Finite Group Databasebeta

← C2×#10612969 #12971412

Subgroups — C2×#10612969 #12971412

Order 1280.

1770 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#125C211yesmaximal, characteristic
2C2×#65912C211yesmaximal, characteristic
3C2×C5×#479C211yesmaximal, characteristic, complemented
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65311C211yesmaximal, characteristic, complemented
6#10612969C2116yesmaximal, direct product factor
7C2×#65173C211yesmaximal, characteristic
8C2×#65165C211yesmaximal, characteristic, complemented
9C2×#65151C211yesmaximal, characteristic
10C2×#65145C211yesmaximal, characteristic, complemented
11C2×#65118C211yesmaximal, characteristic, complemented
12C2×#65124C211yesmaximal, characteristic
13C2×#65098C211yesmaximal, characteristic
14C2×#65094C211yesmaximal, characteristic
15C2×#65086C211yesmaximal, characteristic, complemented
16C2×#65086C211yesmaximal, characteristic, complemented
17C2×C5×#125C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×#4092C2211yescharacteristic
20C2×#4090C2211yescharacteristic
21D5×#125—24no—
22D5×#125C2218yes—
23#65912—24no—
24#65912C2218yes—
25C2×#4043C2211yescharacteristic
26C2×#4042—21no—
27C2×D5×C4⋊C4—21no—
28C2×D5×C4⋊C4—21no—
29C2×D5×C4⋊C4C2211yescharacteristic
30C2×D5×C4⋊C4C2211yescharacteristic
31C2×#4036C2211yescharacteristic
32C2×#4036C2211yescharacteristic
33C2×#4035—21no—
34C2×#4035—21no—
35C2×#4035—21no—
36C2×#4034C2211yescharacteristic
37C2×#4018—21no—
38C2×C42×D5C2211yescharacteristic
39C2×#4016C2211yescharacteristic
40C2×C4×Dic10—21no—
41C2×C4×Dic10C2211yescharacteristic
42C5×#479C2218yescomplemented
43C2×C5×#107C2211yescharacteristic
44C2×C5×#106C2211yescharacteristic
45C2×C5×C4⋊C8C2211yescharacteristic
46C2×C5×#103C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3952C2211yescharacteristic
51C2×#3952C2211yescharacteristic
52C2×#3950C2211yescharacteristic
53C2×#3949C2211yescharacteristic
54C2×#3948C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3947C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58#65352C2218yescomplemented
59#65311C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×C4⋊#168C2211yescharacteristic
67#65173C2218yes—
68#65165C2218yescomplemented
69#65151C2218yes—
70#65145C2218yescomplemented
71#65124C2218yes—
72#65118C2218yescomplemented
73#65098C2218yes—
74#65094C2218yes—
75#65086C2218yescomplemented
76#65086C2218yescomplemented
77C2×#3236—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C4×D5—21no—
80C22×C4×D5—21no—
81C22×C4×D5D411yescharacteristic
82C22×C4×D5D411yescharacteristic
83C22×C4×D5C2311yescharacteristic
84C22×Dic10—21no—
85C22×Dic10C2311yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C5×#125—22no—
89C5×#125C2314yes—
90C4×C5×Q8—22no—
91C4×C5×Q8C2314yes—
92C2×C5×C4⋊C4—21no—
93C2×C5×C4⋊C4—21no—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C42×C5—21no—
99C2×C42×C5C2311yescharacteristic
100#4092—22no—
101#4092C2314yes—
102#4090—22no—
103#4090C2314yes—
104C2×#685—21no—
105C2×#685—21no—
106C2×C4⋊Dic5—21no—
107C2×C4⋊Dic5—21no—
108C2×C4⋊Dic5—21no—
109C2×C4⋊Dic5C2311yescharacteristic
110C2×C4⋊Dic5C2311yescharacteristic
111C2×C4⋊Dic5C2311yescharacteristic
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×#683—21no—
123C2×C4×Dic5—21no—
124C2×C4×Dic5D411yescharacteristic
125C2×C4×Dic5D411yescharacteristic
126C2×C4×Dic5C2311yescharacteristic
127C22×#168C2311yescharacteristic
128C22×#168C2311yescharacteristic
129#4043—22no—
130#4043C2314yes—
131#4042—28no—
132D5×C4⋊C4—28no—
133D5×C4⋊C4—28no—
134D5×C4⋊C4—22no—
135D5×C4⋊C4—22no—
136D5×C4⋊C4C2314yes—
137D5×C4⋊C4C2314yes—
138#4036—22no—
139#4036—22no—
140#4036C2314yes—
141#4036C2314yes—
142#4035—28no—
143#4035—28no—
144#4035—28no—
145#4034—22no—
146#4034C2314yes—
147#4018—28no—
148C42×D5D414yes—
149C42×D5C2314yes—
150#4016—22no—
151#4016C2314yes—
152C4×Dic10—22no—
153C4×Dic10—28no—
154C4×Dic10C2314yes—
155C5×#107C2314yes—
156C5×#106C2314yes—
157C5×C4⋊C8C2314yes—
158C5×#103C2314yes—
159C5×#103C2314yes—
160#3967C2314yes—
161#3967C2314yes—
162#3952C2314yes—
163#3952C2314yes—
164#3950C2314yes—
165#3949C2314yes—
166#3948C2314yes—
167#3948C2314yes—
168#3947C2314yes—
169#3947C2314yes—
170#3942C2314yes—
171#3942C2314yes—
172#3940C2314yes—
173#3940C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176C4⋊#168C2314yes—
177C2×#533—51no—
178C22×#125—51no—
179#3236—516no—
180C2×#501—51no—
181C2×#501—51no—
182C2×#491—51no—
183C2×#491—51no—
184C2×#484—51no—
185C2×#484—51no—
186C2×#483—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#479—51no—
190C2×#479—51no—
191C2×#479D511yescharacteristic, complemented
192C2×#432—51no—
193C23×D5C2×D411yescharacteristic
194C2×C5×Q8—21no—
195C2×C5×Q8—22no—
196C2×C5×Q8—22no—
197C2×C5×Q8C2412yes—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5C2×D411yescharacteristic
203C22×C4×C5C2×D411yescharacteristic
204C22×C4×C5C2411yescharacteristic
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5C2×D411yescharacteristic
210C22×Dic5C2×D411yescharacteristic
211C22×Dic5C2×D411yescharacteristic
212C2×C4×D5—24no—
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×C4×D5—24no—
216C2×C4×D5—24no—
217C2×C4×D5—42no—
218C2×C4×D5—44no—
219C2×C4×D5—44no—
220C2×C4×D5C2×D414yes—
221C2×C4×D5C2×D412yes—
222C2×C4×D5C2×D414yes—
223C2×C4×D5C2412yes—
224C2×Dic10—22no—
225C2×Dic10—22no—
226C2×Dic10—21no—
227C2×Dic10—24no—
228C2×Dic10—44no—
229C2×Dic10C2412yes—
230C2×C5×C8—22no—
231C2×C5×C8—22no—
232C2×C5×C8C2412yes—
233C2×C5×C8C2412yes—
234C5×C4⋊C4—24no—
235C5×C4⋊C4—24no—
236C5×C4⋊C4—24no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4C2412yes—
241C5×C4⋊C4C2412yes—
242C5×C4⋊C4C2412yes—
243C42×C5—24no—
244C42×C5C2×D412yes—
245C42×C5C2412yes—
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⋊Dic5C2412yes—
255C4⋊Dic5C2412yes—
256C4⋊Dic5C2412yes—
257#683—24no—
258#683—24no—
259#683—24no—
260#683—24no—
261#683—24no—
262#683—24no—
263#683—24no—
264#683—24no—
265#683—24no—
266#683—24no—
267#683—24no—
268C4×Dic5—24no—
269C4×Dic5C2×D414yes—
270C4×Dic5C2×D412yes—
271C4×Dic5C2×D414yes—
272C4×Dic5C2412yes—
273C2×#168—22no—
274C2×#168—22no—
275C2×#168C2412yes—
276C2×#168C2412yes—
277#533—58no—
278#533—104no—
279C2×C4⋊Q8—51no—
280C2×C4⋊Q8—51no—
281C2×#125—58no—
282C2×#125—51no—
283C2×#125—51no—
284C2×#125—51no—
285C2×#125—101no—
286C2×#125—101no—
287C2×#125—101no—
288C2×#125—104no—
289C2×#125C2×D511yescharacteristic
290C2×C22⋊Q8—51no—
291C2×C22⋊Q8—51no—
292C2×C22⋊Q8—101no—
293C2×C4×Q8—51no—
294C2×C4×Q8—101no—
295C2×C4×Q8C2×D511yescharacteristic
296C2×#117—101no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—101no—
300C22×C4⋊C4—101no—
301C22×C42—51no—
302#501—58no—
303#501—58no—
304#491—58no—
305#491—58no—
306#484—58no—
307#484—58no—
308#483—58no—
309#483—58no—
310#479—58no—
311#479—58no—
312#479—58no—
313#479C2×D518yescomplemented
314#432—58no—
315C2×#107—51no—
316C2×#107—51no—
317C2×#107—51no—
318C2×#107C2×D511yescharacteristic
319C2×#106—51no—
320C2×#106—51no—
321C2×#106—51no—
322C2×#106C2×D511yescharacteristic
323C2×C4⋊C8—51no—
324C2×C4⋊C8C2×D511yescharacteristic
325C2×#103—51no—
326C2×#103—51no—
327C2×#103—51no—
328C2×#103—51no—
329C2×#103—51no—
330C2×#103—51no—
331C2×#103C2×D511yescharacteristic
332C2×#103C2×D511yescharacteristic
333C2×C22⋊C8—51no—
334C2×C22⋊C8—51no—
335C2×#97—51no—
336C2×#97—51no—
337C23×C5C22×D411yescharacteristic
338C22×D5—22no—
339C22×D5—22no—
340C22×D5#13714yes—
341C22×D5C22×D412yes—
342C5×Q8—22no—
343C5×Q8—22no—
344C5×Q8—42no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—42no—
352C2×C4×C5—42no—
353C2×C4×C5—42no—
354C2×C4×C5—42no—
355C2×C4×C5C22×D412yes—
356C2×C4×C5C22×D412yes—
357C2×C4×C5C22×D411yescharacteristic
358C2×C4×C52−1+412yes—
359C2×C4×C52−1+412yes—
360C2×C4×C5C2511yescharacteristic
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×Dic5C22×D412yes—
373C2×Dic5C22×D412yes—
374C2×Dic5C22×D412yes—
375C4×D5—28no—
376C4×D5—24no—
377C4×D5—22no—
378C4×D5—22no—
379C4×D5—44no—
380C4×D5—48no—
381C4×D5—48no—
382Dic10—22no—
383Dic10—22no—
384Dic10—48no—
385Dic10—42no—
386C5×C8—22no—
387C5×C8—22no—
388#168—22no—
389#168—22no—
390C22×Q8—51no—
391C22×Q8—101no—
392C22×Q8C22×D511yescharacteristic
393C23×C4—51no—
394C23×C4—51no—
395C23×C4—51no—
396C23×C4—101no—
397C23×C4—101no—
398C22×C8—51no—
399C22×C8—51no—
400C22×C8C22×D511yescharacteristic
401C22×C8C22×D511yescharacteristic
402C4⋊Q8—54no—
403C4⋊Q8—54no—
404C4⋊Q8—102no—
405C4⋊Q8—102no—
406#125—22no—
407#125—54no—
408#125—54no—
409#125—54no—
410#125—108no—
411#125—108no—
412#125—102no—
413#125—102no—
414#125—108no—
415#125—102no—
416#125C22×D514yes—
417C22⋊Q8—54no—
418C22⋊Q8—54no—
419C22⋊Q8—102no—
420C22⋊Q8—108no—
421C22⋊Q8—102no—
422C4×Q8—22no—
423C4×Q8—54no—
424C4×Q8—108no—
425C4×Q8—102no—
426C4×Q8C22×D514yes—
427#117—108no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—102no—
438C2×C4⋊C4—108no—
439C2×C4⋊C4—108no—
440C2×C4⋊C4—101no—
441C2×C4⋊C4—101no—
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⋊C4C22×D511yescharacteristic
455C2×C4⋊C4C22×D511yescharacteristic
456C2×C4⋊C4C22×D511yescharacteristic
457C2×C22⋊C4—101no—
458C2×C22⋊C4—101no—
459C2×C42—21no—
460C2×C42—51no—
461C2×C42—51no—
462C2×C42—51no—
463C2×C42—54no—
464C2×C42—54no—
465C2×C42—101no—
466C2×C42C22×D511yescharacteristic
467#107—54no—
468#107—54no—
469#107—54no—
470#107C22×D514yes—
471#106—54no—
472#106—54no—
473#106—54no—
474#106C22×D514yes—
475C4⋊C8—54no—
476C4⋊C8C22×D514yes—
477#103—54no—
478#103—54no—
479#103—54no—
480#103—54no—
481#103—54no—
482#103—54no—
483#103C22×D514yes—
484#103C22×D514yes—
485C22⋊C8—54no—
486C22⋊C8—54no—
487#97—54no—
488#97—54no—
489C22×C5#53612yes—
490C22×C5C2×#13712yes—
491C22×C5#57512yes—
492C22×C5C23×D411yescharacteristic
493C2×D5—22no—
494C2×D5—28no—
495C2×D5—22no—
496C2×D5C2×#13714yes—
497C4×C5—22no—
498C4×C5—22no—
499C4×C5—42no—
500C4×C5—42no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5#53612yes—
504C4×C5C2×2−1+411yescharacteristic
505C4×C5C2×2−1+411yescharacteristic
506Dic5—22no—
507Dic5—22no—
508Dic5—22no—
509Dic5—42no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513C24—51no—
514C2×Q8—21no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—52no—
518C2×Q8—104no—
519C2×Q8—101no—
520C2×Q8—102no—
521C2×Q8—102no—
522C2×Q8—204no—
523C2×Q8C23×D512yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—54no—
532C22×C4—52no—
533C22×C4—52no—
534C22×C4—54no—
535C22×C4—104no—
536C22×C4—104no—
537C22×C4—104no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—202no—
545C22×C4—204no—
546C22×C4—204no—
547C22×C4D4×D511yescharacteristic
548C22×C4D4×D511yescharacteristic
549C22×C4C23×D511yescharacteristic
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—52no—
553C2×C8—52no—
554C2×C8—102no—
555C2×C8—102no—
556C2×C8C23×D512yes—
557C2×C8C23×D512yes—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—52no—
565C4⋊C4—52no—
566C4⋊C4—52no—
567C4⋊C4—104no—
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—104no—
578C4⋊C4—101no—
579C4⋊C4—101no—
580C4⋊C4—101no—
581C4⋊C4—104no—
582C4⋊C4—104no—
583C4⋊C4—104no—
584C4⋊C4C23×D512yes—
585C4⋊C4C23×D512yes—
586C4⋊C4C23×D512yes—
587C22⋊C4—104no—
588C22⋊C4—104no—
589C42—24no—
590C42—54no—
591C42—54no—
592C42—52no—
593C42—52no—
594C42—104no—
595C42D4×D512yes—
596C42C23×D512yes—
597C2×C5#323614yescomplemented
598C2×C5C2×#53611yescharacteristic
599C2×C5C22×#13711yescharacteristic
600C2×C5C2×#57511yescharacteristic
601D5—24no—
602C23—54no—
603C23—52no—
604C23—102no—
605C23—102no—
606C23C2×D4×D511yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—42no—
610Q8—102no—
611Q8—102no—
612Q8—208no—
613Q8—202no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—52no—
625C2×C4—52no—
626C2×C4—52no—
627C2×C4—108no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—102no—
631C2×C4—104no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—204no—
639C2×C4—208no—
640C2×C4—208no—
641C2×C4—202no—
642C2×C4—202no—
643C2×C4—202no—
644C2×C4—202no—
645C2×C4C2×D4×D512yes—
646C2×C4C2×D4×D512yes—
647C2×C4C2×D4×D511yescharacteristic
648C2×C4#414712yes—
649C2×C4#415012yes—
650C2×C4C24×D511yescharacteristic
651C8—22no—
652C8—22no—
653C8—102no—
654C8—102no—
655C5C2×#323611yescharacteristic, complemented, Sylow
656C22—54no—
657C22—102no—
658C22—102no—
659C22—108no—
660C22#6596212yes—
661C22#6610212yes—
662C22D5×#13712yes—
663C22C22×D4×D511yescharacteristic
664C4—22no—
665C4—22no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—102no—
671C4—102no—
672C4—102no—
673C4—202no—
674C4—202no—
675C4—202no—
676C4—202no—
677C4#6596212yes—
678C4C2×#414711yescharacteristic
679C4C2×#415011yescharacteristic
680C2—104no—
681C2#1061296914yesdirect product factor
682C2C2×#6596211yescharacteristic
683C2C2×#6610211yescharacteristic
684C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#479C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#479D5
hypocenterC5C2×#3236
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. C2×C5×#479C2semidirect
4. C2×#65352C2semidirect
5. C2×#65311C2semidirect
6. #10612969C2direct (N × H)
8. C2×#65165C2semidirect
10. C2×#65145C2semidirect
11. C2×#65118C2semidirect
15. C2×#65086C2semidirect
16. C2×#65086C2semidirect
42. C5×#479C22semidirect
58. #65352C22semidirect
59. #65311C22semidirect
68. #65165C22semidirect
70. #65145C22semidirect
72. #65118C22semidirect
75. #65086C22semidirect
76. #65086C22semidirect
191. C2×#479D5semidirect
313. #479C2×D5semidirect
597. C2×C5#3236semidirect
655. C5C2×#3236semidirect
681. C2#10612969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#1252
C2×#659122
C2×C5×#4792
C2×#653522
C2×#653112
#106129692
C2×#651732
C2×#651652
C2×#651512
C2×#651452
C2×#651182
C2×#651242
C2×#650982
C2×#650942
C2×#650862
C2×#32365