⋊C4×C53—44no—
372C22⋊C4×C53—44no—
373C22⋊C4×C53—44no—
374C22⋊C4×C53—44no—
375C22⋊C4×C53—44no—
376C22⋊C4×C53—44no—
377C22⋊C4×C53—44no—
378C22⋊C4×C53—44no—
379C22⋊C4×C53—44no—
380C22⋊C4×C53—44no—
381C22⋊C4×C53—44no—
382C22⋊C4×C53—44no—
383C22⋊C4×C53—44no—
384C22⋊C4×C53—44no—
385C22⋊C4×C53—44no—
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—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×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×C53—41no—
475C23×C53—41no—
476C23×C53—41no—
477C23×C53—41no—
478C23×C53—41no—
479C23×C53—41no—
480C23×C53—41no—
481C23×C53—41no—
482C23×C53—41no—
483C23×C53—41no—
484C23×C53—41no—
485C23×C53—41no—
486C23×C53—41no—
487C23×C53—41no—
488C23×C53—41no—
489C23×C53—41no—
490C23×C53—41no—
491C23×C53—41no—
492C23×C53—41no—
493C23×C53—41no—
494C23×C53—41no—
495C23×C53—41no—
496C23×C53—41no—
497C23×C53—41no—
498C23×C53—41no—
499C23×C53—41no—
500C23×C53—41no—
501C23×C53—41no—
502C23×C53—41no—
503C23×C53—41no—
504C23×C53—41no—
505C23×C53—41no—
506C23×C53—41no—
507C23×C53—41no—
508C23×C53—41no—
509C23×C53—41no—
510C23×C53—41no—
511C23×C53—41no—
512C23×C53—41no—
513C23×C53—41no—
514C23×C53—41no—
515C23×C53—41no—
516C23×C53—41no—
517C23×C53—41no—
518C23×C53—41no—
519C23×C53—41no—
520C23×C53—41no—
521C23×C53—41no—
522C23×C53—41no—
523C23×C53—41no—
524C23×C53—41no—
525C23×C53#12114yes—
526C23×C53C22×D411yescharacteristic
527C23×C53C22×D411yescharacteristic
528C23×C53C22×D411yescharacteristic
529C23×C53C22×D411yescharacteristic
530C23×C53C2×#4111yescharacteristic
531C23×C53C2×#4111yescharacteristic
532C23×C53C2×#4111yescharacteristic
533C23×C53H(5,𝔽2)11yescharacteristic
534C23×C53H(5,𝔽2)11yescharacteristic
535C23×C53H(5,𝔽2)11yescharacteristic
536C23×C53H(5,𝔽2)11yescharacteristic
537C23×C53H(5,𝔽2)11yescharacteristic
538C23×C53H(5,𝔽2)11yescharacteristic
539C23×C53H(5,𝔽2)11yescharacteristic
540C23×C53H(5,𝔽2)11yescharacteristic
541D4×C53—416no—
542D4×C53—416no—
543D4×C53—416no—
544D4×C53—416no—
545D4×C53—416no—
546D4×C53—416no—
547C2×C4×C53—22no—
548C2×C4×C53—22no—
549C2×C4×C53—22no—
550C2×C4×C53—22no—
551C2×C4×C53—22no—
552C2×C4×C53—22no—
553C2×C4×C53—22no—
554C2×C4×C53—22no—
555C2×C4×C53—22no—
556C2×C4×C53—22no—
557C2×C4×C53—22no—
558C2×C4×C53—22no—
559C2×C4×C53—22no—
560C2×C4×C53—22no—
561C2×C4×C53—22no—
562C2×C4×C53—22no—
563C2×C4×C53—22no—
564C2×C4×C53—22no—
565C2×C4×C53—22no—
566C2×C4×C53—22no—
567C2×C4×C53—22no—
568C2×C4×C53—22no—
569C2×C4×C53—22no—
570C2×C4×C53—22no—
571C2×C4×C53—22no—
572C2×C4×C53—22no—
573C2×C4×C53—22no—
574C2×C4×C53—416no—
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×C53—41no—
586C2×C4×C53—41no—
587C2×C4×C53—41no—
588C2×C4×C53—41no—
589C2×C4×C53—41no—
590C2×C4×C53—41no—
591C2×C4×C53—41no—
592C2×C4×C53—41no—
593C2×C4×C53—41no—
594C2×C4×C53—41no—
595C2×C4×C53—41no—
596C2×C4×C53—41no—
597C2×C4×C53—41no—
598C2×C4×C53—41no—
599C2×C4×C53—41no—
600C2×C4×C53—41no—
601C2×C4×C53—41no—
602C2×C4×C53—41no—
603C2×C4×C53—41no—
604C2×C4×C53—41no—
605C2×C4×C53—41no—
606C2×C4×C53—41no—
607C2×C4×C53—41no—
608C2×C4×C53—41no—
609C2×C4×C53—41no—
610C2×C4×C53—41no—
611C2×C4×C53—41no—
612C2×C4×C53—41no—
613C2×C4×C53—41no—
614C2×C4×C53—41no—
615C2×C4×C53—41no—
616C2×C4×C53—41no—
617C2×C4×C53—41no—
618C2×C4×C53—41no—
619C2×C4×C53—41no—
620C2×C4×C53—41no—
621C2×C4×C53—41no—
622C2×C4×C53—41no—
623C2×C4×C53—41no—
624C2×C4×C53—41no—
625#16284C5311yesmaximal, characteristic, direct product factor, Sylow
626C22×C53—24no—
627C22×C53—24no—
628C22×C53—24no—
629C22×C53—42no—
630C22×C53—42no—
631C22×C53—42no—
632C22×C53—42no—
633C22×C53—42no—
634C22×C53—42no—
635C22×C53—42no—
636C22×C53—42no—
637C22×C53—42no—
638C22×C53—42no—
639C22×C53—42no—
640C22×C53—42no—
641C22×C53—42no—
642C22×C53—42no—
643C22×C53—42no—
644C22×C53—42no—
645C22×C53—42no—
646C22×C53—42no—
647C22×C53—42no—
648C22×C53—42no—
649C22×C53—42no—
650C22×C53—42no—
651C22×C53—42no—
652C22×C53—42no—
653C22×C53—42no—
654C22×C53—42no—
655C22×C53—42no—
656C22×C53—42no—
657C22×C53—42no—
658C22×C53—42no—
659C22×C53—42no—
660C22×C53—42no—
661C22×C53—42no—
662C22×C53—81no—
663C22×C53—81no—
664C22×C53—81no—
665C22×C53—81no—
666C22×C53—81no—
667C22×C53—81no—
668C22×C53—81no—
669C22×C53—81no—
670C22×C53—81no—
671C22×C53—81no—
672C22×C53—81no—
673C22×C53—81no—
674C22×C53—81no—
675C22×C53—81no—
676C22×C53—81no—
677C22×C53—81no—
678C22×C53—81no—
679C22×C53—81no—
680C22×C53—81no—
681C22×C53—81no—
682C22×C53—81no—
683C22×C53—81no—
684C22×C53—81no—
685C22×C53—81no—
686C22×C53C2×#12111yescharacteristic
687C22×C53#52511yescharacteristic
688C22×C53#52511yescharacteristic
689C22×C53#53411yescharacteristic
690C22×C53#53411yescharacteristic
691C22×C53#53411yescharacteristic
692C22×C53#53411yescharacteristic
693C22×C53#53511yescharacteristic
694C22×C53#53511yescharacteristic
695C22×C53#53511yescharacteristic
696C22×C53#53511yescharacteristic
697C22×C53#53811yescharacteristic
698C22×C53#53811yescharacteristic
699C22×C53#53811yescharacteristic
700C22×C53#53811yescharacteristic
701C22×C53#53811yescharacteristic
702C22×C53#53811yescharacteristic
703C22×C53#54011yescharacteristic
704C22×C53#54011yescharacteristic
705C22×C53D4211yescharacteristic
706C22×C53D4211yescharacteristic
707C22×C53D4211yescharacteristic
708C22×C53D4211yescharacteristic
709C22×C53D4211yescharacteristic
710C22×C53#54611yescharacteristic
711C22×C53#54611yescharacteristic
712C22×C53#54611yescharacteristic
713C22×C53#54611yescharacteristic
714C22×C53#54611yescharacteristic
715C22×C53#55011yescharacteristic
716C22×C53#55311yescharacteristic
717C22×C53#56011yescharacteristic
718C22×C53#56011yescharacteristic
719C22×C53#56011yescharacteristic
720C22×C53#56011yescharacteristic
721C4×C53—42no—
722C4×C53—42no—
723C4×C53—42no—
724C4×C53—42no—
725C4×C53—42no—
726C4×C53—42no—
727C4×C53—42no—
728C4×C53—42no—
729C4×C53—42no—
730C4×C53—81no—
731C4×C53—81no—
732C2×#394C2×C5311yescharacteristic, complemented
733C2×#392C2×C5311yescharacteristic, complemented
734C2×#392C2×C5311yescharacteristic, complemented
735C2×#392C2×C5311yescharacteristic, complemented
736C2×#392C2×C5311yescharacteristic, complemented
737C2×#386C2×C5311yescharacteristic, complemented
738C2×#386C2×C5311yescharacteristic, complemented
739C2×#386C2×C5311yescharacteristic, complemented
740#1443C2×C5311yescharacteristic, complemented
741#1440C2×C5311yescharacteristic, complemented
742#1440C2×C5311yescharacteristic, complemented
743#1439C2×C5311yescharacteristic, complemented
744#1439C2×C5311yescharacteristic, complemented
745#1438C2×C5311yescharacteristic, complemented
746#1438C2×C5311yescharacteristic, complemented
747C2×C53—44no—
748C2×C53—82no—
749C2×C53—82no—
750C2×C53—82no—
751C2×C53#242411yescharacteristic
752C2×C53#242411yescharacteristic
753C2×C53#245611yescharacteristic
754C2×C53#261711yescharacteristic
755C2×C53#263111yescharacteristic
756C2×C53#263511yescharacteristic
757C2×C53#266811yescharacteristic
758C2×C53#266911yescharacteristic
759C2×C53#266911yescharacteristic
760C2×C53#267311yescharacteristic
761C2×C53#267311yescharacteristic
762C2×C53#267811yescharacteristic
763C2×C53#268811yescharacteristic
764C2×C53#270311yescharacteristic
765C2×C53#282511yescharacteristic
766C23×D4C22×C5311yescharacteristic
767C23×D4C22×C5311yescharacteristic
768C23×D4C22×C5311yescharacteristic
769C23×D4C22×C5311yescharacteristic
770C23×D4C22×C5311yescharacteristic
771C23×D4C22×C5311yescharacteristic
772C24×C4C22×C5311yescharacteristic
773C22×C4⋊C4C22×C5311yescharacteristic
774C22×C22⋊C4C22×C5311yescharacteristic
775C22×C22⋊C4C22×C5311yescharacteristic
776C22×C22⋊C4C22×C5311yescharacteristic
777C22×C22⋊C4C22×C5311yescharacteristic
778C22×C22⋊C4C22×C5311yescharacteristic
779C22×C22⋊C4C22×C5311yescharacteristic
780C22×C22⋊C4C22×C5311yescharacteristic
781C22×C22⋊C4C22×C5311yescharacteristic
782C22×C22⋊C4C22×C5311yescharacteristic
783C22×C22⋊C4C22×C5311yescharacteristic
784C22×C22⋊C4C22×C5311yescharacteristic
785C22×C22⋊C4C22×C5311yescharacteristic
786C22×C22⋊C4C22×C5311yescharacteristic
787C22×C22⋊C4C22×C5311yescharacteristic
788C22×C22⋊C4C22×C5311yescharacteristic
789#394—24no—
790#392—24no—
791#392—24no—
792#392—24no—
793#392—24no—
794#386—24no—
795#386—24no—
796#386—24no—
797C2×#95C22×C5311yescharacteristic
798C2×#95C22×C5311yescharacteristic
799C2×#95C22×C5311yescharacteristic
800C2×#95C22×C5311yescharacteristic
801C2×#95C22×C5311yescharacteristic
802C2×#95C22×C5311yescharacteristic
803C2×#95C22×C5311yescharacteristic
804C2×#95C22×C5311yescharacteristic
805C2×#95C22×C5311yescharacteristic
806C2×#95C22×C5311yescharacteristic
807C2×#95C22×C5311yescharacteristic
808C2×#95C22×C5311yescharacteristic
809C53#1628411yescharacteristic, direct product factor, Sylow
810C25C23×C5311yescharacteristic
811C25C23×C5311yescharacteristic
812C25C23×C5311yescharacteristic
813C25C23×C5311yescharacteristic
814C22×D4—22no—
815C22×D4—22no—
816C22×D4—22no—
817C22×D4—22no—
818C22×D4—22no—
819C22×D4—22no—
820C22×D4—22no—
821C22×D4—22no—
822C22×D4—22no—
823C22×D4—22no—
824C22×D4—22no—
825C22×D4—22no—
826C22×D4—22no—
827C22×D4—22no—
828C22×D4—22no—
829C22×D4—22no—
830C22×D4—22no—
831C22×D4—22no—
832C22×D4—22no—
833C22×D4—22no—
834C22×D4—22no—
835C22×D4—41no—
836C22×D4—41no—
837C22×D4—41no—
838C22×D4—41no—
839C22×D4—41no—
840C22×D4—41no—
841C22×D4—41no—
842C22×D4—41no—
843C22×D4—41no—
844C22×D4—41no—
845C22×D4—41no—
846C22×D4—41no—
847C22×D4—41no—
848C22×D4—41no—
849C22×D4—41no—
850C22×D4—41no—
851C22×D4—41no—
852C22×D4—41no—
853C22×D4—41no—
854C22×D4—41no—
855C22×D4D4×C5314yescomplemented
856C23×C4—22no—
857C23×C4—22no—
858C23×C4—22no—
859C23×C4—41no—
860C23×C4—41no—
861C23×C4—41no—
862C23×C4—41no—
863C23×C4C23×C5311yescharacteristic
864C23×C4C23×C5311yescharacteristic
865C23×C4C23×C5311yescharacteristic
866C23×C4C23×C5311yescharacteristic
867C23×C4C23×C5311yescharacteristic
868C23×C4C23×C5311yescharacteristic
869C23×C4C23×C5311yescharacteristic
870C23×C4C23×C5311yescharacteristic
871C23×C4C23×C5311yescharacteristic
872C23×C4C23×C5311yescharacteristic
873C23×C4C23×C5311yescharacteristic
874C2×C4⋊C4—22no—
875C2×C4⋊C4—41no—
876C2×C4⋊C4—41no—
877C2×C22⋊C4—22no—
878C2×C22⋊C4—22no—
879C2×C22⋊C4—22no—
880C2×C22⋊C4—22no—
881C2×C22⋊C4—22no—
882C2×C22⋊C4—22no—
883C2×C22⋊C4—22no—
884C2×C22⋊C4—22no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—22no—
888C2×C22⋊C4—22no—
889C2×C22⋊C4—22no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—22no—
892C2×C22⋊C4—22no—
893C2×C22⋊C4—22no—
894C2×C22⋊C4—22no—
895C2×C22⋊C4—22no—
896C2×C22⋊C4—22no—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—22no—
899C2×C22⋊C4—22no—
900C2×C22⋊C4—41no—
901C2×C22⋊C4—41no—
902C2×C22⋊C4—41no—
903C2×C22⋊C4—41no—
904C2×C22⋊C4—41no—
905C2×C22⋊C4—41no—
906C2×C22⋊C4—41no—
907C2×C22⋊C4—41no—
908C2×C22⋊C4—41no—
909C2×C22⋊C4—41no—
910C2×C22⋊C4—41no—
911C2×C22⋊C4—41no—
912C2×C22⋊C4—41no—
913C2×C22⋊C4—41no—
914C2×C22⋊C4—41no—
915C2×C22⋊C4—41no—
916C2×C22⋊C4—41no—
917C2×C22⋊C4—41no—
918C2×C22⋊C4—41no—
919C2×C22⋊C4—41no—
920C2×C22⋊C4D4×C5314yescomplemented
921C2×C22⋊C4D4×C5314yescomplemented
922#95—22no—
923#95—22no—
924#95—22no—
925#95—22no—
926#95—22no—
927#95—22no—
928#95—22no—
929#95—22no—
930#95—22no—
931#95—41no—
932#95—41no—
933#95D4×C5314yescomplemented
934C24—21no—
935C24—21no—
936C24—21no—
937C24—21no—
938C24—21no—
939C24—21no—
940C24—21no—
941C24—21no—
942C24—21no—
943C24—21no—
944C24—21no—
945C24—21no—
946C24—21no—
947C24—21no—
948C24—21no—
949C24—21no—
950C24—21no—
951C24—21no—
952C24—21no—
953C24—21no—
954C24—21no—
955C24—21no—
956C24—21no—
957C24—21no—
958C24—21no—
959C24—21no—
960C24—21no—
961C24—21no—
962C24—21no—
963C24—21no—
964C24—21no—
965C24—21no—
966C24—21no—
967C24—21no—
968C24—21no—
969C24—21no—
970C24—21no—
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24C2×D4×C5312yes—
989C24C2×D4×C5312yes—
990C24C2×D4×C5312yes—
991C24C2×D4×C5312yes—
992C24#41×C5312yes—
993C24#41×C5312yes—
994C24C24×C5311yescharacteristic
995C2×D4—28no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—21no—
1042C22×C4—21no—
1043C22×C4—21no—
1044C22×C4—21no—
1045C22×C4—21no—
1046C22×C4—21no—
1047C22×C4—21no—
1048C22×C4—21no—
1049C22×C4—21no—
1050C22×C4—21no—
1051C22×C4—21no—
1052C22×C4—21no—
1053C22×C4—21no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—21no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—21no—
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—21no—
1083C22×C4—21no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—44no—
1111C22×C4—44no—
1112C22×C4C2×D4×C5312yes—
1113C22×C4C2×D4×C5312yes—
1114C22×C4C2×D4×C5312yes—
1115C22×C4C2×D4×C5312yes—
1116C22×C4C2×D4×C5312yes—
1117C22×C4C2×D4×C5312yes—
1118C22×C4C2×D4×C5312yes—
1119C22×C4C2×D4×C5312yes—
1120C22×C4#41×C5312yes—
1121C4⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23#121×C5314yes—
1277C23C22×D4×C5311yescharacteristic
1278C23C22×D4×C5311yescharacteristic
1279C23C22×D4×C5311yescharacteristic
1280C23C22×D4×C5311yescharacteristic
1281C23C2×#41×C5311yescharacteristic
1282C23C2×#41×C5311yescharacteristic
1283C23C2×#41×C5311yescharacteristic
1284C23H(5,𝔽2)×C5311yescharacteristic
1285C23H(5,𝔽2)×C5311yescharacteristic
1286C23H(5,𝔽2)×C5311yescharacteristic
1287C23H(5,𝔽2)×C5311yescharacteristic
1288C23H(5,𝔽2)×C5311yescharacteristic
1289C23H(5,𝔽2)×C5311yescharacteristic
1290C23H(5,𝔽2)×C5311yescharacteristic
1291C23H(5,𝔽2)×C5311yescharacteristic
1292D4—416no—
1293D4—416no—
1294D4—416no—
1295D4—416no—
1296D4—416no—
1297D4—416no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—416no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—41no—
1342C2×C4—41no—
1343C2×C4—41no—
1344C2×C4—41no—
1345C2×C4—41no—
1346C2×C4—41no—
1347C2×C4—41no—
1348C2×C4—41no—
1349C2×C4—41no—
1350C2×C4—41no—
1351C2×C4—41no—
1352C2×C4—41no—
1353C2×C4—41no—
1354C2×C4—41no—
1355C2×C4—41no—
1356C2×C4—41no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C22—24no—
1377C22—24no—
1378C22—24no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—42no—
1392C22—42no—
1393C22—42no—
1394C22—42no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—81no—
1413C22—81no—
1414C22—81no—
1415C22—81no—
1416C22—81no—
1417C22—81no—
1418C22—81no—
1419C22—81no—
1420C22—81no—
1421C22—81no—
1422C22—81no—
1423C22—81no—
1424C22—81no—
1425C22—81no—
1426C22—81no—
1427C22—81no—
1428C22—81no—
1429C22—81no—
1430C22—81no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—81no—
1435C22—81no—
1436C22C2×#121×C5311yescharacteristic
1437C22C53×#52511yescharacteristic
1438C22C53×#52511yescharacteristic
1439C22C53×#53411yescharacteristic
1440C22C53×#53411yescharacteristic
1441C22C53×#53411yescharacteristic
1442C22C53×#53411yescharacteristic
1443C22C53×#53511yescharacteristic
1444C22C53×#53511yescharacteristic
1445C22C53×#53511yescharacteristic
1446C22C53×#53511yescharacteristic
1447C22C53×#53811yescharacteristic
1448C22C53×#53811yescharacteristic
1449C22C53×#53811yescharacteristic
1450C22C53×#53811yescharacteristic
1451C22C53×#53811yescharacteristic
1452C22C53×#53811yescharacteristic
1453C22C53×#54011yescharacteristic
1454C22C53×#54011yescharacteristic
1455C22D42×C5311yescharacteristic
1456C22D42×C5311yescharacteristic
1457C22D42×C5311yescharacteristic
1458C22D42×C5311yescharacteristic
1459C22D42×C5311yescharacteristic
1460C22C53×#54611yescharacteristic
1461C22C53×#54611yescharacteristic
1462C22C53×#54611yescharacteristic
1463C22C53×#54611yescharacteristic
1464C22C53×#54611yescharacteristic
1465C22C53×#55011yescharacteristic
1466C22C53×#55311yescharacteristic
1467C22C53×#56011yescharacteristic
1468C22C53×#56011yescharacteristic
1469C22C53×#56011yescharacteristic
1470C22C53×#56011yescharacteristic
1471C4—42no—
1472C4—42no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—42no—
1477C4—42no—
1478C4—42no—
1479C4—42no—
1480C4—81no—
1481C4—81no—
1482C2—44no—
1483C2—82no—
1484C2—82no—
1485C2—82no—
1486C2C53×#242411yescharacteristic
1487C2C53×#242411yescharacteristic
1488C2C53×#245611yescharacteristic
1489C2C53×#261711yescharacteristic
1490C2C53×#263111yescharacteristic
1491C2C53×#263511yescharacteristic
1492C2C53×#266811yescharacteristic
1493C2C53×#266911yescharacteristic
1494C2C53×#266911yescharacteristic
1495C2C53×#267311yescharacteristic
1496C2C53×#267311yescharacteristic
1497C2C53×#267811yescharacteristic
1498C2C53×#268811yescharacteristic
1499C2C53×#270311yescharacteristic
1500C2C53×#282511yescharacteristic
subgroupG/H
center, socleC24×C53C24
commutator, Frattini, cosocleC24C24×C53
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C53×#394C2semidirect
2. C2×C53×#392C2semidirect
3. C2×C53×#392C2semidirect
4. C2×C53×#392C2semidirect
5. C2×C53×#392C2semidirect
6. C2×C53×#386C2semidirect
7. C2×C53×#386C2semidirect
8. C2×C53×#386C2semidirect
9. C53×#1443C2semidirect
10. C53×#1440C2semidirect
11. C53×#1440C2semidirect
12. C53×#1439C2semidirect
13. C53×#1439C2semidirect
14. C53×#1438C2semidirect
15. C53×#1438C2semidirect
104. C22×D4×C53D4semidirect
169. C2×C22⋊C4×C53D4semidirect
170. C2×C22⋊C4×C53D4semidirect
182. #95×C53D4semidirect
625. #16284C53direct (N × H)
732. C2×#394C2×C53semidirect
733. C2×#392C2×C53semidirect
734. C2×#392C2×C53semidirect
735. C2×#392C2×C53semidirect
736. C2×#392C2×C53semidirect
737. C2×#386C2×C53semidirect
738. C2×#386C2×C53semidirect
739. C2×#386C2×C53semidirect
740. #1443C2×C53semidirect
741. #1440C2×C53semidirect
742. #1440C2×C53semidirect
743. #1439C2×C53semidirect
744. #1439C2×C53semidirect
745. #1438C2×C53semidirect
746. #1438C2×C53semidirect
809. C53#16284direct (N × H)
855. C22×D4D4×C53semidirect
920. C2×C22⋊C4D4×C53semidirect
921. C2×C22⋊C4D4×C53semidirect
933. #95D4×C53semidirect

Maximal subgroups

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

subgroupindex
C2×C53×#3942
C2×C53×#3922
C2×C53×#3862
C53×#14432
C53×#14402
C53×#14392
C53×#14382
#1628453