Finite Group Databasebeta

← C2×#10611709 #12979829

Subgroups — C2×#10611709 #12979829

Order 1280.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65913C211yesmaximal, characteristic
2C2×#65901C211yesmaximal, characteristic, complemented
3C2×C5×#446C211yesmaximal, characteristic, complemented
4#10611709C2116yesmaximal, direct product factor
5C2×#65118C211yesmaximal, characteristic, complemented
6C2×#65118C211yesmaximal, characteristic, complemented
7C2×#65140C211yesmaximal, characteristic, complemented
8C2×#65136C211yesmaximal, characteristic
9C2×#65136C211yesmaximal, characteristic
10C2×#65131C211yesmaximal, characteristic
11C2×#64999C211yesmaximal, characteristic
12C2×#64999C211yesmaximal, characteristic
13C2×#64991C211yesmaximal, characteristic, complemented
14C2×#64991C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic
16C2×#64972C211yesmaximal, characteristic, complemented
17C2×C4×C5×Q8C2211yescharacteristic
18C2×#4092—21no—
19C2×#4090—21no—
20C22×#677C2211yescharacteristic
21#65913—24no—
22#65913C2218yes—
23#65901—24no—
24#65901C2218yescomplemented
25C2×#4042—21no—
26C2×#4042—21no—
27C2×D5×C4⋊C4—21no—
28C2×#4035—21no—
29C2×#4035—21no—
30C2×#4033—21no—
31C2×C4×D20C2211yescharacteristic
32C2×C4×D20C2211yescharacteristic
33C2×C4×D20C2211yescharacteristic
34C2×#4016C2211yescharacteristic
35C2×#4016C2211yescharacteristic
36C2×#4016C2211yescharacteristic
37C2×#4016C2211yescharacteristic
38C2×#4015C2211yescharacteristic
39C2×#4015C2211yescharacteristic
40C2×C4×Dic10C2211yescharacteristic
41C2×C4×Dic10C2211yescharacteristic
42C2×C4×Dic10C2211yescharacteristic
43C5×#446C2218yescomplemented
44C2×C5×C4⋊C8C2211yescharacteristic
45C2×C5×C4⋊C8C2211yescharacteristic
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×#97C2211yescharacteristic
48C2×C5×#97C2211yescharacteristic
49C2×C4×C5×C8C2211yescharacteristic
50C2×#3953C2211yescharacteristic
51C2×#3953C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3950C2211yescharacteristic
54C2×#3950C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3950C2211yescharacteristic
57C2×#3949C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65#65140C2218yescomplemented
66#65136C2218yes—
67#65136C2218yes—
68#65131C2218yes—
69#65118C2218yescomplemented
70#65118C2218yescomplemented
71#64999C2218yes—
72#64999C2218yes—
73#64991C2218yescomplemented
74#64991C2218yescomplemented
75C4×#677C2218yes—
76#64972C2218yescomplemented
77C2×#3388—51nomaximal, Sylow
78C22×C5×Q8D411yescharacteristic
79C22×D20C2311yescharacteristic
80C22×C4×D5—21no—
81C22×C4×D5—21no—
82C22×C4×D5—21no—
83C22×Dic10—21no—
84C22×Dic10—21no—
85C22×Dic10C2311yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C22×C5×C8C2311yescharacteristic
89C22×C5×C8C2311yescharacteristic
90C4×C5×Q8D414yes—
91C4×C5×Q8C2314yes—
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4D411yescharacteristic
94C2×C5×C4⋊C4D411yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C2×C42×C5C2311yescharacteristic
97C2×C42×C5C2311yescharacteristic
98#4092—28no—
99#4090—28no—
100C2×#685—21no—
101C2×#685—21no—
102C2×#685—21no—
103C2×C4⋊Dic5—21no—
104C2×C4⋊Dic5—21no—
105C2×C4⋊Dic5C2311yescharacteristic
106C2×C4⋊Dic5C2311yescharacteristic
107C2×C4⋊Dic5C2311yescharacteristic
108C2×C4⋊Dic5C2311yescharacteristic
109C2×C4⋊Dic5C2311yescharacteristic
110C2×C4⋊Dic5C2311yescharacteristic
111C2×#683—21no—
112C2×#683—21no—
113C2×#683—21no—
114C2×#683—21no—
115C2×#683—21no—
116C2×#683—21no—
117C2×#683—21no—
118C2×#683—21no—
119C2×#683—21no—
120C2×#683—21no—
121C2×#683—21no—
122C2×C4×Dic5—21no—
123C2×C4×Dic5—21no—
124C2×C4×Dic5—21no—
125C2×#677Q818yescomplemented
126C2×#677C2314yes—
127#4042—28no—
128#4042—28no—
129D5×C4⋊C4—28no—
130#4035—28no—
131#4035—28no—
132#4033—28no—
133C4×D20—22no—
134C4×D20—22no—
135C4×D20—22no—
136C4×D20C2314yes—
137C4×D20C2314yes—
138C4×D20C2314yes—
139#4016—22no—
140#4016—22no—
141#4016—22no—
142#4016—22no—
143#4016C2314yes—
144#4016C2314yes—
145#4016C2314yes—
146#4016C2314yes—
147#4015—22no—
148#4015—22no—
149#4015C2314yes—
150#4015C2314yes—
151C4×Dic10—22no—
152C4×Dic10—22no—
153C4×Dic10—22no—
154C4×Dic10C2314yes—
155C4×Dic10C2314yes—
156C4×Dic10C2314yes—
157C5×C4⋊C8C2314yes—
158C5×C4⋊C8C2314yes—
159C5×C4⋊C8C2314yes—
160C5×#97C2314yes—
161C5×#97C2314yes—
162C4×C5×C8C2314yes—
163#3953C2314yes—
164#3953C2314yes—
165#3953C2314yes—
166#3950C2314yes—
167#3950C2314yes—
168#3950C2314yes—
169#3950C2314yes—
170#3949C2314yes—
171#3949C2314yes—
172#3949C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3948C2314yes—
178C2×#557—51no—
179C2×#554—51no—
180#3388—516no—
181C2×#501—51no—
182C2×#501—51no—
183C2×#499—51no—
184C2×#479—51no—
185C2×#479—51no—
186C2×#475—51no—
187C2×#478—51no—
188C2×#478—51no—
189C2×#476—51no—
190C2×#446D511yescharacteristic, complemented
191C2×#440—51no—
192C2×#440—51no—
193C2×C4×SD16—51no—
194C23×D5—21no—
195C2×C5×Q8—42no—
196C2×C5×Q8C2×D414yes—
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2×D411yescharacteristic
203C22×C4×C5C2411yescharacteristic
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C2×D20—21no—
212C2×D20—22no—
213C2×D20C2×Q814yes—
214C2×D20C2412yes—
215C2×C4×D5—24no—
216C2×C4×D5—24no—
217C2×C4×D5—24no—
218C2×C4×D5—44no—
219C2×C4×D5—82no—
220C2×C4×D5—82no—
221C2×Dic10—21no—
222C2×Dic10—22no—
223C2×Dic10—24no—
224C2×Dic10—24no—
225C2×Dic10—44no—
226C2×Dic10—82no—
227C2×Dic10C2×Q814yes—
228C2×Dic10C2412yes—
229C2×C5×C8—22no—
230C2×C5×C8—22no—
231C2×C5×C8—22no—
232C2×C5×C8C2×Q814yes—
233C2×C5×C8C2412yes—
234C2×C5×C8C2412yes—
235C2×C5×C8C2412yes—
236C2×C5×C8C2412yes—
237C5×C4⋊C4C2×D414yes—
238C5×C4⋊C4C2×D414yes—
239C5×C4⋊C4C2×D414yes—
240C42×C5C2×D412yes—
241C42×C5C2×D412yes—
242C42×C5C2×D412yes—
243C42×C5C2412yes—
244C42×C5C2412yes—
245C42×C5C2412yes—
246#685—24no—
247#685—24no—
248#685—24no—
249C4⋊Dic5—21no—
250C4⋊Dic5—21no—
251C4⋊Dic5—21no—
252C4⋊Dic5—21no—
253C4⋊Dic5—21no—
254C4⋊Dic5—24no—
255C4⋊Dic5—24no—
256C4⋊Dic5—21no—
257C4⋊Dic5C2412yes—
258C4⋊Dic5C2412yes—
259C4⋊Dic5C2412yes—
260C4⋊Dic5C2412yes—
261C4⋊Dic5C2412yes—
262C4⋊Dic5C2412yes—
263#683—24no—
264#683—24no—
265#683—24no—
266#683—24no—
267#683—24no—
268#683—24no—
269#683—24no—
270#683—24no—
271#683—24no—
272#683—24no—
273#683—24no—
274C4×Dic5—24no—
275C4×Dic5—24no—
276C4×Dic5—24no—
277#677C2×Q8116yescomplemented
278C22×SD16—51no—
279#557—58no—
280#557—104no—
281#554—58no—
282#554—104no—
283C2×C4⋊Q8—51no—
284C2×C4⋊Q8—51no—
285C2×C4⋊Q8—101no—
286C2×#125—51no—
287C2×#125—51no—
288C2×#125—51no—
289C2×#125—51no—
290C2×#125—101no—
291C2×#125—101no—
292C2×C22⋊Q8—101no—
293C2×C22⋊Q8—101no—
294C2×C22⋊Q8—101no—
295C2×C4×Q8—51no—
296C2×C4×Q8—51no—
297C2×C4×Q8—51no—
298C2×C4×Q8—101no—
299C2×C4×Q8C2×D511yescharacteristic
300C2×C4×D4—51no—
301C2×C4×D4—51no—
302C2×C4×D4—51no—
303C22×C4⋊C4—101no—
304#501—58no—
305#501—58no—
306#499—58no—
307#479—58no—
308#479—58no—
309#478—58no—
310#478—58no—
311#476—58no—
312#475—58no—
313#446C2×D518yescomplemented
314#440—58no—
315#440—58no—
316C4×SD16—58no—
317C2×#107—51no—
318C2×#107—51no—
319C2×#107—51no—
320C2×#107—51no—
321C2×#106—51no—
322C2×#106—51no—
323C2×#106—51no—
324C2×#106—51no—
325C2×#106—51no—
326C2×C4⋊C8C2×D511yescharacteristic
327C2×C4⋊C8C2×D511yescharacteristic
328C2×C4⋊C8C2×D511yescharacteristic
329C2×#103—51no—
330C2×#103—51no—
331C2×#103—51no—
332C2×#102—51no—
333C2×#102—51no—
334C2×#102—51no—
335C2×#97C2×D511yescharacteristic
336C2×#97C2×D511yescharacteristic
337C2×C4×C8C2×D511yescharacteristic
338C23×C5C22×D411yescharacteristic
339C22×D5—24no—
340C22×D5—22no—
341C22×D5—42no—
342C22×D5—42no—
343C5×Q8—44no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5C22×D412yes—
351C2×C4×C5C22×D412yes—
352C2×C4×C5C22×D412yes—
353C2×C4×C5C22×D412yes—
354C2×C4×C5C22×D412yes—
355C2×C4×C5C22×D412yes—
356C2×C4×C5C22×D411yescharacteristic
357C2×C4×C5C22×Q812yes—
358C2×C4×C52−1+412yes—
359C2×C4×C5C2511yescharacteristic
360C2×Dic5—24no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374D20—24no—
375D20—22no—
376D20C22×Q814yes—
377C4×D5—48no—
378C4×D5—84no—
379C4×D5—84no—
380Dic10—24no—
381Dic10—22no—
382Dic10—48no—
383Dic10—84no—
384Dic10C22×Q814yes—
385C5×C8—22no—
386C5×C8—22no—
387C5×C8—22no—
388C5×C8C22×Q814yes—
389C22×Q8—51no—
390C22×Q8—101no—
391C22×Q8—101no—
392C22×Q8D2011yescharacteristic
393C22×D4—51no—
394C23×C4—101no—
395C23×C4—101no—
396C23×C4—101no—
397C2×SD16—58no—
398C2×SD16—54no—
399C22×C8C22×D511yescharacteristic
400C22×C8C22×D511yescharacteristic
401C22×C8C22×D511yescharacteristic
402C22×C8C22×D511yescharacteristic
403C4⋊Q8—54no—
404C4⋊Q8—54no—
405C4⋊Q8—108no—
406C4⋊Q8—102no—
407C4⋊Q8—102no—
408#125—54no—
409#125—54no—
410#125—54no—
411#125—54no—
412#125—108no—
413#125—108no—
414#125—102no—
415#125—102no—
416#125—102no—
417#125—102no—
418C22⋊Q8—108no—
419C22⋊Q8—108no—
420C22⋊Q8—108no—
421C4×Q8—54no—
422C4×Q8—54no—
423C4×Q8—54no—
424C4×Q8—108no—
425C4×Q8—102no—
426C4×Q8—102no—
427C4×Q8—102no—
428C4×Q8D2014yes—
429C4×Q8C22×D514yes—
430C4×D4—54no—
431C4×D4—54no—
432C4×D4—54no—
433C4×D4—102no—
434C4×D4—102no—
435C4×D4—102no—
436C2×C4⋊C4—51no—
437C2×C4⋊C4—51no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—51no—
440C2×C4⋊C4—51no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—101no—
443C2×C4⋊C4—101no—
444C2×C4⋊C4—101no—
445C2×C4⋊C4—101no—
446C2×C4⋊C4—101no—
447C2×C4⋊C4—101no—
448C2×C4⋊C4—101no—
449C2×C4⋊C4—101no—
450C2×C4⋊C4—101no—
451C2×C4⋊C4—101no—
452C2×C4⋊C4—101no—
453C2×C4⋊C4—101no—
454C2×C4⋊C4—101no—
455C2×C4⋊C4—108no—
456C2×C4⋊C4D2011yescharacteristic
457C2×C4⋊C4D2011yescharacteristic
458C2×C4⋊C4D2011yescharacteristic
459C2×C22⋊C4—101no—
460C2×C22⋊C4—101no—
461C2×C22⋊C4—101no—
462C2×C42—101no—
463C2×C42—101no—
464C2×C42—101no—
465C2×C42C22×D511yescharacteristic
466C2×C42C22×D511yescharacteristic
467C2×C42C22×D511yescharacteristic
468#107—54no—
469#107—54no—
470#107—54no—
471#107—54no—
472#106—54no—
473#106—54no—
474#106—54no—
475#106—54no—
476#106—54no—
477C4⋊C8C22×D514yes—
478C4⋊C8C22×D514yes—
479C4⋊C8C22×D514yes—
480#103—54no—
481#103—54no—
482#103—54no—
483#102—54no—
484#102—54no—
485#102—54no—
486#97C22×D514yes—
487#97C22×D514yes—
488C4×C8C22×D514yes—
489C22×C5D4×Q812yes—
490C22×C5#57512yes—
491C22×C5#57712yes—
492C22×C5C23×D411yescharacteristic
493C2×D5—24no—
494C2×D5—48no—
495C2×D5—42no—
496C2×D5—42no—
497C4×C5—22no—
498C4×C5—22no—
499C4×C5—22no—
500C4×C5—22no—
501C4×C5—22no—
502C4×C5—22no—
503C4×C5D4×Q812yes—
504C4×C5C23×Q811yescharacteristic
505C4×C5C2×2−1+411yescharacteristic
506Dic5—24no—
507Dic5—42no—
508Dic5—42no—
509Dic5—42no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513C24—101no—
514C2×Q8—42no—
515C2×Q8—54no—
516C2×Q8—52no—
517C2×Q8—101no—
518C2×Q8—104no—
519C2×Q8—104no—
520C2×Q8—102no—
521C2×Q8—204no—
522C2×Q8—402no—
523C2×Q8C2×D2014yes—
524C2×D4—54no—
525C2×D4—52no—
526C2×D4—101no—
527C2×D4—102no—
528C22×C4—101no—
529C22×C4—101no—
530C22×C4—101no—
531C22×C4—101no—
532C22×C4—101no—
533C22×C4—101no—
534C22×C4—101no—
535C22×C4—104no—
536C22×C4—104no—
537C22×C4—104no—
538C22×C4—204no—
539C22×C4—402no—
540C22×C4—402no—
541C22×C4C2×D2011yescharacteristic
542C22×C4C2×D2011yescharacteristic
543C22×C4C2×D2011yescharacteristic
544C22×C4C2×D2011yescharacteristic
545C22×C4C2×D2011yescharacteristic
546C22×C4C2×D2011yescharacteristic
547C22×C4C23×D511yescharacteristic
548SD16—516no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8Q8×D514yes—
553C2×C8C23×D512yes—
554C2×C8C23×D512yes—
555C2×C8C23×D512yes—
556C2×C8C23×D512yes—
557C4⋊C4—52no—
558C4⋊C4—52no—
559C4⋊C4—52no—
560C4⋊C4—52no—
561C4⋊C4—52no—
562C4⋊C4—52no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4—101no—
569C4⋊C4—104no—
570C4⋊C4—104no—
571C4⋊C4—104no—
572C4⋊C4—104no—
573C4⋊C4—104no—
574C4⋊C4—104no—
575C4⋊C4—104no—
576C4⋊C4—104no—
577C4⋊C4—104no—
578C4⋊C4—104no—
579C4⋊C4—104no—
580C4⋊C4—104no—
581C4⋊C4—104no—
582C4⋊C4C2×D2014yes—
583C4⋊C4C2×D2014yes—
584C4⋊C4C2×D2014yes—
585C22⋊C4—104no—
586C22⋊C4—104no—
587C22⋊C4—104no—
588C42—104no—
589C42—104no—
590C42—104no—
591C42C2×D2012yes—
592C42C2×D2012yes—
593C42C2×D2012yes—
594C42C23×D512yes—
595C42C23×D512yes—
596C42C23×D512yes—
597C2×C5#338814yescomplemented
598C2×C5C2×D4×Q811yescharacteristic
599C2×C5C2×#57511yescharacteristic
600C2×C5C2×#57711yescharacteristic
601D5—44no—
602C23—104no—
603C23—102no—
604C23—202no—
605C23—202no—
606C23C22×D2011yescharacteristic
607Q8—44no—
608Q8—54no—
609Q8—104no—
610Q8—102no—
611Q8—208no—
612Q8—404no—
613D4—54no—
614D4—104no—
615D4—102no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—104no—
623C2×C4—102no—
624C2×C4—102no—
625C2×C4—102no—
626C2×C4—102no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—208no—
631C2×C4—202no—
632C2×C4—202no—
633C2×C4—202no—
634C2×C4—202no—
635C2×C4—202no—
636C2×C4—202no—
637C2×C4—404no—
638C2×C4—404no—
639C2×C4C22×D2012yes—
640C2×C4C22×D2012yes—
641C2×C4C22×D2012yes—
642C2×C4C22×D2012yes—
643C2×C4C22×D2012yes—
644C2×C4C22×D2012yes—
645C2×C4C22×D2011yescharacteristic
646C2×C4C2×Q8×D512yes—
647C2×C4#415012yes—
648C2×C4C24×D511yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8C2×Q8×D514yes—
653C5C2×#338811yescharacteristic, complemented, Sylow
654C22—104no—
655C22—202no—
656C22—202no—
657C22—208no—
658C22Q8×D2012yes—
659C22#6608212yes—
660C22#6608512yes—
661C22C23×D2011yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—104no—
669C4—202no—
670C4—202no—
671C4—202no—
672C4—202no—
673C4—202no—
674C4—202no—
675C4Q8×D2012yes—
676C4C22×Q8×D511yescharacteristic
677C4C2×#415011yescharacteristic
678C2—204no—
679C2#1061170914yesdirect product factor
680C2C2×Q8×D2011yescharacteristic
681C2C2×#6608211yescharacteristic
682C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#446C2
socleC23×C5C22×D4
prime radicalC22×D20C23
hypercenterC2×#446D5
hypocenterC5C2×#3388
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#65901C2semidirect
3. C2×C5×#446C2semidirect
4. #10611709C2direct (N × H)
5. C2×#65118C2semidirect
6. C2×#65118C2semidirect
7. C2×#65140C2semidirect
13. C2×#64991C2semidirect
14. C2×#64991C2semidirect
16. C2×#64972C2semidirect
24. #65901C22semidirect
43. C5×#446C22semidirect
65. #65140C22semidirect
69. #65118C22semidirect
70. #65118C22semidirect
73. #64991C22semidirect
74. #64991C22semidirect
76. #64972C22semidirect
125. C2×#677Q8semidirect
190. C2×#446D5semidirect
277. #677C2×Q8semidirect
313. #446C2×D5semidirect
597. C2×C5#3388semidirect
653. C5C2×#3388semidirect
679. C2#10611709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659132
C2×#659012
C2×C5×#4462
#106117092
C2×#651182
C2×#651402
C2×#651362
C2×#651312
C2×#649992
C2×#649912
C2×C4×#6772
C2×#649722
C2×#33885