Finite Group Databasebeta

← C2×#10612839 #12966821

Subgroups — C2×#10612839 #12966821

Order 1280.

2098 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C211yesmaximal, characteristic
2C2×C4×Q8×D5C211yesmaximal, characteristic
3C2×C5×#477C211yesmaximal, characteristic, complemented
4C2×#65380C211yesmaximal, characteristic, complemented
5C2×#65309C211yesmaximal, characteristic, complemented
6#10612839C2116yesmaximal, direct product factor
7C2×#65166C212yesmaximal, complemented
8C2×#65170C212yesmaximal
9C2×#65140C211yesmaximal, characteristic, complemented
10C2×#65126C211yesmaximal, characteristic
11C2×#65091C212yesmaximal
12C2×#65088C212yesmaximal, complemented
13C22×Q8×D5C2211yescharacteristic
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C4×C5×Q8C2211yescharacteristic
16C2×#4092—21no—
17C2×Q8×Dic5—21no—
18C2×Q8×Dic5C2211yescharacteristic
19C22×#676C2212yes—
20#66062—24no—
21#66062C2218yes—
22C4×Q8×D5—24no—
23C4×Q8×D5C2218yes—
24C2×#4043—21no—
25C2×#4038C2212yes—
26C2×D5×C4⋊C4—21no—
27C2×D5×C4⋊C4C2211yescharacteristic
28C2×#4036C2212yes—
29C2×#4033—21no—
30C2×#4033—21no—
31C2×#4033C2211yescharacteristic
32C2×C42×D5—21no—
33C2×C42×D5C2211yescharacteristic
34C2×#4015C2211yescharacteristic
35C2×C4×Dic10—21no—
36C2×C4×Dic10C2211yescharacteristic
37C5×#477C2218yescomplemented
38C2×C5×#107C2212yes—
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2212yes—
41C2×#3967C2212yes—
42C2×#3949C2212yes—
43C2×#3948C2212yes—
44C2×#3946C2212yes—
45#65380C2218yescomplemented
46#65309C2218yescomplemented
47C2×#3942C2212yes—
48C2×#3940C2212yes—
49C2×#3939C2212yes—
50C2×C4⋊#168C2211yescharacteristic
51#65170C22116yes—
52#65166C22116yescomplemented
53#65140C2218yescomplemented
54#65126C2218yes—
55#65091C22116yes—
56#65088C22116yescomplemented
57C2×#3078—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C5×Q8C2311yescharacteristic
60C2×Q8×D5—22no—
61C2×Q8×D5—24no—
62C2×Q8×D5Q818yescomplemented
63C2×Q8×D5C2314yes—
64C22×C4×D5—21no—
65C22×C4×D5—21no—
66C22×C4×D5D411yescharacteristic
67C22×C4×D5D411yescharacteristic
68C22×C4×D5C2311yescharacteristic
69C22×Dic10—21no—
70C22×Dic10—21no—
71C22×Dic10C2311yescharacteristic
72C22×C5×C8C2312yes—
73C5×C4⋊Q8—22no—
74C5×C4⋊Q8C2314yes—
75C4×C5×Q8—22no—
76C4×C5×Q8C2314yes—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C5×C4⋊C4C2312yes—
81C2×C42×C5—21no—
82C2×C42×C5C2311yescharacteristic
83#4092—28no—
84Q8×Dic5—28no—
85Q8×Dic5—22no—
86Q8×Dic5C2314yes—
87C2×#685—22no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2312yes—
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×#683—22no—
97C2×C4×Dic5—21no—
98C2×C4×Dic5—21no—
99C2×C4×Dic5—21no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5D411yescharacteristic
102C2×C4×Dic5D411yescharacteristic
103C2×C4×Dic5C2311yescharacteristic
104C22×#168C2312yes—
105C2×#676—28no—
106C2×#676C2318yes—
107#4043—28no—
108#4038—24no—
109#4038C2318yes—
110D5×C4⋊C4—28no—
111D5×C4⋊C4—22no—
112D5×C4⋊C4C2314yes—
113#4036—24no—
114#4036C2318yes—
115#4033—28no—
116#4033—28no—
117#4033—22no—
118#4033C2314yes—
119C42×D5—28no—
120C42×D5D414yes—
121C42×D5C2314yes—
122#4015—22no—
123#4015C2314yes—
124C4×Dic10—22no—
125C4×Dic10—28no—
126C4×Dic10C2314yes—
127C5×#107C2318yes—
128C5×C4⋊C8C2314yes—
129C5×#103C2318yes—
130#3967C2318yes—
131#3949C2318yes—
132#3948C2318yes—
133#3946C2318yes—
134#3942C2318yes—
135#3940C2318yes—
136#3939C2318yes—
137C4⋊#168C2314yes—
138C2×#533—51no—
139C22×C4×Q8—51no—
140#3078—516no—
141C2×#479—52no—
142C2×#479—52no—
143C2×#477—51no—
144C2×#477D511yescharacteristic, complemented
145C2×#475—51no—
146C2×#475—51no—
147C2×#428—52no—
148C2×#423—51no—
149C2×#419—52no—
150C23×D5C2×D411yescharacteristic
151C2×C5×Q8—21no—
152C2×C5×Q8—24no—
153C2×C5×Q8—22no—
154C2×C5×Q8—44no—
155C2×C5×Q8C2×Q814yes—
156C2×C5×Q8C2412yes—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—22no—
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2411yescharacteristic
163C22×Dic5—21no—
164C22×Dic5—22no—
165C22×Dic5—21no—
166C22×Dic5C2×D411yescharacteristic
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169Q8×D5—216no—
170Q8×D5—28no—
171Q8×D5C2×Q8116yescomplemented
172C2×C4×D5—28no—
173C2×C4×D5—24no—
174C2×C4×D5—24no—
175C2×C4×D5—24no—
176C2×C4×D5—42no—
177C2×C4×D5—44no—
178C2×C4×D5C2×D414yes—
179C2×C4×D5C2×D414yes—
180C2×C4×D5C2×D412yes—
181C2×C4×D5C2×Q814yes—
182C2×C4×D5#4114yes—
183C2×C4×D5C2412yes—
184C2×Dic10—21no—
185C2×Dic10—22no—
186C2×Dic10—28no—
187C2×Dic10—24no—
188C2×Dic10—24no—
189C2×Dic10—44no—
190C2×Dic10C2×Q814yes—
191C2×Dic10C2412yes—
192C2×C5×C8—24no—
193C2×C5×C8C2414yes—
194C5×C4⋊C4—24no—
195C5×C4⋊C4—24no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4C2412yes—
199C5×C4⋊C4C2414yes—
200C42×C5—24no—
201C42×C5C2×D412yes—
202C42×C5C2412yes—
203#685—28no—
204C4⋊Dic5—21no—
205C4⋊Dic5—22no—
206C4⋊Dic5—24no—
207C4⋊Dic5—24no—
208C4⋊Dic5—28no—
209C4⋊Dic5C2412yes—
210C4⋊Dic5C2414yes—
211#683—24no—
212#683—24no—
213#683—24no—
214#683—28no—
215C4×Dic5—24no—
216C4×Dic5—24no—
217C4×Dic5—24no—
218C4×Dic5—28no—
219C4×Dic5C2×D414yes—
220C4×Dic5C2×D412yes—
221C4×Dic5C2×D414yes—
222C4×Dic5C2412yes—
223C2×#168—24no—
224C2×#168C2414yes—
225#676—216no—
226C23×Q8—51no—
227C22×M16—52no—
228#533—58no—
229#533—104no—
230C2×C4⋊Q8—51no—
231C2×C4⋊Q8C2×D511yescharacteristic
232C2×#125—52no—
233C2×C22⋊Q8—101no—
234C2×C22⋊Q8—101no—
235C2×C4×Q8—51no—
236C2×C4×Q8—58no—
237C2×C4×Q8—51no—
238C2×C4×Q8—51no—
239C2×C4×Q8—101no—
240C2×C4×Q8—101no—
241C2×C4×Q8—101no—
242C2×C4×Q8—104no—
243C2×C4×Q8—101no—
244C2×C4×Q8C2×D511yescharacteristic
245C2×#117—52no—
246C22×C4⋊C4—51no—
247C22×C4⋊C4—101no—
248C22×C42—51no—
249C22×C42—101no—
250#479—516no—
251#479—516no—
252#477—58no—
253#477C2×D518yescomplemented
254#475—58no—
255#475—58no—
256#428—516no—
257C2×#107—52no—
258C2×#107C2×D512yes—
259C2×#106—52no—
260C2×#106—52no—
261#423—58no—
262C2×C4⋊C8—52no—
263C2×C4⋊C8—51no—
264C2×C4⋊C8C2×D511yescharacteristic
265#419—516no—
266C2×#103—52no—
267C2×#103—52no—
268C2×#103—52no—
269C2×#103C2×D512yes—
270C23×C5C22×D411yescharacteristic
271C22×D5—22no—
272C22×D5—22no—
273C22×D5C22⋊Q814yes—
274C22×D5C22×D412yes—
275C5×Q8—24no—
276C5×Q8—22no—
277C5×Q8—48no—
278C5×Q8C22×Q814yes—
279C2×C4×C5—24no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—24no—
284C2×C4×C5—42no—
285C2×C4×C5—44no—
286C2×C4×C5#13714yes—
287C2×C4×C5C22×D412yes—
288C2×C4×C5C22×D411yescharacteristic
289C2×C4×C5C22×D412yes—
290C2×C4×C5C22×Q812yes—
291C2×C4×C5C2×#4112yes—
292C2×C4×C5C2511yescharacteristic
293C2×Dic5—24no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—24no—
299C2×Dic5—44no—
300C2×Dic5—42no—
301C2×Dic5C22⋊Q814yes—
302C2×Dic5C22×D412yes—
303C2×Dic5C22×D412yes—
304C2×Dic5C22×D412yes—
305C4×D5—216no—
306C4×D5—28no—
307C4×D5—44no—
308C4×D5—48no—
309C4×D5C22⋊Q818yes—
310C4×D5C22×Q814yes—
311C4×D5C2×#4114yes—
312Dic10—24no—
313Dic10—22no—
314Dic10—216no—
315Dic10—48no—
316Dic10C22×Q814yes—
317C5×C8—24no—
318#168—24no—
319C22×Q8—21no—
320C22×Q8—58no—
321C22×Q8—54no—
322C22×Q8—51no—
323C22×Q8—101no—
324C22×Q8—102no—
325C22×Q8—104no—
326C22×Q8—101no—
327C22×Q8C22×D511yescharacteristic
328C23×C4—51no—
329C23×C4—51no—
330C23×C4—51no—
331C23×C4—101no—
332C23×C4—101no—
333C2×M16—58no—
334C2×M16—108no—
335C22×C8—52no—
336C22×C8C22×D512yes—
337C4⋊Q8—22no—
338C4⋊Q8—54no—
339C4⋊Q8—102no—
340C4⋊Q8C22×D514yes—
341#125—58no—
342#125—104no—
343C22⋊Q8—108no—
344C22⋊Q8—108no—
345C4×Q8—22no—
346C4×Q8—54no—
347C4×Q8—54no—
348C4×Q8—54no—
349C4×Q8—108no—
350C4×Q8—108no—
351C4×Q8—102no—
352C4×Q8—108no—
353C4×Q8—102no—
354C4×Q8—108no—
355C4×Q8—102no—
356C4×Q8C22×D514yes—
357#117—58no—
358#117—104no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—52no—
363C2×C4⋊C4—54no—
364C2×C4⋊C4—102no—
365C2×C4⋊C4—108no—
366C2×C4⋊C4—101no—
367C2×C4⋊C4—101no—
368C2×C4⋊C4—101no—
369C2×C4⋊C4—102no—
370C2×C4⋊C4—102no—
371C2×C4⋊C4—101no—
372C2×C4⋊C4—101no—
373C2×C4⋊C4C22×D511yescharacteristic
374C2×C4⋊C4C22×D512yes—
375C2×C22⋊C4—102no—
376C2×C42—21no—
377C2×C42—51no—
378C2×C42—51no—
379C2×C42—51no—
380C2×C42—54no—
381C2×C42—54no—
382C2×C42—108no—
383C2×C42—102no—
384C2×C42—101no—
385C2×C42—101no—
386C2×C42—101no—
387C2×C42C22×D511yescharacteristic
388#107—58no—
389#107C22×D518yes—
390#106—58no—
391#106—58no—
392C4⋊C8—58no—
393C4⋊C8—54no—
394C4⋊C8C22×D514yes—
395#103—58no—
396#103—58no—
397#103—58no—
398#103C22×D518yes—
399C22×C5C2×C22⋊Q812yes—
400C22×C5C2×#13712yes—
401C22×C5#57512yes—
402C22×C5C23×D411yescharacteristic
403C2×D5—28no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5C2×C22⋊Q814yes—
407C4×C5—24no—
408C4×C5—22no—
409C4×C5—42no—
410C4×C5—44no—
411C4×C5C2×C22⋊Q812yes—
412C4×C5C2×#13714yes—
413C4×C5C23×Q811yescharacteristic
414C4×C5C22×#4111yescharacteristic
415Dic5—24no—
416Dic5—22no—
417Dic5—22no—
418Dic5—44no—
419Dic5—42no—
420Dic5C2×C22⋊Q814yes—
421C24—51no—
422C2×Q8—21no—
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—44no—
426C2×Q8—516no—
427C2×Q8—54no—
428C2×Q8—52no—
429C2×Q8—104no—
430C2×Q8—108no—
431C2×Q8—1016no—
432C2×Q8—108no—
433C2×Q8—101no—
434C2×Q8—104no—
435C2×Q8—102no—
436C2×Q8—204no—
437C2×Q8Q8×D514yes—
438C2×Q8C23×D512yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—51no—
443C22×C4—52no—
444C22×C4—54no—
445C22×C4—54no—
446C22×C4—52no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—54no—
450C22×C4—54no—
451C22×C4—104no—
452C22×C4—108no—
453C22×C4—104no—
454C22×C4—101no—
455C22×C4—104no—
456C22×C4—101no—
457C22×C4—102no—
458C22×C4—202no—
459C22×C4—204no—
460C22×C4D4×D511yescharacteristic
461C22×C4D4×D511yescharacteristic
462C22×C4C23×D511yescharacteristic
463M16—1016no—
464C2×C8—24no—
465C2×C8—54no—
466C2×C8—104no—
467C2×C8C23×D514yes—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—54no—
473C4⋊C4—52no—
474C4⋊C4—104no—
475C4⋊C4—104no—
476C4⋊C4—104no—
477C4⋊C4—108no—
478C4⋊C4—108no—
479C4⋊C4—101no—
480C4⋊C4—102no—
481C4⋊C4—104no—
482C4⋊C4—104no—
483C4⋊C4C23×D514yes—
484C4⋊C4C23×D512yes—
485C22⋊C4—108no—
486C42—24no—
487C42—54no—
488C42—54no—
489C42—52no—
490C42—52no—
491C42—104no—
492C42—104no—
493C42—108no—
494C42—104no—
495C42D4×D512yes—
496C42C23×D512yes—
497C2×C5#307814yescomplemented
498C2×C5C22×C22⋊Q811yescharacteristic
499C2×C5C22×#13711yescharacteristic
500C2×C5C2×#57511yescharacteristic
501D5—24no—
502C23—54no—
503C23—52no—
504C23—102no—
505C23—102no—
506C23C2×D4×D511yescharacteristic
507Q8—24no—
508Q8—22no—
509Q8—48no—
510Q8—54no—
511Q8—1016no—
512Q8—104no—
513Q8—102no—
514Q8—208no—
515Q8C2×Q8×D514yes—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—54no—
524C2×C4—52no—
525C2×C4—58no—
526C2×C4—54no—
527C2×C4—54no—
528C2×C4—52no—
529C2×C4—52no—
530C2×C4—1016no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—104no—
534C2×C4—102no—
535C2×C4—108no—
536C2×C4—102no—
537C2×C4—104no—
538C2×C4—204no—
539C2×C4—208no—
540C2×C4—204no—
541C2×C4—202no—
542C2×C4#406414yes—
543C2×C4C2×D4×D512yes—
544C2×C4C2×D4×D512yes—
545C2×C4C2×D4×D511yescharacteristic
546C2×C4C2×Q8×D512yes—
547C2×C4D5×#4112yes—
548C2×C4C24×D511yescharacteristic
549C8—24no—
550C8—104no—
551C5C2×#307811yescharacteristic, complemented, Sylow
552C22—54no—
553C22—108no—
554C22—102no—
555C22—102no—
556C22D5×C22⋊Q812yes—
557C22C2×#406412yes—
558C22#6610712yes—
559C22C22×D4×D511yescharacteristic
560C4—24no—
561C4—22no—
562C4—42no—
563C4—44no—
564C4—54no—
565C4—104no—
566C4—102no—
567C4—102no—
568C4—204no—
569C4—202no—
570C4D5×C22⋊Q812yes—
571C4C2×#406414yes—
572C4C22×Q8×D511yescharacteristic
573C4C2×D5×#4111yescharacteristic
574C2—104no—
575C2#1061283914yesdirect product factor
576C2C2×D5×C22⋊Q811yescharacteristic
577C2C22×#406411yescharacteristic
578C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#477C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#477D5
hypocenterC5C2×#3078
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×C5×#477C2semidirect
4. C2×#65380C2semidirect
5. C2×#65309C2semidirect
6. #10612839C2direct (N × H)
7. C2×#65166C2semidirect
9. C2×#65140C2semidirect
12. C2×#65088C2semidirect
37. C5×#477C22semidirect
45. #65380C22semidirect
46. #65309C22semidirect
52. #65166C22semidirect
53. #65140C22semidirect
56. #65088C22semidirect
62. C2×Q8×D5Q8semidirect
144. C2×#477D5semidirect
171. Q8×D5C2×Q8semidirect
253. #477C2×D5semidirect
497. C2×C5#3078semidirect
551. C5C2×#3078semidirect
575. C2#10612839direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660622
C2×C4×Q8×D52
C2×C5×#4772
C2×#653802
C2×#653092
#106128392
C2×#651662
C2×#651702
C2×#651402
C2×#651262
C2×#650912
C2×#650882
C2×#30785