Finite Group Databasebeta

← C2×#10610822 #12966883

Subgroups — C2×#10610822 #12966883

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×#65857C211yesmaximal, characteristic
2C2×#65853C211yesmaximal, characteristic, complemented
3C2×C5×#424C211yesmaximal, characteristic, complemented
4C2×#65422C211yesmaximal, characteristic
5C2×#65410C211yesmaximal, characteristic, complemented
6C2×#65402C211yesmaximal, characteristic
7C22×#3950C211yesmaximal, characteristic, complemented
8#10610822C2116yesmaximal, direct product factor
9C2×#65118C212yesmaximal, complemented
10C2×#65139C212yesmaximal, complemented
11C2×#65136C212yesmaximal, complemented
12C2×#65135C212yesmaximal, complemented
13C22×#709C2211yescharacteristic
14C22×C5×M16C2211yescharacteristic
15C23×C5×C8C2211yescharacteristic
16C2×C5×#117C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20#65857—24no—
21#65857C2218yes—
22#65853—24no—
23#65853C2218yescomplemented
24C2×#4038—21no—
25C2×D5×C4⋊C4—21no—
26C2×#4036—21no—
27C2×#4034—21no—
28C2×#4027—22no—
29C2×#4024—22no—
30C2×C4×D20C2212yes—
31C2×#4016C2212yes—
32C2×#4015C2212yes—
33C2×C4×Dic10C2212yes—
34C5×#424C2218yescomplemented
35C2×C5×C4⋊C8C2212yes—
36C2×C5×C4⋊C8C2212yes—
37#65422C2218yes—
38#65410C2218yescomplemented
39#65402C2218yes—
40C2×#3953C2211yescharacteristic
41C2×#3953C2212yes—
42C2×#3953C2211yescharacteristic
43C2×#3950C2212yes—
44C2×#3950C2212yes—
45C2×#3950C2212yes—
46C2×#3950C2218yescomplemented
47C2×#3949C2212yes—
48C2×#3948C2211yescharacteristic
49C2×#3948C2212yes—
50C2×#3948C2211yescharacteristic
51#65139C22116yescomplemented
52#65136C22116yescomplemented
53#65135C22116yescomplemented
54#65118C22116yescomplemented
55C2×#3083—51nomaximal, Sylow
56C23×C4×C5C2311yescharacteristic
57C22×C22⋊D5—21no—
58C23×Dic5—21no—
59C23×Dic5—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
69C2×C5×M16—24no—
70C2×C5×M16C2314yes—
71C22×C5×C8—24no—
72C22×C5×C8C2312yes—
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2314yes—
76C5×#117D414yes—
77C5×#117C2314yes—
78C2×C5×C4⋊C4D411yescharacteristic
79C2×C5×C4⋊C4D411yescharacteristic
80C2×C5×C22⋊C4D412yes—
81C2×C42×C5C2312yes—
82C2×C22⋊Dic5—21no—
83C2×#685—22no—
84#4072—22no—
85#4072C2314yes—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5C2312yes—
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2312yes—
94C2×C4⋊Dic5C2311yescharacteristic
95C2×C4⋊Dic5C2314yes—
96C2×C4⋊Dic5C2314yes—
97C2×#683—22no—
98C2×#683—22no—
99C2×#683—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—21no—
102#4038—28no—
103D5×C4⋊C4—28no—
104#4036—28no—
105#4034—28no—
106#4027—216no—
107#4024—216no—
108C4×D20—24no—
109C4×D20C2318yes—
110#4016—24no—
111#4016C2318yes—
112#4015—24no—
113#4015C2318yes—
114C4×Dic10—24no—
115C4×Dic10C2318yes—
116C5×C4⋊C8C2318yes—
117C5×C4⋊C8C2318yes—
118#3953C2314yes—
119#3953C2318yes—
120#3953C2314yes—
121#3950C2318yes—
122#3950C2318yes—
123#3950C2318yes—
124#3949C2318yes—
125#3948C2314yes—
126#3948C2318yes—
127#3948C2314yes—
128C2×#544—51no—
129C2×#520—51no—
130#3083—516no—
131C2×#479—52no—
132C2×#477—52no—
133C2×#478—52no—
134C2×#474—52no—
135C2×#428—51no—
136C22×#107—51no—
137C2×#424D511yescharacteristic, complemented
138C2×#417—51no—
139C2×#416—51no—
140C24×C5C2×D411yescharacteristic
141C23×D5—21no—
142C22×C4×C5C2×D412yes—
143C22×C4×C5C2×D412yes—
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D412yes—
146C22×C4×C5C2×Q814yes—
147C22×C4×C5#4114yes—
148C22×C4×C5C2411yescharacteristic
149C22×C4×C5C2412yes—
150C2×C22⋊D5—28no—
151C2×C22⋊D5—24no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—24no—
158C22×Dic5—24no—
159C22×Dic5—82no—
160C22×Dic5—82no—
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—
178C5×M16—28no—
179C2×C5×C8—22no—
180C2×C5×C8—22no—
181C2×C5×C8—28no—
182C2×C5×C8—24no—
183C2×C5×C8C2412yes—
184C2×C5×C8C2412yes—
185C2×C5×C8C2414yes—
186C5×C4⋊C4C2×D414yes—
187C5×C4⋊C4C2×D414yes—
188C5×C22⋊C4C2×D418yes—
189C42×C5C2×D414yes—
190C42×C5C2414yes—
191C22⋊Dic5—24no—
192#685—28no—
193C4⋊Dic5—22no—
194C4⋊Dic5—21no—
195C4⋊Dic5—22no—
196C4⋊Dic5—28no—
197C4⋊Dic5—21no—
198C4⋊Dic5—24no—
199C4⋊Dic5—24no—
200C4⋊Dic5C2412yes—
201C4⋊Dic5C2412yes—
202C4⋊Dic5C2414yes—
203C4⋊Dic5C2414yes—
204#683—28no—
205#683—28no—
206#683—28no—
207C4×Dic5—28no—
208C4×Dic5—24no—
209C22×#41—51no—
210C22×M16C2×D511yescharacteristic
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—101no—
226C2×#117C2×D511yescharacteristic
227C22×C4⋊C4—51no—
228C22×C4⋊C4—51no—
229C22×C4⋊C4—101no—
230#479—516no—
231#478—516no—
232#477—516no—
233#474—516no—
234#428—58no—
235C2×#107—52no—
236C2×#107—52no—
237C2×#107—52no—
238C2×#107—58no—
239C2×#106—52no—
240#424C2×D518yescomplemented
241C2×C4⋊C8C2×D512yes—
242C2×C4⋊C8C2×D512yes—
243#417—58no—
244#416—58no—
245C2×#103—51no—
246C2×#103—52no—
247C2×#103—51no—
248C2×#102—51no—
249C2×#102—52no—
250C2×#102—51no—
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×C5C22⋊Q814yes—
263C2×C4×C5C22⋊Q818yes—
264C2×C4×C5C22×D414yes—
265C2×C4×C5C22×D414yes—
266C2×C4×C5C22×D412yes—
267C2×C4×C5C22×D411yescharacteristic
268C2×C4×C5C22×Q812yes—
269C2×C4×C5C22×Q814yes—
270C2×C4×C5C2×#4112yes—
271C2×C4×C5C2×#4114yes—
272C2×C4×C5C2511yescharacteristic
273C22⋊D5—216no—
274C2×Dic5—24no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—24no—
278C2×Dic5—22no—
279C2×Dic5—24no—
280C2×Dic5—42no—
281C2×Dic5—44no—
282C2×Dic5—44no—
283C2×Dic5—42no—
284C2×Dic5—84no—
285C2×Dic5—84no—
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—
297C5×C8—24no—
298C2×#41—58no—
299C2×#41—54no—
300C2×#41—102no—
301C2×#41—104no—
302C22×Q8—51no—
303C22×Q8—102no—
304C22×D4—51no—
305C22×D4—101no—
306C23×C4—101no—
307C23×C4—101no—
308C23×C4—101no—
309C23×C4—102no—
310C23×C4C22×D511yescharacteristic
311C2×M16—24no—
312C2×M16C22×D514yes—
313C22×C8—24no—
314C22×C8C22×D511yescharacteristic
315C22×C8C22×D511yescharacteristic
316C22×C8C22×D514yes—
317C22×C8C22×D512yes—
318C4⋊Q8—58no—
319C4⋊Q8—108no—
320C4⋊Q8—104no—
321#125—58no—
322#125—108no—
323#125—104no—
324C22⋊Q8—1016no—
325C4×Q8—58no—
326C4×Q8—104no—
327C4×D4—58no—
328C4×D4—1016no—
329C4×D4—104no—
330#117—54no—
331#117—102no—
332#117—108no—
333#117D2014yes—
334#117C22×D514yes—
335C2×C4⋊C4—52no—
336C2×C4⋊C4—54no—
337C2×C4⋊C4—52no—
338C2×C4⋊C4—54no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—102no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4—102no—
345C2×C4⋊C4—102no—
346C2×C4⋊C4—102no—
347C2×C4⋊C4—102no—
348C2×C4⋊C4—102no—
349C2×C4⋊C4—108no—
350C2×C4⋊C4D2011yescharacteristic
351C2×C4⋊C4D2011yescharacteristic
352C2×C22⋊C4—101no—
353C2×C22⋊C4—102no—
354C2×C22⋊C4D2012yes—
355C2×C42—101no—
356C2×C42—102no—
357C2×C42C22×D512yes—
358#107—58no—
359#107—58no—
360#107—58no—
361#106—58no—
362C4⋊C8C22×D518yes—
363C4⋊C8C22×D518yes—
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#57612yes—
376C22×C5#57812yes—
377C22×C5C23×D411yescharacteristic
378C2×D5—24no—
379C2×D5—48no—
380C2×D5—42no—
381C2×D5—42no—
382C4×C5—24no—
383C4×C5—24no—
384C4×C5C2×C22⋊Q812yes—
385C4×C5C2×C22⋊Q814yes—
386C4×C5C23×Q811yescharacteristic
387C4×C5C22×#4111yescharacteristic
388Dic5—24no—
389Dic5—42no—
390Dic5—44no—
391Dic5—44no—
392Dic5—42no—
393C24—101no—
394C24C2×D2011yescharacteristic
395#41—516no—
396#41—108no—
397#41—1016no—
398C2×Q8—54no—
399C2×Q8—52no—
400C2×Q8—101no—
401C2×Q8—108no—
402C2×Q8—102no—
403C2×Q8—404no—
404C2×D4—54no—
405C2×D4—52no—
406C2×D4—104no—
407C2×D4—108no—
408C2×D4—101no—
409C2×D4—102no—
410C22×C4—101no—
411C22×C4—104no—
412C22×C4—108no—
413C22×C4—101no—
414C22×C4—102no—
415C22×C4—101no—
416C22×C4—102no—
417C22×C4—104no—
418C22×C4—104no—
419C22×C4—108no—
420C22×C4—404no—
421C22×C4—402no—
422C22×C4—402no—
423C22×C4C2×D2012yes—
424C22×C4C2×D2012yes—
425C22×C4C2×D2012yes—
426C22×C4C2×D2011yescharacteristic
427C22×C4#71114yes—
428C22×C4Q8×D514yes—
429C22×C4C23×D512yes—
430C22×C4C23×D511yescharacteristic
431M16—28no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—28no—
435C2×C8—24no—
436C2×C8C23×D514yes—
437C2×C8C23×D512yes—
438C2×C8C23×D512yes—
439C4⋊C4—52no—
440C4⋊C4—54no—
441C4⋊C4—52no—
442C4⋊C4—54no—
443C4⋊C4—104no—
444C4⋊C4—102no—
445C4⋊C4—104no—
446C4⋊C4—102no—
447C4⋊C4—101no—
448C4⋊C4—101no—
449C4⋊C4—108no—
450C4⋊C4—108no—
451C4⋊C4—108no—
452C4⋊C4—108no—
453C4⋊C4C2×D2014yes—
454C4⋊C4C2×D2014yes—
455C22⋊C4—104no—
456C22⋊C4—108no—
457C22⋊C4C2×D2018yes—
458C42—104no—
459C42—108no—
460C42C2×D2014yes—
461C42C23×D514yes—
462C2×C5—24no—
463C2×C5#308314yescomplemented
464C2×C5C22×C22⋊Q811yescharacteristic
465C2×C5C2×#57611yescharacteristic
466C2×C5C2×#57811yescharacteristic
467D5—44no—
468C23—22no—
469C23—22no—
470C23—104no—
471C23—102no—
472C23—202no—
473C23—202no—
474C23#404314yes—
475C23C22×D2012yes—
476C23C22×D2011yescharacteristic
477Q8—54no—
478Q8—104no—
479Q8—102no—
480Q8—408no—
481D4—54no—
482D4—1016no—
483D4—104no—
484D4—102no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—104no—
488C2×C4—102no—
489C2×C4—1016no—
490C2×C4—102no—
491C2×C4—104no—
492C2×C4—102no—
493C2×C4—104no—
494C2×C4—204no—
495C2×C4—204no—
496C2×C4—202no—
497C2×C4—202no—
498C2×C4—408no—
499C2×C4—404no—
500C2×C4—404no—
501C2×C4#404314yes—
502C2×C4#404318yes—
503C2×C4C22×D2014yes—
504C2×C4C22×D2014yes—
505C2×C4C22×D2012yes—
506C2×C4C22×D2011yescharacteristic
507C2×C4C2×#71112yes—
508C2×C4C2×#71114yes—
509C2×C4C2×Q8×D512yes—
510C2×C4C2×Q8×D514yes—
511C2×C4C24×D511yescharacteristic
512C8—22no—
513C8—22no—
514C8—24no—
515C5C2×#308311yescharacteristic, complemented, Sylow
516C22—28no—
517C22—22no—
518C22—22no—
519C22—104no—
520C22—208no—
521C22—202no—
522C22—202no—
523C22C2×#404314yes—
524C22C2×#404312yes—
525C22#6608612yes—
526C22#6608712yes—
527C22C23×D2011yescharacteristic
528C4—24no—
529C4—24no—
530C4—104no—
531C4—204no—
532C4—204no—
533C4—202no—
534C4—202no—
535C4C2×#404314yes—
536C4C2×#404312yes—
537C4C22×#71111yescharacteristic
538C4C22×Q8×D511yescharacteristic
539C2—24no—
540C2—204no—
541C2#1061082214yesdirect product factor
542C2C22×#404311yescharacteristic
543C2C2×#6608611yescharacteristic
544C2C2×#6608711yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#424C2
socleC23×C5C22×D4
prime radicalC22×#709C22
hypercenterC2×#424D5
hypocenterC5C2×#3083
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#65853C2semidirect
3. C2×C5×#424C2semidirect
5. C2×#65410C2semidirect
7. C22×#3950C2semidirect
8. #10610822C2direct (N × H)
9. C2×#65118C2semidirect
10. C2×#65139C2semidirect
11. C2×#65136C2semidirect
12. C2×#65135C2semidirect
23. #65853C22semidirect
34. C5×#424C22semidirect
38. #65410C22semidirect
46. C2×#3950C22semidirect
51. #65139C22semidirect
52. #65136C22semidirect
53. #65135C22semidirect
54. #65118C22semidirect
62. C2×#709Q8semidirect
137. C2×#424D5semidirect
163. #709C2×Q8semidirect
240. #424C2×D5semidirect
463. C2×C5#3083semidirect
515. C5C2×#3083semidirect
541. C2#10610822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658572
C2×#658532
C2×C5×#4242
C2×#654222
C2×#654102
C2×#654022
C22×#39502
#106108222
C2×#651182
C2×#651392
C2×#651362
C2×#651352
C2×#30835