Finite Group Databasebeta

← C2×#10611094 #12971507

Subgroups — C2×#10611094 #12971507

Order 1280.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65853C211yesmaximal, characteristic
2C2×#65852C211yesmaximal, characteristic
3C2×C5×#433C211yesmaximal, characteristic
4#10611094C2116yesmaximal, direct product factor
5C2×#65118C211yesmaximal, characteristic, complemented
6C2×#65118C211yesmaximal, characteristic, complemented
7C2×#65139C211yesmaximal, characteristic, complemented
8C2×#65140C211yesmaximal, characteristic, complemented
9C2×#65011C211yesmaximal, characteristic
10C2×#65012C211yesmaximal, characteristic
11C2×#65012C211yesmaximal, characteristic
12C2×#65010C211yesmaximal, characteristic
13C2×#64992C211yesmaximal, characteristic, complemented
14C2×#64991C211yesmaximal, characteristic, complemented
15C2×#64970C211yesmaximal, characteristic, complemented
16C2×#64972C211yesmaximal, characteristic, complemented
17C2×C5×#117C2211yescharacteristic
18C2×#4072C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C2×#4070C2211yescharacteristic
21C2×#4070C2211yescharacteristic
22#65853—24no—
23#65853C2218yes—
24#65852—24no—
25#65852C2218yes—
26C2×#4036—21no—
27C2×#4035—21no—
28C2×#4035—21no—
29C2×#4034—21no—
30C2×#4025—21no—
31C2×#4025—21no—
32C2×#4024—21no—
33C2×#4024—21no—
34C2×#4016C2211yescharacteristic
35C2×#4016C2211yescharacteristic
36C2×#4016C2211yescharacteristic
37C2×#4015C2211yescharacteristic
38C2×#4015C2211yescharacteristic
39C2×#4015C2211yescharacteristic
40C2×C4×Dic10C2211yescharacteristic
41C2×C4×Dic10C2211yescharacteristic
42C5×#433C2218yes—
43C2×C5×C4⋊C8C2211yescharacteristic
44C2×C5×C4⋊C8C2211yescharacteristic
45C2×C5×C22⋊C8C2211yescharacteristic
46C2×C5×C22⋊C8C2211yescharacteristic
47C2×C5×#97C2211yescharacteristic
48C2×C4×C5×C8C2211yescharacteristic
49C2×#3950C2211yescharacteristic
50C2×#3950C2211yescharacteristic
51C2×#3950C2211yescharacteristic
52C2×#3950C2211yescharacteristic
53C2×#3949C2211yescharacteristic
54C2×#3949C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56C2×#3949C2211yescharacteristic
57C2×#3948C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3948C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65#65140C2218yescomplemented
66#65139C2218yescomplemented
67#65118C2218yescomplemented
68#65118C2218yescomplemented
69#65012C2218yes—
70#65012C2218yes—
71#65011C2218yes—
72#65010C2218yes—
73#64992C2218yescomplemented
74#64991C2218yescomplemented
75#64972C2218yescomplemented
76#64970C2218yescomplemented
77C2×#3242—51nomaximal, Sylow
78C23×C4×C5C2311yescharacteristic
79C23×Dic5—21no—
80C22×Dic10—21no—
81C22×Dic10—21no—
82C22×Dic10C2311yescharacteristic
83C22×Dic10C2311yescharacteristic
84C22×C5×C8C2311yescharacteristic
85C22×C5×C8C2311yescharacteristic
86C22×C5×C8C2311yescharacteristic
87C22×C5×C8C2311yescharacteristic
88C5×#117D414yes—
89C5×#117C2314yes—
90C2×C5×C4⋊C4D411yescharacteristic
91C2×C5×C4⋊C4D411yescharacteristic
92C2×C5×C22⋊C4D411yescharacteristic
93C2×C5×C22⋊C4D411yescharacteristic
94C2×C42×C5C2311yescharacteristic
95C2×C42×C5C2311yescharacteristic
96C2×C22⋊Dic5—21no—
97C2×C22⋊Dic5—21no—
98C2×C22⋊Dic5—21no—
99#4072—22no—
100#4072C2314yes—
101C2×C4⋊Dic5—21no—
102C2×C4⋊Dic5—21no—
103C2×C4⋊Dic5—21no—
104C2×C4⋊Dic5—21no—
105C2×C4⋊Dic5—21no—
106C2×C4⋊Dic5—22no—
107C2×C4⋊Dic5C2311yescharacteristic
108C2×C4⋊Dic5C2311yescharacteristic
109C2×C4⋊Dic5C2311yescharacteristic
110C2×C4⋊Dic5C2311yescharacteristic
111C2×C4⋊Dic5C2311yescharacteristic
112C2×C4⋊Dic5C2311yescharacteristic
113C2×C4⋊Dic5C2314yes—
114#4070—22no—
115#4070—22no—
116#4070C2314yes—
117#4070C2314yes—
118C2×#683—21no—
119C2×#683—21no—
120C2×#683—21no—
121C2×#683—21no—
122C2×#683—21no—
123C2×#683—21no—
124C2×#683—21no—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×C4×Dic5—21no—
129C2×C4×Dic5—21no—
130C2×C4×Dic5—21no—
131#4036—28no—
132#4035—28no—
133#4035—28no—
134#4034—28no—
135#4025—28no—
136#4025—28no—
137#4024—28no—
138#4024—28no—
139#4016—22no—
140#4016—22no—
141#4016—22no—
142#4016C2314yes—
143#4016C2314yes—
144#4016C2314yes—
145#4015—22no—
146#4015—22no—
147#4015—22no—
148#4015C2314yes—
149#4015C2314yes—
150#4015C2314yes—
151C4×Dic10—22no—
152C4×Dic10—22no—
153C4×Dic10C2314yes—
154C4×Dic10C2314yes—
155C5×C4⋊C8C2314yes—
156C5×C4⋊C8C2314yes—
157C5×C22⋊C8C2314yes—
158C5×C22⋊C8C2314yes—
159C5×#97C2314yes—
160C4×C5×C8C2314yes—
161#3950C2314yes—
162#3950C2314yes—
163#3950C2314yes—
164#3950C2314yes—
165#3949C2314yes—
166#3949C2314yes—
167#3949C2314yes—
168#3949C2314yes—
169#3948C2314yes—
170#3948C2314yes—
171#3948C2314yes—
172#3948C2314yes—
173#3948C2314yes—
174#3948C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177C2×#544—51no—
178C2×#541—51no—
179#3242—516no—
180C2×#501—51no—
181C2×#499—51no—
182C2×#491—51no—
183C2×#487—51no—
184C2×#484—51no—
185C2×#485—51no—
186C2×#485—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#479—51no—
190C2×#477—51no—
191C2×#475—51no—
192C2×#433D511yescharacteristic
193C24×C5C2×D411yescharacteristic
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2411yescharacteristic
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—24no—
213C22×Dic5—82no—
214C2×Dic10—22no—
215C2×Dic10—22no—
216C2×Dic10—22no—
217C2×Dic10—22no—
218C2×Dic10—21no—
219C2×Dic10—21no—
220C2×Dic10—24no—
221C2×Dic10—24no—
222C2×Dic10—82no—
223C2×Dic10—82no—
224C2×Dic10C2412yes—
225C2×Dic10C2412yes—
226C2×C5×C8—22no—
227C2×C5×C8—22no—
228C2×C5×C8—22no—
229C2×C5×C8—22no—
230C2×C5×C8C2412yes—
231C2×C5×C8C2412yes—
232C2×C5×C8C2412yes—
233C2×C5×C8C2412yes—
234C5×C4⋊C4C2×D414yes—
235C5×C4⋊C4C2×D414yes—
236C5×C22⋊C4C2×D414yes—
237C5×C22⋊C4C2×D414yes—
238C42×C5C2×D412yes—
239C42×C5C2×D412yes—
240C42×C5C2412yes—
241C42×C5C2412yes—
242C22⋊Dic5—24no—
243C22⋊Dic5—24no—
244C22⋊Dic5—24no—
245C4⋊Dic5—21no—
246C4⋊Dic5—21no—
247C4⋊Dic5—21no—
248C4⋊Dic5—21no—
249C4⋊Dic5—21no—
250C4⋊Dic5—24no—
251C4⋊Dic5—24no—
252C4⋊Dic5—24no—
253C4⋊Dic5—24no—
254C4⋊Dic5—21no—
255C4⋊Dic5—24no—
256C4⋊Dic5C2412yes—
257C4⋊Dic5C2412yes—
258C4⋊Dic5C2412yes—
259C4⋊Dic5C2412yes—
260C4⋊Dic5C2412yes—
261C4⋊Dic5C2412yes—
262#683—24no—
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—
272C4×Dic5—24no—
273C4×Dic5—24no—
274C4×Dic5—24no—
275#544—58no—
276#544—104no—
277#541—58no—
278#541—104no—
279C2×C4⋊Q8—51no—
280C2×C4⋊Q8—51no—
281C2×C4⋊Q8—51no—
282C2×C4⋊Q8—101no—
283C2×#126—101no—
284C2×#126—101no—
285C2×#125—51no—
286C2×#125—51no—
287C2×#125—51no—
288C2×#125—101no—
289C2×#125—101no—
290C2×#125—101no—
291C2×C22⋊Q8—51no—
292C2×C22⋊Q8—51no—
293C2×C22⋊Q8—101no—
294C2×C22⋊Q8—101no—
295C2×C4×Q8—51no—
296C2×C4×Q8—51no—
297C2×#117—51no—
298C2×#117C2×D511yescharacteristic
299C22×C4⋊C4—51no—
300#501—58no—
301#499—58no—
302#491—58no—
303#487—58no—
304#485—58no—
305#485—58no—
306#484—58no—
307#483—58no—
308#479—58no—
309#479—58no—
310#477—58no—
311#475—58no—
312#433C2×D518yes—
313C2×#107—51no—
314C2×#107—51no—
315C2×#107—51no—
316C2×#107—51no—
317C2×#106—51no—
318C2×#106—51no—
319C2×#106—51no—
320C2×#106—51no—
321C2×C4⋊C8C2×D511yescharacteristic
322C2×C4⋊C8C2×D511yescharacteristic
323C2×#103—51no—
324C2×#103—51no—
325C2×#103—51no—
326C2×#103—51no—
327C2×#103—51no—
328C2×#103—51no—
329C2×#103—51no—
330C2×#103—51no—
331C2×C22⋊C8C2×D511yescharacteristic
332C2×C22⋊C8C2×D511yescharacteristic
333C2×#97C2×D511yescharacteristic
334C2×C4×C8C2×D511yescharacteristic
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5C22×D412yes—
339C23×C5C22×D411yescharacteristic
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—24no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5C22×D412yes—
349C2×C4×C5C22×D412yes—
350C2×C4×C5C22×D412yes—
351C2×C4×C5C22×D412yes—
352C2×C4×C5C22×D412yes—
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C52−1+412yes—
355C2×C4×C52−1+412yes—
356C2×C4×C5C2511yescharacteristic
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—84no—
374Dic10—22no—
375Dic10—22no—
376Dic10—22no—
377Dic10—22no—
378Dic10—42no—
379Dic10—42no—
380Dic10—84no—
381Dic10—84no—
382C5×C8—22no—
383C5×C8—22no—
384C5×C8—22no—
385C5×C8—22no—
386C22×Q8—51no—
387C22×Q8—51no—
388C22×Q8—101no—
389C22×Q8—101no—
390C23×C4—101no—
391C23×C4C22×D511yescharacteristic
392C22×C8C22×D511yescharacteristic
393C22×C8C22×D511yescharacteristic
394C22×C8C22×D511yescharacteristic
395C22×C8C22×D511yescharacteristic
396C4⋊Q8—54no—
397C4⋊Q8—54no—
398C4⋊Q8—54no—
399C4⋊Q8—108no—
400C4⋊Q8—102no—
401C4⋊Q8—102no—
402C4⋊Q8—102no—
403#126—108no—
404#126—108no—
405#125—54no—
406#125—54no—
407#125—54no—
408#125—108no—
409#125—108no—
410#125—108no—
411#125—102no—
412#125—102no—
413#125—102no—
414C22⋊Q8—54no—
415C22⋊Q8—54no—
416C22⋊Q8—102no—
417C22⋊Q8—102no—
418C22⋊Q8—108no—
419C22⋊Q8—108no—
420C4×Q8—54no—
421C4×Q8—54no—
422C4×Q8—102no—
423C4×Q8—102no—
424#117—54no—
425#117—102no—
426#117D2014yes—
427#117C22×D514yes—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—51no—
435C2×C4⋊C4—101no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—101no—
438C2×C4⋊C4—101no—
439C2×C4⋊C4—101no—
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⋊C4D2011yescharacteristic
452C2×C4⋊C4D2011yescharacteristic
453C2×C22⋊C4—101no—
454C2×C22⋊C4—101no—
455C2×C22⋊C4—101no—
456C2×C22⋊C4D2011yescharacteristic
457C2×C22⋊C4D2011yescharacteristic
458C2×C42—101no—
459C2×C42—101no—
460C2×C42—101no—
461C2×C42C22×D511yescharacteristic
462C2×C42C22×D511yescharacteristic
463#107—54no—
464#107—54no—
465#107—54no—
466#107—54no—
467#106—54no—
468#106—54no—
469#106—54no—
470#106—54no—
471C4⋊C8C22×D514yes—
472C4⋊C8C22×D514yes—
473#103—54no—
474#103—54no—
475#103—54no—
476#103—54no—
477#103—54no—
478#103—54no—
479#103—54no—
480#103—54no—
481C22⋊C8C22×D514yes—
482C22⋊C8C22×D514yes—
483#97C22×D514yes—
484C4×C8C22×D514yes—
485C22×C5—22no—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—44no—
489C22×C5#53612yes—
490C22×C5#57712yes—
491C22×C5#57812yes—
492C22×C5C23×D411yescharacteristic
493C4×C5—22no—
494C4×C5—22no—
495C4×C5—22no—
496C4×C5—22no—
497C4×C5—22no—
498C4×C5#53612yes—
499C4×C5C2×2−1+411yescharacteristic
500C4×C5C2×2−1+411yescharacteristic
501Dic5—42no—
502Dic5—42no—
503Dic5—42no—
504Dic5—42no—
505Dic5—42no—
506Dic5—42no—
507Dic5—42no—
508Dic5—42no—
509C24C2×D2011yescharacteristic
510C2×Q8—52no—
511C2×Q8—52no—
512C2×Q8—101no—
513C2×Q8—101no—
514C2×Q8—104no—
515C2×Q8—104no—
516C2×Q8—102no—
517C2×Q8—102no—
518C2×Q8—102no—
519C2×Q8—102no—
520C2×Q8—402no—
521C2×Q8—402no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—101no—
525C22×C4—101no—
526C22×C4—101no—
527C22×C4—101no—
528C22×C4—101no—
529C22×C4—101no—
530C22×C4—101no—
531C22×C4—101no—
532C22×C4—104no—
533C22×C4—402no—
534C22×C4C2×D2012yes—
535C22×C4C2×D2011yescharacteristic
536C22×C4C2×D2011yescharacteristic
537C22×C4C2×D2011yescharacteristic
538C22×C4C2×D2011yescharacteristic
539C22×C4C2×D2011yescharacteristic
540C22×C4C23×D512yes—
541C22×C4C23×D511yescharacteristic
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8C23×D512yes—
547C2×C8C23×D512yes—
548C2×C8C23×D512yes—
549C2×C8C23×D512yes—
550C4⋊C4—52no—
551C4⋊C4—52no—
552C4⋊C4—52no—
553C4⋊C4—52no—
554C4⋊C4—52no—
555C4⋊C4—52no—
556C4⋊C4—104no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—101no—
563C4⋊C4—104no—
564C4⋊C4—104no—
565C4⋊C4—104no—
566C4⋊C4—104no—
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⋊C4C2×D2014yes—
578C4⋊C4C2×D2014yes—
579C22⋊C4—104no—
580C22⋊C4—104no—
581C22⋊C4—104no—
582C22⋊C4C2×D2014yes—
583C22⋊C4C2×D2014yes—
584C42—104no—
585C42—104no—
586C42—104no—
587C42C2×D2012yes—
588C42C2×D2012yes—
589C42C23×D512yes—
590C42C23×D512yes—
591C2×C5—42no—
592C2×C5#324214yescomplemented
593C2×C5C2×#53611yescharacteristic
594C2×C5C2×#57711yescharacteristic
595C2×C5C2×#57811yescharacteristic
596C23—22no—
597C23—22no—
598C23—22no—
599C23C22×D2012yes—
600C23C22×D2011yescharacteristic
601Q8—102no—
602Q8—102no—
603Q8—102no—
604Q8—102no—
605Q8—202no—
606Q8—202no—
607Q8—404no—
608Q8—404no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—102no—
623C2×C4—102no—
624C2×C4—102no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—202no—
633C2×C4—404no—
634C2×C4C22×D2012yes—
635C2×C4C22×D2012yes—
636C2×C4C22×D2012yes—
637C2×C4C22×D2012yes—
638C2×C4C22×D2012yes—
639C2×C4C22×D2011yescharacteristic
640C2×C4#415012yes—
641C2×C4#415012yes—
642C2×C4C24×D511yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8—22no—
647C5C2×#324211yescharacteristic, complemented, Sylow
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#6586012yes—
653C22#6608512yes—
654C22#6608712yes—
655C22C23×D2011yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—202no—
662C4—202no—
663C4—202no—
664C4—202no—
665C4—202no—
666C4—202no—
667C4—202no—
668C4—202no—
669C4#6586012yes—
670C4C2×#415011yescharacteristic
671C4C2×#415011yescharacteristic
672C2—42no—
673C2#1061109414yesdirect product factor
674C2C2×#6586011yescharacteristic
675C2C2×#6608511yescharacteristic
676C2C2×#6608711yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#433C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenterC2×#433D5
hypocenterC5C2×#3242
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. #10611094C2direct (N × H)
5. C2×#65118C2semidirect
6. C2×#65118C2semidirect
7. C2×#65139C2semidirect
8. C2×#65140C2semidirect
13. C2×#64992C2semidirect
14. C2×#64991C2semidirect
15. C2×#64970C2semidirect
16. C2×#64972C2semidirect
65. #65140C22semidirect
66. #65139C22semidirect
67. #65118C22semidirect
68. #65118C22semidirect
73. #64992C22semidirect
74. #64991C22semidirect
75. #64972C22semidirect
76. #64970C22semidirect
592. C2×C5#3242semidirect
647. C5C2×#3242semidirect
673. C2#10611094direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658532
C2×#658522
C2×C5×#4332
#106110942
C2×#651182
C2×#651392
C2×#651402
C2×#650112
C2×#650122
C2×#650102
C2×#649922
C2×#649912
C2×#649702
C2×#649722
C2×#32425