Finite Group Databasebeta

← C2×#10606821 #12270627

Subgroups — C2×#10606821 #12270627

Order 1280.

2614 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4033C211yesmaximal, characteristic
2C22×C4×Dic10C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic
4C2×#65268C211yesmaximal, characteristic
5C2×#65261C211yesmaximal, characteristic
6C2×#65267C211yesmaximal, characteristic
7C2×#65222C211yesmaximal, characteristic
8#10606821C2116yesmaximal, direct product factor
9C2×#64949C211yesmaximal, characteristic
10C2×#64947C211yesmaximal, characteristic
11C2×#64945C211yesmaximal, characteristic
12C2×#64935C211yesmaximal, characteristic
13C2×#64935C211yesmaximal, characteristic
14C2×#64936C211yesmaximal, characteristic
15C2×#64942C211yesmaximal, characteristic
16C2×#64939C211yesmaximal, characteristic
17C23×Dic10C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×C4⋊Dic5C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C22×C4×Dic5C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C2×#4033—28no—
37C2×#4033C2218yes—
38C2×C4×Dic10—28no—
39C2×C4×Dic10C2218yes—
40C5×#387C2218yes—
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65268C2218yes—
58#65267C2218yes—
59#65261C2218yes—
60#65222C2218yes—
61#64949C2218yes—
62#64947C2218yes—
63#64945C2218yes—
64#64942C2218yes—
65#64939C2218yes—
66#64936C2218yes—
67#64935C2218yes—
68#64935C2218yes—
69C2×#2581—51nomaximal, Sylow
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×Dic10—24no—
86C22×Dic10—24no—
87C22×Dic10—24no—
88C22×Dic10—24no—
89C22×Dic10—24no—
90C22×Dic10Q818yescomplemented
91C22×Dic10C2314yes—
92C22×Dic10C2314yes—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C4⋊C4C2314yes—
97C2×C42×C5—24no—
98C2×C42×C5C2314yes—
99C2×C4⋊Dic5—24no—
100C2×C4⋊Dic5—24no—
101C2×C4⋊Dic5C2314yes—
102C2×C4⋊Dic5C2314yes—
103C2×#683—24no—
104C2×#683—24no—
105C2×#683—24no—
106C2×#683—24no—
107C2×#683—24no—
108C2×#683—24no—
109C2×#683—24no—
110C2×#683—24no—
111C2×#683C2314yes—
112C2×#683C2314yes—
113C2×#683C2314yes—
114C2×#683C2314yes—
115C2×#683C2314yes—
116C2×#683C2314yes—
117C2×#683C2314yes—
118C2×#683C2314yes—
119C2×C4×Dic5—24no—
120C2×C4×Dic5—24no—
121C2×C4×Dic5—24no—
122C2×C4×Dic5D418yes—
123C2×C4×Dic5C2314yes—
124C2×C4×Dic5C2314yes—
125C2×C4×Dic5C2314yes—
126C2×C4×Dic5C2314yes—
127#4033—232no—
128C4×Dic10—232no—
129C5×#95C2314yes—
130C5×#95C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133#3963C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145C22×C4×Q8—51no—
146C22×C4×Q8—51no—
147#2581—516no—
148C2×#400—51no—
149C2×#400—51no—
150C2×#395—51no—
151C2×#395—51no—
152C2×#391—51no—
153C2×#391—51no—
154C2×#389—51no—
155C2×#389—51no—
156C2×#387—51no—
157C2×#387—51no—
158C2×#387—51no—
159C2×#387D511yescharacteristic
160C2×#382—51no—
161C24×C5C2411yescharacteristic
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5C2×D414yes—
181C22×C4×C5C2×Q814yes—
182C22×C4×C5#4114yes—
183C22×C4×C5C2412yes—
184C22×C4×C5C2412yes—
185C22×C4×C5C2412yes—
186C22×C4×C5C2412yes—
187C22×C4×C5C2412yes—
188C22×C4×C5C2412yes—
189C22×C4×C5C2412yes—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5C2×D414yes—
209C22×Dic5C2×D414yes—
210C22×Dic5C2×Q814yes—
211C22×Dic5C2×Q814yes—
212C22×Dic5#4114yes—
213C22×Dic5#4114yes—
214C22×Dic5C2412yes—
215C22×Dic5C2412yes—
216C22×Dic5C2412yes—
217C22×Dic5C2412yes—
218C22×Dic5C2412yes—
219C22×Dic5C2412yes—
220C22×Dic5C2412yes—
221C22×Dic5C2412yes—
222C2×Dic10—232no—
223C2×Dic10—28no—
224C2×Dic10—232no—
225C2×Dic10—28no—
226C2×Dic10—28no—
227C2×Dic10—28no—
228C2×Dic10—28no—
229C2×Dic10C2×Q8116yescomplemented
230C5×C4⋊C4—28no—
231C5×C4⋊C4—28no—
232C42×C5—28no—
233C4⋊Dic5—28no—
234C4⋊Dic5—28no—
235#683—28no—
236#683—28no—
237#683—28no—
238#683—28no—
239#683—28no—
240#683—28no—
241#683—28no—
242#683—28no—
243C4×Dic5—28no—
244C4×Dic5—28no—
245C4×Dic5—28no—
246C4×Dic5C2×D4116yes—
247C23×Q8—51no—
248C23×Q8—51no—
249C2×C4×Q8—58no—
250C2×C4×Q8—58no—
251C2×C4×Q8—108no—
252C2×C4×Q8—108no—
253C22×C4⋊C4—51no—
254C22×C4⋊C4—51no—
255C22×C4⋊C4—51no—
256C22×C4⋊C4—51no—
257C22×C4⋊C4—51no—
258C22×C4⋊C4—51no—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4C2×D511yescharacteristic
264C22×C4⋊C4C2×D511yescharacteristic
265C22×C42—51no—
266C22×C42—51no—
267C22×C42—51no—
268C22×C42—51no—
269C22×C42C2×D511yescharacteristic
270#400—58no—
271#400—58no—
272#395—58no—
273#395—58no—
274#391—58no—
275#391—58no—
276#389—58no—
277#389—58no—
278#387—58no—
279#387—58no—
280#387—58no—
281#387C2×D518yes—
282#382—58no—
283C2×#95—51no—
284C2×#95—51no—
285C2×#95—51no—
286C2×#95—51no—
287C2×#95—51no—
288C2×#95—51no—
289C2×#95—51no—
290C2×#95—51no—
291C2×#95—51no—
292C2×#95—51no—
293C2×#95—51no—
294C2×#95—51no—
295C2×#95C2×D511yescharacteristic
296C2×#95C2×D511yescharacteristic
297C2×#95C2×D511yescharacteristic
298C2×#95C2×D511yescharacteristic
299C23×C5C22×D412yes—
300C23×C5C22×Q812yes—
301C23×C5C2×#4112yes—
302C23×C5C2×#4112yes—
303C23×C5C2×#4112yes—
304C23×C52−1+412yes—
305C23×C52−1+412yes—
306C23×C5C2511yescharacteristic
307C2×C4×C5—28no—
308C2×C4×C5—28no—
309C2×C4×C5—28no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—44no—
329C2×C4×C5—44no—
330C2×C4×C5—44no—
331C2×C4×C5—44no—
332C2×C4×C5C22×D414yes—
333C2×C4×C5C22×Q814yes—
334C2×C4×C5C2×#4114yes—
335C2×Dic5—28no—
336C2×Dic5—28no—
337C2×Dic5—28no—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—44no—
357C2×Dic5—44no—
358C2×Dic5—44no—
359C2×Dic5—44no—
360C2×Dic5C22⋊Q8116yes—
361C2×Dic5C22×D414yes—
362C2×Dic5C22×D414yes—
363C2×Dic5C22×Q814yes—
364C2×Dic5C22×Q814yes—
365C2×Dic5C2×#4114yes—
366C2×Dic5C2×#4114yes—
367Dic10—232no—
368Dic10—232no—
369C22×Q8—58no—
370C22×Q8—54no—
371C22×Q8—54no—
372C22×Q8—104no—
373C22×Q8—104no—
374C22×Q8—104no—
375C22×Q8—104no—
376C22×Q8—104no—
377C23×C4—51no—
378C23×C4—51no—
379C23×C4—51no—
380C23×C4—51no—
381C23×C4—51no—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4—51no—
385C23×C4C22×D511yescharacteristic
386C23×C4C22×D511yescharacteristic
387C23×C4C22×D511yescharacteristic
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D511yescharacteristic
390C23×C4C22×D511yescharacteristic
391C23×C4C22×D511yescharacteristic
392C4×Q8—1032no—
393C4×Q8—1032no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—54no—
397C2×C4⋊C4—54no—
398C2×C4⋊C4—54no—
399C2×C4⋊C4—54no—
400C2×C4⋊C4—54no—
401C2×C4⋊C4—54no—
402C2×C4⋊C4—54no—
403C2×C4⋊C4—54no—
404C2×C4⋊C4—54no—
405C2×C4⋊C4—54no—
406C2×C4⋊C4—104no—
407C2×C4⋊C4—104no—
408C2×C4⋊C4—104no—
409C2×C4⋊C4—104no—
410C2×C4⋊C4—104no—
411C2×C4⋊C4—104no—
412C2×C4⋊C4—104no—
413C2×C4⋊C4—104no—
414C2×C4⋊C4—104no—
415C2×C4⋊C4—104no—
416C2×C4⋊C4C22×D514yes—
417C2×C4⋊C4C22×D514yes—
418C2×C42—24no—
419C2×C42—58no—
420C2×C42—54no—
421C2×C42—54no—
422C2×C42—54no—
423C2×C42—54no—
424C2×C42—104no—
425C2×C42—104no—
426C2×C42—104no—
427C2×C42C22×D514yes—
428#95—54no—
429#95—54no—
430#95—54no—
431#95—54no—
432#95—54no—
433#95—54no—
434#95—54no—
435#95—54no—
436#95—54no—
437#95—54no—
438#95—54no—
439#95—54no—
440#95C22×D514yes—
441#95C22×D514yes—
442#95C22×D514yes—
443#95C22×D514yes—
444C22×C5C2×C22⋊Q814yes—
445C22×C5#52514yes—
446C22×C5#53614yes—
447C22×C5#55614yes—
448C22×C5#55614yes—
449C22×C5#55714yes—
450C22×C5#55714yes—
451C22×C5C23×D411yescharacteristic
452C22×C5C23×Q811yescharacteristic
453C22×C5C22×#4111yescharacteristic
454C22×C5C22×#4111yescharacteristic
455C22×C5C22×#4111yescharacteristic
456C22×C5C2×2−1+411yescharacteristic
457C22×C5C2×2−1+411yescharacteristic
458C4×C5—24no—
459C4×C5—24no—
460C4×C5—24no—
461C4×C5—42no—
462C4×C5—42no—
463C4×C5—42no—
464C4×C5—42no—
465Dic5—24no—
466Dic5—24no—
467Dic5—24no—
468Dic5—42no—
469Dic5—42no—
470Dic5—42no—
471Dic5—42no—
472Dic5C2×C22⋊Q818yes—
473C24C23×D511yescharacteristic
474C2×Q8—516no—
475C2×Q8—108no—
476C2×Q8—108no—
477C2×Q8—1032no—
478C2×Q8—108no—
479C2×Q8—108no—
480C2×Q8—1032no—
481C2×Q8—108no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—54no—
501C22×C4—54no—
502C22×C4—54no—
503C22×C4—52no—
504C22×C4—54no—
505C22×C4—54no—
506C22×C4—54no—
507C22×C4—52no—
508C22×C4—52no—
509C22×C4—52no—
510C22×C4—52no—
511C22×C4—52no—
512C22×C4—52no—
513C22×C4—52no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4—102no—
519C22×C4—102no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—102no—
525C22×C4—102no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—102no—
530C22×C4—102no—
531C22×C4—102no—
532C22×C4#70914yes—
533C22×C4D4×D514yes—
534C22×C4Q8×D514yes—
535C22×C4C23×D512yes—
536C22×C4C23×D512yes—
537C22×C4C23×D512yes—
538C22×C4C23×D512yes—
539C22×C4C23×D512yes—
540C22×C4C23×D512yes—
541C22×C4C23×D512yes—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—108no—
545C4⋊C4—108no—
546C4⋊C4—108no—
547C4⋊C4—108no—
548C4⋊C4—108no—
549C4⋊C4—108no—
550C4⋊C4—108no—
551C4⋊C4—108no—
552C4⋊C4—108no—
553C4⋊C4—108no—
554C42—28no—
555C42—516no—
556C42—108no—
557C42—108no—
558C42—108no—
559C2×C5#258118yescomplemented
560C2×C5C22×C22⋊Q811yescharacteristic
561C2×C5C2×#52511yescharacteristic
562C2×C5C2×#53611yescharacteristic
563C2×C5C2×#55611yescharacteristic
564C2×C5C2×#55611yescharacteristic
565C2×C5C2×#55711yescharacteristic
566C2×C5C2×#55711yescharacteristic
567C23C2×#70912yes—
568C23C2×D4×D512yes—
569C23C2×Q8×D512yes—
570C23D5×#4112yes—
571C23D5×#4112yes—
572C23#415012yes—
573C23#415012yes—
574C23C24×D511yescharacteristic
575Q8—1032no—
576Q8—1032no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—28no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—516no—
603C2×C4—54no—
604C2×C4—54no—
605C2×C4—54no—
606C2×C4—54no—
607C2×C4—54no—
608C2×C4—54no—
609C2×C4—108no—
610C2×C4—108no—
611C2×C4—108no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
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—102no—
626C2×C4—102no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—204no—
631C2×C4—204no—
632C2×C4—204no—
633C2×C4—204no—
634C2×C4C2×#70914yes—
635C2×C4C2×D4×D514yes—
636C2×C4C2×Q8×D514yes—
637C5C2×#258111yescharacteristic, complemented, Sylow
638C22#6586714yes—
639C22#6588114yes—
640C22#6590114yes—
641C22D5×C22⋊Q814yes—
642C22#6598214yes—
643C22#6601914yes—
644C22#6603614yes—
645C22C22×#70911yescharacteristic
646C22C22×D4×D511yescharacteristic
647C22C22×Q8×D511yescharacteristic
648C22C2×D5×#4111yescharacteristic
649C22C2×D5×#4111yescharacteristic
650C22C2×#415011yescharacteristic
651C22C2×#415011yescharacteristic
652C4—24no—
653C4—24no—
654C4—24no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—58no—
660C4—104no—
661C4—104no—
662C4—104no—
663C4—202no—
664C4—202no—
665C4—202no—
666C4—202no—
667C2#1060682118yesdirect product factor
668C2C2×#6586711yescharacteristic
669C2C2×#6588111yescharacteristic
670C2C2×#6590111yescharacteristic
671C2C2×D5×C22⋊Q811yescharacteristic
672C2C2×#6598211yescharacteristic
673C2C2×#6601911yescharacteristic
674C2C2×#6603611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socle, prime radicalC24×C5C24
hypercenterC2×#387D5
hypocenterC5C2×#2581
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
8. #10606821C2direct (N × H)
90. C22×Dic10Q8semidirect
229. C2×Dic10C2×Q8semidirect
559. C2×C5#2581semidirect
637. C5C2×#2581semidirect
667. C2#10606821direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40332
C22×C4×Dic102
C2×C5×#3872
C2×#652682
C2×#652612
C2×#652672
C2×#652222
#106068212
C2×#649492
C2×#649472
C2×#649452
C2×#649352
C2×#649362
C2×#649422
C2×#649392
C2×#25815