Finite Group Databasebeta

← C2×#10600772 #12066556

Subgroups — C2×#10600772 #12066556

Order 1280.

1510 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66125C211yesmaximal, characteristic
2C2×C5×#407C211yesmaximal, characteristic, complemented
3C2×#65501C211yesmaximal, characteristic, complemented
4#10600772C218yesmaximal, direct product factor
5C2×#64687C212yesmaximal, complemented
6C2×#64690C212yesmaximal, complemented
7C24×C4×C5C2211yescharacteristic
8C22×#709C411yescharacteristic, complemented
9C22×C5×M16—21no—
10C2×#4099—21no—
11C22×C22⋊Dic5—21no—
12#66125—22no—
13#66125—22no—
14#66125C414yescomplemented
15#66125C2214yes—
16C2×#4076C411yescharacteristic, complemented
17C2×#4076C2211yescharacteristic
18C2×#4075—21no—
19C2×C4×C22⋊D5—21no—
20C2×C4×C22⋊D5—21no—
21C2×#4072C411yescharacteristic, complemented
22C22×C4⋊Dic5—21no—
23C2×#4070C411yescharacteristic, complemented
24C2×#4070C2211yescharacteristic
25C5×#407—22no—
26C5×#407C2214yescomplemented
27C2×C5×C22⋊C8—21no—
28C2×C5×C22⋊C8C2212yes—
29#65501—22no—
30#65501C2214yescomplemented
31C2×#3963C2212yes—
32#64690C2218yescomplemented
33#64687C2218yescomplemented
34C2×#1513—51nomaximal, Sylow
35C25×C5D411yescharacteristic
36C23×C4×C5—44no—
37C23×C4×C5C2×C411yescharacteristic
38C23×C4×C5C2×C411yescharacteristic
39C23×C4×C5C2×C412yes—
40C23×C4×C5D411yescharacteristic
41C23×C4×C5D412yes—
42C23×C4×C5D411yescharacteristic
43C23×C4×C5D411yescharacteristic
44C23×C4×C5D412yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2312yes—
47C22×C22⋊D5—21no—
48C22×C22⋊D5—21no—
49C22×C22⋊D5—21no—
50C23×Dic5—22no—
51C2×#709—22no—
52C2×#709—44no—
53C2×#709C2×C414yescomplemented
54C22×D20C2×C411yescharacteristic
55C22×C4×D5—21no—
56C22×Dic10C2×C411yescharacteristic
57C2×C5×M16—24no—
58C2×C5×M16—44no—
59C22×C5×C8—22no—
60#4099—24no—
61#4099—24no—
62C2×C22⋊Dic5—21no—
63C2×C22⋊Dic5—21no—
64C2×C22⋊Dic5—21no—
65C2×C22⋊Dic5—24no—
66C2×C22⋊Dic5—44no—
67#4076—22no—
68#4076—21no—
69#4076—21no—
70#4076C2×C412yes—
71#4076C2×C414yescomplemented
72#4076C2312yes—
73#4075—24no—
74#4075—24no—
75C4×C22⋊D5—24no—
76C4×C22⋊D5—24no—
77C4×C22⋊D5—24no—
78C4×C22⋊D5—24no—
79C2×#685—21no—
80C2×#685—21no—
81#4072—22no—
82#4072C2×C414yescomplemented
83C2×C4⋊Dic5—24no—
84C2×C4⋊Dic5—44no—
85C2×C4⋊Dic5C2×C411yescharacteristic
86C2×C4⋊Dic5C2×C411yescharacteristic
87#4070—22no—
88#4070—21no—
89#4070—21no—
90#4070C2×C412yes—
91#4070C2×C414yescomplemented
92#4070C2312yes—
93C2×#683—21no—
94C2×#683—21no—
95C2×C4×Dic5—21no—
96C5×C22⋊C8—24no—
97C5×C22⋊C8—22no—
98C5×C22⋊C8C2314yes—
99#3963—22no—
100#3963C2314yes—
101C2×#525—51no—
102C2×#407D511yescharacteristic, complemented
103C2×#380—51no—
104#1513—58no—
105C2×#328—52no—
106C2×#327—52no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—42no—
110C24×C5—42no—
111C24×C5C22⋊C411yescharacteristic
112C24×C5C22⋊C411yescharacteristic
113C24×C5C22⋊C412yes—
114C24×C5C2×D411yescharacteristic
115C24×C5C2×D412yes—
116C23×D5—21no—
117C22×C4×C5—24no—
118C22×C4×C5—24no—
119C22×C4×C5—24no—
120C22×C4×C5—44no—
121C22×C4×C5—44no—
122C22×C4×C5—44no—
123C22×C4×C5—44no—
124C22×C4×C5—42no—
125C22×C4×C5—42no—
126C22×C4×C5—42no—
127C22×C4×C5C22⋊C412yes—
128C22×C4×C5C22⋊C411yescharacteristic
129C22×C4×C5C22⋊C412yes—
130C22×C4×C5C22⋊C412yes—
131C22×C4×C5C22⋊C412yes—
132C22×C4×C5C22⋊C412yes—
133C22×C4×C5C22⋊C411yescharacteristic
134C22×C4×C5C22×C411yescharacteristic
135C22×C4×C5C22×C412yes—
136C22×C4×C5C22×C411yescharacteristic
137C22×C4×C5C22×C412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D411yescharacteristic
140C22×C4×C5C2×D411yescharacteristic
141C22×C4×C5C2×D412yes—
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D412yes—
144C22×C4×C5C2411yescharacteristic
145C2×C22⋊D5—24no—
146C2×C22⋊D5—22no—
147C2×C22⋊D5—24no—
148C2×C22⋊D5—22no—
149C2×C22⋊D5—44no—
150C2×C22⋊D5—44no—
151C2×C22⋊D5—42no—
152C2×C22⋊D5—42no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—24no—
157C22×Dic5—44no—
158C22×Dic5—44no—
159C22×Dic5—44no—
160#709—48no—
161#709—48no—
162C2×D20—21no—
163C2×D20—42no—
164C2×D20C22×C412yes—
165C2×C4×D5—24no—
166C2×C4×D5—44no—
167C2×Dic10—21no—
168C2×Dic10—42no—
169C2×Dic10C22×C412yes—
170C5×M16—48no—
171C2×C5×C8—24no—
172C2×C5×C8—44no—
173C22⋊Dic5—22no—
174C22⋊Dic5—24no—
175C22⋊Dic5—24no—
176C22⋊Dic5—22no—
177C22⋊Dic5—48no—
178#685—22no—
179#685—24no—
180#685—22no—
181C4⋊Dic5—21no—
182C4⋊Dic5—21no—
183C4⋊Dic5—48no—
184C4⋊Dic5C22×C412yes—
185C4⋊Dic5C22×C412yes—
186#683—22no—
187#683—24no—
188#683—22no—
189C4×Dic5—24no—
190C22×#41—51no—
191C24×C4C2×D511yescharacteristic
192C22×M16—21no—
193#525—54no—
194#525—54no—
195#525—102no—
196#525—102no—
197C2×#123—101no—
198C2×C22⋊Q8—51no—
199C2×C22⋊Q8—51no—
200C2×#121—51no—
201C2×#121—51no—
202C2×#120—101no—
203C2×C4×D4—101no—
204C2×C4×D4—101no—
205C2×#117—51no—
206C22×C4⋊C4—101no—
207C22×C22⋊C4—101no—
208#407—22no—
209#407C2×D514yescomplemented
210C2×C22⋊C8—21no—
211C2×C22⋊C8C2×D512yes—
212#380—54no—
213#380—102no—
214C2×#95—52no—
215#328—58no—
216#327—58no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—22no—
220C23×C5—22no—
221C23×C5—22no—
222C23×C5—22no—
223C23×C5—24no—
224C23×C5—22no—
225C23×C5—22no—
226C23×C5—22no—
227C23×C5—22no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5—42no—
232C23×C5—48no—
233C23×C5—48no—
234C23×C5C2×C22⋊C412yes—
235C23×C5C2×C22⋊C412yes—
236C23×C5C2×C22⋊C411yescharacteristic
237C23×C5C2×C22⋊C411yescharacteristic
238C23×C5AGL(1,ℤ/8)12yes—
239C23×C5#13712yes—
240C23×C5C22×D411yescharacteristic
241C22×D5—22no—
242C22×D5—42no—
243C22×D5—42no—
244C22×D5—42no—
245C2×C4×C5—22no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—24no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—41no—
257C2×C4×C5—42no—
258C2×C4×C5—41no—
259C2×C4×C5—41no—
260C2×C4×C5—42no—
261C2×C4×C5—41no—
262C2×C4×C5#9914yes—
263C2×C4×C5C2×C22⋊C411yescharacteristic
264C2×C4×C5C2×C22⋊C412yes—
265C2×C4×C5C2×C22⋊C411yescharacteristic
266C2×C4×C5C2×C22⋊C412yes—
267C2×C4×C5C23×C411yescharacteristic
268C2×C4×C5C22×D411yescharacteristic
269C22⋊D5—48no—
270C22⋊D5—48no—
271C22⋊D5—42no—
272C22⋊D5—42no—
273C22⋊D5—44no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5—44no—
281C2×Dic5—44no—
282C2×Dic5—44no—
283C2×Dic5—88no—
284D20—42no—
285D20—42no—
286C4×D5—48no—
287Dic10—42no—
288Dic10—42no—
289C5×C8—44no—
290C25D2011yescharacteristic
291C2×#41—54no—
292C2×#41—102no—
293C2×#41—204no—
294C22×Q8—51no—
295C22×D4—51no—
296C22×D4—101no—
297C22×D4—101no—
298C22×D4—101no—
299C23×C4—44no—
300C23×C4—101no—
301C23×C4—102no—
302C23×C4C4×D511yescharacteristic
303C23×C4C4×D511yescharacteristic
304C23×C4C4×D512yes—
305C23×C4D2011yescharacteristic
306C23×C4D2012yes—
307C23×C4C22⋊D511yescharacteristic
308C23×C4C22⋊D511yescharacteristic
309C23×C4C22⋊D512yes—
310C23×C4C22×D511yescharacteristic
311C23×C4C22×D512yes—
312C2×M16—24no—
313C2×M16—44no—
314C22×C8—22no—
315#123—104no—
316#123—104no—
317C22⋊Q8—52no—
318C22⋊Q8—54no—
319C22⋊Q8—52no—
320C22⋊Q8—102no—
321C22⋊Q8—101no—
322C22⋊Q8—101no—
323#121—52no—
324#121—54no—
325#121—52no—
326#121—102no—
327#121—101no—
328#121—101no—
329#120—104no—
330#120—104no—
331C4×D4—104no—
332C4×D4—104no—
333C4×D4—104no—
334C4×D4—104no—
335#117—54no—
336#117—102no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—101no—
340C2×C4⋊C4—101no—
341C2×C4⋊C4—104no—
342C2×C4⋊C4—204no—
343C2×C22⋊C4—101no—
344C2×C22⋊C4—101no—
345C2×C22⋊C4—101no—
346C2×C22⋊C4—101no—
347C2×C22⋊C4—101no—
348C2×C22⋊C4—104no—
349C2×C22⋊C4—204no—
350C2×C42—101no—
351C22⋊C8—24no—
352C22⋊C8—22no—
353C22⋊C8C22×D514yes—
354#95—54no—
355#95—102no—
356C22×C5—21no—
357C22×C5—21no—
358C22×C5—21no—
359C22×C5—21no—
360C22×C5—24no—
361C22×C5—24no—
362C22×C5—22no—
363C22×C5—22no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5—22no—
367C22×C5—22no—
368C22×C5—44no—
369C22×C5—44no—
370C22×C5—48no—
371C22×C5—44no—
372C22×C5—44no—
373C22×C5C2×#9912yes—
374C22×C5#41712yes—
375C22×C5#41712yes—
376C22×C5#42112yes—
377C22×C5C22×C22⋊C411yescharacteristic
378C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C5C2×#13711yescharacteristic
380C2×D5—42no—
381C2×D5—42no—
382C2×D5—42no—
383C2×D5—84no—
384C4×C5—21no—
385C4×C5—21no—
386C4×C5—21no—
387C4×C5—21no—
388C4×C5—22no—
389C4×C5C2×#9914yes—
390Dic5—42no—
391Dic5—42no—
392Dic5—42no—
393Dic5—84no—
394C24—22no—
395C24—22no—
396C24—42no—
397C24—42no—
398C24—101no—
399C24#68511yescharacteristic
400C24#68511yescharacteristic
401C24#68512yes—
402C24C2×D2011yescharacteristic
403C24C2×D2012yes—
404#41—208no—
405#41—208no—
406C2×Q8—52no—
407C2×Q8—101no—
408C2×Q8—202no—
409C2×D4—52no—
410C2×D4—102no—
411C2×D4—104no—
412C2×D4—102no—
413C2×D4—104no—
414C2×D4—101no—
415C2×D4—202no—
416C2×D4—204no—
417C2×D4—204no—
418C2×D4—202no—
419C2×D4—202no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—104no—
434C22×C4—104no—
435C22×C4—204no—
436C22×C4—204no—
437C22×C4—204no—
438C22×C4—204no—
439C22×C4#68512yes—
440C22×C4#68512yes—
441C22×C4#68512yes—
442C22×C4#68511yescharacteristic
443C22×C4#68512yes—
444C22×C4#68512yes—
445C22×C4#68511yescharacteristic
446C22×C4C2×C4×D512yes—
447C22×C4C2×C4×D511yescharacteristic
448C22×C4C2×C4×D512yes—
449C22×C4C2×C4×D511yescharacteristic
450C22×C4C2×D2012yes—
451C22×C4C2×D2011yescharacteristic
452C22×C4C2×C22⋊D512yes—
453C22×C4C2×C22⋊D511yescharacteristic
454C22×C4C2×C22⋊D511yescharacteristic
455C22×C4C2×C22⋊D512yes—
456C22×C4C23×D511yescharacteristic
457M16—48no—
458C2×C8—24no—
459C2×C8—44no—
460C4⋊C4—52no—
461C4⋊C4—52no—
462C4⋊C4—102no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—104no—
466C4⋊C4—102no—
467C4⋊C4—208no—
468C22⋊C4—102no—
469C22⋊C4—104no—
470C22⋊C4—104no—
471C22⋊C4—102no—
472C22⋊C4—102no—
473C22⋊C4—104no—
474C22⋊C4—102no—
475C22⋊C4—208no—
476C42—104no—
477C2×C5—21no—
478C2×C5—21no—
479C2×C5—22no—
480C2×C5—42no—
481C2×C5—42no—
482C2×C5#151314yescomplemented
483C2×C5C22×#9911yescharacteristic
484C2×C5C2×#41711yescharacteristic
485C2×C5C2×#42111yescharacteristic
486D5—82no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—48no—
503C23—48no—
504C23—102no—
505C23—202no—
506C23—202no—
507C23—202no—
508C23#405412yes—
509C23#405512yes—
510C23C2×#68512yes—
511C23C2×#68512yes—
512C23C2×#68511yescharacteristic
513C23C2×#68511yescharacteristic
514C23C22×D2011yescharacteristic
515Q8—202no—
516Q8—202no—
517D4—202no—
518D4—202no—
519D4—208no—
520D4—208no—
521D4—202no—
522D4—202no—
523D4—204no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—202no—
545C2×C4—202no—
546C2×C4—202no—
547C2×C4—208no—
548C2×C4—204no—
549C2×C4—204no—
550C2×C4—204no—
551C2×C4—408no—
552C2×C4#393814yes—
553C2×C4C2×#68511yescharacteristic
554C2×C4C2×#68512yes—
555C2×C4C2×#68511yescharacteristic
556C2×C4C2×#68512yes—
557C2×C4C22×C4×D511yescharacteristic
558C2×C4C22×C22⋊D511yescharacteristic
559C8—44no—
560C5C2×#151311yescharacteristic, complemented, Sylow
561C22—24no—
562C22—24no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—44no—
574C22—44no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—202no—
579C22—202no—
580C22—202no—
581C22—404no—
582C22C2×#393812yes—
583C22#6542212yes—
584C22#6542212yes—
585C22#6542812yes—
586C22C2×#405411yescharacteristic
587C22C2×#405511yescharacteristic
588C22C22×#68511yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—202no—
595C4—202no—
596C4—202no—
597C4—404no—
598C4C2×#393814yes—
599C2—21no—
600C2—21no—
601C2—22no—
602C2—42no—
603C2—42no—
604C2—402no—
605C2#1060077214yesdirect product factor
606C2C22×#393811yescharacteristic
607C2C2×#6542211yescharacteristic
608C2C2×#6542811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#407C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#66125C2
cosocleC22×C4×C5C24
hypercenterC2×#407D5
hypocenterC5C2×#1513
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C5×#407C2semidirect
3. C2×#65501C2semidirect
4. #10600772C2direct (N × H)
5. C2×#64687C2semidirect
6. C2×#64690C2semidirect
8. C22×#709C4semidirect
14. #66125C4semidirect
16. C2×#4076C4semidirect
21. C2×#4072C4semidirect
23. C2×#4070C4semidirect
26. C5×#407C22semidirect
30. #65501C22semidirect
32. #64690C22semidirect
33. #64687C22semidirect
53. C2×#709C2×C4semidirect
71. #4076C2×C4semidirect
82. #4072C2×C4semidirect
91. #4070C2×C4semidirect
102. C2×#407D5semidirect
209. #407C2×D5semidirect
482. C2×C5#1513semidirect
560. C5C2×#1513semidirect
605. C2#10600772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661252
C2×C5×#4072
C2×#655012
#106007722
C2×#646872
C2×#646902
C2×#15135