Finite Group Databasebeta

← C2×#10613699 #12979822

Subgroups — C2×#10613699 #12979822

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×#66055C211yesmaximal, characteristic, complemented
2C2×#66024C211yesmaximal, characteristic
3C2×C5×#501C211yesmaximal, characteristic, complemented
4C2×#65373C211yesmaximal, characteristic
5C2×#65352C211yesmaximal, characteristic, complemented
6#10613699C2116yesmaximal, direct product factor
7C2×#65166C211yesmaximal, characteristic, complemented
8C2×#65180C211yesmaximal, characteristic
9C2×#65167C211yesmaximal, characteristic, complemented
10C2×#65178C211yesmaximal, characteristic
11C2×#65143C211yesmaximal, characteristic, complemented
12C2×#65160C211yesmaximal, characteristic
13C2×#65145C211yesmaximal, characteristic, complemented
14C2×#65141C211yesmaximal, characteristic
15C2×#64999C211yesmaximal, characteristic
16C2×#64990C211yesmaximal, characteristic, complemented
17C2×C5×C4⋊Q8C2211yescharacteristic
18C2×C5×#125C2211yescharacteristic
19C2×Q8×Dic5—21no—
20C2×#4090—21no—
21C22×#677C2211yescharacteristic
22#66055—24no—
23#66055C2218yescomplemented
24#66024—24no—
25#66024C2218yes—
26C2×#4043—21no—
27C2×#4042—21no—
28C2×#4042—21no—
29C2×#4039C2211yescharacteristic
30C2×#4039C2211yescharacteristic
31C2×D5×C4⋊C4—21no—
32C2×#4036C2211yescharacteristic
33C2×#4036C2211yescharacteristic
34C2×#4036C2211yescharacteristic
35C2×#4035—21no—
36C2×#4035—21no—
37C2×#4034C2211yescharacteristic
38C2×#4033C2211yescharacteristic
39C2×#4033C2211yescharacteristic
40C2×C4×D20C2211yescharacteristic
41C2×C4×Dic10C2211yescharacteristic
42C2×C4×Dic10C2211yescharacteristic
43C5×#501C2218yescomplemented
44C2×C5×#107C2211yescharacteristic
45C2×C5×#107C2211yescharacteristic
46C2×C5×#106C2211yescharacteristic
47C2×C5×#106C2211yescharacteristic
48C2×C5×#97C2211yescharacteristic
49C2×#3953C2211yescharacteristic
50C2×#3950C2211yescharacteristic
51C2×#3948C2211yescharacteristic
52C2×#3947C2211yescharacteristic
53C2×#3946C2211yescharacteristic
54C2×#3946C2211yescharacteristic
55C2×C8×Dic5C2211yescharacteristic
56#65373C2218yes—
57#65352C2218yescomplemented
58C2×#3942C2211yescharacteristic
59C2×#3942C2211yescharacteristic
60C2×#3941C2211yescharacteristic
61C2×#3941C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3940C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×C4⋊#168C2211yescharacteristic
67#65180C2218yes—
68#65178C2218yes—
69#65167C2218yescomplemented
70#65166C2218yescomplemented
71#65160C2218yes—
72#65145C2218yescomplemented
73#65143C2218yescomplemented
74#65141C2218yes—
75#64999C2218yes—
76#64990C2218yescomplemented
77C2×#3388—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×D20C2311yescharacteristic
80C22×C4×D5—21no—
81C22×C4×D5—21no—
82C22×C4×D5—21no—
83C22×Dic10—21no—
84C22×Dic10D411yescharacteristic
85C22×Dic10C2311yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C5×C4⋊Q8—22no—
89C5×C4⋊Q8C2314yes—
90C5×#125—22no—
91C5×#125C2314yes—
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×C5×C4⋊C4C2311yescharacteristic
99C2×C42×C5C2311yescharacteristic
100Q8×Dic5—28no—
101#4090—28no—
102C2×#685—21no—
103C2×#685—21no—
104C2×#685—21no—
105C2×C4⋊Dic5—21no—
106C2×C4⋊Dic5—21no—
107C2×C4⋊Dic5—21no—
108C2×C4⋊Dic5D411yescharacteristic
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×#683D411yescharacteristic
119C2×#683D411yescharacteristic
120C2×C4×Dic5—21no—
121C2×C4×Dic5—21no—
122C2×C4×Dic5—21no—
123C2×C4×Dic5C2311yescharacteristic
124C2×C4×Dic5C2311yescharacteristic
125C22×#168C2311yescharacteristic
126C22×#168C2311yescharacteristic
127C2×#677Q818yescomplemented
128C2×#677C2314yes—
129#4043—28no—
130#4042—28no—
131#4042—28no—
132#4039—22no—
133#4039—22no—
134#4039C2314yes—
135#4039C2314yes—
136D5×C4⋊C4—28no—
137#4036—22no—
138#4036—22no—
139#4036—22no—
140#4036C2314yes—
141#4036C2314yes—
142#4036C2314yes—
143#4035—28no—
144#4035—28no—
145#4034—22no—
146#4034C2314yes—
147#4033—22no—
148#4033—22no—
149#4033C2314yes—
150#4033C2314yes—
151C4×D20—22no—
152C4×D20C2314yes—
153C4×Dic10—22no—
154C4×Dic10D414yes—
155C4×Dic10C2314yes—
156C4×Dic10C2314yes—
157C5×#107C2314yes—
158C5×#107C2314yes—
159C5×#106C2314yes—
160C5×#106C2314yes—
161C5×#97C2314yes—
162#3953C2314yes—
163#3950C2314yes—
164#3948C2314yes—
165#3947C2314yes—
166#3946C2314yes—
167#3946C2314yes—
168C8×Dic5C2314yes—
169#3942C2314yes—
170#3942C2314yes—
171#3941C2314yes—
172#3941C2314yes—
173#3940C2314yes—
174#3940C2314yes—
175#3940C2314yes—
176#3939C2314yes—
177C4⋊#168C2314yes—
178C2×#557—51no—
179C2×#554—51no—
180#3388—516no—
181C2×#501—51no—
182C2×#501D511yescharacteristic, complemented
183C2×#499—51no—
184C2×#479—51no—
185C2×#479—51no—
186C2×#475—51no—
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—24no—
196C2×C5×Q8—44no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2×D411yescharacteristic
203C22×C4×C5C2411yescharacteristic
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5C2×D411yescharacteristic
208C22×Dic5C2×D411yescharacteristic
209C22×Dic5C2×D411yescharacteristic
210C22×Dic5C2×D411yescharacteristic
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—42no—
225C2×Dic10—82no—
226C2×Dic10C2×D414yes—
227C2×Dic10C2×Q814yes—
228C2×Dic10C2412yes—
229C2×C5×C8—22no—
230C2×C5×C8C2×Q814yes—
231C2×C5×C8C2412yes—
232C2×C5×C8C2412yes—
233C5×C4⋊C4—24no—
234C5×C4⋊C4—24no—
235C5×C4⋊C4—24no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4C2412yes—
241C5×C4⋊C4C2412yes—
242C5×C4⋊C4C2412yes—
243C5×C4⋊C4C2412yes—
244C42×C5C2×D412yes—
245C42×C5C2412yes—
246#685—24no—
247#685—24no—
248#685—24no—
249C4⋊Dic5—21no—
250C4⋊Dic5—21no—
251C4⋊Dic5—24no—
252C4⋊Dic5—24no—
253C4⋊Dic5—24no—
254C4⋊Dic5C2×D414yes—
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#683C2×D414yes—
265#683C2×D414yes—
266C4×Dic5—24no—
267C4×Dic5—24no—
268C4×Dic5—24no—
269C4×Dic5C2×D412yes—
270C4×Dic5C2×D412yes—
271C4×Dic5C2412yes—
272C4×Dic5C2412yes—
273C2×#168—22no—
274C2×#168—22no—
275C2×#168C2412yes—
276C2×#168C2412yes—
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—101no—
285C2×C4⋊Q8C2×D511yescharacteristic
286C2×#125—51no—
287C2×#125—51no—
288C2×#125—51no—
289C2×#125—101no—
290C2×#125—101no—
291C2×#125C2×D511yescharacteristic
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—51no—
299C2×C4×Q8—101no—
300C2×C4×D4—51no—
301C2×C4×D4—51no—
302C2×C4×D4—51no—
303C22×C4⋊C4—101no—
304#501—58no—
305#501C2×D518yescomplemented
306#499—58no—
307#479—58no—
308#479—58no—
309#478—58no—
310#478—58no—
311#476—58no—
312#475—58no—
313#446—58no—
314#440—58no—
315#440—58no—
316C4×SD16—58no—
317C2×#107—51no—
318C2×#107—51no—
319C2×#107C2×D511yescharacteristic
320C2×#107C2×D511yescharacteristic
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⋊C8—51no—
329C2×#103—51no—
330C2×#103—51no—
331C2×#103—51no—
332C2×#102—51no—
333C2×#102—51no—
334C2×#102—51no—
335C2×#97—51no—
336C2×#97C2×D511yescharacteristic
337C2×C4×C8—51no—
338C23×C5C22×D411yescharacteristic
339C22×D5—24no—
340C22×D5—22no—
341C22×D5—42no—
342C22×D5—42no—
343C5×Q8—48no—
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×C5—42no—
351C2×C4×C5—42no—
352C2×C4×C5—42no—
353C2×C4×C5—42no—
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×Dic5C22×D412yes—
371C2×Dic5C22×D412yes—
372C2×Dic5C22×D412yes—
373C2×Dic5C22×D412yes—
374D20—24no—
375D20—22no—
376D20C22×Q814yes—
377C4×D5—48no—
378C4×D5—84no—
379C4×D5—84no—
380Dic10—24no—
381Dic10—22no—
382Dic10—44no—
383Dic10—84no—
384Dic10C22×Q814yes—
385C5×C8—22no—
386C5×C8C22×Q814yes—
387#168—22no—
388#168—22no—
389C22×Q8—21no—
390C22×Q8—51no—
391C22×Q8—51no—
392C22×Q8—101no—
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—22no—
409#125—54no—
410#125—54no—
411#125—54no—
412#125—102no—
413#125—102no—
414#125—102no—
415#125—108no—
416#125—108no—
417#125C22×D514yes—
418C22⋊Q8—108no—
419C22⋊Q8—108no—
420C22⋊Q8—108no—
421C4×Q8—54no—
422C4×Q8—54no—
423C4×Q8—54no—
424C4×Q8—54no—
425C4×Q8—54no—
426C4×Q8—102no—
427C4×Q8—102no—
428C4×Q8—108no—
429C4×Q8—102no—
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—21no—
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⋊C4C22×D511yescharacteristic
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—51no—
463C2×C42—51no—
464C2×C42—101no—
465C2×C42—101no—
466C2×C42—101no—
467C2×C42C22×D511yescharacteristic
468#107—54no—
469#107—54no—
470#107C22×D514yes—
471#107C22×D514yes—
472#106—54no—
473#106—54no—
474#106—54no—
475#106C22×D514yes—
476#106C22×D514yes—
477C4⋊C8—54no—
478C4⋊C8—54no—
479C4⋊C8—54no—
480#103—54no—
481#103—54no—
482#103—54no—
483#102—54no—
484#102—54no—
485#102—54no—
486#97—54no—
487#97C22×D514yes—
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—22no—
498C4×C5—22no—
499C4×C5—42no—
500C4×C5—42no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5D4×Q812yes—
504C4×C5C23×Q811yescharacteristic
505C4×C5C2×2−1+411yescharacteristic
506Dic5—24no—
507Dic5—22no—
508Dic5—22no—
509Dic5—22no—
510Dic5—22no—
511Dic5—42no—
512Dic5—42no—
513C24—101no—
514C2×Q8—24no—
515C2×Q8—44no—
516C2×Q8—54no—
517C2×Q8—54no—
518C2×Q8—52no—
519C2×Q8—104no—
520C2×Q8—101no—
521C2×Q8—102no—
522C2×Q8—202no—
523C2×Q8—402no—
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—52no—
551C2×C8—52no—
552C2×C8—102no—
553C2×C8—102no—
554C2×C8Q8×D514yes—
555C2×C8C23×D512yes—
556C2×C8C23×D512yes—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—54no—
565C4⋊C4—54no—
566C4⋊C4—54no—
567C4⋊C4—52no—
568C4⋊C4—52no—
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—104no—
581C4⋊C4C23×D512yes—
582C4⋊C4C23×D512yes—
583C4⋊C4C23×D512yes—
584C4⋊C4C23×D512yes—
585C22⋊C4—104no—
586C22⋊C4—104no—
587C22⋊C4—104no—
588C42—52no—
589C42—52no—
590C42—52no—
591C42—52no—
592C42—104no—
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—48no—
608Q8—54no—
609Q8—104no—
610Q8—102no—
611Q8—204no—
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—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—52no—
627C2×C4—52no—
628C2×C4—52no—
629C2×C4—52no—
630C2×C4—104no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—208no—
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#414712yes—
648C2×C4C24×D511yescharacteristic
649C8—22no—
650C8—102no—
651C8—102no—
652C8C2×Q8×D514yes—
653C5C2×#338811yescharacteristic, complemented, Sylow
654C22—104no—
655C22—208no—
656C22—202no—
657C22—202no—
658C22#6606112yes—
659C22#6610712yes—
660C22#6611212yes—
661C22C22×D4×D511yescharacteristic
662C4—22no—
663C4—22no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—104no—
669C4—102no—
670C4—102no—
671C4—102no—
672C4—102no—
673C4—202no—
674C4—202no—
675C4#6606112yes—
676C4C22×Q8×D511yescharacteristic
677C4C2×#414711yescharacteristic
678C2—204no—
679C2#1061369914yesdirect product factor
680C2C2×#6606111yescharacteristic
681C2C2×#6610711yescharacteristic
682C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#501C2
socleC23×C5C22×D4
prime radicalC22×D20C23
hypercenterC2×#501D5
hypocenterC5C2×#3388
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#66055C2semidirect
3. C2×C5×#501C2semidirect
5. C2×#65352C2semidirect
6. #10613699C2direct (N × H)
7. C2×#65166C2semidirect
9. C2×#65167C2semidirect
11. C2×#65143C2semidirect
13. C2×#65145C2semidirect
16. C2×#64990C2semidirect
23. #66055C22semidirect
43. C5×#501C22semidirect
57. #65352C22semidirect
69. #65167C22semidirect
70. #65166C22semidirect
72. #65145C22semidirect
73. #65143C22semidirect
76. #64990C22semidirect
127. C2×#677Q8semidirect
182. C2×#501D5semidirect
277. #677C2×Q8semidirect
305. #501C2×D5semidirect
597. C2×C5#3388semidirect
653. C5C2×#3388semidirect
679. C2#10613699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660552
C2×#660242
C2×C5×#5012
C2×#653732
C2×#653522
#106136992
C2×#651662
C2×#651802
C2×#651672
C2×#651782
C2×#651432
C2×#651602
C2×#651452
C2×#651412
C2×#649992
C2×#649902
C2×#33885