Finite Group Databasebeta

← #12115358

Subgroups — #12115358

Order 1280.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65872C211yesmaximal, characteristic
2C2×C5×C8×D4C211yesmaximal, characteristic, complemented
3C2×#65300C211yesmaximal, characteristic, complemented
4#10602768C211yesmaximal, characteristic, complemented
5#10602768C211yesmaximal, characteristic, complemented
6#10602758C211yesmaximal, characteristic, complemented
7C2×#64770C211yesmaximal, characteristic, complemented
8#10601269C211yesmaximal, characteristic, complemented
9#10601266C211yesmaximal, characteristic, complemented
10#10600746C211yesmaximal, characteristic, complemented
11#10600745C211yesmaximal, characteristic, complemented
12#10600704C211yesmaximal, characteristic, complemented
13#10600703C211yesmaximal, characteristic, complemented
14#10600581C211yesmaximal, characteristic, complemented
15#10600546C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×#4085C411yescharacteristic
20C2×#4081C411yescharacteristic
21C2×C4×C22⋊D5C2211yescharacteristic
22C2×C4×C22⋊D5C2211yescharacteristic
23C2×#4072C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×#681C2211yescharacteristic
26C23×#168C2211yescharacteristic
27#65872—24no—
28#65872—24no—
29C2×#4044C411yescharacteristic
30C2×#4035C411yescharacteristic
31C2×#4032C411yescharacteristic
32C2×#4031C411yescharacteristic
33C2×#4025C411yescharacteristic
34C2×#4024C411yescharacteristic
35C2×#4018C2211yescharacteristic
36C2×C4×Dic10C2211yescharacteristic
37C5×C8×D4—24no—
38C2×C5×C4⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×C22⋊C8C2211yescharacteristic
41C2×C4×C5×C8C2211yescharacteristic
42C2×C22⋊#168C2211yescharacteristic
43C2×C22⋊#168C2211yescharacteristic
44C2×#3952C2211yescharacteristic
45C2×#3952C2211yescharacteristic
46C2×#3952C2211yescharacteristic
47C2×#3952C2211yescharacteristic
48#65300—24no—
49C2×C4⋊#168C2211yescharacteristic
50C2×#3935C2211yescharacteristic
51#64770C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64770C2211yescharacteristic
55#64770C2211yescharacteristic
56#64770C2211yescharacteristic
57#64770C2211yescharacteristic
58#64770C2211yescharacteristic
59#64770C2211yescharacteristic
60#64770C2211yescharacteristic
61#64770C2211yescharacteristic
62#64770C2211yescharacteristic
63#22470—51nomaximal, Sylow
64C22×C5×D4C2×C411yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C22×C22⋊D5C2×C411yescharacteristic
68C22×C22⋊D5C2×C411yescharacteristic
69C23×Dic5C2×C411yescharacteristic
70C23×Dic5C2×C411yescharacteristic
71C22×C4×D5C2311yescharacteristic
72C22×Dic10C2×C411yescharacteristic
73C22×C5×C8—22no—
74C22×C5×C8—22no—
75C22×C5×C8—22no—
76C22×C5×C8—22no—
77C22×C5×C8—41no—
78C22×C5×C8—41no—
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C4×C5×D4D414yes—
84C4×C5×D4D414yes—
85C2×C5×C4⋊C4C2×C411yescharacteristic
86C2×C5×C22⋊C4C2×C411yescharacteristic
87C2×C5×C22⋊C4C2×C411yescharacteristic
88C2×C42×C5C2311yescharacteristic
89C2×C22⋊Dic5C2×C411yescharacteristic
90C2×C22⋊Dic5C2×C411yescharacteristic
91C2×C22⋊Dic5C2×C411yescharacteristic
92C2×C22⋊Dic5C2×C411yescharacteristic
93#4085—24no—
94#4081—24no—
95C4×C22⋊D5—22no—
96C4×C22⋊D5—22no—
97C4×C22⋊D5—22no—
98C4×C22⋊D5—22no—
99C2×#685C2×C411yescharacteristic
100C2×#685C2×C411yescharacteristic
101C2×#685C2×C411yescharacteristic
102C2×#685C2×C411yescharacteristic
103#4072—22no—
104#4072—22no—
105C2×C4⋊Dic5C2×C411yescharacteristic
106C2×C4⋊Dic5C2×C411yescharacteristic
107C2×C4⋊Dic5C2×C411yescharacteristic
108C2×#683C2×C411yescharacteristic
109C2×#683C2×C411yescharacteristic
110C2×#683C2×C411yescharacteristic
111C2×#683C2×C411yescharacteristic
112C2×#683C2×C411yescharacteristic
113C2×#683C2×C411yescharacteristic
114C2×C4×Dic5—22no—
115C2×C4×Dic5—22no—
116C2×C4×Dic5C2×C411yescharacteristic
117C2×C4×Dic5C2×C411yescharacteristic
118C2×C4×Dic5C2311yescharacteristic
119C2×C4×Dic5C2311yescharacteristic
120C2×C4×Dic5C2311yescharacteristic
121C2×#681—22no—
122C2×#681—22no—
123C2×#681—41no—
124C22×#168—22no—
125C22×#168—22no—
126C22×#168—41no—
127C22×#168C2311yescharacteristic
128C22×#168C2311yescharacteristic
129C22×#168C2311yescharacteristic
130C22×#168C2311yescharacteristic
131#4044—24no—
132#4035—24no—
133#4032—24no—
134#4031—24no—
135#4025—24no—
136#4024—24no—
137#4018—22no—
138#4018—22no—
139C4×Dic10—22no—
140C4×Dic10—22no—
141C5×C4⋊C8—22no—
142C5×C22⋊C8—22no—
143C5×C22⋊C8—22no—
144C4×C5×C8—22no—
145C22⋊#168—22no—
146C22⋊#168—22no—
147#3952—22no—
148#3952—22no—
149#3952—41no—
150#3952—41no—
151C4⋊#168—22no—
152#3935—22no—
153C2×#529—51no—
154C2×#435—51no—
155C2×C8×D4D511yescharacteristic, complemented
156#1985—51no—
157#1984—51no—
158#1870—51no—
159#1869—51no—
160#1869—51no—
161#1869—51no—
162#1818—51no—
163#1817—51no—
164#1798—51no—
165#1750—51no—
166#1729—51no—
167C2×#336—51no—
168C24×C5C22×C411yescharacteristic
169C24×C5C22×C411yescharacteristic
170C23×D5C22×C411yescharacteristic
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4C22⋊C414yes—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5C22×C411yescharacteristic
183C22×C4×C5C22×C411yescharacteristic
184C22×C4×C5C22×C411yescharacteristic
185C22×C4×C5C22×C411yescharacteristic
186C22×C4×C5C2×D412yes—
187C22×C4×C5C2×D412yes—
188C22×C4×C5C2×D412yes—
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2411yescharacteristic
191C2×C22⋊D5—22no—
192C2×C22⋊D5—22no—
193C2×C22⋊D5—22no—
194C2×C22⋊D5—22no—
195C2×C22⋊D5—22no—
196C2×C22⋊D5—41no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—41no—
203C22×Dic5C22×C411yescharacteristic
204C22×Dic5C22×C411yescharacteristic
205C22×Dic5C22×C411yescharacteristic
206C22×Dic5C22×C411yescharacteristic
207C22×Dic5C22×C411yescharacteristic
208C22×Dic5C22×C411yescharacteristic
209C22×Dic5C22×C411yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—21no—
212C2×C4×D5—21no—
213C2×C4×D5—21no—
214C2×C4×D5—21no—
215C2×C4×D5—21no—
216C2×Dic10—22no—
217C2×Dic10—22no—
218C2×Dic10—41no—
219C2×C5×C8—21no—
220C2×C5×C8—21no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—44no—
231C2×C5×C8—44no—
232C2×C5×C8#4112yes—
233C5×C4⋊C4C22⋊C414yes—
234C5×C22⋊C4C22⋊C414yes—
235C5×C22⋊C4C22⋊C414yes—
236C42×C5C2×D412yes—
237C42×C5C2×D412yes—
238C22⋊Dic5—22no—
239C22⋊Dic5—22no—
240C22⋊Dic5—22no—
241C22⋊Dic5—22no—
242#685—22no—
243#685—22no—
244#685—22no—
245#685—22no—
246C4⋊Dic5—22no—
247C4⋊Dic5—22no—
248C4⋊Dic5—22no—
249#683—22no—
250#683—22no—
251#683—22no—
252#683—22no—
253#683—22no—
254#683—22no—
255C4×Dic5—22no—
256C4×Dic5—22no—
257C4×Dic5—21no—
258C4×Dic5—21no—
259C4×Dic5—21no—
260C4×Dic5—21no—
261C4×Dic5—21no—
262C4×Dic5—21no—
263#681—44no—
264C2×#168—21no—
265C2×#168—21no—
266C2×#168—21no—
267C2×#168—21no—
268C2×#168—21no—
269C2×#168—21no—
270C2×#168—21no—
271C2×#168—21no—
272C2×#168—21no—
273C2×#168—21no—
274C2×#168—21no—
275C2×#168—44no—
276C2×#168#4112yes—
277C22×M16—51no—
278C23×C8—51no—
279C23×C8C2×D511yescharacteristic
280C23×C8C2×D511yescharacteristic
281#529—104no—
282#529—104no—
283C2×#126—51no—
284C2×#126—51no—
285C2×#125—51no—
286C2×#124—51no—
287C2×#123—51no—
288C2×#123—51no—
289C2×C22⋊Q8—51no—
290C2×#121—51no—
291C2×C4×Q8—51no—
292C2×C4×D4—51no—
293C2×C4×D4—51no—
294C2×C4×D4C2×D511yescharacteristic
295C2×#117—51no—
296C2×#117—51no—
297C22×C42—51no—
298#435—104no—
299C8×D4—24no—
300C2×C4⋊C8—51no—
301C2×C4⋊C8C2×D511yescharacteristic
302C2×C22⋊C8—51no—
303C2×C22⋊C8—51no—
304C2×C22⋊C8—51no—
305C2×C22⋊C8—51no—
306C2×C22⋊C8—51no—
307C2×C22⋊C8—51no—
308C2×C22⋊C8C2×D511yescharacteristic
309C2×C22⋊C8C2×D511yescharacteristic
310C2×#97—51no—
311C2×C4×C8C2×D511yescharacteristic
312#336—51no—
313#336—51no—
314#336—51no—
315#336—51no—
316#336—51no—
317#336—51no—
318#336—51no—
319#336—51no—
320#336—51no—
321#336—51no—
322#336—51no—
323#336—51no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5C2×C22⋊C412yes—
335C23×C5C2×C22⋊C412yes—
336C23×C5#13112yes—
337C23×C5#13112yes—
338C23×C5C23×C411yescharacteristic
339C22×D5—21no—
340C22×D5—21no—
341C22×D5—21no—
342C22×D5—21no—
343C22×D5—21no—
344C22×D5—21no—
345C22×D5—21no—
346C5×D4—28no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5C2×C22⋊C412yes—
364C2×C4×C5C2×C22⋊C412yes—
365C2×C4×C5C2×C22⋊C412yes—
366C2×C4×C5C2×C22⋊C412yes—
367C2×C4×C5C22×D411yescharacteristic
368C2×C4×C5C22×D411yescharacteristic
369C2×C4×C5C2×#4111yescharacteristic
370C2×C4×C5C2×#4111yescharacteristic
371C2×C4×C5H(5,𝔽2)11yescharacteristic
372C2×C4×C52−1+411yescharacteristic
373C22⋊D5—44no—
374C22⋊D5—44no—
375C2×Dic5—21no—
376C2×Dic5—21no—
377C2×Dic5—21no—
378C2×Dic5—21no—
379C2×Dic5—21no—
380C2×Dic5—21no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—21no—
384C2×Dic5—21no—
385C2×Dic5—21no—
386C2×Dic5—21no—
387C2×Dic5—21no—
388C2×Dic5—21no—
389C2×Dic5—21no—
390C2×Dic5—21no—
391C2×Dic5—21no—
392C2×Dic5—21no—
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5#13112yes—
398C4×D5—41no—
399C4×D5—41no—
400C4×D5—41no—
401C4×D5—41no—
402Dic10—44no—
403C5×C8—22no—
404C5×C8—41no—
405C5×C8—41no—
406C5×C8—41no—
407#168—22no—
408#168—41no—
409#168—41no—
410#168—41no—
411C22×Q8—51no—
412C22×D4—51no—
413C22×D4—51no—
414C22×D4C4×D511yescharacteristic
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C2×M16—102no—
421C2×M16—102no—
422C2×M16—201no—
423C22×C8—22no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—41no—
428C22×C8—41no—
429C22×C8—51no—
430C22×C8—51no—
431C22×C8—51no—
432C22×C8—51no—
433C22×C8—102no—
434C22×C8—102no—
435C22×C8—201no—
436C22×C8C22×D511yescharacteristic
437C22×C8C22×D511yescharacteristic
438C22×C8C22×D511yescharacteristic
439C22×C8C22×D511yescharacteristic
440#126—104no—
441#126—104no—
442#125—104no—
443#124—104no—
444#123—104no—
445#123—104no—
446C22⋊Q8—104no—
447#121—104no—
448C4×Q8—102no—
449C4×Q8—102no—
450C4×D4—102no—
451C4×D4—102no—
452C4×D4—102no—
453C4×D4—102no—
454C4×D4D2014yes—
455C4×D4C22⋊D514yes—
456#117—102no—
457#117—102no—
458#117—102no—
459#117—102no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4—51no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4C4×D511yescharacteristic
470C2×C22⋊C4—51no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—51no—
477C2×C22⋊C4—51no—
478C2×C22⋊C4C4×D511yescharacteristic
479C2×C22⋊C4C4×D511yescharacteristic
480C2×C42—51no—
481C2×C42—51no—
482C2×C42—51no—
483C2×C42—51no—
484C2×C42—51no—
485C2×C42—102no—
486C2×C42—102no—
487C2×C42C22×D511yescharacteristic
488C4⋊C8—22no—
489C4⋊C8—102no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—102no—
493C22⋊C8—102no—
494C22⋊C8—102no—
495C22⋊C8—102no—
496C22⋊C8—201no—
497C22⋊C8—201no—
498#97—102no—
499C4×C8—22no—
500C22×C5—22no—
501C22×C5—22no—
502C22×C5—22no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—22no—
507C22×C5—22no—
508C22×C5—22no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5#40814yes—
514C22×C5C22×C22⋊C411yescharacteristic
515C22×C5C4×#4111yescharacteristic
516C22×C5#52011yescharacteristic
517C22×C5C2×#13111yescharacteristic
518C22×C5C2×#13111yescharacteristic
519C22×C5C2×#13111yescharacteristic
520C22×C5#56811yescharacteristic
521C2×D5—41no—
522C2×D5—41no—
523C2×D5—41no—
524C2×D5—41no—
525C2×D5—41no—
526C2×D5—41no—
527C2×D5—41no—
528C4×C5—22no—
529C4×C5—22no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5#54611yescharacteristic
533C4×C5#54611yescharacteristic
534C4×C5#54711yescharacteristic
535C4×C5#54711yescharacteristic
536Dic5—22no—
537Dic5—41no—
538Dic5—41no—
539Dic5—41no—
540Dic5—41no—
541Dic5—41no—
542Dic5—41no—
543C24—51no—
544C24C2×C4×D511yescharacteristic
545C24C2×C4×D511yescharacteristic
546C2×Q8—102no—
547C2×Q8—102no—
548C2×Q8—201no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—102no—
552C2×D4—102no—
553C2×D4—102no—
554C2×D4—102no—
555C2×D4—102no—
556C2×D4—201no—
557C2×D4#68514yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—51no—
567C22×C4—51no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—51no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—201no—
585C22×C4C2×C4×D511yescharacteristic
586C22×C4C2×C4×D511yescharacteristic
587C22×C4C2×C4×D511yescharacteristic
588C22×C4C2×C4×D511yescharacteristic
589C22×C4C2×D2012yes—
590C22×C4C2×D2012yes—
591C22×C4C2×C22⋊D512yes—
592C22×C4C2×C22⋊D512yes—
593C22×C4C23×D511yescharacteristic
594M16—204no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—44no—
607C2×C8—44no—
608C2×C8—52no—
609C2×C8—101no—
610C2×C8—101no—
611C2×C8—101no—
612C2×C8—101no—
613C2×C8—101no—
614C2×C8—101no—
615C2×C8—101no—
616C2×C8—101no—
617C2×C8—101no—
618C2×C8—101no—
619C2×C8—101no—
620C2×C8—204no—
621C2×C8#71112yes—
622C4⋊C4—102no—
623C4⋊C4—102no—
624C4⋊C4—102no—
625C4⋊C4—102no—
626C4⋊C4—102no—
627C4⋊C4—102no—
628C4⋊C4—102no—
629C4⋊C4—102no—
630C4⋊C4—102no—
631C4⋊C4#68514yes—
632C22⋊C4—102no—
633C22⋊C4—102no—
634C22⋊C4—102no—
635C22⋊C4—102no—
636C22⋊C4—102no—
637C22⋊C4—102no—
638C22⋊C4—102no—
639C22⋊C4—102no—
640C22⋊C4#68514yes—
641C22⋊C4#68514yes—
642C42—101no—
643C42—101no—
644C42—101no—
645C42—101no—
646C42—101no—
647C42—101no—
648C42—102no—
649C42—102no—
650C42C2×D2012yes—
651C42C2×C22⋊D512yes—
652C2×C5—24no—
653C2×C5—42no—
654C2×C5#233911yescharacteristic
655C2×C5C2×#40811yescharacteristic
656C2×C5#288011yescharacteristic
657C2×C5#296611yescharacteristic
658C2×C5#296811yescharacteristic
659C2×C5#299211yescharacteristic
660C2×C5#299411yescharacteristic
661D5—81no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—101no—
673C23—101no—
674C23—101no—
675C23—101no—
676C23—101no—
677C23—101no—
678C23—101no—
679C23#404712yes—
680C23#404712yes—
681C23C2×#68512yes—
682C23C2×#68512yes—
683C23C22×C4×D511yescharacteristic
684Q8—204no—
685D4—28no—
686D4—204no—
687D4—204no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—52no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—101no—
713C2×C4—101no—
714C2×C4—101no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—101no—
718C2×C4—101no—
719C2×C4—101no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—204no—
726C2×C4—204no—
727C2×C4—201no—
728C2×C4—201no—
729C2×C4—201no—
730C2×C4—201no—
731C2×C4C2×#68512yes—
732C2×C4C2×#68512yes—
733C2×C4C2×#68512yes—
734C2×C4C2×#68512yes—
735C2×C4C22×D2011yescharacteristic
736C2×C4C2×#71111yescharacteristic
737C2×C4#414411yescharacteristic
738C2×C4D5×#4111yescharacteristic
739C2×C4#415011yescharacteristic
740C2×C4C22×C22⋊D511yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—102no—
746C8—201no—
747C8—201no—
748C8—201no—
749C5#2247011yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—201no—
767C22—201no—
768C22—201no—
769C22—201no—
770C22#6539914yes—
771C22C4×#71111yescharacteristic
772C22#6588011yescharacteristic
773C22C2×#404711yescharacteristic
774C22C2×#404711yescharacteristic
775C22D5×#13111yescharacteristic
776C22#6608411yescharacteristic
777C22C22×#68511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—102no—
783C4—201no—
784C4—201no—
785C4—201no—
786C4—201no—
787C4—201no—
788C4—201no—
789C4#6588811yescharacteristic
790C4#6588911yescharacteristic
791C4#6614011yescharacteristic
792C4#6615811yescharacteristic
793C2—24no—
794C2—42no—
795C2—401no—
796C2#1061113111yescharacteristic
797C2#1061113311yescharacteristic
798C2#1061113811yescharacteristic
799C2#1061114011yescharacteristic
800C2#1061406111yescharacteristic
801C2C2×#6539911yescharacteristic
802C2#1061552411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC2×C5×C8×D4C2
prime radicalC2×#4085C4
cosocleC22×C4×C5C24
hypercenterC2×C8×D4D5
hypocenterC5#22470
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×C8×D4C2semidirect
3. C2×#65300C2semidirect
4. #10602768C2semidirect
5. #10602768C2semidirect
6. #10602758C2semidirect
7. C2×#64770C2semidirect
8. #10601269C2semidirect
9. #10601266C2semidirect
10. #10600746C2semidirect
11. #10600745C2semidirect
12. #10600704C2semidirect
13. #10600703C2semidirect
14. #10600581C2semidirect
15. #10600546C2semidirect
155. C2×C8×D4D5semidirect
749. C5#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#658722
C2×C5×C8×D42
C2×#653002
#106027682
#106027582
C2×#647702
#106012692
#106012662
#106007462
#106007452
#106007042
#106007032
#106005812
#106005462
#224705