Finite Group Databasebeta

← C2×#20279502 #27553822

Subgroups — C2×#20279502 #27553822

Order 13568.

2246 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20279502C2116yesmaximal, direct product factor
2C2×C53⋊#401C211yesmaximal, characteristic, complemented
3C2×#16810564C211yesmaximal, characteristic, complemented
4C2×#16810548C211yesmaximal, characteristic
5C2×#16810535C211yesmaximal, characteristic
6C2×#16810529C211yesmaximal, characteristic, complemented
7C2×#16810527C211yesmaximal, characteristic, complemented
8C2×#16810517C211yesmaximal, characteristic
9C2×#16810511C211yesmaximal, characteristic
10C2×#16810508C211yesmaximal, characteristic, complemented
11C2×#16810507C211yesmaximal, characteristic, complemented
12C2×#16810507C211yesmaximal, characteristic, complemented
13C2×#16810496C211yesmaximal, characteristic
14C2×#16810486C211yesmaximal, characteristic
15C2×#16810469C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C53⋊#401C2218yescomplemented
30#16810564C2218yescomplemented
31#16810548C2218yes—
32#16810535C2218yes—
33#16810529C2218yescomplemented
34#16810527C2218yescomplemented
35#16810517C2218yes—
36#16810511C2218yes—
37#16810508C2218yescomplemented
38#16810507C2218yescomplemented
39#16810507C2218yescomplemented
40#16810496C2218yes—
41#16810486C2218yes—
42#16810469C2218yescomplemented
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C24×C4×C53C2211yescharacteristic
60C22×C22⋊C4×C53C2211yescharacteristic
61C22×C22⋊C4×C53C2211yescharacteristic
62C22×C42×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C4×C22⋊C4×C53C2218yes—
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C22×Dic106—24no—
68C22×Dic106—24no—
69C22×Dic106—42no—
70C22×Dic106C2314yes—
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C2×C4⋊Dic53—24no—
80C2×C4⋊Dic53C2314yes—
81C2×#11719919—24no—
82C2×#11719919—24no—
83C2×#11719919—42no—
84C2×#11719919—42no—
85C2×#11719919C2314yes—
86C2×#11719919C2314yes—
87C2×#11719919C2314yes—
88C2×#11719919C2314yes—
89C2×C22⋊Dic53—24no—
90C2×C22⋊Dic53—24no—
91C2×C22⋊Dic53—24no—
92C2×C22⋊Dic53—42no—
93C2×C22⋊Dic53C2314yes—
94C2×C22⋊Dic53C2314yes—
95C2×C22⋊Dic53C2314yes—
96C2×C22⋊Dic53C2314yes—
97C2×C4×Dic53—24no—
98C2×C4×Dic53—24no—
99C2×C4×Dic53C2314yes—
100C2×C4×Dic53C2314yes—
101#13133124C2314yes—
102#13133124C2314yes—
103#13133124C2314yes—
104#13133124C2314yes—
105#13133124C2314yes—
106#13133124C2314yes—
107#13133124C2314yes—
108#13133124C2314yes—
109#13133124C2314yes—
110#13133124C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117C25×C53C2311yescharacteristic
118C23×C4×C53—24no—
119C23×C4×C53—24no—
120C23×C4×C53—42no—
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2314yes—
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C2×C22⋊C4×C53—24no—
129C2×C22⋊C4×C53—24no—
130C2×C22⋊C4×C53C2314yes—
131C2×C22⋊C4×C53C2314yes—
132C2×C42×C53—24no—
133C2×C42×C53—42no—
134C2×C42×C53C2314yes—
135C2×C42×C53C2314yes—
136#95×C53C2314yes—
137#95×C53C2314yes—
138C24×C53—22no—
139C24×C53—22no—
140C24×C53—22no—
141C24×C53—22no—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53#4114yes—
145C24×C53C2412yes—
146C24×C53C2411yescharacteristic
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—28no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—28no—
164C22×C4×C53—44no—
165C22×C4×C53—416no—
166C22×C4×C53#4114yes—
167C22×C4×C53#4114yes—
168C22×C4×C53#4114yes—
169C22×C4×C53C2412yes—
170C22×C4×C53C2412yes—
171C22×C4×C53C2412yes—
172C22×C4×C53C2412yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53#4114yes—
199C22×Dic53C2412yes—
200C22×Dic53C2412yes—
201C22×Dic53C2412yes—
202C22×Dic53C2412yes—
203C22×Dic53C2412yes—
204C22×Dic53C2412yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C2×Dic106—28no—
208C2×Dic106—28no—
209C2×Dic106—44no—
210C2×Dic106—416no—
211C22⋊C4×C53—28no—
212C22⋊C4×C53—28no—
213C42×C53—28no—
214C42×C53—44no—
215C22⋊Dic53—28no—
216C22⋊Dic53—28no—
217C22⋊Dic53—28no—
218C22⋊Dic53—44no—
219C4⋊Dic53—28no—
220#11719919—28no—
221#11719919—28no—
222#11719919—44no—
223#11719919—44no—
224C4×Dic53—28no—
225C4×Dic53—28no—
226C23×C53—28no—
227C23×C53—28no—
228C23×C53—28no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—44no—
236C23×C53—44no—
237C23×C53—44no—
238C23×C53—44no—
239C23×C53C2×#4112yes—
240C23×C53C2×#4112yes—
241C23×C53C2×#4114yes—
242C23×C53C2×#4112yes—
243C23×C53C2×#4112yes—
244C23×C53C2×#4112yes—
245C23×C53H(5,𝔽2)12yes—
246C23×C532−1+412yes—
247C23×C53C2511yescharacteristic
248C2×C4×C53—28no—
249C2×C4×C53—28no—
250C2×C4×C53—28no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—416no—
267C2×C4×C53—44no—
268C2×C4×C53—44no—
269C2×C4×C53—44no—
270C2×C4×C53C2×#4114yes—
271C2×C4×C53C2×#4114yes—
272C2×C4×C53C2×#4114yes—
273C2×Dic53—28no—
274C2×Dic53—22no—
275C2×Dic53—22no—
276C2×Dic53—22no—
277C2×Dic53—22no—
278C2×Dic53—22no—
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—22no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—44no—
298C2×Dic53—44no—
299C2×Dic53—44no—
300C2×Dic53—44no—
301C2×Dic53—44no—
302C2×Dic53—44no—
303C2×Dic53—44no—
304C2×Dic53C2×#4114yes—
305Dic106—416no—
306C2×#2527—531nomaximal, Sylow
307C22×C53—24no—
308C22×C53—24no—
309C22×C53—24no—
310C22×C53—42no—
311C22×C53—42no—
312C22×C53—42no—
313C22×C53—42no—
314C22×C53—416no—
315C22×C53#52914yes—
316C22×C53#52914yes—
317C22×C53#54214yes—
318C22×C53#55114yes—
319C22×C53#55114yes—
320C22×C53#55214yes—
321C22×C53#55614yes—
322C22×C53C22×#4111yescharacteristic
323C22×C53C22×#4111yescharacteristic
324C22×C53C22×#4111yescharacteristic
325C22×C53C22×#4111yescharacteristic
326C22×C53C22×#4111yescharacteristic
327C22×C53C2×H(5,𝔽2)11yescharacteristic
328C22×C53C2×2−1+411yescharacteristic
329C4×C53—24no—
330C4×C53—24no—
331C4×C53—24no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53—42no—
335Dic53—24no—
336Dic53—42no—
337Dic53—42no—
338Dic53—42no—
339Dic53—42no—
340Dic53—42no—
341Dic53—42no—
342Dic53—42no—
343#2527—5316no—
344C2×#401—531no—
345C2×#400—531no—
346C2×#397—531no—
347C2×#393—531no—
348C2×#391—531no—
349C2×#391—531no—
350C2×#388—531no—
351C2×#388—531no—
352C2×#387—531no—
353C2×#387—531no—
354C2×#387—531no—
355C2×#385—531no—
356C2×#381—531no—
357C2×C4×C22⋊C4D5311yescharacteristic
358C2×#376—531no—
359C2×C53—44no—
360C2×C53#252718yescomplemented
361C2×C53C2×#52911yescharacteristic
362C2×C53C2×#52911yescharacteristic
363C2×C53C2×#54211yescharacteristic
364C2×C53C2×#55111yescharacteristic
365C2×C53C2×#55111yescharacteristic
366C2×C53C2×#55211yescharacteristic
367C2×C53C2×#55611yescharacteristic
368C23×Q8—531no—
369C24×C4C2×D5311yescharacteristic
370C22×C4⋊C4—531no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4—531no—
373C22×C4⋊C4—531no—
374C22×C4⋊C4—531no—
375C22×C22⋊C4—531no—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4—531no—
379C22×C22⋊C4C2×D5311yescharacteristic
380C22×C22⋊C4C2×D5311yescharacteristic
381C22×C42—531no—
382C22×C42—531no—
383C22×C42C2×D5311yescharacteristic
384C22×C42C2×D5311yescharacteristic
385#401—538no—
386#400—538no—
387#397—538no—
388#393—538no—
389#391—538no—
390#391—538no—
391#388—538no—
392#388—538no—
393#387—538no—
394#387—538no—
395#387—538no—
396#385—538no—
397#381—538no—
398C4×C22⋊C4C2×D5318yes—
399#376—538no—
400C2×#95—531no—
401C2×#95—531no—
402C2×#95—531no—
403C2×#95—531no—
404C2×#95—531no—
405C2×#95—531no—
406C2×#95—531no—
407C2×#95—531no—
408C2×#95—531no—
409C2×#95—531no—
410C2×#95—531no—
411C2×#95—531no—
412C2×#95—531no—
413C2×#95—531no—
414C2×#95—531no—
415C2×#95—531no—
416C2×#95C2×D5311yescharacteristic
417C2×#95C2×D5311yescharacteristic
418C53C2×#252711yescharacteristic, complemented, Sylow
419C25C22×D5311yescharacteristic
420C22×Q8—534no—
421C22×Q8—1064no—
422C22×Q8—1064no—
423C22×Q8—2122no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—42no—
427C23×C4—531no—
428C23×C4—531no—
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4C22×D5311yescharacteristic
436C23×C4C22×D5311yescharacteristic
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5314yes—
439C23×C4C22×D5311yescharacteristic
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C2×C4⋊C4—534no—
443C2×C4⋊C4—534no—
444C2×C4⋊C4—534no—
445C2×C4⋊C4—534no—
446C2×C4⋊C4—534no—
447C2×C4⋊C4—1064no—
448C2×C4⋊C4—1064no—
449C2×C4⋊C4—1064no—
450C2×C4⋊C4—2122no—
451C2×C4⋊C4—2122no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—534no—
455C2×C22⋊C4—534no—
456C2×C22⋊C4—534no—
457C2×C22⋊C4—534no—
458C2×C22⋊C4—1064no—
459C2×C22⋊C4—1064no—
460C2×C22⋊C4—1064no—
461C2×C22⋊C4—2122no—
462C2×C22⋊C4C22×D5314yes—
463C2×C22⋊C4C22×D5314yes—
464C2×C42—24no—
465C2×C42—42no—
466C2×C42—534no—
467C2×C42—534no—
468C2×C42—1064no—
469C2×C42—1064no—
470C2×C42C22×D5314yes—
471C2×C42C22×D5314yes—
472#95—534no—
473#95—534no—
474#95—534no—
475#95—534no—
476#95—534no—
477#95—534no—
478#95—534no—
479#95—534no—
480#95—534no—
481#95—534no—
482#95—534no—
483#95—534no—
484#95—534no—
485#95—534no—
486#95—534no—
487#95—534no—
488#95C22×D5314yes—
489#95C22×D5314yes—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24#1171994514yes—
497C24C23×D5312yes—
498C24C23×D5311yescharacteristic
499C2×Q8—1068no—
500C2×Q8—1068no—
501C2×Q8—2124no—
502C2×Q8—21216no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—44no—
521C22×C4—416no—
522C22×C4—534no—
523C22×C4—532no—
524C22×C4—532no—
525C22×C4—532no—
526C22×C4—532no—
527C22×C4—532no—
528C22×C4—532no—
529C22×C4—532no—
530C22×C4—532no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4#1171994514yes—
555C22×C4#1171994514yes—
556C22×C4#1171994714yes—
557C22×C4C23×D5312yes—
558C22×C4C23×D5312yes—
559C22×C4C23×D5312yes—
560C22×C4C23×D5312yes—
561C22×C4C23×D5312yes—
562C22×C4C23×D5312yes—
563C4⋊C4—1068no—
564C4⋊C4—1068no—
565C4⋊C4—1068no—
566C4⋊C4—2124no—
567C4⋊C4—2124no—
568C22⋊C4—28no—
569C22⋊C4—28no—
570C22⋊C4—1068no—
571C22⋊C4—1068no—
572C22⋊C4—1068no—
573C22⋊C4—2124no—
574C42—28no—
575C42—44no—
576C42—1068no—
577C42—1068no—
578C23—28no—
579C23—28no—
580C23—28no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—44no—
588C23—44no—
589C23—44no—
590C23—44no—
591C23#41×D5312yes—
592C23C2×#1171994712yes—
593C23C2×#1171994514yes—
594C23C2×#1171994512yes—
595C23C2×#1171994512yes—
596C23C2×#1171994512yes—
597C23#1313326212yes—
598C23#1313326412yes—
599C23C24×D5311yescharacteristic
600Q8—21216no—
601C2×C4—28no—
602C2×C4—28no—
603C2×C4—28no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—416no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—534no—
624C2×C4—1068no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1062no—
632C2×C4—1062no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
646C2×C4—1062no—
647C2×C4—1062no—
648C2×C4—2124no—
649C2×C4—2124no—
650C2×C4—2124no—
651C2×C4—2124no—
652C2×C4—2124no—
653C2×C4—2124no—
654C2×C4—2124no—
655C2×C4C2×#1171994714yes—
656C2×C4C2×#1171994514yes—
657C2×C4C2×#1171994514yes—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—42no—
662C22—42no—
663C22—416no—
664C22—42no—
665C22—42no—
666C22#1681115314yes—
667C22#1681115714yes—
668C22#1681123814yes—
669C22#1681129914yes—
670C22#1681130214yes—
671C22#1681130614yes—
672C22#1681134314yes—
673C22C2×#41×D5311yescharacteristic
674C22C22×#1171994711yescharacteristic
675C22C22×#1171994511yescharacteristic
676C22C22×#1171994511yescharacteristic
677C22C22×#1171994511yescharacteristic
678C22C2×#1313326211yescharacteristic
679C22C2×#1313326411yescharacteristic
680C4—24no—
681C4—24no—
682C4—24no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—1064no—
687C4—2122no—
688C4—2122no—
689C4—2122no—
690C4—2122no—
691C4—2122no—
692C4—2122no—
693C4—2122no—
694C2—44no—
695C2#2027950218yesdirect product factor
696C2C2×#1681115311yescharacteristic
697C2C2×#1681115711yescharacteristic
698C2C2×#1681123811yescharacteristic
699C2C2×#1681129911yescharacteristic
700C2C2×#1681130211yescharacteristic
701C2C2×#1681130611yescharacteristic
702C2C2×#1681134311yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C4×C22⋊C4×C53C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C2×#2527
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #20279502C2direct (N × H)
2. C2×C53⋊#401C2semidirect
3. C2×#16810564C2semidirect
6. C2×#16810529C2semidirect
7. C2×#16810527C2semidirect
10. C2×#16810508C2semidirect
11. C2×#16810507C2semidirect
12. C2×#16810507C2semidirect
15. C2×#16810469C2semidirect
29. C53⋊#401C22semidirect
30. #16810564C22semidirect
33. #16810529C22semidirect
34. #16810527C22semidirect
37. #16810508C22semidirect
38. #16810507C22semidirect
39. #16810507C22semidirect
42. #16810469C22semidirect
360. C2×C53#2527semidirect
418. C53C2×#2527semidirect
695. C2#20279502direct (N × H)

Maximal subgroups

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

subgroupindex
#202795022
C2×C53⋊#4012
C2×#168105642
C2×#168105482
C2×#168105352
C2×#168105292
C2×#168105272
C2×#168105172
C2×#168105112
C2×#168105082
C2×#168105072
C2×#168104962
C2×#168104862
C2×#168104692
C2×C4×C22⋊C4×C532
C2×#252753