Finite Group Databasebeta

← #12100784

Subgroups — #12100784

Order 1280.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2C2×#66153C211yesmaximal, characteristic, complemented
3C2×#65525C211yesmaximal, characteristic, complemented
4#10615805C211yesmaximal, characteristic, complemented
5#10615803C211yesmaximal, characteristic, complemented
6#10602909C218yesmaximal, complemented
7C2×#64779C211yesmaximal, characteristic, complemented
8#10602787C211yesmaximal, characteristic, complemented
9C22×C5×#41C2211yescharacteristic
10C22×C5×#41C2211yescharacteristic
11C5×#575—22no—
12C5×#575—22no—
13C5×#575C414yescomplemented
14C5×#575C2214yes—
15C2×C5×#137—21no—
16C2×C5×#137C412yescomplemented
17C2×C5×AGL(1,ℤ/8)—21no—
18C2×C5×AGL(1,ℤ/8)C412yescomplemented
19C2×C5×#135—22no—
20C22×C5×M16C2211yescharacteristic
21#66153—22no—
22#66153—22no—
23#66153—22no—
24#66153C2214yescomplemented
25C2×#4094—22no—
26C2×#4094—22no—
27C2×#4072C2211yescharacteristic
28C22×#681—22no—
29C22×#681C2211yescharacteristic
30C22×#681C2211yescharacteristic
31C22×#681C2211yescharacteristic
32#65525—22no—
33#65525C2214yescomplemented
34C2×#3969—22no—
35#65523—22no—
36#65523C2214yescomplemented
37#65522C2214yescomplemented
38#65521—22no—
39#65514—21no—
40#65504—21no—
41#65496—22no—
42#64779C2214yescomplemented
43#64778C2214yescomplemented
44#20939—51nomaximal, Sylow
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41—21no—
51C2×C5×#41—21no—
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41—21no—
55C2×C5×#41—21no—
56C2×C5×#41—21no—
57C2×C5×#41—21no—
58C2×C5×#41—21no—
59C2×C5×#41—21no—
60C2×C5×#41—21no—
61C2×C5×#41C2×C412yes—
62C2×C5×#41C2×C412yes—
63C2×C5×#41C2×C412yes—
64C2×C5×#41D412yes—
65C2×C5×#41D412yes—
66C2×C5×#41D412yes—
67C2×C5×#41C2312yes—
68C2×C5×#41C2312yes—
69C22×C5×Q8C2×C411yescharacteristic
70C22×C5×Q8D411yescharacteristic
71C22×C5×D4—21no—
72C22×C5×D4—21no—
73C22×C5×D4C2×C411yescharacteristic
74C22×C5×D4D411yescharacteristic
75C23×C4×C5—21no—
76C23×C4×C5—21no—
77C23×C4×C5C2311yescharacteristic
78C5×#137—24no—
79C5×#137—24no—
80C5×#137—24no—
81C5×#137C2×C418yescomplemented
82C5×AGL(1,ℤ/8)—24no—
83C5×AGL(1,ℤ/8)—24no—
84C5×AGL(1,ℤ/8)—24no—
85C5×AGL(1,ℤ/8)C2×C418yescomplemented
86C5×#135—28no—
87C5×#135—28no—
88C2×C5×Q16—22no—
89C2×C5×SD16—22no—
90C2×C5×SD16—22no—
91C2×C5×D8—22no—
92C2×C5×M16—21no—
93C2×C5×M16—21no—
94C2×C5×M16—21no—
95C2×C5×M16C2×C412yes—
96C2×C5×M16C2×C412yes—
97C2×C5×M16C2312yes—
98C22×C5×C8—21no—
99C2×C22⋊Dic5—21no—
100#4094—28no—
101#4094—28no—
102#4094—28no—
103#4094—28no—
104#4072—21no—
105#4072—21no—
106#4072—21no—
107#4072C2312yes—
108C2×C4⋊Dic5—21no—
109C2×C4×Dic5—21no—
110C2×#681—24no—
111C2×#681—28no—
112C2×#681—21no—
113C2×#681—21no—
114C2×#681—21no—
115C2×#681—21no—
116C2×#681—21no—
117C2×#681—21no—
118C2×#681—21no—
119C2×#681—28no—
120C2×#681—21no—
121C2×#681—21no—
122C2×#681—21no—
123C2×#681—21no—
124C2×#681—21no—
125C2×#681—21no—
126C2×#681D412yes—
127C2×#681D412yes—
128C2×#681D412yes—
129C2×#681C2312yes—
130C2×#681C2312yes—
131C22×#168—24no—
132C22×#168—21no—
133C22×#168D412yes—
134C22×#168C2312yes—
135#3969—28no—
136#3967—24no—
137#3964—24no—
138C22⋊#168—28no—
139C2×#575D511yescharacteristic
140C2×#568—51no—
141C2×#421—51no—
142#2896—51no—
143#2879—51no—
144#1881—58no—
145C2×#344—51no—
146#1738—51no—
147C24×C5—21no—
148C24×C5—21no—
149C24×C5#4111yescharacteristic
150C5×#41—22no—
151C5×#41—22no—
152C5×#41—22no—
153C5×#41—22no—
154C5×#41—22no—
155C5×#41—22no—
156C5×#41—22no—
157C5×#41—22no—
158C5×#41—22no—
159C5×#41—22no—
160C5×#41—22no—
161C5×#41—22no—
162C5×#41—22no—
163C5×#41—22no—
164C5×#41—22no—
165C5×#41—22no—
166C5×#41—22no—
167C5×#41—22no—
168C5×#41—22no—
169C5×#41—22no—
170C5×#41—41no—
171C5×#41—41no—
172C5×#41—41no—
173C5×#41—41no—
174C5×#41—41no—
175C5×#41—41no—
176C5×#41—41no—
177C5×#41—41no—
178C5×#41C22⋊C414yes—
179C5×#41C22⋊C414yes—
180C5×#41C22×C414yes—
181C5×#41C2×D414yes—
182C2×C5×Q8—21no—
183C2×C5×Q8—21no—
184C2×C5×Q8—21no—
185C2×C5×Q8—21no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8C22⋊C412yes—
191C2×C5×Q8C22⋊C412yes—
192C2×C5×Q8C22×C412yes—
193C2×C5×Q8C2×D412yes—
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—41no—
211C2×C5×D4—41no—
212C2×C5×D4—41no—
213C2×C5×D4—41no—
214C2×C5×D4C22⋊C412yes—
215C2×C5×D4C22⋊C412yes—
216C2×C5×D4C22×C412yes—
217C2×C5×D4C2×D412yes—
218C22×C4×C5—21no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—21no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—41no—
229C22×C4×C5—41no—
230C22×C4×C5—41no—
231C22×C4×C5—41no—
232C22×C4×C5C22×C411yescharacteristic
233C22×C4×C5C22×C411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2×D411yescharacteristic
242C22×C4×C5#4111yescharacteristic
243C22×C4×C5#4111yescharacteristic
244C22×C4×C5#4111yescharacteristic
245C22×C4×C5C2411yescharacteristic
246C22×Dic5—41no—
247C5×Q16—28no—
248C5×SD16—28no—
249C5×SD16—28no—
250C5×D8—28no—
251C5×M16—22no—
252C5×M16—22no—
253C5×M16—22no—
254C5×M16C22×C414yes—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8—22no—
258C22⋊Dic5—22no—
259C22⋊Dic5—41no—
260C4⋊Dic5—22no—
261C4⋊Dic5—41no—
262C4×Dic5—22no—
263C4×Dic5—41no—
264#681—216no—
265#681—22no—
266#681—22no—
267#681—22no—
268#681—22no—
269#681—22no—
270#681—22no—
271#681—22no—
272#681—41no—
273#681—41no—
274#681—41no—
275#681—41no—
276#681C2×D414yes—
277C2×#168—216no—
278C2×#168—22no—
279C2×#168—22no—
280C2×#168—22no—
281C2×#168—22no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—22no—
285C2×#168—22no—
286C2×#168C2×D414yes—
287C22×#41C2×D511yescharacteristic
288C22×#41C2×D511yescharacteristic
289#575—22no—
290#575—22no—
291#575Dic514yescomplemented
292#575C2×D514yes—
293C2×#137—21no—
294C2×#137Dic512yescomplemented
295C2×AGL(1,ℤ/8)—21no—
296C2×AGL(1,ℤ/8)Dic512yescomplemented
297C2×#135—22no—
298#568—54no—
299#568—102no—
300#568—102no—
301#568—102no—
302C2×#131—102no—
303C2×#131—102no—
304C22×M16—51no—
305C22×M16—51no—
306C22×M16—51no—
307C22×M16—102no—
308C22×M16C2×D511yescharacteristic
309C2×#117—51no—
310#421—54no—
311#421—102no—
312C2×#104—102no—
313#419—101no—
314#418—101no—
315#417—102no—
316#416—54no—
317#408—54no—
318#408—102no—
319#407—102no—
320#344—54no—
321#341—54no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—41no—
327C23×C5—41no—
328C23×C5—81no—
329C23×C5—82no—
330C23×C5—82no—
331C23×C5C4×D411yescharacteristic
332C23×C5C4×D411yescharacteristic
333C23×C5#12111yescharacteristic
334C23×C5#12111yescharacteristic
335C23×C5#12311yescharacteristic
336C23×C5#12311yescharacteristic
337C23×C5C2×#4111yescharacteristic
338C5×Q8—22no—
339C5×Q8—22no—
340C5×Q8—22no—
341C5×Q8—22no—
342C5×Q8—22no—
343C5×Q8—41no—
344C5×Q8—41no—
345C5×Q8C2×C22⋊C414yes—
346C5×D4—24no—
347C5×D4—24no—
348C5×D4—24no—
349C5×D4—24no—
350C5×D4—22no—
351C5×D4—22no—
352C5×D4—22no—
353C5×D4—22no—
354C5×D4—22no—
355C5×D4—42no—
356C5×D4—42no—
357C5×D4—42no—
358C5×D4—42no—
359C5×D4—41no—
360C5×D4—41no—
361C5×D4C2×C22⋊C414yes—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—24no—
366C2×C4×C5—24no—
367C2×C4×C5—24no—
368C2×C4×C5—24no—
369C2×C4×C5—22no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5C2×C22⋊C411yescharacteristic
377C2×C4×C5C2×C22⋊C411yescharacteristic
378C2×C4×C5C2×C22⋊C411yescharacteristic
379C2×C4×C5C2×C22⋊C411yescharacteristic
380C2×C4×C5C4×D411yescharacteristic
381C2×C4×C5C4×D411yescharacteristic
382C2×C4×C5C4×D411yescharacteristic
383C2×C4×C5C4×D411yescharacteristic
384C2×C4×C5C4×D411yescharacteristic
385C2×C4×C5C4×D411yescharacteristic
386C2×C4×C5#12011yescharacteristic
387C2×C4×C5#12011yescharacteristic
388C2×C4×C5#12011yescharacteristic
389C2×C4×C5#12011yescharacteristic
390C2×C4×C5#12111yescharacteristic
391C2×C4×C5#12111yescharacteristic
392C2×C4×C5#12111yescharacteristic
393C2×C4×C5#12111yescharacteristic
394C2×C4×C5#12111yescharacteristic
395C2×C4×C5#12111yescharacteristic
396C2×C4×C5#12311yescharacteristic
397C2×C4×C5#12311yescharacteristic
398C2×C4×C5C23×C411yescharacteristic
399C2×C4×C5C22×D411yescharacteristic
400C2×C4×C5C22×D411yescharacteristic
401C2×C4×C5C22×D411yescharacteristic
402C2×C4×C5C22×D411yescharacteristic
403C2×C4×C5C2×#4111yescharacteristic
404C2×Dic5—42no—
405C2×Dic5—82no—
406C5×C8—24no—
407#168—24no—
408#168—24no—
409#168—42no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41C2×Dic512yes—
427C2×#41C2×Dic512yes—
428C2×#41C2×Dic512yes—
429C2×#41C22⋊D512yes—
430C2×#41C22⋊D512yes—
431C2×#41C22⋊D512yes—
432C2×#41C22×D512yes—
433C2×#41C22×D512yes—
434C22×Q8C2×Dic511yescharacteristic
435C22×Q8C22⋊D511yescharacteristic
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C2×Dic511yescharacteristic
439C22×D4C22⋊D511yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4C22×D511yescharacteristic
443#137—24no—
444#137—24no—
445#137—24no—
446#137C2×Dic518yescomplemented
447AGL(1,ℤ/8)—24no—
448AGL(1,ℤ/8)—24no—
449AGL(1,ℤ/8)—24no—
450AGL(1,ℤ/8)C2×Dic518yescomplemented
451#135—28no—
452#135—28no—
453C2×Q16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×D8—22no—
457#131—108no—
458#131—108no—
459#131—108no—
460#131—108no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—52no—
465C2×M16—52no—
466C2×M16—52no—
467C2×M16—52no—
468C2×M16—52no—
469C2×M16—108no—
470C2×M16—104no—
471C2×M16—108no—
472C2×M16—101no—
473C2×M16—101no—
474C2×M16—101no—
475C2×M16—101no—
476C2×M16—101no—
477C2×M16—101no—
478C2×M16—101no—
479C2×M16—101no—
480C2×M16—101no—
481C2×M16—101no—
482C2×M16—101no—
483C2×M16—101no—
484C2×M16—101no—
485C2×M16C2×Dic512yes—
486C2×M16C2×Dic512yes—
487C2×M16C22×D512yes—
488C22×C8—21no—
489C22×C8—52no—
490C22×C8—52no—
491C22×C8—104no—
492C22×C8—101no—
493#117—52no—
494#117—101no—
495#117—101no—
496#117—101no—
497C2×C4⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—101no—
500#104—108no—
501#103—104no—
502#102—104no—
503C22⋊C8—108no—
504C22×C5—24no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—44no—
513C22×C5—44no—
514C22×C5—42no—
515C22×C5—82no—
516C22×C5—82no—
517C22×C5—82no—
518C22×C5—82no—
519C22×C5#38611yescharacteristic
520C22×C5#38611yescharacteristic
521C22×C5#38611yescharacteristic
522C22×C5#38611yescharacteristic
523C22×C5C2×C4×D411yescharacteristic
524C22×C5C2×#12111yescharacteristic
525C22×C5C2×#12311yescharacteristic
526C4×C5—24no—
527C4×C5—42no—
528C4×C5#38611yescharacteristic
529C4×C5#38611yescharacteristic
530C4×C5#38611yescharacteristic
531C4×C5#38611yescharacteristic
532C4×C5C22×C22⋊C411yescharacteristic
533C4×C5C2×C4×D411yescharacteristic
534C4×C5C2×#12011yescharacteristic
535C4×C5C2×#12111yescharacteristic
536Dic5—82no—
537C24—21no—
538C24—21no—
539C24#71111yescharacteristic
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41C22⋊Dic514yes—
569#41C22⋊Dic514yes—
570#41C22×Dic514yes—
571#41C2×C22⋊D514yes—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8C22⋊Dic512yes—
581C2×Q8C22⋊Dic512yes—
582C2×Q8C22×Dic512yes—
583C2×Q8C2×C22⋊D512yes—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4C22⋊Dic512yes—
605C2×D4C22⋊Dic512yes—
606C2×D4C22×Dic512yes—
607C2×D4C2×C22⋊D512yes—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—201no—
623C22×C4D4×D511yescharacteristic
624C22×C4D4×D511yescharacteristic
625C22×C4D4×D511yescharacteristic
626C22×C4D4×D511yescharacteristic
627C22×C4#71111yescharacteristic
628C22×C4#71111yescharacteristic
629C22×C4#71111yescharacteristic
630C22×C4C22×Dic511yescharacteristic
631C22×C4C22×Dic511yescharacteristic
632C22×C4C2×C22⋊D511yescharacteristic
633C22×C4C2×C22⋊D511yescharacteristic
634C22×C4C2×C22⋊D511yescharacteristic
635C22×C4C2×C22⋊D511yescharacteristic
636C22×C4C23×D511yescharacteristic
637Q16—28no—
638SD16—28no—
639SD16—28no—
640D8—28no—
641M16—22no—
642M16—22no—
643M16—22no—
644M16—54no—
645M16—1016no—
646M16—102no—
647M16—102no—
648M16—102no—
649M16—102no—
650M16—102no—
651M16—102no—
652M16—102no—
653M16—201no—
654M16—201no—
655M16—201no—
656M16—201no—
657M16C22×Dic514yes—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—54no—
662C2×C8—1016no—
663C2×C8—102no—
664C2×C8—102no—
665C2×C8—102no—
666C2×C8—102no—
667C2×C8—102no—
668C2×C8—102no—
669C2×C8—102no—
670C2×C8—102no—
671C4⋊C4—102no—
672C4⋊C4—201no—
673C22⋊C4—102no—
674C22⋊C4—201no—
675C42—102no—
676C42—201no—
677C2×C5—21no—
678C2×C5—21no—
679C2×C5—21no—
680C2×C5—21no—
681C2×C5—21no—
682C2×C5—21no—
683C2×C5—21no—
684C2×C5—44no—
685C2×C5—82no—
686C2×C5C2×#38611yescharacteristic
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—81no—
694C23—82no—
695C23—82no—
696C23D4×Dic511yescharacteristic
697C23D4×Dic511yescharacteristic
698C23#408111yescharacteristic
699C23#408111yescharacteristic
700C23#408511yescharacteristic
701C23#408511yescharacteristic
702C23C2×#71111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8C2×C22⋊Dic514yes—
711D4—24no—
712D4—24no—
713D4—24no—
714D4—24no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—42no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—41no—
725D4—41no—
726D4C2×C22⋊Dic514yes—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—202no—
742C2×C4—402no—
743C2×C4D4×Dic511yescharacteristic
744C2×C4D4×Dic511yescharacteristic
745C2×C4D4×Dic511yescharacteristic
746C2×C4D4×Dic511yescharacteristic
747C2×C4D4×Dic511yescharacteristic
748C2×C4D4×Dic511yescharacteristic
749C2×C4#408111yescharacteristic
750C2×C4#408111yescharacteristic
751C2×C4#408311yescharacteristic
752C2×C4#408311yescharacteristic
753C2×C4#408311yescharacteristic
754C2×C4#408311yescharacteristic
755C2×C4#408511yescharacteristic
756C2×C4#408511yescharacteristic
757C2×C4#408511yescharacteristic
758C2×C4#408511yescharacteristic
759C2×C4#408511yescharacteristic
760C2×C4#408511yescharacteristic
761C2×C4C2×C22⋊Dic511yescharacteristic
762C2×C4C2×C22⋊Dic511yescharacteristic
763C2×C4C2×C22⋊Dic511yescharacteristic
764C2×C4C2×C22⋊Dic511yescharacteristic
765C2×C4C2×D4×D511yescharacteristic
766C2×C4C2×D4×D511yescharacteristic
767C2×C4C2×#71111yescharacteristic
768C2×C4C23×Dic511yescharacteristic
769C2×C4C22×C22⋊D511yescharacteristic
770C2×C4C22×C22⋊D511yescharacteristic
771C8—24no—
772C8—104no—
773C8—104no—
774C8—202no—
775C5#2093911yescharacteristic, complemented, Sylow
776C22—24no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22#6550911yescharacteristic
792C22#6550911yescharacteristic
793C22#6550911yescharacteristic
794C22#6550911yescharacteristic
795C22C2×D4×Dic511yescharacteristic
796C22C2×#408111yescharacteristic
797C22C2×#408511yescharacteristic
798C4—24no—
799C4—42no—
800C4—402no—
801C4#6550911yescharacteristic
802C4#6550911yescharacteristic
803C4#6550911yescharacteristic
804C4#6550911yescharacteristic
805C4C2×D4×Dic511yescharacteristic
806C4C2×#408311yescharacteristic
807C4C2×#408511yescharacteristic
808C4C22×C22⋊Dic511yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—44no—
817C2—82no—
818C2C2×#6550911yescharacteristic
subgroupG/H
centerC4C2×#4083
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
Fitting, prime radicalC2×C5×#575C2
socleC2×C5C2×#386
cosocleC22×C4×C5C24
hypercenterC2×#575D5
hypocenterC5#20939
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. C2×#66153C2semidirect
3. C2×#65525C2semidirect
4. #10615805C2semidirect
5. #10615803C2semidirect
6. #10602909C2semidirect
7. C2×#64779C2semidirect
8. #10602787C2semidirect
13. C5×#575C4semidirect
16. C2×C5×#137C4semidirect
18. C2×C5×AGL(1,ℤ/8)C4semidirect
24. #66153C22semidirect
33. #65525C22semidirect
36. #65523C22semidirect
37. #65522C22semidirect
42. #64779C22semidirect
43. #64778C22semidirect
81. C5×#137C2×C4semidirect
85. C5×AGL(1,ℤ/8)C2×C4semidirect
291. #575Dic5semidirect
294. C2×#137Dic5semidirect
296. C2×AGL(1,ℤ/8)Dic5semidirect
446. #137C2×Dic5semidirect
450. AGL(1,ℤ/8)C2×Dic5semidirect
775. C5#20939semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5752
C2×#661532
C2×#655252
#106158052
#106158032
#106029092
C2×#647792
#106027872
#209395