Finite Group Databasebeta

← #12101217

Subgroups — #12101217

Order 1280.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2#10619161C211yesmaximal, characteristic, complemented
3C2×#65529C211yesmaximal, characteristic, complemented
4C2×#65525C211yesmaximal, characteristic, complemented
5C2×#65525C211yesmaximal, characteristic, complemented
6#10602907C218yesmaximal, complemented
7C2×#64779C211yesmaximal, characteristic, complemented
8#10602775C211yesmaximal, 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#66161—22no—
22#66161—22no—
23#41×Dic5—22no—
24#41×Dic5C2214yescomplemented
25#66146—21no—
26#66132—21no—
27#66132—22no—
28C2×#4072—22no—
29C2×#4072C2211yescharacteristic
30C2×#4072C2211yescharacteristic
31C2×#4072C2211yescharacteristic
32C22×#681C2211yescharacteristic
33#65529—22no—
34#65529C2214yescomplemented
35#65525—22no—
36#65525—22no—
37#65525—22no—
38#65525C2214yescomplemented
39C2×#3969—22no—
40C2×#3969C2214yescomplemented
41C2×#3966—22no—
42#64779C2214yescomplemented
43#64775C2214yescomplemented
44#21000—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×C412yescomplemented
64C2×C5×#41D412yes—
65C2×C5×#41D412yes—
66C2×C5×#41D412yes—
67C2×C5×#41C2312yes—
68C2×C5×#41C2312yes—
69C22×C5×Q8C2×C411yescharacteristic, complemented
70C22×C5×Q8D411yescharacteristic
71C22×C5×D4—21no—
72C22×C5×D4—21no—
73C22×C5×D4C2×C411yescharacteristic, complemented
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×C412yescomplemented
96C2×C5×M16C2×C412yescomplemented
97C2×C5×M16C2312yes—
98C22×C5×C8—21no—
99C2×C22⋊Dic5—24no—
100C2×C22⋊Dic5—21no—
101C2×C22⋊Dic5—21no—
102C2×C22⋊Dic5D412yes—
103Q8×Dic5—24no—
104Q8×Dic5—24no—
105D4×Dic5—28no—
106D4×Dic5—24no—
107D4×Dic5—24no—
108D4×Dic5—28no—
109#4072—24no—
110#4072—24no—
111#4072—21no—
112#4072—21no—
113#4072—21no—
114#4072—21no—
115#4072—21no—
116#4072—24no—
117#4072—21no—
118#4072—21no—
119#4072D412yes—
120#4072D412yes—
121#4072D412yes—
122#4072C2312yes—
123#4072C2312yes—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4×Dic5—21no—
129C2×C4×Dic5—24no—
130C2×C4×Dic5—21no—
131C2×C4×Dic5C2312yes—
132C2×#681—21no—
133C2×#681—21no—
134C2×#681—21no—
135C2×#681—21no—
136C2×#681—21no—
137C2×#681C2312yes—
138C22×#168—21no—
139#3969—28no—
140#3969—28no—
141#3966—28no—
142C2×#575D511yescharacteristic
143#3428—51no—
144C2×#421—51no—
145C2×#421—51no—
146C2×#410—51no—
147#1906—58no—
148C2×#344—51no—
149#1733—51no—
150C24×C5—21no—
151C24×C5—21no—
152C24×C5C2×D411yescharacteristic
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—22no—
171C5×#41—22no—
172C5×#41—22no—
173C5×#41—41no—
174C5×#41—41no—
175C5×#41—41no—
176C5×#41—41no—
177C5×#41—41no—
178C5×#41—41no—
179C5×#41—41no—
180C5×#41—41no—
181C5×#41C22⋊C414yes—
182C5×#41C22⋊C414yes—
183C5×#41C22×C414yes—
184C5×#41C2×D414yes—
185C2×C5×Q8—21no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—21no—
192C2×C5×Q8—21no—
193C2×C5×Q8C22⋊C412yes—
194C2×C5×Q8C22⋊C412yes—
195C2×C5×Q8C22×C412yes—
196C2×C5×Q8C2×D412yes—
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4—41no—
214C2×C5×D4—41no—
215C2×C5×D4—41no—
216C2×C5×D4—41no—
217C2×C5×D4C22⋊C412yes—
218C2×C5×D4C22⋊C412yes—
219C2×C5×D4C22×C412yes—
220C2×C5×D4C2×D412yes—
221C22×C4×C5—21no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—21no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5—41no—
232C22×C4×C5—41no—
233C22×C4×C5—41no—
234C22×C4×C5—41no—
235C22×C4×C5C22×C411yescharacteristic
236C22×C4×C5C22×C411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2×D411yescharacteristic
241C22×C4×C5C2×D411yescharacteristic
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5#4111yescharacteristic
245C22×C4×C5#4111yescharacteristic
246C22×C4×C5#4111yescharacteristic
247C22×C4×C5#4111yescharacteristic
248C22×C4×C5C2411yescharacteristic
249C22×Dic5—28no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—41no—
253C5×Q16—28no—
254C5×SD16—28no—
255C5×SD16—28no—
256C5×D8—28no—
257C5×M16—22no—
258C5×M16—22no—
259C5×M16—22no—
260C5×M16C22×C414yes—
261C2×C5×C8—22no—
262C2×C5×C8—22no—
263C2×C5×C8—22no—
264C22⋊Dic5—28no—
265C22⋊Dic5—22no—
266C22⋊Dic5—22no—
267C22⋊Dic5—22no—
268C22⋊Dic5—22no—
269C22⋊Dic5—41no—
270C22⋊Dic5C2×D414yes—
271C4⋊Dic5—28no—
272C4⋊Dic5—22no—
273C4⋊Dic5—22no—
274C4⋊Dic5—22no—
275C4⋊Dic5—22no—
276C4⋊Dic5—22no—
277C4⋊Dic5—41no—
278C4×Dic5—28no—
279C4×Dic5—22no—
280C4×Dic5—22no—
281C4×Dic5—22no—
282C4×Dic5—22no—
283C4×Dic5—41no—
284C4×Dic5C2×D414yes—
285#681—22no—
286#681—22no—
287#681—41no—
288#681—41no—
289C2×#168—22no—
290C2×#168—41no—
291C2×#168—41no—
292C22×#41C2×D511yescharacteristic
293C22×#41C2×D511yescharacteristic
294#575—22no—
295#575—22no—
296#575Dic514yescomplemented
297#575C2×D514yes—
298C2×#137—21no—
299C2×#137Dic512yescomplemented
300C2×AGL(1,ℤ/8)—21no—
301C2×AGL(1,ℤ/8)Dic512yescomplemented
302C2×#135—22no—
303C22×M16—51no—
304C22×M16C2×D511yescharacteristic
305#520—102no—
306#520—102no—
307#519—101no—
308#518—102no—
309#518—101no—
310C4×#41—54no—
311C4×#41—102no—
312C2×#117—51no—
313C2×#117—51no—
314C2×#117—51no—
315C2×#117—102no—
316#421—54no—
317#421—102no—
318#421—102no—
319#421—102no—
320C2×#104—54no—
321C2×#104—102no—
322#410—54no—
323#410—102no—
324C2×#99—102no—
325#344—54no—
326#339—54no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—41no—
332C23×C5—41no—
333C23×C5—81no—
334C23×C5—82no—
335C23×C5—82no—
336C23×C5C4×D411yescharacteristic
337C23×C5C4×D411yescharacteristic
338C23×C5#12011yescharacteristic
339C23×C5#12011yescharacteristic
340C23×C5#12111yescharacteristic
341C23×C5#12111yescharacteristic
342C23×C5C22×D411yescharacteristic
343C5×Q8—22no—
344C5×Q8—22no—
345C5×Q8—22no—
346C5×Q8—22no—
347C5×Q8—22no—
348C5×Q8—41no—
349C5×Q8—41no—
350C5×Q8C2×C22⋊C414yes—
351C5×D4—24no—
352C5×D4—24no—
353C5×D4—24no—
354C5×D4—24no—
355C5×D4—22no—
356C5×D4—22no—
357C5×D4—22no—
358C5×D4—22no—
359C5×D4—22no—
360C5×D4—42no—
361C5×D4—42no—
362C5×D4—42no—
363C5×D4—42no—
364C5×D4—41no—
365C5×D4—41no—
366C5×D4C2×C22⋊C414yes—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—24no—
371C2×C4×C5—24no—
372C2×C4×C5—24no—
373C2×C4×C5—24no—
374C2×C4×C5—22no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5C2×C22⋊C411yescharacteristic
382C2×C4×C5C2×C22⋊C411yescharacteristic
383C2×C4×C5C2×C22⋊C411yescharacteristic
384C2×C4×C5C2×C22⋊C411yescharacteristic
385C2×C4×C5C4×D411yescharacteristic
386C2×C4×C5C4×D411yescharacteristic
387C2×C4×C5C4×D411yescharacteristic
388C2×C4×C5C4×D411yescharacteristic
389C2×C4×C5C4×D411yescharacteristic
390C2×C4×C5C4×D411yescharacteristic
391C2×C4×C5#12011yescharacteristic
392C2×C4×C5#12011yescharacteristic
393C2×C4×C5#12111yescharacteristic
394C2×C4×C5#12111yescharacteristic
395C2×C4×C5#12111yescharacteristic
396C2×C4×C5#12111yescharacteristic
397C2×C4×C5#12111yescharacteristic
398C2×C4×C5#12111yescharacteristic
399C2×C4×C5#12311yescharacteristic
400C2×C4×C5#12311yescharacteristic
401C2×C4×C5#12311yescharacteristic
402C2×C4×C5#12311yescharacteristic
403C2×C4×C5C23×C411yescharacteristic
404C2×C4×C5C22×D411yescharacteristic
405C2×C4×C5C22×D411yescharacteristic
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C2×#4111yescharacteristic
408C2×C4×C5C2×#4111yescharacteristic
409C2×Dic5—24no—
410C2×Dic5—24no—
411C2×Dic5—42no—
412C2×Dic5—82no—
413C2×Dic5—82no—
414C2×Dic5—88no—
415C2×Dic5—82no—
416C5×C8—24no—
417#168—42no—
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×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41C2×Dic512yes—
435C2×#41C2×Dic512yes—
436C2×#41C2×Dic512yescomplemented
437C2×#41C22⋊D512yes—
438C2×#41C22⋊D512yes—
439C2×#41C22⋊D512yes—
440C2×#41C22×D512yes—
441C2×#41C22×D512yes—
442C22×Q8C2×Dic511yescharacteristic, complemented
443C22×Q8C22⋊D511yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C2×Dic511yescharacteristic, complemented
447C22×D4C22⋊D511yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4C22×D511yescharacteristic
451#137—24no—
452#137—24no—
453#137—24no—
454#137C2×Dic518yescomplemented
455AGL(1,ℤ/8)—24no—
456AGL(1,ℤ/8)—24no—
457AGL(1,ℤ/8)—24no—
458AGL(1,ℤ/8)C2×Dic518yescomplemented
459#135—28no—
460#135—28no—
461C2×Q16—22no—
462C2×SD16—22no—
463C2×SD16—22no—
464C2×D8—22no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—52no—
469C2×M16—101no—
470C2×M16—101no—
471C2×M16—101no—
472C2×M16—101no—
473C2×M16—101no—
474C2×M16C2×Dic512yescomplemented
475C2×M16C2×Dic512yescomplemented
476C2×M16C22×D512yes—
477C22×C8—21no—
478C22×C8—101no—
479C4×Q8—104no—
480C4×Q8—104no—
481C4×D4—108no—
482C4×D4—108no—
483C4×D4—104no—
484C4×D4—104no—
485#117—52no—
486#117—52no—
487#117—52no—
488#117—52no—
489#117—52no—
490#117—104no—
491#117—104no—
492#117—104no—
493#117—101no—
494#117—101no—
495#117—101no—
496#117—101no—
497#117—101no—
498#117—101no—
499#117—101no—
500C2×C4⋊C4—104no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C22⋊C4—52no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C42—52no—
509C2×C42—104no—
510C2×C42—101no—
511C2×C42—101no—
512#104—108no—
513#104—108no—
514#99—108no—
515C22×C5—24no—
516C22×C5—41no—
517C22×C5—41no—
518C22×C5—41no—
519C22×C5—41no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
523C22×C5—44no—
524C22×C5—42no—
525C22×C5—82no—
526C22×C5—82no—
527C22×C5—82no—
528C22×C5—82no—
529C22×C5—82no—
530C22×C5#38611yescharacteristic
531C22×C5#38611yescharacteristic
532C22×C5#38611yescharacteristic
533C22×C5#38611yescharacteristic
534C22×C5C2×C4×D411yescharacteristic
535C22×C5C2×#12011yescharacteristic
536C22×C5C2×#12111yescharacteristic
537C4×C5—24no—
538C4×C5—42no—
539C4×C5#38611yescharacteristic
540C4×C5#38611yescharacteristic
541C4×C5#38611yescharacteristic
542C4×C5#38611yescharacteristic
543C4×C5C22×C22⋊C411yescharacteristic
544C4×C5C2×C4×D411yescharacteristic
545C4×C5C2×#12111yescharacteristic
546C4×C5C2×#12311yescharacteristic
547Dic5—44no—
548Dic5—44no—
549Dic5—82no—
550C24—21no—
551C24—21no—
552C24D4×D511yescharacteristic
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41C22⋊Dic514yes—
582#41C22⋊Dic514yes—
583#41C22×Dic514yes—
584#41C2×C22⋊D514yes—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C22⋊Dic512yes—
594C2×Q8C22⋊Dic512yes—
595C2×Q8C22×Dic512yes—
596C2×Q8C2×C22⋊D512yes—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4C22⋊Dic512yes—
618C2×D4C22⋊Dic512yes—
619C2×D4C22×Dic512yes—
620C2×D4C2×C22⋊D512yes—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—108no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—201no—
639C22×C4D4×D511yescharacteristic
640C22×C4D4×D511yescharacteristic
641C22×C4D4×D511yescharacteristic
642C22×C4#71111yescharacteristic
643C22×C4#71111yescharacteristic
644C22×C4#71111yescharacteristic
645C22×C4#71111yescharacteristic
646C22×C4C22×Dic511yescharacteristic
647C22×C4C22×Dic511yescharacteristic
648C22×C4C2×C22⋊D511yescharacteristic
649C22×C4C2×C22⋊D511yescharacteristic
650C22×C4C2×C22⋊D511yescharacteristic
651C22×C4C2×C22⋊D511yescharacteristic
652C22×C4C23×D511yescharacteristic
653Q16—28no—
654SD16—28no—
655SD16—28no—
656D8—28no—
657M16—22no—
658M16—22no—
659M16—22no—
660M16—102no—
661M16—102no—
662M16—201no—
663M16—201no—
664M16C22×Dic514yes—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—102no—
669C2×C8—201no—
670C2×C8—201no—
671C4⋊C4—108no—
672C4⋊C4—102no—
673C4⋊C4—102no—
674C4⋊C4—102no—
675C4⋊C4—102no—
676C4⋊C4—102no—
677C4⋊C4—201no—
678C22⋊C4—54no—
679C22⋊C4—108no—
680C22⋊C4—102no—
681C22⋊C4—102no—
682C22⋊C4—102no—
683C22⋊C4—102no—
684C22⋊C4—201no—
685C42—54no—
686C42—108no—
687C42—102no—
688C42—102no—
689C42—102no—
690C42—102no—
691C42—201no—
692C2×C5—21no—
693C2×C5—21no—
694C2×C5—21no—
695C2×C5—21no—
696C2×C5—21no—
697C2×C5—21no—
698C2×C5—21no—
699C2×C5—44no—
700C2×C5—82no—
701C2×C5C2×#38611yescharacteristic
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—81no—
709C23—82no—
710C23—82no—
711C23D4×Dic511yescharacteristic
712C23D4×Dic511yescharacteristic
713C23#408311yescharacteristic
714C23#408311yescharacteristic
715C23#408511yescharacteristic
716C23#408511yescharacteristic
717C23C2×D4×D511yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—41no—
724Q8—41no—
725Q8C2×C22⋊Dic514yes—
726D4—24no—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—41no—
740D4—41no—
741D4C2×C22⋊Dic514yes—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—104no—
757C2×C4—104no—
758C2×C4—202no—
759C2×C4—402no—
760C2×C4—402no—
761C2×C4—408no—
762C2×C4—402no—
763C2×C4D4×Dic511yescharacteristic
764C2×C4D4×Dic511yescharacteristic
765C2×C4D4×Dic511yescharacteristic
766C2×C4D4×Dic511yescharacteristic
767C2×C4D4×Dic511yescharacteristic
768C2×C4D4×Dic511yescharacteristic
769C2×C4#408111yescharacteristic
770C2×C4#408111yescharacteristic
771C2×C4#408111yescharacteristic
772C2×C4#408111yescharacteristic
773C2×C4#408311yescharacteristic
774C2×C4#408311yescharacteristic
775C2×C4#408511yescharacteristic
776C2×C4#408511yescharacteristic
777C2×C4#408511yescharacteristic
778C2×C4#408511yescharacteristic
779C2×C4#408511yescharacteristic
780C2×C4#408511yescharacteristic
781C2×C4C2×C22⋊Dic511yescharacteristic
782C2×C4C2×C22⋊Dic511yescharacteristic
783C2×C4C2×C22⋊Dic511yescharacteristic
784C2×C4C2×C22⋊Dic511yescharacteristic
785C2×C4C2×D4×D511yescharacteristic
786C2×C4C2×#71111yescharacteristic
787C2×C4C2×#71111yescharacteristic
788C2×C4C23×Dic511yescharacteristic
789C2×C4C22×C22⋊D511yescharacteristic
790C2×C4C22×C22⋊D511yescharacteristic
791C8—24no—
792C8—202no—
793C5#2100011yescharacteristic, complemented, Sylow
794C22—24no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—42no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#6550911yescharacteristic
810C22#6550911yescharacteristic
811C22#6550911yescharacteristic
812C22#6550911yescharacteristic
813C22C2×D4×Dic511yescharacteristic
814C22C2×#408311yescharacteristic
815C22C2×#408511yescharacteristic
816C4—24no—
817C4—42no—
818C4—204no—
819C4—204no—
820C4—402no—
821C4#6550911yescharacteristic
822C4#6550911yescharacteristic
823C4#6550911yescharacteristic
824C4#6550911yescharacteristic
825C4C2×D4×Dic511yescharacteristic
826C4C2×#408111yescharacteristic
827C4C2×#408511yescharacteristic
828C4C22×C22⋊Dic511yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—44no—
837C2—82no—
838C2C2×#6550911yescharacteristic
subgroupG/H
centerC4C2×#4085
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
Fitting, prime radicalC2×C5×#575C2
socleC2×C5C2×#386
cosocleC22×C4×C5C24
hypercenterC2×#575D5
hypocenterC5#21000
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. #10619161C2semidirect
3. C2×#65529C2semidirect
4. C2×#65525C2semidirect
5. C2×#65525C2semidirect
6. #10602907C2semidirect
7. C2×#64779C2semidirect
8. #10602775C2semidirect
13. C5×#575C4semidirect
16. C2×C5×#137C4semidirect
18. C2×C5×AGL(1,ℤ/8)C4semidirect
24. #41×Dic5C22semidirect
34. #65529C22semidirect
38. #65525C22semidirect
40. C2×#3969C22semidirect
42. #64779C22semidirect
43. #64775C22semidirect
63. C2×C5×#41C2×C4semidirect
69. C22×C5×Q8C2×C4semidirect
73. C22×C5×D4C2×C4semidirect
81. C5×#137C2×C4semidirect
85. C5×AGL(1,ℤ/8)C2×C4semidirect
95. C2×C5×M16C2×C4semidirect
96. C2×C5×M16C2×C4semidirect
296. #575Dic5semidirect
299. C2×#137Dic5semidirect
301. C2×AGL(1,ℤ/8)Dic5semidirect
436. C2×#41C2×Dic5semidirect
442. C22×Q8C2×Dic5semidirect
446. C22×D4C2×Dic5semidirect
454. #137C2×Dic5semidirect
458. AGL(1,ℤ/8)C2×Dic5semidirect
474. C2×M16C2×Dic5semidirect
475. C2×M16C2×Dic5semidirect
793. C5#21000semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5752
#106191612
C2×#655292
C2×#655252
#106029072
C2×#647792
#106027752
#210005