Finite Group Databasebeta

← C2×#10612739 #12979834

Subgroups — C2×#10612739 #12979834

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×#66064C211yesmaximal, characteristic
2C2×#65903C211yesmaximal, characteristic, complemented
3C2×C5×#475C211yesmaximal, characteristic, complemented
4C2×#65369C211yesmaximal, characteristic, complemented
5C2×#65315C211yesmaximal, characteristic
6#10612739C2116yesmaximal, direct product factor
7C2×#65160C211yesmaximal, characteristic
8C2×#65159C211yesmaximal, characteristic
9C2×#65145C211yesmaximal, characteristic, complemented
10C2×#65147C211yesmaximal, characteristic, complemented
11C2×#65136C211yesmaximal, characteristic
12C2×#65117C211yesmaximal, characteristic, complemented
13C2×#65085C211yesmaximal, characteristic, complemented
14C2×#65088C211yesmaximal, characteristic, complemented
15C2×#65106C211yesmaximal, characteristic
16C2×#65077C211yesmaximal, characteristic
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×#4092—21no—
20C2×#4092—21no—
21C2×Q8×Dic5C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C22×#688C2211yescharacteristic
24#66064—24no—
25#66064C2218yes—
26#65903—24no—
27#65903C2218yescomplemented
28C2×#4043—21no—
29C2×#4039C2211yescharacteristic
30C2×#4039C2211yescharacteristic
31C2×D5×C4⋊C4—21no—
32C2×#4036—21no—
33C2×#4036C2211yescharacteristic
34C2×#4036C2211yescharacteristic
35C2×#4036C2211yescharacteristic
36C2×#4034—21no—
37C2×#4034C2211yescharacteristic
38C2×C4×D20C2211yescharacteristic
39C2×#4016—21no—
40C2×#4016C2211yescharacteristic
41C2×C4×Dic10—21no—
42C2×C4×Dic10C2211yescharacteristic
43C5×#475C2218yescomplemented
44C2×C5×#106C2211yescharacteristic
45C2×C5×#106C2211yescharacteristic
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3953C2211yescharacteristic
51C2×#3953C2211yescharacteristic
52C2×#3950C2211yescharacteristic
53C2×#3949C2211yescharacteristic
54C2×#3947C2211yescharacteristic
55C2×#3946C2211yescharacteristic
56C2×#3946C2211yescharacteristic
57C2×C8×Dic5C2211yescharacteristic
58#65369C2218yescomplemented
59#65315C2218yes—
60C2×#3941C2211yescharacteristic
61C2×#3940C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3939C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3935C2211yescharacteristic
67#65160C2218yes—
68#65159C2218yes—
69#65147C2218yescomplemented
70#65145C2218yescomplemented
71#65136C2218yes—
72#65117C2218yescomplemented
73#65106C2218yes—
74#65088C2218yescomplemented
75#65085C2218yescomplemented
76#65077C2218yes—
77C2×#3388—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×D20C2311yescharacteristic
81C22×C4×D5—21no—
82C22×C4×D5—21no—
83C22×C4×D5—21no—
84C22×Dic10—21no—
85C22×Dic10D411yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C5×C4⋊Q8—22no—
89C5×C4⋊Q8C2314yes—
90C4×C5×Q8—22no—
91C4×C5×Q8C2314yes—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C42×C5—21no—
98C2×C42×C5C2311yescharacteristic
99#4092—28no—
100#4092—28no—
101Q8×Dic5—22no—
102Q8×Dic5—22no—
103Q8×Dic5C2314yes—
104Q8×Dic5C2314yes—
105C2×#688Q818yescomplemented
106C2×#688C2314yes—
107C2×#685—21no—
108C2×#685—21no—
109C2×#685—21no—
110C2×C4⋊Dic5—21no—
111C2×C4⋊Dic5—21no—
112C2×C4⋊Dic5—21no—
113C2×C4⋊Dic5—21no—
114C2×C4⋊Dic5—21no—
115C2×C4⋊Dic5D411yescharacteristic
116C2×C4⋊Dic5C2311yescharacteristic
117C2×C4⋊Dic5C2311yescharacteristic
118C2×C4⋊Dic5C2311yescharacteristic
119C2×#683—21no—
120C2×#683—21no—
121C2×#683—21no—
122C2×#683—21no—
123C2×#683—21no—
124C2×#683—21no—
125C2×#683D411yescharacteristic
126C2×#683D411yescharacteristic
127C2×C4×Dic5—21no—
128C2×C4×Dic5—21no—
129C2×C4×Dic5C2311yescharacteristic
130C2×C4×Dic5C2311yescharacteristic
131C22×#168C2311yescharacteristic
132C22×#168C2311yescharacteristic
133#4043—28no—
134#4039—22no—
135#4039—22no—
136#4039C2314yes—
137#4039C2314yes—
138D5×C4⋊C4—28no—
139#4036—28no—
140#4036—22no—
141#4036—22no—
142#4036—22no—
143#4036C2314yes—
144#4036C2314yes—
145#4036C2314yes—
146#4034—28no—
147#4034—22no—
148#4034C2314yes—
149C4×D20—22no—
150C4×D20C2314yes—
151#4016—22no—
152#4016—28no—
153#4016C2314yes—
154C4×Dic10—28no—
155C4×Dic10D414yes—
156C4×Dic10C2314yes—
157C5×#106C2314yes—
158C5×#106C2314yes—
159C5×C4⋊C8C2314yes—
160C5×#103C2314yes—
161C5×#103C2314yes—
162#3967C2314yes—
163#3953C2314yes—
164#3953C2314yes—
165#3950C2314yes—
166#3949C2314yes—
167#3947C2314yes—
168#3946C2314yes—
169#3946C2314yes—
170C8×Dic5C2314yes—
171#3941C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3935C2314yes—
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×#475D511yescharacteristic, complemented
187C2×#478—51no—
188C2×#478—51no—
189C2×#476—51no—
190C2×#446—51no—
191C2×#440—51no—
192C2×#440—51no—
193C2×C4×SD16—51no—
194C23×D5—21no—
195C2×C5×Q8—21no—
196C2×C5×Q8—24no—
197C2×C5×Q8—22no—
198C2×C5×Q8—82no—
199C2×C5×Q8C2×Q814yes—
200C2×C5×Q8C2412yes—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5C2×D411yescharacteristic
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2411yescharacteristic
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5C2×D411yescharacteristic
212C22×Dic5C2×D411yescharacteristic
213C22×Dic5C2×D411yescharacteristic
214C22×Dic5C2×D411yescharacteristic
215C2×D20—21no—
216C2×D20—22no—
217C2×D20C2×Q814yes—
218C2×D20C2412yes—
219C2×C4×D5—24no—
220C2×C4×D5—24no—
221C2×C4×D5—24no—
222C2×C4×D5—44no—
223C2×C4×D5—82no—
224C2×C4×D5—82no—
225C2×Dic10—24no—
226C2×Dic10—42no—
227C2×Dic10—44no—
228C2×Dic10C2×D414yes—
229C2×C5×C8—22no—
230C2×C5×C8—22no—
231C2×C5×C8C2412yes—
232C2×C5×C8C2412yes—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—24no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4C2412yes—
239C5×C4⋊C4C2412yes—
240C5×C4⋊C4C2412yes—
241C42×C5—24no—
242C42×C5C2×D412yes—
243C42×C5C2412yes—
244#688C2×Q8116yescomplemented
245#685—24no—
246#685—24no—
247#685—24no—
248C4⋊Dic5—21no—
249C4⋊Dic5—21no—
250C4⋊Dic5—21no—
251C4⋊Dic5—24no—
252C4⋊Dic5—24no—
253C4⋊Dic5—24no—
254C4⋊Dic5—24no—
255C4⋊Dic5—24no—
256C4⋊Dic5C2×D414yes—
257C4⋊Dic5C2412yes—
258C4⋊Dic5C2412yes—
259C4⋊Dic5C2412yes—
260#683—24no—
261#683—24no—
262#683—24no—
263#683—24no—
264#683—24no—
265#683—24no—
266#683C2×D414yes—
267#683C2×D414yes—
268C4×Dic5—24no—
269C4×Dic5—24no—
270C4×Dic5C2×D412yes—
271C4×Dic5C2×D412yes—
272C4×Dic5C2412yes—
273C4×Dic5C2412yes—
274C2×#168—22no—
275C2×#168C2×Q814yes—
276C2×#168C2412yes—
277C2×#168C2412yes—
278C22×SD16—51no—
279#557—58no—
280#557—104no—
281#554—58no—
282#554—104no—
283C2×C4⋊Q8—51no—
284C2×C4⋊Q8—101no—
285C2×C4⋊Q8C2×D511yescharacteristic
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#475C2×D518yescomplemented
313#446—58no—
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×#106C2×D511yescharacteristic
325C2×#106C2×D511yescharacteristic
326C2×C4⋊C8—51no—
327C2×C4⋊C8—51no—
328C2×C4⋊C8C2×D511yescharacteristic
329C2×#103—51no—
330C2×#103C2×D511yescharacteristic
331C2×#103C2×D511yescharacteristic
332C2×#102—51no—
333C2×#102—51no—
334C2×#102—51no—
335C2×#97—51no—
336C2×#97—51no—
337C2×C4×C8—51no—
338C23×C5C22×D411yescharacteristic
339C22×D5—24no—
340C22×D5—22no—
341C22×D5—42no—
342C22×D5—42no—
343C5×Q8—24no—
344C5×Q8—22no—
345C5×Q8—84no—
346C5×Q8C22×Q814yes—
347C2×C4×C5—24no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5C22×D412yes—
358C2×C4×C5C22×D412yes—
359C2×C4×C5C22×D411yescharacteristic
360C2×C4×C5C22×Q812yes—
361C2×C4×C52−1+412yes—
362C2×C4×C5C2511yescharacteristic
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5C22×D412yes—
374C2×Dic5C22×D412yes—
375C2×Dic5C22×D412yes—
376C2×Dic5C22×D412yes—
377D20—24no—
378D20—22no—
379D20C22×Q814yes—
380C4×D5—48no—
381C4×D5—84no—
382C4×D5—84no—
383Dic10—44no—
384Dic10—48no—
385C5×C8—22no—
386C5×C8—22no—
387#168—22no—
388#168C22×Q814yes—
389C22×Q8—21no—
390C22×Q8—51no—
391C22×Q8—101no—
392C22×Q8C22×D511yescharacteristic
393C22×D4—51no—
394C23×C4—101no—
395C23×C4—101no—
396C23×C4—101no—
397C2×SD16—58no—
398C2×SD16—54no—
399C22×C8—51no—
400C22×C8—51no—
401C22×C8C22×D511yescharacteristic
402C22×C8C22×D511yescharacteristic
403C4⋊Q8—22no—
404C4⋊Q8—54no—
405C4⋊Q8—102no—
406C4⋊Q8—108no—
407C4⋊Q8C22×D514yes—
408#125—54no—
409#125—54no—
410#125—54no—
411#125—54no—
412#125—108no—
413#125—102no—
414#125—102no—
415#125—102no—
416#125—108no—
417#125—102no—
418C22⋊Q8—108no—
419C22⋊Q8—108no—
420C22⋊Q8—108no—
421C4×Q8—22no—
422C4×Q8—54no—
423C4×Q8—54no—
424C4×Q8—54no—
425C4×Q8—54no—
426C4×Q8—108no—
427C4×Q8—102no—
428C4×Q8—102no—
429C4×Q8C22×D514yes—
430C4×D4—54no—
431C4×D4—54no—
432C4×D4—54no—
433C4×D4—102no—
434C4×D4—102no—
435C4×D4—102no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—51no—
439C2×C4⋊C4—51no—
440C2×C4⋊C4—51no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—51no—
443C2×C4⋊C4—51no—
444C2×C4⋊C4—108no—
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—101no—
456C2×C4⋊C4C22×D511yescharacteristic
457C2×C4⋊C4C22×D511yescharacteristic
458C2×C4⋊C4C22×D511yescharacteristic
459C2×C22⋊C4—101no—
460C2×C22⋊C4—101no—
461C2×C22⋊C4—101no—
462C2×C42—21no—
463C2×C42—51no—
464C2×C42—51no—
465C2×C42—101no—
466C2×C42—101no—
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#106C22×D514yes—
476#106C22×D514yes—
477C4⋊C8—54no—
478C4⋊C8—54no—
479C4⋊C8C22×D514yes—
480#103—54no—
481#103C22×D514yes—
482#103C22×D514yes—
483#102—54no—
484#102—54no—
485#102—54no—
486#97—54no—
487#97—54no—
488C4×C8—54no—
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—24no—
498C4×C5—22no—
499C4×C5—22no—
500C4×C5—42no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5D4×Q812yes—
504C4×C5C23×Q811yescharacteristic
505C4×C5C2×2−1+411yescharacteristic
506Dic5—22no—
507Dic5—22no—
508Dic5—22no—
509Dic5—22no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513C24—101no—
514C2×Q8—21no—
515C2×Q8—24no—
516C2×Q8—22no—
517C2×Q8—54no—
518C2×Q8—82no—
519C2×Q8—104no—
520C2×Q8—202no—
521C2×Q8—204no—
522C2×Q8Q8×D514yes—
523C2×Q8C23×D512yes—
524C2×D4—54no—
525C2×D4—52no—
526C2×D4—101no—
527C2×D4—102no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—51no—
533C22×C4—51no—
534C22×C4—51no—
535C22×C4—51no—
536C22×C4—104no—
537C22×C4—104no—
538C22×C4—101no—
539C22×C4—101no—
540C22×C4—101no—
541C22×C4—104no—
542C22×C4—204no—
543C22×C4—402no—
544C22×C4—402no—
545C22×C4D4×D511yescharacteristic
546C22×C4D4×D511yescharacteristic
547C22×C4C23×D511yescharacteristic
548SD16—516no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—54no—
552C2×C8—52no—
553C2×C8—52no—
554C2×C8—102no—
555C2×C8C23×D512yes—
556C2×C8C23×D512yes—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—54no—
563C4⋊C4—54no—
564C4⋊C4—54no—
565C4⋊C4—52no—
566C4⋊C4—52no—
567C4⋊C4—52no—
568C4⋊C4—104no—
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—101no—
578C4⋊C4—101no—
579C4⋊C4—101no—
580C4⋊C4—104no—
581C4⋊C4—104no—
582C4⋊C4C23×D512yes—
583C4⋊C4C23×D512yes—
584C4⋊C4C23×D512yes—
585C22⋊C4—104no—
586C22⋊C4—104no—
587C22⋊C4—104no—
588C42—24no—
589C42—52no—
590C42—52no—
591C42—52no—
592C42—52no—
593C42—104no—
594C42—104no—
595C42D4×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—
606C23C2×D4×D511yescharacteristic
607Q8—24no—
608Q8—22no—
609Q8—84no—
610Q8—204no—
611Q8—208no—
612Q8C2×Q8×D514yes—
613D4—54no—
614D4—104no—
615D4—102no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—52no—
627C2×C4—52no—
628C2×C4—52no—
629C2×C4—52no—
630C2×C4—102no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—208no—
638C2×C4—202no—
639C2×C4—202no—
640C2×C4—202no—
641C2×C4—404no—
642C2×C4—404no—
643C2×C4C2×D4×D512yes—
644C2×C4C2×D4×D512yes—
645C2×C4C2×D4×D511yescharacteristic
646C2×C4C2×Q8×D512yes—
647C2×C4#415012yes—
648C2×C4C24×D511yescharacteristic
649C8—22no—
650C8—22no—
651C8—54no—
652C8—102no—
653C5C2×#338811yescharacteristic, complemented, Sylow
654C22—104no—
655C22—208no—
656C22—202no—
657C22—202no—
658C22#6596612yes—
659C22#6609612yes—
660C22#6611112yes—
661C22C22×D4×D511yescharacteristic
662C4—24no—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—102no—
669C4—102no—
670C4—102no—
671C4—102no—
672C4—202no—
673C4—202no—
674C4—202no—
675C4#6596612yes—
676C4C22×Q8×D511yescharacteristic
677C4C2×#415011yescharacteristic
678C2—204no—
679C2#1061273914yesdirect product factor
680C2C2×#6596611yescharacteristic
681C2C2×#6609611yescharacteristic
682C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#475C2
socleC23×C5C22×D4
prime radicalC22×D20C23
hypercenterC2×#475D5
hypocenterC5C2×#3388
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#65903C2semidirect
3. C2×C5×#475C2semidirect
4. C2×#65369C2semidirect
6. #10612739C2direct (N × H)
9. C2×#65145C2semidirect
10. C2×#65147C2semidirect
12. C2×#65117C2semidirect
13. C2×#65085C2semidirect
14. C2×#65088C2semidirect
27. #65903C22semidirect
43. C5×#475C22semidirect
58. #65369C22semidirect
69. #65147C22semidirect
70. #65145C22semidirect
72. #65117C22semidirect
74. #65088C22semidirect
75. #65085C22semidirect
105. C2×#688Q8semidirect
186. C2×#475D5semidirect
244. #688C2×Q8semidirect
312. #475C2×D5semidirect
597. C2×C5#3388semidirect
653. C5C2×#3388semidirect
679. C2#10612739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660642
C2×#659032
C2×C5×#4752
C2×#653692
C2×#653152
#106127392
C2×#651602
C2×#651592
C2×#651452
C2×#651472
C2×#651362
C2×#651172
C2×#650852
C2×#650882
C2×#651062
C2×#650772
C2×#33885