Finite Group Databasebeta

← C2×#20280687 #27550535

Subgroups — C2×#20280687 #27550535

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280687C2116yesmaximal, direct product factor
2C2×#16810564C211yesmaximal, characteristic, complemented
3C2×#16810564C211yesmaximal, characteristic, complemented
4C2×#16810563C211yesmaximal, characteristic, complemented
5C2×#16810561C211yesmaximal, characteristic, complemented
6C2×#16810557C211yesmaximal, characteristic, complemented
7C2×#16810556C211yesmaximal, characteristic, complemented
8C2×#16810554C211yesmaximal, characteristic, complemented
9C2×#16810553C211yesmaximal, characteristic, complemented
10C2×#16810498C211yesmaximal, characteristic
11C2×#16810496C211yesmaximal, characteristic
12C2×#16810495C211yesmaximal, characteristic
13C2×#16810481C211yesmaximal, characteristic
14C2×#16810481C211yesmaximal, characteristic
15C22×#13133124C211yesmaximal, characteristic
16C2×C53×#385C211yesmaximal, characteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31#16810564C2218yescomplemented
32#16810564C2218yescomplemented
33#16810563C2218yescomplemented
34#16810561C2218yescomplemented
35#16810557C2218yescomplemented
36#16810556C2218yescomplemented
37#16810554C2218yescomplemented
38#16810553C2218yescomplemented
39#16810498C2218yes—
40#16810496C2218yes—
41#16810495C2218yes—
42#16810481C2218yes—
43#16810481C2218yes—
44C2×#13133124C2218yes—
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×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C53×#385C2218yes—
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C23×Dic53—24no—
68C23×Dic53—42no—
69C23×Dic53—42no—
70C23×Dic53—42no—
71C23×Dic53—42no—
72C23×Dic53Q818yes—
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2314yes—
82C23×Dic53C2314yes—
83C2×C4⋊Dic53—42no—
84C2×C4⋊Dic53—42no—
85C2×C4⋊Dic53C2314yes—
86C2×C4⋊Dic53C2314yes—
87C2×#11719919—42no—
88C2×#11719919—42no—
89C2×#11719919—42no—
90C2×#11719919—42no—
91C2×#11719919—42no—
92C2×#11719919—42no—
93C2×#11719919—42no—
94C2×#11719919—42no—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×C22⋊Dic53—24no—
104C2×C22⋊Dic53—24no—
105C2×C22⋊Dic53C2314yes—
106C2×C22⋊Dic53C2314yes—
107#13133124C2314yes—
108#13133124C2314yes—
109#13133124C2314yes—
110#13133124C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121C25×C53C2311yescharacteristic
122C23×C4×C53—24no—
123C23×C4×C53—42no—
124C23×C4×C53—42no—
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2314yes—
132C2×C4⋊C4×C53—42no—
133C2×C4⋊C4×C53—42no—
134C2×C4⋊C4×C53C2314yes—
135C2×C4⋊C4×C53C2314yes—
136C2×C22⋊C4×C53—24no—
137C2×C22⋊C4×C53—24no—
138C2×C22⋊C4×C53C2314yes—
139C2×C22⋊C4×C53C2314yes—
140#95×C53C2314yes—
141#95×C53C2314yes—
142C24×C53—22no—
143C24×C53—22no—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53C2×Q814yes—
147C24×C53#4114yes—
148C24×C53#4114yes—
149C24×C53C2412yes—
150C24×C53C2411yescharacteristic
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—28no—
156C22×C4×C53—22no—
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—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—44no—
171C22×C4×C53—44no—
172C22×C4×C53—416no—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
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—28no—
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—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—416no—
203C22×Dic53—44no—
204C22×Dic53—44no—
205C22×Dic53—44no—
206C22×Dic53—44no—
207C22×Dic53—416no—
208C22×Dic53C2×Q814yes—
209C22×Dic53C2×Q814yes—
210C22×Dic53C2×Q8116yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C4⋊C4×C53—44no—
220C4⋊C4×C53—44no—
221C22⋊C4×C53—28no—
222C22⋊C4×C53—28no—
223C22⋊Dic53—28no—
224C22⋊Dic53—28no—
225C4⋊Dic53—44no—
226C4⋊Dic53—44no—
227#11719919—44no—
228#11719919—44no—
229#11719919—44no—
230#11719919—44no—
231#11719919—44no—
232#11719919—44no—
233#11719919—44no—
234#11719919—44no—
235C23×C53—28no—
236C23×C53—28no—
237C23×C53—28no—
238C23×C53—28no—
239C23×C53—28no—
240C23×C53—28no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53#125116yes—
246C23×C53C22×Q814yes—
247C23×C53C22×Q812yes—
248C23×C53C2×#4114yes—
249C23×C53C2×#4112yes—
250C23×C53C2×#4114yes—
251C23×C53C2×#4112yes—
252C23×C53H(5,𝔽2)12yes—
253C23×C53H(5,𝔽2)12yes—
254C23×C53H(5,𝔽2)12yes—
255C23×C532−1+412yes—
256C23×C53C2511yescharacteristic
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—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—416no—
276C2×C4×C53—44no—
277C2×C4×C53—44no—
278C2×C4×C53—44no—
279C2×C4×C53—44no—
280C2×C4×C53—44no—
281C2×C4×C53—44no—
282C2×Dic53—28no—
283C2×Dic53—28no—
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—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—416no—
307C2×Dic53—416no—
308C2×Dic53—44no—
309C2×Dic53—44no—
310C2×Dic53—44no—
311C2×Dic53—44no—
312C2×Dic53—44no—
313C2×Dic53—44no—
314C2×Dic53C22×Q814yes—
315C2×Dic53C22×Q814yes—
316C2×#2646—531nomaximal, Sylow
317C22×C53—232no—
318C22×C53—24no—
319C22×C53—24no—
320C22×C53—24no—
321C22×C53—24no—
322C22×C53—24no—
323C22×C53—24no—
324C22×C53C2×#12518yes—
325C22×C53C2×#12514yes—
326C22×C53#53814yes—
327C22×C53#53814yes—
328C22×C53#53914yes—
329C22×C53#53914yes—
330C22×C53#54314yes—
331C22×C53#54414yes—
332C22×C53C23×Q811yescharacteristic
333C22×C53C22×#4111yescharacteristic
334C22×C53C22×#4111yescharacteristic
335C22×C53C2×H(5,𝔽2)11yescharacteristic
336C22×C53C2×H(5,𝔽2)11yescharacteristic
337C22×C53C2×H(5,𝔽2)11yescharacteristic
338C22×C53C2×2−1+411yescharacteristic
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53—42no—
344C4×C53—42no—
345Dic53—24no—
346Dic53—24no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353#2646—5316no—
354C2×#400—531no—
355C2×#400—531no—
356C2×#400—531no—
357C2×#400—531no—
358C2×#398—531no—
359C2×#398—531no—
360C2×#398—531no—
361C2×#398—531no—
362C2×#385—531no—
363C2×#385—531no—
364C2×#385—531no—
365C2×#385D5311yescharacteristic
366C2×#380—531no—
367C2×#380—531no—
368C22×#95—531no—
369C2×C53—28no—
370C2×C53#264618yescomplemented
371C2×C53C22×#12511yescharacteristic
372C2×C53C2×#53811yescharacteristic
373C2×C53C2×#53811yescharacteristic
374C2×C53C2×#53911yescharacteristic
375C2×C53C2×#53911yescharacteristic
376C2×C53C2×#54311yescharacteristic
377C2×C53C2×#54411yescharacteristic
378C24×C4—531no—
379C24×C4—531no—
380C24×C4C2×D5311yescharacteristic
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—531no—
384C22×C4⋊C4—531no—
385C22×C4⋊C4—531no—
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4—531no—
390C22×C4⋊C4—531no—
391C22×C4⋊C4C2×D5311yescharacteristic
392C22×C4⋊C4C2×D5311yescharacteristic
393C22×C22⋊C4—531no—
394C22×C22⋊C4—531no—
395C22×C22⋊C4C2×D5311yescharacteristic
396C22×C22⋊C4C2×D5311yescharacteristic
397#400—538no—
398#400—538no—
399#400—538no—
400#400—538no—
401#398—538no—
402#398—538no—
403#398—538no—
404#398—538no—
405#385—538no—
406#385—538no—
407#385—538no—
408#385C2×D5318yes—
409#380—538no—
410#380—538no—
411C2×#95—538no—
412C2×#95—531no—
413C2×#95—531no—
414C2×#95—531no—
415C2×#95—531no—
416C2×#95—531no—
417C2×#95—531no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95—531no—
423C2×#95—531no—
424C2×#95—531no—
425C2×#95—531no—
426C2×#95C2×D5311yescharacteristic
427C2×#95C2×D5311yescharacteristic
428C53C2×#264611yescharacteristic, complemented, Sylow
429C25C22×D5311yescharacteristic
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—538no—
436C23×C4—534no—
437C23×C4—531no—
438C23×C4—531no—
439C23×C4—531no—
440C23×C4—531no—
441C23×C4—531no—
442C23×C4—531no—
443C23×C4—534no—
444C23×C4—1064no—
445C23×C4—2122no—
446C23×C4—2122no—
447C23×C4—2122no—
448C23×C4—2122no—
449C23×C4C22×D5311yescharacteristic
450C23×C4C22×D5311yescharacteristic
451C23×C4C22×D5311yescharacteristic
452C23×C4C22×D5311yescharacteristic
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C23×C4C22×D5314yes—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—534no—
459C2×C4⋊C4—534no—
460C2×C4⋊C4—534no—
461C2×C4⋊C4—534no—
462C2×C4⋊C4—534no—
463C2×C4⋊C4—534no—
464C2×C4⋊C4—534no—
465C2×C4⋊C4—534no—
466C2×C4⋊C4—534no—
467C2×C4⋊C4—534no—
468C2×C4⋊C4—2122no—
469C2×C4⋊C4—2122no—
470C2×C4⋊C4—2122no—
471C2×C4⋊C4—2122no—
472C2×C4⋊C4—2122no—
473C2×C4⋊C4—2122no—
474C2×C4⋊C4—2122no—
475C2×C4⋊C4—2122no—
476C2×C4⋊C4—2122no—
477C2×C4⋊C4—2122no—
478C2×C4⋊C4C22×D5314yes—
479C2×C4⋊C4C22×D5314yes—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—534no—
483C2×C22⋊C4—534no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—1064no—
486C2×C22⋊C4C22×D5314yes—
487C2×C22⋊C4C22×D5314yes—
488#95—534no—
489#95—534no—
490#95—534no—
491#95—534no—
492#95—534no—
493#95—534no—
494#95—534no—
495#95—534no—
496#95—534no—
497#95—534no—
498#95—534no—
499#95—534no—
500#95—534no—
501#95—534no—
502#95C22×D5314yes—
503#95C22×D5314yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24#1171994514yes—
509C24#1171994714yes—
510C24Q8×D5314yes—
511C24C23×D5312yes—
512C24C23×D5311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—416no—
535C22×C4—534no—
536C22×C4—534no—
537C22×C4—532no—
538C22×C4—532no—
539C22×C4—5316no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—532no—
543C22×C4—532no—
544C22×C4—532no—
545C22×C4—532no—
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—1068no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—2124no—
570C22×C4—2124no—
571C22×C4—21216no—
572C22×C4—2124no—
573C22×C4—2124no—
574C22×C4—21216no—
575C22×C4C23×D5312yes—
576C22×C4C23×D5312yes—
577C22×C4C23×D5312yes—
578C22×C4C23×D5312yes—
579C22×C4C23×D5312yes—
580C22×C4C23×D5312yes—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—2124no—
584C4⋊C4—2124no—
585C4⋊C4—2124no—
586C4⋊C4—2124no—
587C4⋊C4—2124no—
588C4⋊C4—2124no—
589C4⋊C4—2124no—
590C4⋊C4—2124no—
591C4⋊C4—2124no—
592C4⋊C4—2124no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—1068no—
596C22⋊C4—1068no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23#13133207116yes—
608C23C2×Q8×D5314yes—
609C23C2×Q8×D5312yes—
610C23C2×#1171994714yes—
611C23C2×#1171994712yes—
612C23C2×#1171994514yes—
613C23C2×#1171994512yes—
614C23#1313326212yes—
615C23#1313326212yes—
616C23#1313326312yes—
617C23#1313326412yes—
618C23C24×D5311yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—416no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—534no—
645C2×C4—534no—
646C2×C4—1062no—
647C2×C4—1062no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1068no—
651C2×C4—1068no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—21216no—
671C2×C4—21216no—
672C2×C4—2124no—
673C2×C4—2124no—
674C2×C4—2124no—
675C2×C4—2124no—
676C2×C4—2124no—
677C2×C4—2124no—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—24no—
682C22—24no—
683C22—232no—
684C22—24no—
685C22C2×#1313320718yes—
686C22C2×#1313320714yes—
687C22#1681120614yes—
688C22#1681120814yes—
689C22#1681121514yes—
690C22#1681121714yes—
691C22#1681124814yes—
692C22#1681125214yes—
693C22C22×Q8×D5311yescharacteristic
694C22C22×#1171994711yescharacteristic
695C22C22×#1171994511yescharacteristic
696C22C2×#1313326211yescharacteristic
697C22C2×#1313326211yescharacteristic
698C22C2×#1313326311yescharacteristic
699C22C2×#1313326411yescharacteristic
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—1064no—
707C4—1064no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C2—28no—
715C2#2028068718yesdirect product factor
716C2C22×#1313320711yescharacteristic
717C2C2×#1681120611yescharacteristic
718C2C2×#1681120811yescharacteristic
719C2C2×#1681121511yescharacteristic
720C2C2×#1681121711yescharacteristic
721C2C2×#1681124811yescharacteristic
722C2C2×#1681125211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53C2×#2646
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #20280687C2direct (N × H)
2. C2×#16810564C2semidirect
3. C2×#16810564C2semidirect
4. C2×#16810563C2semidirect
5. C2×#16810561C2semidirect
6. C2×#16810557C2semidirect
7. C2×#16810556C2semidirect
8. C2×#16810554C2semidirect
9. C2×#16810553C2semidirect
31. #16810564C22semidirect
32. #16810564C22semidirect
33. #16810563C22semidirect
34. #16810561C22semidirect
35. #16810557C22semidirect
36. #16810556C22semidirect
37. #16810554C22semidirect
38. #16810553C22semidirect
370. C2×C53#2646semidirect
428. C53C2×#2646semidirect
715. C2#20280687direct (N × H)

Maximal subgroups

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

subgroupindex
#202806872
C2×#168105642
C2×#168105632
C2×#168105612
C2×#168105572
C2×#168105562
C2×#168105542
C2×#168105532
C2×#168104982
C2×#168104962
C2×#168104952
C2×#168104812
C22×#131331242
C2×C53×#3852
C2×#264653