Finite Group Databasebeta

← C2×#520270 #72298792

Subgroups — C2×#520270 #72298792

Order 1024.

79517 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#2847C211yesmaximal, characteristic
3C22×#2361C213yesmaximal, complemented
4C22×C4×#120C212yesmaximal, complemented
5C2×#14694C212yesmaximal, complemented
6#520270C2132yesmaximal, direct product factor
7C2×#14137C213yesmaximal, complemented
8C2×#14130C213yesmaximal, complemented
9C2×#14019C216yesmaximal, complemented
10C2×#14015C216yesmaximal, complemented
11C2×C22⋊C4×C4⋊C4C213yesmaximal, complemented
12C2×C4×#379C211yesmaximal, characteristic, complemented
13C26×C4C2211yescharacteristic
14C26×C4C2212yes—
15C23×#121C2213yes—
16C23×#120C2212yes—
17C23×C4×D4C2216yes—
18C23×C4×D4C2211yescharacteristic, complemented
19C24×C4⋊C4—248no—
20C24×C4⋊C4C2213yes—
21C24×C4⋊C4C2216yes—
22C24×C4⋊C4C2213yes—
23C24×C4⋊C4C22116yescomplemented
24C2×#2847C4132yescomplemented
25C2×#2847C22116yes—
26C2×#2361—248no—
27C2×#2361C22148yescomplemented
28C2×C4×#120—232no—
29C2×C4×#120C22132yescomplemented
30C22×#390C2213yescomplemented
31C22×#389C2213yescomplemented
32C22×#388C2216yescomplemented
33C22×#386C2216yes—
34C22×#386C2216yes—
35C22×#386C2216yes—
36C22×#386C2216yes—
37C22×#385C2216yes—
38C22×#385C2216yescomplemented
39C22×#380C2213yes—
40C22×#379C2211yescharacteristic
41C22×#379C2211yescharacteristic
42C22×C4×C4⋊C4C2213yescomplemented
43C22×C4×C22⋊C4C2213yes—
44C22×C4×C22⋊C4C2213yes—
45C22×C4×C22⋊C4C2216yes—
46#14694C22132yescomplemented
47#14137C22148yescomplemented
48#14130C22148yescomplemented
49#14019C22196yescomplemented
50#14015C22196yescomplemented
51C2×#1444C2216yescomplemented
52C2×#1442C2216yescomplemented
53C2×#1439C22112yescomplemented
54C22⋊C4×C4⋊C4C22148yescomplemented
55C4×#379C22116yescomplemented
56C2×#1436C22112yescomplemented
57C2×C4⋊#95C2216yescomplemented
58C2×C22⋊#95C2216yes—
59C2×C22⋊#95C2213yes—
60C2×C22⋊#95C2216yes—
61C2×C22⋊#95C2213yes—
62C27C2311yescharacteristic
63C24×D4C2316yes—
64C24×D4C2311yescharacteristic
65C25×C4—224no—
66C25×C4—224no—
67C25×C4—248no—
68C25×C4—216no—
69C25×C4—424no—
70C25×C4C2×C4116yescomplemented
71C25×C4C2313yes—
72C25×C4C2318yes—
73C25×C4C2316yes—
74C25×C4C23116yes—
75C25×C4C2312yes—
76C25×C4C2316yes—
77C25×C4C2313yes—
78C22×#121—224no—
79C22×#121—224no—
80C22×#121C2×C4148yescomplemented
81C22×#121C23124yes—
82C22×#120—216no—
83C22×#120—216no—
84C22×#120C2×C4132yescomplemented
85C22×#120C23116yes—
86C22×C4×D4—248no—
87C22×C4×D4—224no—
88C22×C4×D4—248no—
89C22×C4×D4—424no—
90C22×C4×D4C23148yes—
91C22×C4×D4C2318yescomplemented
92C23×C4⋊C4—2512no—
93C23×C4⋊C4—248no—
94C23×C4⋊C4—224no—
95C23×C4⋊C4—296no—
96C23×C4⋊C4—248no—
97C23×C4⋊C4—248no—
98C23×C4⋊C4—2384no—
99C23×C4⋊C4D4148yescomplemented
100C23×C4⋊C4C2316yes—
101C23×C4⋊C4C23124yes—
102C23×C4⋊C4C23148yes—
103C23×C4⋊C4C2316yes—
104C23×C4⋊C4C2313yes—
105C23×C4⋊C4C2313yes—
106C23×C4⋊C4C2316yes—
107C23×C4⋊C4C23124yes—
108C23×C4⋊C4C2311yescharacteristic
109C23×C22⋊C4C2312yes—
110C23×C22⋊C4C2313yes—
111C23×C22⋊C4C2313yes—
112C23×C22⋊C4C2316yes—
113C23×C22⋊C4C2316yes—
114C23×C22⋊C4C2316yes—
115C23×C22⋊C4C2313yes—
116C23×C22⋊C4C2313yes—
117C23×C22⋊C4C2316yes—
118C23×C42C2311yescharacteristic
119C23×C42C2313yes—
120C23×C42C2316yes—
121#2847C2×C41256yescomplemented
122#2361—2384no—
123C4×#120—2256no—
124C2×#390—224no—
125C2×#390C23124yescomplemented
126C2×#389—224no—
127C2×#389C23124yescomplemented
128C2×#388—248no—
129C2×#388C23148yescomplemented
130C2×#386—248no—
131C2×#386—248no—
132C2×#386—424no—
133C2×#386C2×C4196yescomplemented
134C2×#386C23148yes—
135C2×#386C23148yes—
136C2×#386C23148yes—
137C2×#386C23148yes—
138C2×#385—248no—
139C2×#385—248no—
140C2×#385C23148yes—
141C2×#385C23148yescomplemented
142C2×#380C2×C4148yescomplemented
143C2×#380C23124yes—
144C2×#379—28no—
145C2×#379D4116yescomplemented
146C2×#379C2318yes—
147C2×#379C2318yes—
148C2×C4×C4⋊C4—224no—
149C2×C4×C4⋊C4C23124yescomplemented
150C2×C4×C22⋊C4—224no—
151C2×C4×C22⋊C4—224no—
152C2×C4×C22⋊C4—248no—
153C2×C4×C22⋊C4C23124yes—
154C2×C4×C22⋊C4C23124yes—
155C2×C4×C22⋊C4C23148yes—
156C22×#95C2316yes—
157C22×#95C23112yes—
158C22×#95C2313yes—
159C22×#95C2316yes—
160C22×#95C2313yes—
161C22×#95C2316yes—
162C22×#95C23112yes—
163C22×#95C2316yes—
164#1444C23148yescomplemented
165#1442C23148yescomplemented
166#1439C23196yescomplemented
167#1436C23196yescomplemented
168C4⋊#95C23148yescomplemented
169C22⋊#95C23148yes—
170C22⋊#95C23148yes—
171C22⋊#95C23124yes—
172C22⋊#95C23124yes—
173C26—212no—
174C26—212no—
175C26—212no—
176C26—212no—
177C26C22×C418yes—
178C26C2×D418yes—
179C26#4118yes—
180C26C2412yes—
181C26C2414yes—
182C26C2413yes—
183C23×D4—224no—
184C23×D4—224no—
185C23×D4—224no—
186C23×D4—224no—
187C23×D4—224no—
188C23×D4—224no—
189C23×D4—212no—
190C23×D4—212no—
191C23×D4C22×C4148yes—
192C23×D4C22×C418yescomplemented
193C23×D4C24124yes—
194C23×D4C2414yes—
195C24×C4—2384no—
196C24×C4—2128no—
197C24×C4—212no—
198C24×C4—212no—
199C24×C4—2384no—
200C24×C4—224no—
201C24×C4—296no—
202C24×C4—224no—
203C24×C4—224no—
204C24×C4—296no—
205C24×C4—224no—
206C24×C4—2256no—
207C24×C4—224no—
208C24×C4—224no—
209C24×C4—224no—
210C24×C4—248no—
211C24×C4—2192no—
212C24×C4—248no—
213C24×C4—224no—
214C24×C4—264no—
215C24×C4—224no—
216C24×C4—28no—
217C24×C4—224no—
218C24×C4—424no—
219C24×C4—424no—
220C24×C4—496no—
221C24×C4—412no—
222C24×C4—4384no—
223C24×C4—4384no—
224C24×C4C22×C4124yes—
225C24×C4C22×C4124yes—
226C24×C4C22×C4164yescomplemented
227C24×C4C2×D4148yes—
228C24×C4C2×D4124yes—
229C24×C4#41124yes—
230C24×C4C2411yescharacteristic
231C24×C4C2413yes—
232C24×C4C24112yes—
233C24×C4C2416yes—
234C24×C4C2416yes—
235C24×C4C2411yescharacteristic
236C24×C4C2413yes—
237C24×C4C24124yes—
238C24×C4C2418yes—
239C24×C4C24124yes—
240C24×C4C24112yes—
241C24×C4C2413yes—
242C24×C4C2412yes—
243C24×C4C2411yescharacteristic
244C2×#121—2384no—
245C2×#121—296no—
246C2×#121—296no—
247C2×#121C22×C41192yescomplemented
248C2×#120—2256no—
249C2×#120—264no—
250C2×#120—264no—
251C2×#120C22×C41128yescomplemented
252C2×C4×D4—2192no—
253C2×C4×D4—296no—
254C2×C4×D4—2192no—
255C2×C4×D4—496no—
256C2×C4×D4—4384no—
257C2×C4×D4—464no—
258C22×C4⋊C4—2768no—
259C22×C4⋊C4—2384no—
260C22×C4⋊C4—22048no—
261C22×C4⋊C4—248no—
262C22×C4⋊C4—2192no—
263C22×C4⋊C4—224no—
264C22×C4⋊C4—296no—
265C22×C4⋊C4—248no—
266C22×C4⋊C4—224no—
267C22×C4⋊C4—212no—
268C22×C4⋊C4—212no—
269C22×C4⋊C4—2384no—
270C22×C4⋊C4—2384no—
271C22×C4⋊C4—2192no—
272C22×C4⋊C4—2192no—
273C22×C4⋊C4—224no—
274C22×C4⋊C4—224no—
275C22×C4⋊C4—412no—
276C22×C4⋊C4C22×C4124yescomplemented
277C22×C4⋊C4C2×D4148yes—
278C22×C4⋊C4C2×D4124yes—
279C22×C4⋊C4C2×D4124yes—
280C22×C4⋊C4C2×D41192yescomplemented
281C22×C4⋊C4C24124yes—
282C22×C4⋊C4C24124yes—
283C22×C4⋊C4C24112yes—
284C22×C4⋊C4C24112yes—
285C22×C4⋊C4C24124yes—
286C22×C4⋊C4C2414yes—
287C22×C22⋊C4—212no—
288C22×C22⋊C4—224no—
289C22×C22⋊C4—224no—
290C22×C22⋊C4—212no—
291C22×C22⋊C4—212no—
292C22×C22⋊C4—212no—
293C22×C22⋊C4—224no—
294C22×C22⋊C4—224no—
295C22×C22⋊C4—212no—
296C22×C22⋊C4—212no—
297C22×C22⋊C4—212no—
298C22×C22⋊C4—212no—
299C22×C22⋊C4—212no—
300C22×C22⋊C4—212no—
301C22×C22⋊C4—224no—
302C22×C22⋊C4—224no—
303C22×C22⋊C4—224no—
304C22×C22⋊C4—224no—
305C22×C22⋊C4—412no—
306C22×C22⋊C4—424no—
307C22×C22⋊C4C22×C4148yes—
308C22×C22⋊C4C22×C4148yescomplemented
309C22×C22⋊C4C2×D4124yes—
310C22×C22⋊C4C2×D4124yes—
311C22×C22⋊C4C2418yes—
312C22×C22⋊C4C24112yes—
313C22×C22⋊C4C24112yes—
314C22×C22⋊C4C24124yes—
315C22×C22⋊C4C24124yes—
316C22×C22⋊C4C24124yes—
317C22×C22⋊C4C24112yes—
318C22×C22⋊C4C24112yes—
319C22×C22⋊C4C24124yes—
320C22×C42—224no—
321C22×C42—212no—
322C22×C42—224no—
323C22×C42—212no—
324C22×C42—224no—
325C22×C42—412no—
326C22×C42C2414yes—
327C22×C42C24112yes—
328C22×C42C24124yes—
329#390—296no—
330#389—296no—
331#388—2192no—
332#386—2192no—
333#386—2192no—
334#386—496no—
335#386C22×C41384yescomplemented
336#385—2192no—
337#385—2192no—
338#380C22×C41192yescomplemented
339#379—232no—
340#379C2×D4164yescomplemented
341C4×C4⋊C4—296no—
342C4×C22⋊C4—296no—
343C4×C22⋊C4—296no—
344C4×C22⋊C4—2192no—
345C2×#95—212no—
346C2×#95—248no—
347C2×#95—212no—
348C2×#95—224no—
349C2×#95—224no—
350C2×#95—224no—
351C2×#95—424no—
352C2×#95C22×C4148yescomplemented
353C2×#95C24124yes—
354C2×#95C24124yes—
355C2×#95C24112yes—
356C2×#95C24124yes—
357C2×#95C24112yes—
358C2×#95C24148yes—
359C2×#95C24148yes—
360C2×#95C24124yes—
361C25—232no—
362C25—296no—
363C25—296no—
364C25—296no—
365C25—2192no—
366C25—296no—
367C25—296no—
368C25—296no—
369C25—296no—
370C25—296no—
371C25—296no—
372C25—224no—
373C25—212no—
374C25—224no—
375C25—212no—
376C25—224no—
377C25—212no—
378C25—224no—
379C25—212no—
380C25—212no—
381C25—24no—
382C25—212no—
383C25—24no—
384C25—212no—
385C25—212no—
386C25C4×D4164yescomplemented
387C25C23×C418yes—
388C25C23×C4116yes—
389C25C23×C4112yes—
390C25C22×D4116yes—
391C25C22×D4112yes—
392C25C22×D4112yes—
393C25C2×#41116yes—
394C25C2×#41112yes—
395C25C2×#41112yes—
396C25H(5,𝔽2)112yes—
397C252−1+4112yes—
398C25C2514yes—
399C25C2516yes—
400C25C2511yescharacteristic
401C22×D4—2192no—
402C22×D4—2192no—
403C22×D4—2192no—
404C22×D4—248no—
405C22×D4—248no—
406C22×D4—248no—
407C22×D4—248no—
408C22×D4—248no—
409C22×D4—248no—
410C22×D4—296no—
411C22×D4—224no—
412C22×D4—224no—
413C22×D4—496no—
414C22×D4—496no—
415C22×D4—496no—
416C22×D4—496no—
417C22×D4—416no—
418C22×D4—448no—
419C22×D4C23×C4196yes—
420C22×D4C23×C4116yescomplemented
421C23×C4—296no—
422C23×C4—2256no—
423C23×C4—2192no—
424C23×C4—296no—
425C23×C4—2768no—
426C23×C4—22048no—
427C23×C4—296no—
428C23×C4—224no—
429C23×C4—212no—
430C23×C4—24no—
431C23×C4—224no—
432C23×C4—212no—
433C23×C4—212no—
434C23×C4—2192no—
435C23×C4—2192no—
436C23×C4—2768no—
437C23×C4—296no—
438C23×C4—296no—
439C23×C4—2192no—
440C23×C4—248no—
441C23×C4—248no—
442C23×C4—248no—
443C23×C4—248no—
444C23×C4—2192no—
445C23×C4—2512no—
446C23×C4—2192no—
447C23×C4—26no—
448C23×C4—212no—
449C23×C4—26no—
450C23×C4—212no—
451C23×C4—212no—
452C23×C4—248no—
453C23×C4—224no—
454C23×C4—248no—
455C23×C4—212no—
456C23×C4—212no—
457C23×C4—212no—
458C23×C4—26no—
459C23×C4—26no—
460C23×C4—212no—
461C23×C4—224no—
462C23×C4—212no—
463C23×C4—248no—
464C23×C4—212no—
465C23×C4—212no—
466C23×C4—2192no—
467C23×C4—296no—
468C23×C4—296no—
469C23×C4—26no—
470C23×C4—26no—
471C23×C4—248no—
472C23×C4—22no—
473C23×C4—26no—
474C23×C4—212no—
475C23×C4—212no—
476C23×C4—248no—
477C23×C4—26no—
478C23×C4—26no—
479C23×C4—216no—
480C23×C4—248no—
481C23×C4—496no—
482C23×C4—448no—
483C23×C4—448no—
484C23×C4—424no—
485C23×C4—496no—
486C23×C4—4192no—
487C23×C4—4192no—
488C23×C4—4192no—
489C23×C4—4768no—
490C23×C4—4192no—
491C23×C4—4768no—
492C23×C4—42048no—
493C23×C4—496no—
494C23×C4—496no—
495C23×C4—432no—
496C23×C4—848no—
497C23×C4C4×D41192yescomplemented
498C23×C4C23×C4124yes—
499C23×C4C23×C4148yes—
500C23×C4C23×C4112yes—
501C23×C4C23×C4148yes—
502C23×C4C23×C414yes—
503C23×C4C22×D4112yes—
504C23×C4C22×D4124yes—
505C23×C4C22×D414yes—
506C23×C4C22×D4196yes—
507C23×C4C22×D4112yes—
508C23×C4C22×D4148yes—
509C23×C4C22×D4124yes—
510C23×C4C22×D4112yes—
511C23×C4C2×#41112yes—
512C23×C4C2×#41148yes—
513C23×C4C2×#41112yes—
514C23×C4C2512yes—
515C23×C4C2516yes—
516C23×C4C25112yes—
517C23×C4C2516yes—
518C23×C4C2512yes—
519C23×C4C25112yes—
520C23×C4C2516yes—
521C23×C4C2514yes—
522C23×C4C2512yes—
523#121—2768no—
524#120—2512no—
525C4×D4—4768no—
526C4×D4—4128no—
527C2×C4⋊C4—2192no—
528C2×C4⋊C4—21536no—
529C2×C4⋊C4—2768no—
530C2×C4⋊C4—296no—
531C2×C4⋊C4—2192no—
532C2×C4⋊C4—296no—
533C2×C4⋊C4—296no—
534C2×C4⋊C4—248no—
535C2×C4⋊C4—296no—
536C2×C4⋊C4—248no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—2768no—
540C2×C4⋊C4—248no—
541C2×C4⋊C4—248no—
542C2×C4⋊C4—424no—
543C2×C4⋊C4—496no—
544C2×C4⋊C4#120164yescomplemented
545C2×C4⋊C4C23×C4148yescomplemented
546C2×C4⋊C4C22×D4196yes—
547C2×C4⋊C4C22×D4148yes—
548C2×C4⋊C4C22×D4148yes—
549C2×C22⋊C4—2192no—
550C2×C22⋊C4—296no—
551C2×C22⋊C4—296no—
552C2×C22⋊C4—224no—
553C2×C22⋊C4—248no—
554C2×C22⋊C4—248no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—2192no—
559C2×C22⋊C4—248no—
560C2×C22⋊C4—248no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—248no—
568C2×C22⋊C4—248no—
569C2×C22⋊C4—248no—
570C2×C22⋊C4—248no—
571C2×C22⋊C4—424no—
572C2×C22⋊C4—496no—
573C2×C22⋊C4—448no—
574C2×C22⋊C4—448no—
575C2×C22⋊C4—432no—
576C2×C22⋊C4—448no—
577C2×C22⋊C4—848no—
578C2×C22⋊C4C23×C4196yes—
579C2×C22⋊C4C23×C4196yescomplemented
580C2×C22⋊C4C22×D4148yes—
581C2×C22⋊C4C22×D4148yes—
582C2×C42—248no—
583C2×C42—224no—
584C2×C42—248no—
585C2×C42—224no—
586C2×C42—248no—
587C2×C42—424no—
588C2×C42—496no—
589C2×C42—416no—
590C2×C42—448no—
591#95—224no—
592#95—296no—
593#95—224no—
594#95—248no—
595#95—248no—
596#95—248no—
597#95—448no—
598#95C23×C4196yescomplemented
599C24—232no—
600C24—296no—
601C24—2256no—
602C24—296no—
603C24—2256no—
604C24—2768no—
605C24—2192no—
606C24—296no—
607C24—2768no—
608C24—2256no—
609C24—2768no—
610C24—212no—
611C24—212no—
612C24—212no—
613C24—212no—
614C24—2768no—
615C24—296no—
616C24—248no—
617C24—296no—
618C24—248no—
619C24—224no—
620C24—224no—
621C24—248no—
622C24—296no—
623C24—248no—
624C24—296no—
625C24—248no—
626C24—296no—
627C24—248no—
628C24—296no—
629C24—248no—
630C24—224no—
631C24—248no—
632C24—224no—
633C24—248no—
634C24—248no—
635C24—248no—
636C24—248no—
637C24—212no—
638C24—24no—
639C24—212no—
640C24—24no—
641C24—212no—
642C24—212no—
643C24—248no—
644C24—216no—
645C24—248no—
646C24—48no—
647C24—424no—
648C24—424no—
649C24—424no—
650C24—424no—
651C24—424no—
652C24—424no—
653C24—424no—
654C24—448no—
655C24C2×C4×D4148yes—
656C24C2×C4×D4148yes—
657C24C2×C4×D4164yescomplemented
658C24#520148yes—
659C24D42148yes—
660C24#547148yes—
661C24#548148yes—
662C24#553148yes—
663C24C24×C418yes—
664C24C24×C4112yes—
665C24C24×C412yes—
666C24C23×D4112yes—
667C24C23×D4112yes—
668C24C23×D416yes—
669C24C23×D412yes—
670C24C22×#41112yes—
671C24C22×#41112yes—
672C24C22×#4116yes—
673C24C22×#4112yes—
674C24C2×H(5,𝔽2)112yes—
675C24C2×H(5,𝔽2)16yes—
676C24C2×2−1+4112yes—
677C24C2×2−1+416yes—
678C24C2611yescharacteristic
679C2×D4—2192no—
680C2×D4—2192no—
681C2×D4—2192no—
682C2×D4—296no—
683C2×D4—4768no—
684C2×D4—496no—
685C2×D4—496no—
686C2×D4—496no—
687C2×D4—496no—
688C2×D4—416no—
689C2×D4—448no—
690C2×D4—4128no—
691C22×C4—296no—
692C22×C4—2192no—
693C22×C4—296no—
694C22×C4—2768no—
695C22×C4—22048no—
696C22×C4—24no—
697C22×C4—212no—
698C22×C4—212no—
699C22×C4—212no—
700C22×C4—296no—
701C22×C4—248no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—248no—
705C22×C4—248no—
706C22×C4—248no—
707C22×C4—2192no—
708C22×C4—2192no—
709C22×C4—296no—
710C22×C4—296no—
711C22×C4—2192no—
712C22×C4—2768no—
713C22×C4—2192no—
714C22×C4—212no—
715C22×C4—212no—
716C22×C4—212no—
717C22×C4—26no—
718C22×C4—26no—
719C22×C4—224no—
720C22×C4—212no—
721C22×C4—212no—
722C22×C4—212no—
723C22×C4—212no—
724C22×C4—224no—
725C22×C4—26no—
726C22×C4—26no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—212no—
730C22×C4—248no—
731C22×C4—248no—
732C22×C4—248no—
733C22×C4—248no—
734C22×C4—224no—
735C22×C4—224no—
736C22×C4—248no—
737C22×C4—2192no—
738C22×C4—248no—
739C22×C4—248no—
740C22×C4—2192no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—212no—
744C22×C4—22no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—496no—
750C22×C4—496no—
751C22×C4—4192no—
752C22×C4—4192no—
753C22×C4—4768no—
754C22×C4—4192no—
755C22×C4—4192no—
756C22×C4—42048no—
757C22×C4—496no—
758C22×C4—4768no—
759C22×C4—44no—
760C22×C4—412no—
761C22×C4—424no—
762C22×C4—496no—
763C22×C4—448no—
764C22×C4—424no—
765C22×C4—424no—
766C22×C4—424no—
767C22×C4—448no—
768C22×C4—412no—
769C22×C4—412no—
770C22×C4—424no—
771C22×C4—44no—
772C22×C4—412no—
773C22×C4—412no—
774C22×C4—412no—
775C22×C4—424no—
776C22×C4—412no—
777C22×C4—412no—
778C22×C4—424no—
779C22×C4—432no—
780C22×C4—848no—
781C22×C4—8128no—
782C22×C4C2×C4×D4148yes—
783C22×C4C2×C4×D4148yes—
784C22×C4C2×C4×D41192yescomplemented
785C22×C4C2×#120132yes—
786C22×C4C2×#120116yes—
787C22×C4#525148yes—
788C22×C4C24×C4124yes—
789C22×C4C24×C4112yes—
790C22×C4C24×C414yes—
791C22×C4C23×D4112yes—
792C22×C4C23×D4124yes—
793C22×C4C23×D414yes—
794C22×C4C23×D4112yes—
795C22×C4C23×D4124yes—
796C22×C4C23×D4112yes—
797C22×C4C22×#41112yes—
798C22×C4C22×#41112yes—
799C4⋊C4—2192no—
800C4⋊C4—296no—
801C4⋊C4—2192no—
802C4⋊C4—296no—
803C4⋊C4—496no—
804C4⋊C4C2×#120164yescomplemented
805C22⋊C4—2192no—
806C22⋊C4—296no—
807C22⋊C4—296no—
808C22⋊C4—2192no—
809C22⋊C4—496no—
810C22⋊C4—448no—
811C22⋊C4—448no—
812C22⋊C4—432no—
813C22⋊C4—848no—
814C42—496no—
815C42—416no—
816C42—448no—
817C23—2128no—
818C23—2128no—
819C23—2384no—
820C23—22048no—
821C23—2384no—
822C23—2128no—
823C23—2384no—
824C23—296no—
825C23—2192no—
826C23—212no—
827C23—224no—
828C23—224no—
829C23—224no—
830C23—224no—
831C23—212no—
832C23—224no—
833C23—2192no—
834C23—2384no—
835C23—296no—
836C23—2192no—
837C23—224no—
838C23—224no—
839C23—212no—
840C23—212no—
841C23—224no—
842C23—296no—
843C23—296no—
844C23—2192no—
845C23—224no—
846C23—224no—
847C23—296no—
848C23—224no—
849C23—224no—
850C23—296no—
851C23—224no—
852C23—28no—
853C23—224no—
854C23—412no—
855C23—424no—
856C23—412no—
857C23—496no—
858C23—496no—
859C23—44no—
860C23—412no—
861C23—412no—
862C23—412no—
863C23—432no—
864C23—412no—
865C23—412no—
866C23—848no—
867C23—816no—
868C23—848no—
869C23—816no—
870C23#23611192yescomplemented
871C23C22×C4×D4124yes—
872C23C22×C4×D4124yes—
873C23C22×C4×D414yes—
874C23C22×C4×D4112yes—
875C23C2×#520124yes—
876C23C2×#520112yes—
877C23C22×#12014yes—
878C23C2×#525112yes—
879C23C2×D42124yes—
880C23C2×D42112yes—
881C23C2×#547124yes—
882C23C2×#547112yes—
883C23C2×#548124yes—
884C23C2×#548112yes—
885C23C2×#553124yes—
886C23C2×#553112yes—
887C23#3484112yes—
888C23#3486112yes—
889C23#3492124yes—
890C23C25×C411yescharacteristic
891C23C24×D413yes—
892C23C24×D411yescharacteristic
893C23C23×#4113yes—
894C23C23×#4111yescharacteristic
895C23C22×H(5,𝔽2)13yes—
896C23C22×2−1+413yes—
897D4—4384no—
898D4—464no—
899C2×C4—2384no—
900C2×C4—224no—
901C2×C4—224no—
902C2×C4—212no—
903C2×C4—212no—
904C2×C4—224no—
905C2×C4—224no—
906C2×C4—296no—
907C2×C4—264no—
908C2×C4—2384no—
909C2×C4—224no—
910C2×C4—224no—
911C2×C4—224no—
912C2×C4—224no—
913C2×C4—224no—
914C2×C4—212no—
915C2×C4—212no—
916C2×C4—224no—
917C2×C4—224no—
918C2×C4—4384no—
919C2×C4—4384no—
920C2×C4—448no—
921C2×C4—424no—
922C2×C4—46no—
923C2×C4—412no—
924C2×C4—46no—
925C2×C4—496no—
926C2×C4—42no—
927C2×C4—46no—
928C2×C4—412no—
929C2×C4—424no—
930C2×C4—412no—
931C2×C4—412no—
932C2×C4—412no—
933C2×C4—496no—
934C2×C4—416no—
935C2×C4—46no—
936C2×C4—412no—
937C2×C4—46no—
938C2×C4—42no—
939C2×C4—46no—
940C2×C4—46no—
941C2×C4—46no—
942C2×C4—412no—
943C2×C4—864no—
944C2×C4—88no—
945C2×C4—824no—
946C2×C4C4×#120164yescomplemented
947C2×C4C22×C4×D4124yes—
948C2×C4C22×C4×D4124yes—
949C2×C4C22×#120116yes—
950C2×C4C22×#12018yes—
951C2×C4C2×#525124yes—
952C22—2512no—
953C22—224no—
954C22—248no—
955C22—224no—
956C22—2384no—
957C22—248no—
958C22—224no—
959C22—224no—
960C22—248no—
961C22—224no—
962C22—224no—
963C22—248no—
964C22—424no—
965C22—48no—
966C22—424no—
967C22—864no—
968C22—84no—
969C22—812no—
970C22—84no—
971C22—812no—
972C22C2×C4×#12018yes—
973C22C2×#2361124yes—
974C22C2×#2361148yescomplemented
975C22#34200124yes—
976C22D4×#12018yes—
977C22#36103124yes—
978C22#3657518yes—
979C22#36581124yes—
980C22C23×C4×D413yes—
981C22C23×C4×D411yescharacteristic
982C22C22×#52013yes—
983C22C23×#12011yescharacteristic
984C22C22×#52513yes—
985C22C22×D4213yes—
986C22C22×#54813yes—
987C22C22×#54713yes—
988C22C22×#55313yes—
989C22C2×#348413yes—
990C22C2×#349216yes—
991C22C2×#348613yes—
992C4—224no—
993C4—216no—
994C4—424no—
995C4—424no—
996C4—44no—
997C4—412no—
998C4—82no—
999C4—86no—
1000C4C2×C4×#120116yescomplemented
1001C2—248no—
1002C2—88no—
1003C2#520270116yesdirect product factor
1004C2C22×C4×#12011yescharacteristic
1005C2C22×#236113yes—
1006C2C2×#3420013yes—
1007C2C2×D4×#12011yescharacteristic
1008C2C2×#3610313yes—
1009C2C2×#3657511yescharacteristic
1010C2C2×#3658113yes—
subgroupG/H
center, socleC25C25
commutatorC23C25×C4
Frattini, cosocleC24C26
prime radicalC22×#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C25×C4⋊C4C2semidirect
3. C22×#2361C2semidirect
4. C22×C4×#120C2semidirect
5. C2×#14694C2semidirect
6. #520270C2direct (N × H)
7. C2×#14137C2semidirect
8. C2×#14130C2semidirect
9. C2×#14019C2semidirect
10. C2×#14015C2semidirect
11. C2×C22⋊C4×C4⋊C4C2semidirect
12. C2×C4×#379C2semidirect
18. C23×C4×D4C22semidirect
23. C24×C4⋊C4C22semidirect
24. C2×#2847C4semidirect
27. C2×#2361C22semidirect
29. C2×C4×#120C22semidirect
30. C22×#390C22semidirect
31. C22×#389C22semidirect
32. C22×#388C22semidirect
38. C22×#385C22semidirect
42. C22×C4×C4⋊C4C22semidirect
46. #14694C22semidirect
47. #14137C22semidirect
48. #14130C22semidirect
49. #14019C22semidirect
50. #14015C22semidirect
51. C2×#1444C22semidirect
52. C2×#1442C22semidirect
53. C2×#1439C22semidirect
54. C22⋊C4×C4⋊C4C22semidirect
55. C4×#379C22semidirect
56. C2×#1436C22semidirect
57. C2×C4⋊#95C22semidirect
70. C25×C4C2×C4semidirect
80. C22×#121C2×C4semidirect
84. C22×#120C2×C4semidirect
91. C22×C4×D4C23semidirect
99. C23×C4⋊C4D4semidirect
121. #2847C2×C4semidirect
125. C2×#390C23semidirect
127. C2×#389C23semidirect
129. C2×#388C23semidirect
133. C2×#386C2×C4semidirect
141. C2×#385C23semidirect
142. C2×#380C2×C4semidirect
145. C2×#379D4semidirect
149. C2×C4×C4⋊C4C23semidirect
164. #1444C23semidirect
165. #1442C23semidirect
166. #1439C23semidirect
167. #1436C23semidirect
168. C4⋊#95C23semidirect
192. C23×D4C22×C4semidirect
226. C24×C4C22×C4semidirect
247. C2×#121C22×C4semidirect
251. C2×#120C22×C4semidirect
276. C22×C4⋊C4C22×C4semidirect
280. C22×C4⋊C4C2×D4semidirect
308. C22×C22⋊C4C22×C4semidirect
335. #386C22×C4semidirect
338. #380C22×C4semidirect
340. #379C2×D4semidirect
352. C2×#95C22×C4semidirect
386. C25C4×D4semidirect
420. C22×D4C23×C4semidirect
497. C23×C4C4×D4semidirect
544. C2×C4⋊C4#120semidirect
545. C2×C4⋊C4C23×C4semidirect
579. C2×C22⋊C4C23×C4semidirect
598. #95C23×C4semidirect
657. C24C2×C4×D4semidirect
784. C22×C4C2×C4×D4semidirect
804. C4⋊C4C2×#120semidirect
870. C23#2361semidirect
946. C2×C4C4×#120semidirect
974. C22C2×#2361semidirect
1000. C4C2×C4×#120semidirect
1003. C2#520270direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C4⋊C42
C22×#28472
C22×#23612
C22×C4×#1202
C2×#146942
#5202702
C2×#141372
C2×#141302
C2×#140192
C2×#140152
C2×C22⋊C4×C4⋊C42
C2×C4×#3792