Finite Group Databasebeta

← C2×#10599075 #12066637

Subgroups — C2×#10599075 #12066637

Order 1280.

1366 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65930C211yesmaximal, characteristic
2C2×#65007C211yesmaximal, characteristic, complemented
3C2×#64939C211yesmaximal, characteristic, complemented
4C2×C5×#327C211yesmaximal, characteristic, complemented
5C2×#64757C211yesmaximal, characteristic, complemented
6C2×#64690C211yesmaximal, characteristic, complemented
7C2×#64671C211yesmaximal, characteristic, complemented
8#10599075C218yesmaximal, direct product factor
9C22×#711—21no—
10C2×C5×#121C2211yescharacteristic
11C2×#4086C411yescharacteristic, complemented
12C2×#4085—21no—
13C2×D4×Dic5C411yescharacteristic, complemented
14C2×#4076C2211yescharacteristic
15C22×#683—21no—
16C22×C4×Dic5C2211yescharacteristic
17#65930—22no—
18#65930—22no—
19#65930C414yescomplemented
20#65930C2214yes—
21C2×#4039C411yescharacteristic, complemented
22C2×#4034C411yescharacteristic, complemented
23C2×#4031—21no—
24C2×#4027—21no—
25C2×C5×C22⋊C8C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×#3963—21no—
28C2×#3963C2211yescharacteristic
29C2×C22⋊#168C2211yescharacteristic
30C2×#3946—21no—
31C2×C8×Dic5—21no—
32#65007—22no—
33#65007C2214yescomplemented
34#64939—22no—
35#64939C2214yescomplemented
36C5×#327C2214yescomplemented
37#64757C2214yescomplemented
38#64690C2214yescomplemented
39#64671C2214yescomplemented
40C2×#1517—51nomaximal, Sylow
41C22×C5×D4—21no—
42C22×C5×D4C2×C411yescharacteristic
43C23×C4×C5—21no—
44C23×C4×C5C2311yescharacteristic
45C22×C22⋊D5—21no—
46C22×C22⋊D5—21no—
47C22×C22⋊D5—21no—
48C23×Dic5—21no—
49C23×Dic5—21no—
50C23×Dic5D411yescharacteristic
51C23×Dic5D411yescharacteristic
52C2×#711—24no—
53C2×#711—24no—
54C2×#711—44no—
55C2×#711—44no—
56C22×D20C2×C411yescharacteristic
57C22×C4×D5—21no—
58C22×Dic10—21no—
59C22×C5×C8—21no—
60C5×#121—21no—
61C5×#121—21no—
62C5×#121C2×C412yes—
63C5×#121C2312yes—
64C2×C5×C4⋊C4C2×C411yescharacteristic
65C2×C5×C22⋊C4—21no—
66C2×C22⋊Dic5—21no—
67#4086—22no—
68#4086C2×C414yescomplemented
69#4085—24no—
70#4085—24no—
71D4×Dic5—22no—
72D4×Dic5C2×C414yescomplemented
73#4076—21no—
74#4076—21no—
75#4076C2×C412yes—
76#4076C2312yes—
77C2×#685—21no—
78C2×#685—21no—
79C2×C4⋊Dic5C2×C411yescharacteristic
80C2×#683—21no—
81C2×#683—24no—
82C2×#683—44no—
83C2×C4×Dic5C2×C411yescharacteristic
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5C2×C412yes—
86C2×C4×Dic5D412yes—
87C2×C4×Dic5D411yescharacteristic
88C2×C4×Dic5D411yescharacteristic
89C2×C4×Dic5D412yes—
90C2×C4×Dic5C2312yes—
91C22×#168—21no—
92#4039—22no—
93#4039C2×C414yescomplemented
94#4034—22no—
95#4034C2×C414yescomplemented
96#4031—24no—
97#4031—24no—
98#4027—24no—
99#4027—24no—
100C5×C22⋊C8—21no—
101C5×C22⋊C8C2312yes—
102C5×#95—21no—
103C5×#95C2312yes—
104#3963—21no—
105#3963—24no—
106#3963C2312yes—
107C22⋊#168—21no—
108C22⋊#168C2312yes—
109#3946—24no—
110C8×Dic5—24no—
111C2×#532—51no—
112C2×#431—51no—
113C2×#382—51no—
114#1517—58no—
115C2×#327—51no—
116C2×#327—51no—
117C2×#327—51no—
118C2×#327D511yescharacteristic, complemented
119C24×C5—21no—
120C24×C5C2×D411yescharacteristic
121C23×D5—21no—
122C2×C5×D4—22no—
123C2×C5×D4—22no—
124C2×C5×D4—21no—
125C2×C5×D4—42no—
126C2×C5×D4—42no—
127C2×C5×D4—42no—
128C2×C5×D4C22×C412yes—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
131C22×C4×C5—42no—
132C22×C4×C5—42no—
133C22×C4×C5—42no—
134C22×C4×C5—42no—
135C22×C4×C5C22×C411yescharacteristic
136C22×C4×C5C22×C411yescharacteristic
137C22×C4×C5C2×D411yescharacteristic
138C22×C4×C5C2×D411yescharacteristic
139C22×C4×C5C2×D411yescharacteristic
140C22×C4×C5C2411yescharacteristic
141C2×C22⋊D5—22no—
142C2×C22⋊D5—22no—
143C2×C22⋊D5—24no—
144C2×C22⋊D5—24no—
145C2×C22⋊D5—44no—
146C2×C22⋊D5—42no—
147C2×C22⋊D5—42no—
148C2×C22⋊D5—44no—
149C22×Dic5—21no—
150C22×Dic5—24no—
151C22×Dic5—22no—
152C22×Dic5—42no—
153C22×Dic5—44no—
154C22×Dic5—42no—
155C22×Dic5—42no—
156C22×Dic5—42no—
157C22×Dic5C22⋊C411yescharacteristic
158C22×Dic5C22⋊C411yescharacteristic
159C22×Dic5C22⋊C412yes—
160C22×Dic5C22⋊C411yescharacteristic
161C22×Dic5C22⋊C411yescharacteristic
162C22×Dic5C22⋊C412yes—
163C22×Dic5D814yes—
164C22×Dic5SD1614yes—
165C22×Dic5C2×D412yes—
166C22×Dic5C2×D412yes—
167#711—416no—
168#711—48no—
169#711—48no—
170C2×D20—21no—
171C2×D20—42no—
172C2×D20C22×C412yes—
173C2×C4×D5—24no—
174C2×C4×D5—44no—
175C2×Dic10—24no—
176C2×Dic10—44no—
177C2×C5×C8—22no—
178C2×C5×C8—42no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4C22×C412yes—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C22⋊Dic5—24no—
184#685—22no—
185#685—22no—
186#685—24no—
187C4⋊Dic5—21no—
188C4⋊Dic5C22×C412yes—
189#683—24no—
190#683—48no—
191C4×Dic5C22⋊C412yes—
192C4×Dic5C22⋊C412yes—
193C4×Dic5C22⋊C412yes—
194C4×Dic5C22⋊C412yes—
195C4×Dic5C22×C412yes—
196C4×Dic5C22×C412yes—
197C4×Dic5C2×D412yes—
198C4×Dic5C2×D412yes—
199C2×#168—22no—
200C2×#168—42no—
201C22×#41—101no—
202#532—54no—
203#532—54no—
204#532—102no—
205#532—102no—
206C2×C4⋊Q8—51no—
207C2×#127—51no—
208C2×#124—101no—
209C2×#121—51no—
210C2×#121—101no—
211C2×#121C2×D511yescharacteristic
212C2×C4×D4—51no—
213C2×C4×D4—51no—
214C2×C4×D4—101no—
215C22×C4⋊C4—101no—
216C22×C42—51no—
217#431—54no—
218#431—102no—
219C2×C4⋊C8—101no—
220C2×C22⋊C8—51no—
221C2×C22⋊C8C2×D511yescharacteristic
222C2×C4×C8—101no—
223#382—54no—
224#382—102no—
225C2×#95—51no—
226C2×#95—101no—
227C2×#95C2×D511yescharacteristic
228#327—54no—
229#327—54no—
230#327—54no—
231#327C2×D514yescomplemented
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5C2×C22⋊C411yescharacteristic
239C23×C5C2×C22⋊C411yescharacteristic
240C23×C5C2×D812yes—
241C23×C5C2×SD1612yes—
242C23×C5C22×D411yescharacteristic
243C22×D5—22no—
244C22×D5—42no—
245C22×D5—42no—
246C22×D5—42no—
247C5×D4—42no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—42no—
251C5×D4—44no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—84no—
264C2×C4×C5C2×C22⋊C411yescharacteristic
265C2×C4×C5C2×C22⋊C411yescharacteristic
266C2×C4×C5C23×C411yescharacteristic
267C2×C4×C5C22×D411yescharacteristic
268C22⋊D5—48no—
269C22⋊D5—42no—
270C22⋊D5—42no—
271C22⋊D5—44no—
272C22⋊D5—48no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—42no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—48no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—84no—
284C2×Dic5#10214yes—
285C2×Dic5#10214yes—
286C2×Dic5#10218yes—
287C2×Dic5C2×C22⋊C412yes—
288C2×Dic5C2×C22⋊C412yes—
289C2×Dic5C2×C22⋊C412yes—
290C2×Dic5C2×C22⋊C412yes—
291C2×Dic5C2×D814yes—
292C2×Dic5C2×SD1614yes—
293D20—42no—
294D20—42no—
295C4×D5—48no—
296Dic10—48no—
297C5×C8—42no—
298#168—42no—
299C2×#41—104no—
300C2×#41—104no—
301C2×#41—204no—
302C2×#41—204no—
303C22×Q8—101no—
304C22×D4—21no—
305C22×D4—51no—
306C22×D4—101no—
307C22×D4—101no—
308C22×D4—101no—
309C22×D4C4×D511yescharacteristic
310C23×C4—21no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—101no—
314C23×C4—101no—
315C23×C4—101no—
316C23×C4C22×D511yescharacteristic
317C22×C8—21no—
318C22×C8—101no—
319C4⋊Q8—54no—
320C4⋊Q8—102no—
321#127—54no—
322#127—102no—
323#124—104no—
324#124—104no—
325#121—21no—
326#121—21no—
327#121—52no—
328#121—52no—
329#121—104no—
330#121—104no—
331#121—101no—
332#121—101no—
333#121C4×D512yes—
334#121C22×D512yes—
335C4×D4—54no—
336C4×D4—54no—
337C4×D4—104no—
338C4×D4—104no—
339C4×D4—102no—
340C4×D4—102no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—104no—
344C2×C4⋊C4—204no—
345C2×C4⋊C4C4×D511yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—101no—
348C2×C22⋊C4—101no—
349C2×C22⋊C4—101no—
350C2×C42—51no—
351C2×C42—51no—
352C2×C42—52no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—52no—
356C2×C42—52no—
357C2×C42—52no—
358C4⋊C8—104no—
359C22⋊C8—21no—
360C22⋊C8—52no—
361C22⋊C8—101no—
362C22⋊C8C22×D512yes—
363C4×C8—104no—
364#95—21no—
365#95—52no—
366#95—104no—
367#95—101no—
368#95C22×D512yes—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—21no—
373C22×C5—24no—
374C22×C5—24no—
375C22×C5—42no—
376C22×C5—42no—
377C22×C5—42no—
378C22×C5—84no—
379C22×C5#41012yes—
380C22×C5C2×#10212yes—
381C22×C5C2×#10212yes—
382C22×C5#42112yes—
383C22×C5C22×C22⋊C411yescharacteristic
384C22×C5C22×D811yescharacteristic
385C22×C5C22×SD1611yescharacteristic
386C2×D5—42no—
387C2×D5—42no—
388C2×D5—42no—
389C2×D5—84no—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—21no—
394C4×C5—42no—
395C4×C5—82no—
396Dic5—22no—
397Dic5—22no—
398Dic5—42no—
399Dic5—82no—
400Dic5C2×#10214yes—
401Dic5C2×#10214yes—
402C24—21no—
403C24—101no—
404C24D4×D511yescharacteristic
405#41—2016no—
406#41—208no—
407#41—208no—
408C2×Q8—104no—
409C2×Q8—204no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—21no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—52no—
417C2×D4—104no—
418C2×D4—104no—
419C2×D4—102no—
420C2×D4—102no—
421C2×D4—101no—
422C2×D4—202no—
423C2×D4—204no—
424C2×D4—204no—
425C2×D4—202no—
426C2×D4—202no—
427C2×D4C2×C4×D512yes—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—52no—
435C22×C4—52no—
436C22×C4—51no—
437C22×C4—51no—
438C22×C4—54no—
439C22×C4—54no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—52no—
443C22×C4—52no—
444C22×C4—104no—
445C22×C4—104no—
446C22×C4—101no—
447C22×C4—102no—
448C22×C4—204no—
449C22×C4—204no—
450C22×C4—202no—
451C22×C4—202no—
452C22×C4—202no—
453C22×C4—202no—
454C22×C4C2×C4×D511yescharacteristic
455C22×C4C2×C4×D511yescharacteristic
456C22×C4D4×D511yescharacteristic
457C22×C4D4×D511yescharacteristic
458C22×C4D4×D511yescharacteristic
459C22×C4C23×D511yescharacteristic
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—102no—
463C2×C8—202no—
464C4⋊C4—21no—
465C4⋊C4—52no—
466C4⋊C4—104no—
467C4⋊C4—101no—
468C4⋊C4—208no—
469C4⋊C4C2×C4×D512yes—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—104no—
473C22⋊C4—104no—
474C22⋊C4—102no—
475C22⋊C4—102no—
476C42—52no—
477C42—52no—
478C42—52no—
479C42—52no—
480C42—52no—
481C42—52no—
482C42—52no—
483C42—52no—
484C2×C5—21no—
485C2×C5—21no—
486C2×C5—22no—
487C2×C5—82no—
488C2×C5#151714yescomplemented
489C2×C5C2×#41011yescharacteristic
490C2×C5C22×#10211yescharacteristic
491C2×C5C2×#42111yescharacteristic
492D5—82no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—102no—
500C23—202no—
501C23—202no—
502C23—202no—
503C23D5×C22⋊C411yescharacteristic
504C23D5×C22⋊C411yescharacteristic
505C23D5×D812yes—
506C23D5×SD1612yes—
507C23C2×D4×D511yescharacteristic
508Q8—208no—
509D4—42no—
510D4—42no—
511D4—44no—
512D4—42no—
513D4—42no—
514D4—202no—
515D4—202no—
516D4—208no—
517D4—208no—
518D4—204no—
519D4—202no—
520D4—202no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—54no—
535C2×C4—54no—
536C2×C4—58no—
537C2×C4—54no—
538C2×C4—54no—
539C2×C4—52no—
540C2×C4—52no—
541C2×C4—84no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—208no—
546C2×C4—208no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—202no—
550C2×C4—202no—
551C2×C4—202no—
552C2×C4—202no—
553C2×C4—404no—
554C2×C4D5×C22⋊C411yescharacteristic
555C2×C4D5×C22⋊C411yescharacteristic
556C2×C4C22×C4×D511yescharacteristic
557C2×C4C2×D4×D511yescharacteristic
558C8—42no—
559C8—202no—
560C5C2×#151711yescharacteristic, complemented, Sylow
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—202no—
572C22—202no—
573C22—202no—
574C22—404no—
575C22#6502912yes—
576C22D5×#10212yes—
577C22D5×#10212yes—
578C22#6511012yes—
579C22C2×D5×C22⋊C411yescharacteristic
580C22C2×D5×D811yescharacteristic
581C22C2×D5×SD1611yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—54no—
588C4—54no—
589C4—82no—
590C4—102no—
591C4—102no—
592C4—202no—
593C4—402no—
594C2—21no—
595C2—22no—
596C2—21no—
597C2—82no—
598C2—402no—
599C2#1059907514yesdirect product factor
600C2C2×#6502911yescharacteristic
601C2C2×D5×#10211yescharacteristic
602C2C2×#6511011yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#327C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#65930C2
cosocleC22×C4×C5C24
hypercenterC2×#327D5
hypocenterC5C2×#1517
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#65007C2semidirect
3. C2×#64939C2semidirect
4. C2×C5×#327C2semidirect
5. C2×#64757C2semidirect
6. C2×#64690C2semidirect
7. C2×#64671C2semidirect
8. #10599075C2direct (N × H)
11. C2×#4086C4semidirect
13. C2×D4×Dic5C4semidirect
19. #65930C4semidirect
21. C2×#4039C4semidirect
22. C2×#4034C4semidirect
33. #65007C22semidirect
35. #64939C22semidirect
36. C5×#327C22semidirect
37. #64757C22semidirect
38. #64690C22semidirect
39. #64671C22semidirect
68. #4086C2×C4semidirect
72. D4×Dic5C2×C4semidirect
93. #4039C2×C4semidirect
95. #4034C2×C4semidirect
118. C2×#327D5semidirect
231. #327C2×D5semidirect
488. C2×C5#1517semidirect
560. C5C2×#1517semidirect
599. C2#10599075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659302
C2×#650072
C2×#649392
C2×C5×#3272
C2×#647572
C2×#646902
C2×#646712
#105990752
C2×#15175