Finite Group Databasebeta

← C2×#10610861 #12966898

Subgroups — C2×#10610861 #12966898

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65838C211yesmaximal, characteristic
2C2×#65834C211yesmaximal, characteristic, complemented
3C22×C5×#106C211yesmaximal, characteristic, complemented
4C2×#65402C211yesmaximal, characteristic
5C2×#65391C211yesmaximal, characteristic, complemented
6C2×#65255C211yesmaximal, characteristic
7C2×#65253C211yesmaximal, characteristic, complemented
8C2×#65146C212yesmaximal, complemented
9C2×#65143C212yesmaximal, complemented
10#10610861C2116yesmaximal, direct product factor
11C2×#65160C212yesmaximal, complemented
12C2×#65159C212yesmaximal, complemented
13C22×#709C2211yescharacteristic
14C23×C5×C8C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C2×C4×C22⋊D5—22no—
18C2×#4072C2211yescharacteristic
19C2×#4072C2211yescharacteristic
20C2×#4070—22no—
21C22×#681C2211yescharacteristic
22#65838—24no—
23#65838C2218yes—
24C2×#4039C2212yes—
25C2×#4038—21no—
26C2×D5×C4⋊C4—21no—
27#65834—24no—
28#65834C2218yescomplemented
29C2×#4036—21no—
30C2×#4036C2212yes—
31C2×#4034—21no—
32C2×#4034C2212yes—
33C2×#4033C2212yes—
34C2×C5×#106C2212yes—
35C2×C5×#106C2212yes—
36C2×C5×#106C2218yescomplemented
37#65402C2218yes—
38C2×#3953C2211yescharacteristic
39C2×#3953C2211yescharacteristic
40C2×#3948C2211yescharacteristic
41C2×#3948C2211yescharacteristic
42#65391C2218yescomplemented
43C2×#3946C2212yes—
44C2×#3946C2212yes—
45C2×#3942C2212yes—
46#65255C2218yes—
47C2×#3941C2212yes—
48#65253C2218yescomplemented
49C2×#3940C2212yes—
50C2×#3939C2212yes—
51#65160C22116yescomplemented
52#65159C22116yescomplemented
53#65146C22116yescomplemented
54#65143C22116yescomplemented
55C2×#3084—51nomaximal, Sylow
56C23×C4×C5—21no—
57C23×C4×C5—21no—
58C23×C4×C5C2311yescharacteristic
59C22×C22⋊D5—21no—
60C2×#709—22no—
61C2×#709—24no—
62C2×#709Q818yescomplemented
63C2×#709C2314yes—
64C22×D20C2311yescharacteristic
65C22×C4×D5—21no—
66C22×C4×D5—22no—
67C22×Dic10—22no—
68C22×Dic10C2311yescharacteristic
69C22×C5×C8—24no—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2314yes—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—22no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4C2312yes—
78C2×C5×C4⋊C4C2312yes—
79C2×C5×C4⋊C4C2314yes—
80C2×C5×C4⋊C4C2314yes—
81C2×C22⋊Dic5—21no—
82C2×C22⋊Dic5D412yes—
83C4×C22⋊D5—216no—
84C2×#685—22no—
85#4072—22no—
86#4072D414yes—
87#4072C2314yes—
88#4072C2314yes—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5D411yescharacteristic
91C2×C4⋊Dic5D411yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2311yescharacteristic
94#4070—216no—
95C2×#683—22no—
96C2×#683—22no—
97C2×#683—22no—
98C2×C4×Dic5—21no—
99C2×C4×Dic5—22no—
100C2×C4×Dic5C2312yes—
101C2×#681—24no—
102C2×#681C2314yes—
103C22×#168C2312yes—
104#4039—24no—
105#4039C2318yes—
106#4038—28no—
107D5×C4⋊C4—28no—
108#4036—28no—
109#4036—24no—
110#4036C2318yes—
111#4034—28no—
112#4034—24no—
113#4034C2318yes—
114#4033—24no—
115#4033C2318yes—
116C5×#106C2318yes—
117C5×#106C2318yes—
118#3953C2314yes—
119#3953C2314yes—
120#3948C2314yes—
121#3948C2314yes—
122#3946C2318yes—
123#3946C2318yes—
124#3942C2318yes—
125#3941C2318yes—
126#3940C2318yes—
127#3939C2318yes—
128C2×#544—51no—
129C2×#520—51no—
130#3084—516no—
131C2×#479—52no—
132C2×#475—52no—
133C2×#478—52no—
134C2×#476—52no—
135C2×#428—51no—
136C22×#106D511yescharacteristic, complemented
137C2×#424—51no—
138C2×#417—51no—
139C2×#416—51no—
140C24×C5C2×D411yescharacteristic
141C23×D5—21no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—24no—
145C22×C4×C5—24no—
146C22×C4×C5—82no—
147C22×C4×C5—82no—
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D412yes—
150C22×C4×C5C2×Q814yes—
151C22×C4×C5#4114yes—
152C22×C4×C5C2411yescharacteristic
153C22×C4×C5C2412yes—
154C2×C22⋊D5—28no—
155C2×C22⋊D5—24no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5C2×D412yes—
160C22×Dic5C2×D412yes—
161#709—216no—
162#709—28no—
163#709C2×Q8116yescomplemented
164C2×D20—21no—
165C2×D20—22no—
166C2×D20C2×Q814yes—
167C2×D20C2412yes—
168C2×C4×D5—28no—
169C2×C4×D5—24no—
170C2×C4×D5—28no—
171C2×C4×D5—84no—
172C2×Dic10—21no—
173C2×Dic10—22no—
174C2×Dic10—28no—
175C2×Dic10—84no—
176C2×Dic10C2×Q814yes—
177C2×Dic10C2412yes—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—28no—
181C2×C5×C8C2412yes—
182C2×C5×C8C2412yes—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—24no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—24no—
187C5×C4⋊C4C2414yes—
188C5×C4⋊C4C2414yes—
189C22⋊Dic5—24no—
190C22⋊Dic5C2×D418yes—
191#685—28no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—28no—
195C4⋊Dic5C2×D414yes—
196C4⋊Dic5C2×D414yes—
197C4⋊Dic5C2412yes—
198C4⋊Dic5C2412yes—
199#683—28no—
200#683—28no—
201#683—28no—
202C4×Dic5—24no—
203C4×Dic5—28no—
204C4×Dic5C2×D414yes—
205C4×Dic5C2414yes—
206#681—28no—
207C2×#168—24no—
208C2×#168C2414yes—
209C22×#41—51no—
210C22×M16—51no—
211C23×C8C2×D511yescharacteristic
212#544—58no—
213#544—104no—
214C2×C4⋊Q8—52no—
215C2×C4⋊Q8—101no—
216C2×#125—52no—
217C2×#125—101no—
218C2×C22⋊Q8—102no—
219#520—58no—
220#520—104no—
221C2×C4×Q8—52no—
222C2×C4×D4—52no—
223C2×C4×D4—102no—
224C2×#117—51no—
225C2×#117—51no—
226C2×#117—101no—
227C22×C4⋊C4—101no—
228C22×C4⋊C4C2×D511yescharacteristic
229C22×C4⋊C4C2×D511yescharacteristic
230#479—516no—
231#478—516no—
232#476—516no—
233#475—516no—
234#428—58no—
235C2×#107—52no—
236C2×#106—52no—
237C2×#106C2×D512yes—
238C2×#106C2×D512yes—
239C2×#106C2×D518yescomplemented
240#424—58no—
241C2×C4⋊C8—52no—
242C2×C4⋊C8—52no—
243#417—58no—
244#416—58no—
245C2×#103—51no—
246C2×#103—51no—
247C2×#103—52no—
248C2×#102—51no—
249C2×#102—51no—
250C2×#102—52no—
251C23×C5—22no—
252C23×C5—22no—
253C23×C5C22⋊Q814yes—
254C23×C5C22×D412yes—
255C23×C5C22×D411yescharacteristic
256C22×D5—24no—
257C22×D5—22no—
258C22×D5—42no—
259C22×D5—42no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—44no—
263C2×C4×C5—44no—
264C2×C4×C5—84no—
265C2×C4×C5—84no—
266C2×C4×C5C22⋊Q814yes—
267C2×C4×C5C22⋊Q818yes—
268C2×C4×C5C22×D412yes—
269C2×C4×C5C22×D411yescharacteristic
270C2×C4×C5C22×Q812yes—
271C2×C4×C5C22×Q814yes—
272C2×C4×C5C2×#4112yes—
273C2×C4×C5C2×#4114yes—
274C2×C4×C5C2511yescharacteristic
275C22⋊D5—216no—
276C2×Dic5—24no—
277C2×Dic5—24no—
278C2×Dic5—24no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—22no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5C22×D414yes—
285C2×Dic5C22×D414yes—
286D20—24no—
287D20—22no—
288D20C22×Q814yes—
289C4×D5—216no—
290C4×D5—88no—
291Dic10—24no—
292Dic10—22no—
293Dic10—88no—
294Dic10C22×Q814yes—
295C5×C8—22no—
296C5×C8—22no—
297#168—24no—
298C2×#41—58no—
299C2×#41—54no—
300C2×#41—104no—
301C2×#41—102no—
302C22×Q8—51no—
303C22×Q8—102no—
304C22×D4—51no—
305C22×D4—101no—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—102no—
309C23×C4—101no—
310C23×C4C22×D511yescharacteristic
311C2×M16—54no—
312C2×M16—104no—
313C22×C8—24no—
314C22×C8—52no—
315C22×C8C22×D511yescharacteristic
316C22×C8C22×D511yescharacteristic
317C22×C8C22×D514yes—
318C4⋊Q8—58no—
319C4⋊Q8—104no—
320C4⋊Q8—108no—
321#125—58no—
322#125—104no—
323#125—108no—
324C22⋊Q8—1016no—
325C4×Q8—58no—
326C4×Q8—104no—
327C4×D4—58no—
328C4×D4—104no—
329C4×D4—1016no—
330#117—54no—
331#117—54no—
332#117—54no—
333#117—108no—
334#117—102no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—108no—
344C2×C4⋊C4—102no—
345C2×C4⋊C4—102no—
346C2×C4⋊C4—102no—
347C2×C4⋊C4—102no—
348C2×C4⋊C4C22×D512yes—
349C2×C4⋊C4C22×D514yes—
350C2×C4⋊C4C22×D512yes—
351C2×C4⋊C4C22×D514yes—
352C2×C22⋊C4—52no—
353C2×C22⋊C4—102no—
354C2×C22⋊C4—101no—
355C2×C42—52no—
356C2×C42—102no—
357C2×C42—101no—
358#107—58no—
359#106—58no—
360#106C22×D518yes—
361#106C22×D518yes—
362C4⋊C8—58no—
363C4⋊C8—58no—
364#103—54no—
365#103—54no—
366#103—58no—
367#102—54no—
368#102—54no—
369#102—58no—
370C22×C5—28no—
371C22×C5—22no—
372C22×C5—22no—
373C22×C5C2×C22⋊Q814yes—
374C22×C5C2×C22⋊Q812yes—
375C22×C5#57712yes—
376C22×C5#57712yes—
377C22×C5C23×D411yescharacteristic
378C2×D5—24no—
379C2×D5—48no—
380C2×D5—42no—
381C2×D5—42no—
382C4×C5—44no—
383C4×C5—44no—
384C4×C5C2×C22⋊Q812yes—
385C4×C5C2×C22⋊Q814yes—
386C4×C5C23×Q811yescharacteristic
387C4×C5C22×#4111yescharacteristic
388Dic5—24no—
389Dic5—24no—
390Dic5—24no—
391Dic5—42no—
392Dic5—42no—
393C24—101no—
394C24D4×D511yescharacteristic
395#41—516no—
396#41—108no—
397#41—1016no—
398C2×Q8—54no—
399C2×Q8—52no—
400C2×Q8—108no—
401C2×Q8—102no—
402C2×Q8—101no—
403C2×Q8—404no—
404C2×D4—54no—
405C2×D4—52no—
406C2×D4—104no—
407C2×D4—108no—
408C2×D4—102no—
409C2×D4—101no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—52no—
415C22×C4—52no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—108no—
419C22×C4—101no—
420C22×C4—104no—
421C22×C4—108no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—404no—
425C22×C4#70914yes—
426C22×C4D4×D512yes—
427C22×C4D4×D511yescharacteristic
428C22×C4Q8×D514yes—
429C22×C4C23×D512yes—
430C22×C4C23×D511yescharacteristic
431M16—108no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—54no—
436C2×C8—104no—
437C2×C8C23×D512yes—
438C2×C8C23×D512yes—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—24no—
443C4⋊C4—54no—
444C4⋊C4—54no—
445C4⋊C4—52no—
446C4⋊C4—52no—
447C4⋊C4—108no—
448C4⋊C4—108no—
449C4⋊C4—108no—
450C4⋊C4—108no—
451C4⋊C4—101no—
452C4⋊C4—101no—
453C4⋊C4C23×D514yes—
454C4⋊C4C23×D514yes—
455C22⋊C4—58no—
456C22⋊C4—108no—
457C22⋊C4—104no—
458C42—54no—
459C42—54no—
460C42—108no—
461C42—104no—
462C2×C5—24no—
463C2×C5#308414yescomplemented
464C2×C5C22×C22⋊Q811yescharacteristic
465C2×C5C2×#57711yescharacteristic
466C2×C5C2×#57711yescharacteristic
467D5—44no—
468C23—22no—
469C23—22no—
470C23—104no—
471C23—102no—
472C23—202no—
473C23—202no—
474C23#404214yes—
475C23C2×D4×D512yes—
476C23C2×D4×D511yescharacteristic
477Q8—54no—
478Q8—104no—
479Q8—102no—
480Q8—408no—
481D4—54no—
482D4—1016no—
483D4—104no—
484D4—102no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—54no—
490C2×C4—54no—
491C2×C4—84no—
492C2×C4—84no—
493C2×C4—104no—
494C2×C4—104no—
495C2×C4—104no—
496C2×C4—102no—
497C2×C4—1016no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—202no—
501C2×C4—202no—
502C2×C4—408no—
503C2×C4#404214yes—
504C2×C4#404218yes—
505C2×C4C2×#70912yes—
506C2×C4C2×#70914yes—
507C2×C4C2×D4×D511yescharacteristic
508C2×C4C2×D4×D512yes—
509C2×C4C2×Q8×D512yes—
510C2×C4C2×Q8×D514yes—
511C2×C4C24×D511yescharacteristic
512C8—22no—
513C8—22no—
514C8—104no—
515C5C2×#308411yescharacteristic, complemented, Sylow
516C22—28no—
517C22—22no—
518C22—22no—
519C22—104no—
520C22—208no—
521C22—202no—
522C22—202no—
523C22C2×#404214yes—
524C22C2×#404212yes—
525C22#6609612yes—
526C22#6609612yes—
527C22C22×D4×D511yescharacteristic
528C4—44no—
529C4—44no—
530C4—104no—
531C4—104no—
532C4—104no—
533C4—202no—
534C4—202no—
535C4C2×#404214yes—
536C4C2×#404212yes—
537C4C22×#70911yescharacteristic
538C4C22×Q8×D511yescharacteristic
539C2—24no—
540C2—204no—
541C2#1061086114yesdirect product factor
542C2C22×#404211yescharacteristic
543C2C2×#6609611yescharacteristic
544C2C2×#6609611yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#106C2
socleC23×C5C22×D4
prime radicalC22×#709C22
hypercenterC22×#106D5
hypocenterC5C2×#3084
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
2. C2×#65834C2semidirect
3. C22×C5×#106C2semidirect
5. C2×#65391C2semidirect
7. C2×#65253C2semidirect
8. C2×#65146C2semidirect
9. C2×#65143C2semidirect
10. #10610861C2direct (N × H)
11. C2×#65160C2semidirect
12. C2×#65159C2semidirect
28. #65834C22semidirect
36. C2×C5×#106C22semidirect
42. #65391C22semidirect
48. #65253C22semidirect
51. #65160C22semidirect
52. #65159C22semidirect
53. #65146C22semidirect
54. #65143C22semidirect
62. C2×#709Q8semidirect
136. C22×#106D5semidirect
163. #709C2×Q8semidirect
239. C2×#106C2×D5semidirect
463. C2×C5#3084semidirect
515. C5C2×#3084semidirect
541. C2#10610861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658382
C2×#658342
C22×C5×#1062
C2×#654022
C2×#653912
C2×#652552
C2×#652532
C2×#651462
C2×#651432
#106108612
C2×#651602
C2×#651592
C2×#30845