Finite Group Databasebeta

← C2×#20280671 #27550545

Subgroups — C2×#20280671 #27550545

Order 13568.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280671C2116yesmaximal, direct product factor
2C2×C53⋊#401C211yesmaximal, characteristic, complemented
3C2×#16810565C211yesmaximal, characteristic, complemented
4C2×#16810562C211yesmaximal, characteristic, complemented
5C2×#16810561C211yesmaximal, characteristic, complemented
6C2×#16810552C211yesmaximal, characteristic, complemented
7C2×#16810550C211yesmaximal, characteristic, complemented
8C2×#16810549C211yesmaximal, characteristic, complemented
9C2×#16810545C211yesmaximal, characteristic, complemented
10C2×#16810502C211yesmaximal, characteristic
11C2×#16810500C211yesmaximal, characteristic
12C2×#16810500C211yesmaximal, characteristic
13C2×#16810498C211yesmaximal, characteristic, complemented
14C2×#16810495C211yesmaximal, characteristic, complemented
15C22×#13133124C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C24×Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C53⋊#401C2218yescomplemented
32#16810565C2218yescomplemented
33#16810562C2218yescomplemented
34#16810561C2218yescomplemented
35#16810552C2218yescomplemented
36#16810550C2218yescomplemented
37#16810549C2218yescomplemented
38#16810545C2218yescomplemented
39#16810502C2218yes—
40#16810500C2218yes—
41#16810500C2218yes—
42#16810498C2218yescomplemented
43#16810495C2218yescomplemented
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×#13133124C2218yescomplemented
59C24×C4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C53×#385C2218yescomplemented
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C24×D53C2311yescharacteristic
68C22×C22⋊D53—24no—
69C22×C22⋊D53—24no—
70C22×C22⋊D53—24no—
71C22×C22⋊D53C2314yes—
72C23×Dic53—24no—
73C23×Dic53—24no—
74C23×Dic53—42no—
75C23×Dic53—42no—
76C23×Dic53—42no—
77C23×Dic53—42no—
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C23×Dic53C2311yescharacteristic
85C23×Dic53C2314yes—
86C23×Dic53C2314yes—
87C2×C4⋊Dic53—42no—
88C2×C4⋊Dic53—42no—
89C2×C4⋊Dic53C2314yes—
90C2×C4⋊Dic53C2314yes—
91C2×#11719919—42no—
92C2×#11719919—42no—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×C22⋊Dic53—24no—
96C2×C22⋊Dic53C2314yes—
97C2×#11719921—42no—
98C2×#11719921—42no—
99C2×#11719921—42no—
100C2×#11719921—42no—
101C2×#11719921—42no—
102C2×#11719921—42no—
103C2×#11719921C2314yes—
104C2×#11719921C2314yes—
105C2×#11719921C2314yes—
106C2×#11719921C2314yes—
107C2×#11719921C2314yes—
108C2×#11719921C2314yes—
109#13133124C2314yes—
110#13133124C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123C25×C53C2311yescharacteristic
124C23×C4×C53—24no—
125C23×C4×C53—42no—
126C23×C4×C53—42no—
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2314yes—
134C2×C4⋊C4×C53—42no—
135C2×C4⋊C4×C53—42no—
136C2×C4⋊C4×C53C2314yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C22⋊C4×C53—24no—
139C2×C22⋊C4×C53—24no—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142#95×C53C2314yes—
143#95×C53C2314yes—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53#4114yes—
149C24×C53#4114yes—
150C24×C53#4114yes—
151C24×C53C2412yes—
152C24×C53C2411yescharacteristic
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53—22no—
158C23×D53—22no—
159C23×D53—22no—
160C23×D53C2412yes—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—28no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—44no—
181C22×C4×C53—44no—
182C22×C4×C53—416no—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C2×C22⋊D53—28no—
190C2×C22⋊D53—28no—
191C2×C22⋊D53—28no—
192C2×C22⋊D53—416no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—28no—
196C22×Dic53—28no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—44no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C22×Dic53—416no—
221C22×Dic53—416no—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C4⋊C4×C53—44no—
230C4⋊C4×C53—44no—
231C22⋊C4×C53—28no—
232C22⋊C4×C53—28no—
233C22⋊Dic53—28no—
234#11719921—44no—
235#11719921—44no—
236#11719921—44no—
237#11719921—44no—
238#11719921—44no—
239#11719921—44no—
240C4⋊Dic53—44no—
241C4⋊Dic53—44no—
242#11719919—44no—
243#11719919—44no—
244C23×C53—28no—
245C23×C53—28no—
246C23×C53—28no—
247C23×C53—28no—
248C23×C53—28no—
249C23×C53—28no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53#126116yes—
255C23×C53C2×#4114yes—
256C23×C53C2×#4112yes—
257C23×C53C2×#4114yes—
258C23×C53C2×#4112yes—
259C23×C53C2×#4114yes—
260C23×C53C2×#4112yes—
261C23×C53H(5,𝔽2)12yes—
262C23×C53H(5,𝔽2)12yes—
263C23×C53H(5,𝔽2)12yes—
264C23×C532−1+412yes—
265C23×C53C2511yescharacteristic
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—44no—
274C22×D53—44no—
275C22×D53—44no—
276C22×D53—44no—
277C22×D53—44no—
278C22×D53—44no—
279C22×D53—44no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—416no—
299C2×C4×C53—44no—
300C2×C4×C53—44no—
301C2×C4×C53—44no—
302C2×C4×C53—44no—
303C2×C4×C53—44no—
304C2×C4×C53—44no—
305C22⋊D53—416no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—416no—
328C2×Dic53—416no—
329C2×Dic53—44no—
330C2×Dic53—44no—
331C2×Dic53—44no—
332C2×Dic53—44no—
333C2×Dic53—44no—
334C2×Dic53—44no—
335C2×Dic53—44no—
336C2×#2643—531nomaximal, Sylow
337C22×C53—232no—
338C22×C53—24no—
339C22×C53—24no—
340C22×C53—24no—
341C22×C53—24no—
342C22×C53—24no—
343C22×C53—24no—
344C22×C53C2×#12618yes—
345C22×C53C2×#12614yes—
346C22×C53#53814yes—
347C22×C53#53814yes—
348C22×C53#53814yes—
349C22×C53#53914yes—
350C22×C53#53914yes—
351C22×C53#53914yes—
352C22×C53C22×#4111yescharacteristic
353C22×C53C22×#4111yescharacteristic
354C22×C53C22×#4111yescharacteristic
355C22×C53C2×H(5,𝔽2)11yescharacteristic
356C22×C53C2×H(5,𝔽2)11yescharacteristic
357C22×C53C2×H(5,𝔽2)11yescharacteristic
358C22×C53C2×2−1+411yescharacteristic
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—88no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379Dic53—42no—
380#2643—5316no—
381C2×#401—531no—
382C2×#400—531no—
383C2×#400—531no—
384C2×#400—531no—
385C2×#397—531no—
386C2×#397—531no—
387C2×#397—531no—
388C2×#396—531no—
389C2×#386—531no—
390C2×#386—531no—
391C2×#386—531no—
392C2×#385—531no—
393C2×#385—531no—
394C2×#385D5311yescharacteristic, complemented
395C22×#95—531no—
396C2×C53—28no—
397C2×C53#264318yescomplemented
398C2×C53C22×#12611yescharacteristic
399C2×C53C2×#53811yescharacteristic
400C2×C53C2×#53811yescharacteristic
401C2×C53C2×#53811yescharacteristic
402C2×C53C2×#53911yescharacteristic
403C2×C53C2×#53911yescharacteristic
404C2×C53C2×#53911yescharacteristic
405D53—82no—
406C23×D4—531no—
407C24×C4—531no—
408C24×C4—531no—
409C24×C4C2×D5311yescharacteristic
410C22×C4⋊C4—531no—
411C22×C4⋊C4—531no—
412C22×C4⋊C4—531no—
413C22×C4⋊C4—531no—
414C22×C4⋊C4C2×D5311yescharacteristic
415C22×C4⋊C4C2×D5311yescharacteristic
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4—531no—
420C22×C22⋊C4—531no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4C2×D5311yescharacteristic
424C22×C22⋊C4C2×D5311yescharacteristic
425#401—538no—
426#400—538no—
427#400—538no—
428#400—538no—
429#397—538no—
430#397—538no—
431#397—538no—
432#396—538no—
433#386—538no—
434#386—538no—
435#386—538no—
436#385—538no—
437#385—538no—
438#385C2×D5318yescomplemented
439C2×#95—538no—
440C2×#95—531no—
441C2×#95—531no—
442C2×#95—531no—
443C2×#95—531no—
444C2×#95—531no—
445C2×#95—531no—
446C2×#95—531no—
447C2×#95—531no—
448C2×#95—531no—
449C2×#95—531no—
450C2×#95—531no—
451C2×#95—531no—
452C2×#95—531no—
453C2×#95—531no—
454C2×#95C2×D5311yescharacteristic
455C2×#95C2×D5311yescharacteristic
456C53C2×#264311yescharacteristic, complemented, Sylow
457C25—531no—
458C25C22×D5311yescharacteristic
459C22×D4—534no—
460C22×D4—1064no—
461C22×D4—1064no—
462C22×D4—1064no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—42no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—534no—
474C23×C4—534no—
475C23×C4—1064no—
476C23×C4—1064no—
477C23×C4—2122no—
478C23×C4—2122no—
479C23×C4—2122no—
480C23×C4—2122no—
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C23×C4C22×D5311yescharacteristic
484C23×C4C22×D5311yescharacteristic
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5311yescharacteristic
487C23×C4C22×D5314yes—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—534no—
491C2×C4⋊C4—534no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—534no—
494C2×C4⋊C4—2122no—
495C2×C4⋊C4—2122no—
496C2×C4⋊C4—2122no—
497C2×C4⋊C4—2122no—
498C2×C4⋊C4C22×D5314yes—
499C2×C4⋊C4C22×D5314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—534no—
505C2×C22⋊C4—534no—
506C2×C22⋊C4—534no—
507C2×C22⋊C4—534no—
508C2×C22⋊C4—534no—
509C2×C22⋊C4—1064no—
510C2×C22⋊C4—2122no—
511C2×C22⋊C4—2122no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4—2122no—
516C2×C22⋊C4C22×D5314yes—
517C2×C22⋊C4C22×D5314yes—
518#95—534no—
519#95—534no—
520#95—534no—
521#95—534no—
522#95—534no—
523#95—534no—
524#95—534no—
525#95—534no—
526#95—534no—
527#95—534no—
528#95—534no—
529#95—534no—
530#95—534no—
531#95—534no—
532#95C22×D5314yes—
533#95C22×D5314yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—532no—
539C24—1062no—
540C24—1062no—
541C24—1062no—
542C24—1062no—
543C24—1062no—
544C24—1062no—
545C24—1062no—
546C24#1171994514yes—
547C24#1171994714yes—
548C24#1171994914yes—
549C24C23×D5312yes—
550C24C23×D5311yescharacteristic
551C2×D4—1068no—
552C2×D4—1068no—
553C2×D4—1068no—
554C2×D4—21216no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—416no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—1062no—
585C22×C4—1068no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1068no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—2124no—
608C22×C4—2124no—
609C22×C4—2124no—
610C22×C4—2124no—
611C22×C4—21216no—
612C22×C4—21216no—
613C22×C4C23×D5312yes—
614C22×C4C23×D5312yes—
615C22×C4C23×D5312yes—
616C22×C4C23×D5312yes—
617C22×C4C23×D5312yes—
618C22×C4C23×D5312yes—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—2124no—
622C4⋊C4—2124no—
623C4⋊C4—2124no—
624C4⋊C4—2124no—
625C22⋊C4—28no—
626C22⋊C4—28no—
627C22⋊C4—1068no—
628C22⋊C4—2124no—
629C22⋊C4—2124no—
630C22⋊C4—2124no—
631C22⋊C4—2124no—
632C22⋊C4—2124no—
633C22⋊C4—2124no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—2124no—
652C23—2124no—
653C23—2124no—
654C23—2124no—
655C23—2124no—
656C23—2124no—
657C23—2124no—
658C23#13133212116yes—
659C23C2×#1171994714yes—
660C23C2×#1171994712yes—
661C23C2×#1171994514yes—
662C23C2×#1171994512yes—
663C23C2×#1171994914yes—
664C23C2×#1171994912yes—
665C23#1313326212yes—
666C23#1313326212yes—
667C23#1313326312yes—
668C23#1313326412yes—
669C23C24×D5311yescharacteristic
670D4—21216no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—416no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—21216no—
718C2×C4—21216no—
719C2×C4—2124no—
720C2×C4—2124no—
721C2×C4—2124no—
722C2×C4—2124no—
723C2×C4—2124no—
724C2×C4—2124no—
725C2×C4—2124no—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—232no—
733C22—4248no—
734C22—2122no—
735C22—2122no—
736C22—2122no—
737C22—2122no—
738C22—2122no—
739C22—2122no—
740C22—2122no—
741C22C2×#1313321218yes—
742C22C2×#1313321214yes—
743C22#1681120614yes—
744C22#1681120814yes—
745C22#1681121314yes—
746C22#1681121514yes—
747C22#1681121714yes—
748C22#1681122214yes—
749C22C22×#1171994711yescharacteristic
750C22C22×#1171994511yescharacteristic
751C22C22×#1171994911yescharacteristic
752C22C2×#1313326211yescharacteristic
753C22C2×#1313326211yescharacteristic
754C22C2×#1313326311yescharacteristic
755C22C2×#1313326411yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—2122no—
763C4—2122no—
764C4—2122no—
765C4—2122no—
766C4—2122no—
767C4—2122no—
768C4—2122no—
769C2—28no—
770C2—4242no—
771C2#2028067118yesdirect product factor
772C2C22×#1313321211yescharacteristic
773C2C2×#1681120611yescharacteristic
774C2C2×#1681120811yescharacteristic
775C2C2×#1681121311yescharacteristic
776C2C2×#1681121511yescharacteristic
777C2C2×#1681121711yescharacteristic
778C2C2×#1681122211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53C2×#2643
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #20280671C2direct (N × H)
2. C2×C53⋊#401C2semidirect
3. C2×#16810565C2semidirect
4. C2×#16810562C2semidirect
5. C2×#16810561C2semidirect
6. C2×#16810552C2semidirect
7. C2×#16810550C2semidirect
8. C2×#16810549C2semidirect
9. C2×#16810545C2semidirect
13. C2×#16810498C2semidirect
14. C2×#16810495C2semidirect
15. C22×#13133124C2semidirect
16. C2×C53×#385C2semidirect
31. C53⋊#401C22semidirect
32. #16810565C22semidirect
33. #16810562C22semidirect
34. #16810561C22semidirect
35. #16810552C22semidirect
36. #16810550C22semidirect
37. #16810549C22semidirect
38. #16810545C22semidirect
42. #16810498C22semidirect
43. #16810495C22semidirect
58. C2×#13133124C22semidirect
64. C53×#385C22semidirect
394. C2×#385D53semidirect
397. C2×C53#2643semidirect
438. #385C2×D53semidirect
456. C53C2×#2643semidirect
771. C2#20280671direct (N × H)

Maximal subgroups

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

subgroupindex
#202806712
C2×C53⋊#4012
C2×#168105652
C2×#168105622
C2×#168105612
C2×#168105522
C2×#168105502
C2×#168105492
C2×#168105452
C2×#168105022
C2×#168105002
C2×#168104982
C2×#168104952
C22×#131331242
C2×C53×#3852
C2×#264353