Finite Group Databasebeta

← C2×#10614291 #12966893

Subgroups — C2×#10614291 #12966893

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×C5×#520C211yesmaximal, characteristic
2C2×#65853C211yesmaximal, characteristic, complemented
3C2×#65521C211yesmaximal, characteristic
4C2×#65522C211yesmaximal, characteristic
5#10614291C2116yesmaximal, direct product factor
6C2×#65311C212yesmaximal, complemented
7C2×#65309C212yesmaximal, complemented
8C2×#65298C212yesmaximal, complemented
9C2×#65297C212yesmaximal, complemented
10C2×#65288C211yesmaximal, characteristic, complemented
11C2×#65253C211yesmaximal, characteristic, complemented
12C22×#3940C211yesmaximal, characteristic, complemented
13C22×C5×#41C2211yescharacteristic
14C5×#520—24no—
15C5×#520C2218yes—
16C2×C4×C5×Q8C2212yes—
17C2×C4×C5×D4—22no—
18C2×C4×C5×D4C2212yes—
19C2×C5×#117—21no—
20C2×C5×#117C2211yescharacteristic
21C22×C5×C4⋊C4—21no—
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×#4072C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C22×#681C2211yescharacteristic
26C23×#168C2211yescharacteristic
27#65853—24no—
28#65853C2218yescomplemented
29C2×#4036—21no—
30C2×#4034—21no—
31C2×#4024—22no—
32C2×#4016C2212yes—
33C2×#4015C2212yes—
34#65522C2218yes—
35#65521C2218yes—
36C2×#3967C2211yescharacteristic
37C2×#3967C2212yes—
38C2×#3967C2211yescharacteristic
39C2×#3964C2211yescharacteristic
40C2×#3964C2212yes—
41C2×#3964C2211yescharacteristic
42#65311C22116yescomplemented
43#65309C22116yescomplemented
44#65298C22116yescomplemented
45#65297C22116yescomplemented
46#65288C2218yescomplemented
47#65253C2218yescomplemented
48C2×#3940C2212yes—
49C2×#3940C2212yes—
50C2×#3940C2212yes—
51C2×#3940C2218yescomplemented
52C2×#3939C2212yes—
53C2×C4⋊#168C2212yes—
54C2×C4⋊#168C2212yes—
55C2×#3084—51nomaximal, Sylow
56C2×C5×#41—22no—
57C2×C5×#41—24no—
58C2×C5×#41Q818yescomplemented
59C2×C5×#41C2314yes—
60C22×C5×Q8C2311yescharacteristic
61C22×C5×D4—21no—
62C22×C5×D4C2311yescharacteristic
63C23×C4×C5—21no—
64C23×C4×C5—21no—
65C23×C4×C5—22no—
66C23×C4×C5C2311yescharacteristic
67C23×Dic5—21no—
68C22×Dic10—22no—
69C4×C5×Q8—24no—
70C4×C5×Q8C2318yes—
71C4×C5×D4—216no—
72C4×C5×D4—24no—
73C4×C5×D4C2318yes—
74C5×#117—28no—
75C5×#117D414yes—
76C5×#117C2314yes—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—22no—
79C2×C5×C4⋊C4—22no—
80C2×C5×C4⋊C4—28no—
81C2×C5×C4⋊C4D411yescharacteristic
82C2×C5×C4⋊C4D411yescharacteristic
83C2×C5×C4⋊C4C2312yes—
84C2×C5×C4⋊C4C2314yes—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4D412yes—
87C2×C42×C5—22no—
88C2×C42×C5C2312yes—
89C2×C22⋊Dic5—21no—
90#4072—22no—
91#4072C2314yes—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—21no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5C2311yescharacteristic
96C2×C4⋊Dic5C2312yes—
97C2×C4⋊Dic5C2311yescharacteristic
98C2×C4⋊Dic5C2314yes—
99C2×#683—22no—
100C2×#683—22no—
101C2×C4×Dic5—21no—
102C2×#681—24no—
103C2×#681C2314yes—
104C22×#168—24no—
105C22×#168C2314yes—
106C22×#168C2311yescharacteristic
107C22×#168C2311yescharacteristic
108C22×#168C2312yes—
109#4036—28no—
110#4034—28no—
111#4024—216no—
112#4016—24no—
113#4016C2318yes—
114#4015—24no—
115#4015C2318yes—
116#3967C2314yes—
117#3967C2318yes—
118#3967C2314yes—
119#3964C2314yes—
120#3964C2318yes—
121#3964C2314yes—
122#3940C2318yes—
123#3940C2318yes—
124#3940C2318yes—
125#3939C2318yes—
126C4⋊#168C2318yes—
127C4⋊#168C2318yes—
128C2×#544—51no—
129C2×#520D511yescharacteristic
130#3084—516no—
131C2×#479—52no—
132C2×#475—52no—
133C2×#478—52no—
134C2×#476—52no—
135C2×#428—51no—
136C22×#106—51no—
137C2×#424—51no—
138C2×#417—51no—
139C2×#416—51no—
140C24×C5—21no—
141C24×C5C2×D411yescharacteristic
142C5×#41—216no—
143C5×#41—28no—
144C5×#41C2×Q8116yescomplemented
145C2×C5×Q8—21no—
146C2×C5×Q8—22no—
147C2×C5×Q8C2×Q814yes—
148C2×C5×Q8C2412yes—
149C2×C5×D4—28no—
150C2×C5×D4—24no—
151C2×C5×D4—21no—
152C2×C5×D4—22no—
153C2×C5×D4C2×Q814yes—
154C2×C5×D4C2412yes—
155C22×C4×C5—21no—
156C22×C4×C5—28no—
157C22×C4×C5—24no—
158C22×C4×C5—22no—
159C22×C4×C5—24no—
160C22×C4×C5—28no—
161C22×C4×C5—84no—
162C22×C4×C5—82no—
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×Q814yes—
168C22×C4×C5#4114yes—
169C22×C4×C5C2411yescharacteristic
170C22×C4×C5C2412yes—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—22no—
174C22×Dic5—24no—
175C22×Dic5—82no—
176C2×Dic10—28no—
177C2×Dic10—84no—
178C5×C4⋊C4—24no—
179C5×C4⋊C4—28no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4C2×D414yes—
182C5×C4⋊C4C2×D414yes—
183C5×C4⋊C4C2414yes—
184C5×C22⋊C4—28no—
185C5×C22⋊C4C2×D418yes—
186C42×C5—28no—
187C42×C5C2×D414yes—
188C42×C5C2414yes—
189C22⋊Dic5—24no—
190C4⋊Dic5—21no—
191C4⋊Dic5—22no—
192C4⋊Dic5—28no—
193C4⋊Dic5—21no—
194C4⋊Dic5—24no—
195C4⋊Dic5C2412yes—
196C4⋊Dic5C2412yes—
197C4⋊Dic5C2414yes—
198#683—28no—
199#683—28no—
200C4×Dic5—24no—
201#681—28no—
202C2×#168—22no—
203C2×#168—22no—
204C2×#168—28no—
205C2×#168—24no—
206C2×#168C2414yes—
207C2×#168C2412yes—
208C2×#168C2412yes—
209C22×#41C2×D511yescharacteristic
210C22×M16—51no—
211C23×C8—51no—
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—24no—
220#520C2×D518yes—
221C2×C4×Q8C2×D512yes—
222C2×C4×D4—22no—
223C2×C4×D4C2×D512yes—
224C2×#117—21no—
225C2×#117—51no—
226C2×#117C2×D511yescharacteristic
227C22×C4⋊C4—21no—
228C22×C4⋊C4—51no—
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×#106—52no—
238C2×#106—52no—
239C2×#106—58no—
240#424—58no—
241C2×C4⋊C8—52no—
242C2×C4⋊C8—52no—
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×C5—24no—
254C23×C5—22no—
255C23×C5—42no—
256C23×C5—42no—
257C23×C5C22⋊Q814yes—
258C23×C5C22×D412yes—
259C23×C5C22×D411yescharacteristic
260C5×Q8—24no—
261C5×Q8—22no—
262C5×Q8C22×Q814yes—
263C5×D4—216no—
264C5×D4—24no—
265C5×D4—22no—
266C5×D4C22×Q814yes—
267C2×C4×C5—24no—
268C2×C4×C5—24no—
269C2×C4×C5—24no—
270C2×C4×C5—22no—
271C2×C4×C5—216no—
272C2×C4×C5—24no—
273C2×C4×C5—44no—
274C2×C4×C5—88no—
275C2×C4×C5—84no—
276C2×C4×C5C22⋊Q814yes—
277C2×C4×C5C22⋊Q818yes—
278C2×C4×C5C22×D414yes—
279C2×C4×C5C22×D414yes—
280C2×C4×C5C22×D412yes—
281C2×C4×C5C22×D411yescharacteristic
282C2×C4×C5C22×Q812yes—
283C2×C4×C5C22×Q814yes—
284C2×C4×C5C2×#4112yes—
285C2×C4×C5C2×#4114yes—
286C2×C4×C5C2511yescharacteristic
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—24no—
290C2×Dic5—42no—
291C2×Dic5—44no—
292C2×Dic5—42no—
293C2×Dic5—84no—
294Dic10—88no—
295#168—22no—
296#168—22no—
297#168—24no—
298C2×#41—24no—
299C2×#41—22no—
300C2×#41Dic1018yescomplemented
301C2×#41C22×D514yes—
302C22×Q8—102no—
303C22×Q8C22×D511yescharacteristic
304C22×D4—21no—
305C22×D4C22×D511yescharacteristic
306C23×C4—21no—
307C23×C4—21no—
308C23×C4—22no—
309C23×C4—101no—
310C23×C4C22×D511yescharacteristic
311C2×M16—54no—
312C2×M16—104no—
313C22×C8—51no—
314C22×C8—51no—
315C22×C8—54no—
316C22×C8—52no—
317C22×C8—104no—
318C4⋊Q8—58no—
319C4⋊Q8—108no—
320C4⋊Q8—104no—
321#125—58no—
322#125—108no—
323#125—104no—
324C22⋊Q8—1016no—
325C4×Q8—24no—
326C4×Q8C22×D518yes—
327C4×D4—216no—
328C4×D4—24no—
329C4×D4C22×D518yes—
330#117—28no—
331#117—54no—
332#117—102no—
333#117C22⋊D514yes—
334#117C22×D514yes—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—52no—
340C2×C4⋊C4—54no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4—102no—
345C2×C4⋊C4—102no—
346C2×C4⋊C4—102no—
347C2×C4⋊C4—102no—
348C2×C4⋊C4C22⋊D511yescharacteristic
349C2×C4⋊C4C22⋊D511yescharacteristic
350C2×C4⋊C4C22×D512yes—
351C2×C4⋊C4C22×D514yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—101no—
354C2×C22⋊C4C22⋊D512yes—
355C2×C42—22no—
356C2×C42—101no—
357C2×C42C22×D512yes—
358#107—58no—
359#106—58no—
360#106—58no—
361#106—58no—
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×C5—24no—
374C22×C5—48no—
375C22×C5—42no—
376C22×C5—42no—
377C22×C5C2×C22⋊Q814yes—
378C22×C5C2×C22⋊Q812yes—
379C22×C5#57712yes—
380C22×C5#57712yes—
381C22×C5C23×D411yescharacteristic
382C4×C5—24no—
383C4×C5—24no—
384C4×C5—24no—
385C4×C5—44no—
386C4×C5C2×C22⋊Q814yes—
387C4×C5C2×C22⋊Q812yes—
388C4×C5C23×Q811yescharacteristic
389C4×C5C22×#4111yescharacteristic
390Dic5—42no—
391Dic5—44no—
392Dic5—42no—
393C24—21no—
394C24C2×C22⋊D511yescharacteristic
395#41—28no—
396#41—216no—
397#41C2×Dic10116yescomplemented
398C2×Q8—22no—
399C2×Q8—21no—
400C2×Q8—108no—
401C2×Q8—404no—
402C2×Q8C2×Dic1014yes—
403C2×Q8C23×D512yes—
404C2×D4—24no—
405C2×D4—28no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4C2×Dic1014yes—
409C2×D4C23×D512yes—
410C22×C4—21no—
411C22×C4—24no—
412C22×C4—28no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—28no—
416C22×C4—84no—
417C22×C4—82no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—102no—
421C22×C4—104no—
422C22×C4—402no—
423C22×C4C2×Dic1014yes—
424C22×C4#70914yes—
425C22×C4C2×C22⋊D512yes—
426C22×C4C2×C22⋊D512yes—
427C22×C4C2×C22⋊D512yes—
428C22×C4C2×C22⋊D511yescharacteristic
429C22×C4C23×D512yes—
430C22×C4C23×D511yescharacteristic
431M16—108no—
432C2×C8—52no—
433C2×C8—52no—
434C2×C8—54no—
435C2×C8—102no—
436C2×C8—102no—
437C2×C8—108no—
438C2×C8—104no—
439C4⋊C4—24no—
440C4⋊C4—28no—
441C4⋊C4—22no—
442C4⋊C4—54no—
443C4⋊C4—52no—
444C4⋊C4—52no—
445C4⋊C4—104no—
446C4⋊C4—102no—
447C4⋊C4—101no—
448C4⋊C4—101no—
449C4⋊C4—108no—
450C4⋊C4—108no—
451C4⋊C4—108no—
452C4⋊C4C2×C22⋊D514yes—
453C4⋊C4C2×C22⋊D514yes—
454C4⋊C4C23×D514yes—
455C22⋊C4—28no—
456C22⋊C4—104no—
457C22⋊C4C2×C22⋊D518yes—
458C42—28no—
459C42—104no—
460C42C2×C22⋊D514yes—
461C42C23×D514yes—
462C2×C5—24no—
463C2×C5—44no—
464C2×C5#308414yescomplemented
465C2×C5C22×C22⋊Q811yescharacteristic
466C2×C5C2×#57711yescharacteristic
467C2×C5C2×#57711yescharacteristic
468C23—22no—
469C23—22no—
470C23—24no—
471C23—22no—
472C23—42no—
473C23—42no—
474C23#407014yes—
475C23C22×C22⋊D512yes—
476C23C22×C22⋊D511yescharacteristic
477Q8—24no—
478Q8—22no—
479Q8—408no—
480Q8C22×Dic1014yes—
481D4—216no—
482D4—24no—
483D4—22no—
484D4C22×Dic1014yes—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—216no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—88no—
493C2×C4—84no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—104no—
497C2×C4—202no—
498C2×C4—204no—
499C2×C4—202no—
500C2×C4—404no—
501C2×C4#407014yes—
502C2×C4#407018yes—
503C2×C4C22×Dic1012yes—
504C2×C4C22×Dic1014yes—
505C2×C4C2×#70912yes—
506C2×C4C2×#70914yes—
507C2×C4C22×C22⋊D514yes—
508C2×C4C22×C22⋊D514yes—
509C2×C4C22×C22⋊D512yes—
510C2×C4C22×C22⋊D511yescharacteristic
511C2×C4C24×D511yescharacteristic
512C8—102no—
513C8—102no—
514C8—104no—
515C5C2×#308411yescharacteristic, complemented, Sylow
516C22—28no—
517C22—22no—
518C22—22no—
519C22—24no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22C2×#407014yes—
524C22C2×#407012yes—
525C22#6617012yes—
526C22#6617112yes—
527C22C23×C22⋊D511yescharacteristic
528C4—24no—
529C4—24no—
530C4—24no—
531C4—44no—
532C4—202no—
533C4—204no—
534C4—202no—
535C4C2×#407014yes—
536C4C2×#407012yes—
537C4C23×Dic1011yescharacteristic
538C4C22×#70911yescharacteristic
539C2—24no—
540C2—44no—
541C2#1061429114yesdirect product factor
542C2C22×#407011yescharacteristic
543C2C2×#6617011yescharacteristic
544C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#520C2
socleC23×C5C22×D4
prime radicalC22×C5×#41C22
hypercenterC2×#520D5
hypocenterC5C2×#3084
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#65853C2semidirect
5. #10614291C2direct (N × H)
6. C2×#65311C2semidirect
7. C2×#65309C2semidirect
8. C2×#65298C2semidirect
9. C2×#65297C2semidirect
10. C2×#65288C2semidirect
11. C2×#65253C2semidirect
12. C22×#3940C2semidirect
28. #65853C22semidirect
42. #65311C22semidirect
43. #65309C22semidirect
44. #65298C22semidirect
45. #65297C22semidirect
46. #65288C22semidirect
47. #65253C22semidirect
51. C2×#3940C22semidirect
58. C2×C5×#41Q8semidirect
144. C5×#41C2×Q8semidirect
300. C2×#41Dic10semidirect
397. #41C2×Dic10semidirect
464. C2×C5#3084semidirect
515. C5C2×#3084semidirect
541. C2#10614291direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5202
C2×#658532
C2×#655212
C2×#655222
#106142912
C2×#653112
C2×#653092
C2×#652982
C2×#652972
C2×#652882
C2×#652532
C22×#39402
C2×#30845