Finite Group Databasebeta

← C2×#10613143 #12967301

Subgroups — C2×#10613143 #12967301

Order 1280.

2570 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65956C211yesmaximal, characteristic, complemented
2C22×#4039C211yesmaximal, characteristic
3C2×C5×#483C211yesmaximal, characteristic, complemented
4C2×#65335C211yesmaximal, characteristic
5C2×#65260C211yesmaximal, characteristic, complemented
6#10613143C2116yesmaximal, direct product factor
7C2×#65159C212yesmaximal, complemented
8C2×#65141C212yesmaximal, complemented
9C2×#65107C212yesmaximal, complemented
10C2×#65077C212yesmaximal, complemented
11C2×#65020C211yesmaximal, characteristic
12C2×#65007C211yesmaximal, characteristic, complemented
13C23×D20C2211yescharacteristic
14C23×C4×D5—21no—
15C2×C5×C22⋊Q8C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C2×Q8×Dic5C2211yescharacteristic, complemented
18C2×#4090C2211yescharacteristic, complemented
19C22×#688C2212yes—
20C22×#685—21no—
21C2×#4070C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C22×#677C2212yes—
24#65956—24no—
25#65956C2218yescomplemented
26C2×#4039—21no—
27C2×#4039—21no—
28C2×#4039—24no—
29C2×#4039C2212yes—
30C2×#4039C2212yes—
31C2×#4039C2218yes—
32C2×#4035—21no—
33C2×#4034C2211yescharacteristic, complemented
34C2×#4033—21no—
35C2×#4033C2211yescharacteristic, complemented
36C2×#4024—21no—
37C2×#4023—21no—
38C5×#483C2218yescomplemented
39C2×C5×#106C2212yescomplemented
40C2×C5×#103C2212yescomplemented
41C2×C5×C22⋊C8C2211yescharacteristic
42C2×C22⋊#168C2211yescharacteristic
43C2×#3953C2212yes—
44C2×#3946C2212yescomplemented
45C2×C8×Dic5C2212yescomplemented
46#65335C2218yes—
47#65260C2218yescomplemented
48C2×#3942C2212yescomplemented
49C2×#3941C2212yes—
50C2×#3940C2212yescomplemented
51#65159C22116yescomplemented
52#65141C22116yescomplemented
53#65107C22116yescomplemented
54#65077C22116yescomplemented
55#65020C2218yes—
56#65007C2218yescomplemented
57C2×#3101—51nomaximal, Sylow
58C24×D5—21no—
59C22×C5×Q8C2311yescharacteristic
60C23×C4×C5—21no—
61C23×C4×C5C2311yescharacteristic
62C23×Dic5D411yescharacteristic
63C23×Dic5D411yescharacteristic
64C22×D20—21no—
65C22×D20—22no—
66C22×D20—28no—
67C22×D20C2314yes—
68C22×D20C2312yes—
69C22×C4×D5—22no—
70C22×C4×D5—22no—
71C22×C4×D5—28no—
72C22×C4×D5—48no—
73C22×Dic10—21no—
74C22×Dic10C2311yescharacteristic
75C22×C5×C8C2312yes—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8C2314yes—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—22no—
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C4⋊C4C2312yes—
83C2×C5×C4⋊C4C2314yes—
84C2×C5×C22⋊C4—21no—
85C2×C22⋊Dic5—21no—
86Q8×Dic5—22no—
87Q8×Dic5C2314yescomplemented
88#4090—22no—
89#4090C2314yescomplemented
90C2×#688—28no—
91C2×#688C2318yes—
92C2×#685—22no—
93C2×#685—22no—
94C2×#685—28no—
95C2×C4⋊Dic5—21no—
96C2×C4⋊Dic5C2311yescharacteristic
97#4070—22no—
98#4070C2314yes—
99C2×#683—21no—
100C2×#683—21no—
101C2×#683—21no—
102C2×#683—21no—
103C2×#683—21no—
104C2×C4×Dic5—21no—
105C2×C4×Dic5—21no—
106C2×C4×Dic5D411yescharacteristic
107C2×C4×Dic5D411yescharacteristic
108C2×C4×Dic5D414yes—
109C2×C4×Dic5C2311yescharacteristic
110C2×C4×Dic5C2311yescharacteristic
111C2×C4×Dic5C2314yes—
112C22×#168C2312yes—
113C2×#677—28no—
114C2×#677C2318yes—
115#4039—28no—
116#4039—24no—
117#4039—24no—
118#4039—28no—
119#4039C2318yes—
120#4039C2318yes—
121#4035—28no—
122#4034—22no—
123#4034C2314yescomplemented
124#4033—28no—
125#4033—22no—
126#4033C2314yescomplemented
127#4024—28no—
128#4023—28no—
129C5×#106C2318yescomplemented
130C5×#103C2318yescomplemented
131C5×C22⋊C8C2314yes—
132C22⋊#168C2314yes—
133#3953C2318yes—
134#3946C2318yescomplemented
135C8×Dic5C2318yescomplemented
136#3942C2318yescomplemented
137#3941C2318yes—
138#3940C2318yescomplemented
139C2×#533—51no—
140C22×C4×D4—51no—
141#3101—516no—
142C2×#483—51no—
143C2×#483D511yescharacteristic, complemented
144C2×#476—52no—
145C2×#461—52no—
146C2×#450—51no—
147C2×#450—51no—
148C2×C4×SD16—52no—
149C2×C4×SD16—52no—
150C2×#431—51no—
151C24×C5C2×D411yescharacteristic
152C23×D5—28no—
153C23×D5—24no—
154C23×D5—22no—
155C23×D5—44no—
156C23×D5—44no—
157C2×C5×Q8—21no—
158C2×C5×Q8—24no—
159C2×C5×Q8C2412yes—
160C22×C4×C5—24no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—24no—
164C22×C4×C5—22no—
165C22×C4×C5—44no—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D412yes—
168C22×C4×C5C2412yes—
169C22×C4×C5C2411yescharacteristic
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—42no—
173C22×Dic5SD1618yescomplemented
174C22×Dic5C2×D411yescharacteristic
175C22×Dic5C2×D411yescharacteristic
176C22×Dic5C2×D414yes—
177C22×Dic5C2×D411yescharacteristic
178C22×Dic5C2×D411yescharacteristic
179C22×Dic5C2×D414yes—
180C2×D20—28no—
181C2×D20—216no—
182C2×D20—24no—
183C2×D20—22no—
184C2×D20—24no—
185C2×D20—216no—
186C2×D20#4118yes—
187C2×D20C2414yes—
188C2×C4×D5—28no—
189C2×C4×D5—28no—
190C2×C4×D5—48no—
191C2×C4×D5—48no—
192C2×C4×D5—432no—
193C2×Dic10—24no—
194C2×Dic10—21no—
195C2×Dic10—24no—
196C2×Dic10—44no—
197C2×Dic10C2412yes—
198C2×C5×C8—24no—
199C2×C5×C8C2414yes—
200C5×C4⋊C4—24no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—24no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4C2414yes—
205C5×C4⋊C4C2412yes—
206C5×C22⋊C4—24no—
207C22⋊Dic5—24no—
208#688—216no—
209#685—28no—
210#685—28no—
211C4⋊Dic5—21no—
212C4⋊Dic5—24no—
213C4⋊Dic5C2412yes—
214#683—24no—
215#683—24no—
216#683—24no—
217#683—24no—
218#683—24no—
219C4×Dic5—24no—
220C4×Dic5—24no—
221C4×Dic5C2×D414yes—
222C4×Dic5C2×D412yes—
223C4×Dic5C2×D412yes—
224C4×Dic5C2×D414yes—
225C4×Dic5C2412yes—
226C4×Dic5C2412yes—
227C2×#168—24no—
228C2×#168C2414yes—
229#677—216no—
230C23×D4—51no—
231C24×C4—101no—
232C22×SD16—52no—
233C22×SD16—52no—
234#533—58no—
235#533—104no—
236C2×C4⋊Q8—51no—
237C2×C4⋊Q8—51no—
238C2×#125—101no—
239C2×C22⋊Q8—51no—
240C2×C22⋊Q8—101no—
241C2×C22⋊Q8C2×D511yescharacteristic
242C2×C4×Q8—51no—
243C2×C4×Q8—51no—
244C2×C4×Q8—101no—
245C2×C4×D4—58no—
246C2×C4×D4—52no—
247C2×C4×D4—52no—
248C2×C4×D4—101no—
249C2×C4×D4—101no—
250C2×C4×D4—104no—
251C2×#117—101no—
252C22×C4⋊C4C2×D511yescharacteristic
253C22×C22⋊C4—101no—
254C22×C42—51no—
255#483—58no—
256#483C2×D518yescomplemented
257#476—516no—
258#461—516no—
259#450—58no—
260#450—58no—
261C4×SD16—516no—
262C4×SD16—516no—
263#431—58no—
264C2×#106—52no—
265C2×#106C2×D512yescomplemented
266C2×C4⋊C8—52no—
267C2×#103—52no—
268C2×#103C2×D512yescomplemented
269C2×#102—52no—
270C2×#102—52no—
271C2×C22⋊C8—51no—
272C2×C22⋊C8C2×D511yescharacteristic
273C2×C4×C8—52no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5C2×SD1614yes—
277C23×C5C22×D412yes—
278C23×C5C22×D411yescharacteristic
279C22×D5—216no—
280C22×D5—28no—
281C22×D5—24no—
282C22×D5—432no—
283C22×D5—48no—
284C22×D5—48no—
285C22×D5—44no—
286C22×D5—44no—
287C5×Q8—24no—
288C5×Q8—42no—
289C2×C4×C5—22no—
290C2×C4×C5—24no—
291C2×C4×C5—24no—
292C2×C4×C5—22no—
293C2×C4×C5—22no—
294C2×C4×C5—24no—
295C2×C4×C5—42no—
296C2×C4×C5—48no—
297C2×C4×C5—44no—
298C2×C4×C5—42no—
299C2×C4×C5C22×D412yes—
300C2×C4×C5C22×D411yescharacteristic
301C2×C4×C5C2×#4114yes—
302C2×C4×C5C2511yescharacteristic
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—44no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5C2×SD1614yes—
311C2×Dic5C2×SD1614yes—
312C2×Dic5C2×SD16116yescomplemented
313C2×Dic5C22×D412yes—
314C2×Dic5C22×D412yes—
315C2×Dic5C22×D412yes—
316C2×Dic5C22×D412yes—
317D20—216no—
318D20—28no—
319D20—24no—
320D20C2×#4118yes—
321C4×D5—416no—
322C4×D5—416no—
323Dic10—24no—
324Dic10—48no—
325Dic10—42no—
326C5×C8—24no—
327#168—24no—
328C25—101no—
329C22×Q8—51no—
330C22×Q8—101no—
331C22×Q8C22×D511yescharacteristic
332C22×D4—52no—
333C22×D4—54no—
334C22×D4—108no—
335C22×D4—102no—
336C22×D4—101no—
337C23×C4—21no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—108no—
341C23×C4—102no—
342C23×C4—102no—
343C23×C4—208no—
344C23×C4C22×D511yescharacteristic
345C2×SD16—58no—
346C2×SD16—58no—
347C2×SD16—108no—
348C2×SD16—108no—
349C22×C8—52no—
350C22×C8C22×D512yes—
351C4⋊Q8—54no—
352C4⋊Q8—54no—
353C4⋊Q8—102no—
354C4⋊Q8—102no—
355#125—108no—
356C22⋊Q8—22no—
357C22⋊Q8—54no—
358C22⋊Q8—108no—
359C22⋊Q8—102no—
360C22⋊Q8C22×D514yes—
361C4×Q8—54no—
362C4×Q8—54no—
363C4×Q8—102no—
364C4×Q8—108no—
365C4×Q8—102no—
366C4×D4—58no—
367C4×D4—58no—
368C4×D4—108no—
369C4×D4—104no—
370C4×D4—108no—
371C4×D4—104no—
372#117—108no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4—101no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4—101no—
383C2×C4⋊C4C22×D512yes—
384C2×C4⋊C4C22×D514yes—
385C2×C4⋊C4C22×D511yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—108no—
388C2×C22⋊C4—102no—
389C2×C22⋊C4—102no—
390C2×C22⋊C4—101no—
391C2×C42—51no—
392C2×C42—51no—
393C2×C42—54no—
394C2×C42—51no—
395C2×C42—51no—
396C2×C42—54no—
397C2×C42—101no—
398C2×C42—101no—
399#106—58no—
400#106C22×D518yescomplemented
401C4⋊C8—58no—
402#103—58no—
403#103C22×D518yescomplemented
404#102—58no—
405#102—58no—
406C22⋊C8—54no—
407C22⋊C8C22×D514yes—
408C4×C8—58no—
409C22×C5—28no—
410C22×C5—22no—
411C22×C5—22no—
412C22×C5#52512yes—
413C22×C5C22×SD1614yes—
414C22×C5C22×SD1612yes—
415C22×C5#57512yes—
416C22×C5C23×D411yescharacteristic
417C2×D5—28no—
418C2×D5—432no—
419C2×D5—416no—
420C2×D5—44no—
421C2×D5—44no—
422C4×C5—22no—
423C4×C5—42no—
424C4×C5—44no—
425C4×C5—42no—
426C4×C5#52512yes—
427C4×C5C22×#4112yes—
428Dic5—22no—
429Dic5—22no—
430Dic5—42no—
431Dic5—42no—
432Dic5C22×SD1614yes—
433Dic5C22×SD1614yes—
434C24—108no—
435C24—104no—
436C24—102no—
437C24—204no—
438C24—204no—
439C24D4×D511yescharacteristic
440C2×Q8—21no—
441C2×Q8—24no—
442C2×Q8—52no—
443C2×Q8—104no—
444C2×Q8—101no—
445C2×Q8—104no—
446C2×Q8—204no—
447C2×Q8C23×D512yes—
448C2×D4—58no—
449C2×D4—54no—
450C2×D4—1016no—
451C2×D4—108no—
452C2×D4—1016no—
453C2×D4—104no—
454C2×D4—102no—
455C2×D4—104no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—54no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—58no—
466C22×C4—51no—
467C22×C4—51no—
468C22×C4—54no—
469C22×C4—108no—
470C22×C4—108no—
471C22×C4—101no—
472C22×C4—101no—
473C22×C4—208no—
474C22×C4—208no—
475C22×C4—2032no—
476C22×C4—202no—
477C22×C4D4×D512yes—
478C22×C4D4×D511yescharacteristic
479C22×C4C23×D512yes—
480C22×C4C23×D511yescharacteristic
481SD16—1016no—
482SD16—1016no—
483C2×C8—24no—
484C2×C8—54no—
485C2×C8—104no—
486C2×C8C23×D514yes—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—24no—
490C4⋊C4—21no—
491C4⋊C4—52no—
492C4⋊C4—104no—
493C4⋊C4—104no—
494C4⋊C4—104no—
495C4⋊C4—104no—
496C4⋊C4—104no—
497C4⋊C4—101no—
498C4⋊C4—104no—
499C4⋊C4C23×D512yes—
500C4⋊C4C23×D514yes—
501C22⋊C4—24no—
502C22⋊C4—108no—
503C22⋊C4—108no—
504C22⋊C4—104no—
505C42—52no—
506C42—54no—
507C42—54no—
508C42—52no—
509C42—52no—
510C42—52no—
511C42—104no—
512C42—104no—
513C2×C5—24no—
514C2×C5#310114yescomplemented
515C2×C5C2×#52511yescharacteristic
516C2×C5C23×SD1611yescharacteristic
517C2×C5C2×#57511yescharacteristic
518D5—48no—
519C23—22no—
520C23—22no—
521C23—1016no—
522C23—108no—
523C23—104no—
524C23—2032no—
525C23—208no—
526C23—208no—
527C23—204no—
528C23—204no—
529C23D5×SD1614yes—
530C23C2×D4×D512yes—
531C23C2×D4×D511yescharacteristic
532Q8—24no—
533Q8—42no—
534Q8—104no—
535Q8—208no—
536Q8—202no—
537D4—58no—
538D4—1016no—
539D4—108no—
540D4—104no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—54no—
552C2×C4—54no—
553C2×C4—516no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—102no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—102no—
562C2×C4—2016no—
563C2×C4—2016no—
564C2×C4—204no—
565C2×C4—202no—
566C2×C4—202no—
567C2×C4C2×D4×D512yes—
568C2×C4C2×D4×D511yescharacteristic
569C2×C4D5×#4114yes—
570C2×C4C24×D511yescharacteristic
571C8—24no—
572C8—104no—
573C5C2×#310111yescharacteristic, complemented, Sylow
574C22—22no—
575C22—28no—
576C22—22no—
577C22—108no—
578C22—2032no—
579C22—2016no—
580C22—204no—
581C22—204no—
582C22#6599012yes—
583C22C2×D5×SD1614yes—
584C22C2×D5×SD1612yes—
585C22#6611112yes—
586C22C22×D4×D511yescharacteristic
587C4—22no—
588C4—42no—
589C4—44no—
590C4—42no—
591C4—54no—
592C4—54no—
593C4—102no—
594C4—102no—
595C4—202no—
596C4—202no—
597C4#6599012yes—
598C4C2×D5×#4112yes—
599C2—24no—
600C2—208no—
601C2#1061314314yesdirect product factor
602C2C2×#6599011yescharacteristic
603C2C22×D5×SD1611yescharacteristic
604C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#483C2
socleC23×C5C22×D4
prime radicalC23×D20C22
hypercenterC2×#483D5
hypocenterC5C2×#3101
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#65956C2semidirect
3. C2×C5×#483C2semidirect
5. C2×#65260C2semidirect
6. #10613143C2direct (N × H)
7. C2×#65159C2semidirect
8. C2×#65141C2semidirect
9. C2×#65107C2semidirect
10. C2×#65077C2semidirect
12. C2×#65007C2semidirect
17. C2×Q8×Dic5C22semidirect
18. C2×#4090C22semidirect
25. #65956C22semidirect
33. C2×#4034C22semidirect
35. C2×#4033C22semidirect
38. C5×#483C22semidirect
39. C2×C5×#106C22semidirect
40. C2×C5×#103C22semidirect
44. C2×#3946C22semidirect
45. C2×C8×Dic5C22semidirect
47. #65260C22semidirect
48. C2×#3942C22semidirect
50. C2×#3940C22semidirect
51. #65159C22semidirect
52. #65141C22semidirect
53. #65107C22semidirect
54. #65077C22semidirect
56. #65007C22semidirect
87. Q8×Dic5C23semidirect
89. #4090C23semidirect
123. #4034C23semidirect
126. #4033C23semidirect
129. C5×#106C23semidirect
130. C5×#103C23semidirect
134. #3946C23semidirect
135. C8×Dic5C23semidirect
136. #3942C23semidirect
138. #3940C23semidirect
143. C2×#483D5semidirect
173. C22×Dic5SD16semidirect
256. #483C2×D5semidirect
265. C2×#106C2×D5semidirect
268. C2×#103C2×D5semidirect
312. C2×Dic5C2×SD16semidirect
400. #106C22×D5semidirect
403. #103C22×D5semidirect
514. C2×C5#3101semidirect
573. C5C2×#3101semidirect
601. C2#10613143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659562
C22×#40392
C2×C5×#4832
C2×#653352
C2×#652602
#106131432
C2×#651592
C2×#651412
C2×#651072
C2×#650772
C2×#650202
C2×#650072
C2×#31015