Finite Group Databasebeta

← C2×#10607962 #12268352

Subgroups — C2×#10607962 #12268352

Order 1280.

3678 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C212yesmaximal
2C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×C4×D20C211yesmaximal, characteristic
4C2×C5×#389C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65276C211yesmaximal, characteristic, complemented
7C2×#65276C211yesmaximal, characteristic, complemented
8C2×#65273C212yesmaximal, complemented
9C2×#65217C211yesmaximal, characteristic, complemented
10#10607962C2116yesmaximal, direct product factor
11C2×#64964C212yesmaximal, complemented
12C2×#64953C212yesmaximal, complemented
13C23×D20C2211yescharacteristic
14C23×C4×D5C2212yes—
15C23×C4×D5C2211yescharacteristic
16C23×C4×D5C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2212yes—
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×#685C2212yes—
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×#683C2212yes—
30C22×#683C2212yes—
31C2×#4040—216no—
32C2×#4040C22116yes—
33C2×D5×C4⋊C4—28no—
34C2×D5×C4⋊C4C2218yescomplemented
35C2×C4×D20—28no—
36C2×C4×D20C2218yes—
37C5×#389C2218yescomplemented
38C2×C5×#95C2212yes—
39C2×#3963C2212yes—
40C2×#3963C2212yes—
41C2×#3963C2212yes—
42C2×#3963C2212yes—
43#65276C2218yescomplemented
44#65276C2218yescomplemented
45#65276C2218yescomplemented
46#65273C22116yescomplemented
47#65217C2218yescomplemented
48#64964C22116yescomplemented
49#64953C22116yescomplemented
50C2×#2486—51nomaximal, Sylow
51C24×D5C2311yescharacteristic
52C24×D5C2311yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2312yes—
55C23×C4×C5C2312yes—
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×Dic5C2312yes—
59C23×Dic5C2312yes—
60C23×Dic5C2311yescharacteristic
61C23×Dic5C2311yescharacteristic
62C22×D20—24no—
63C22×D20—24no—
64C22×D20D418yes—
65C22×D20C2314yes—
66C22×C4×D5—24no—
67C22×C4×D5—24no—
68C22×C4×D5—28no—
69C22×C4×D5—28no—
70C22×C4×D5—28no—
71C22×C4×D5—24no—
72C22×C4×D5—24no—
73C22×C4×D5—24no—
74C22×C4×D5D418yes—
75C22×C4×D5C2314yes—
76C22×C4×D5C2318yes—
77C22×C4×D5C2314yes—
78C2×C5×C4⋊C4—24no—
79C2×C5×C4⋊C4—28no—
80C2×C5×C4⋊C4—24no—
81C2×C5×C4⋊C4C2314yes—
82C2×C5×C4⋊C4C2318yes—
83C2×C5×C4⋊C4C2314yes—
84C2×C42×C5—24no—
85C2×C42×C5C2314yes—
86C2×#685—24no—
87C2×#685—28no—
88C2×#685—28no—
89C2×#685—28no—
90C2×#685—24no—
91C2×#685C2314yes—
92C2×#685C2314yes—
93C2×#685C2318yes—
94C2×#685C2318yes—
95C2×#685C2318yes—
96C2×C4⋊Dic5—24no—
97C2×C4⋊Dic5—24no—
98C2×C4⋊Dic5—24no—
99C2×C4⋊Dic5C2314yes—
100C2×C4⋊Dic5C2314yes—
101C2×C4⋊Dic5C2314yes—
102C2×#683—28no—
103C2×#683—28no—
104C2×#683C2318yes—
105C2×#683C2318yes—
106#4040—264no—
107D5×C4⋊C4—232no—
108C4×D20—232no—
109C5×#95C2318yes—
110#3963C2318yes—
111#3963C2318yes—
112#3963C2318yes—
113#3963C2318yes—
114C22×#123—52no—
115C22×C4×D4—51no—
116C23×C4⋊C4—51no—
117#2486—516no—
118C2×#398—52no—
119C2×#397—52no—
120C2×#389—51no—
121C2×#389D511yescharacteristic, complemented
122C2×#381—52no—
123C2×#380—51no—
124C2×#380—51no—
125C2×#380—51no—
126C24×C5C2411yescharacteristic
127C23×D5—22no—
128C23×D5—22no—
129C23×D5—22no—
130C23×D5—22no—
131C23×D5—22no—
132C23×D5—22no—
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5C2×D414yes—
138C23×D5C2×D414yes—
139C23×D5C2×D414yes—
140C23×D5#4114yes—
141C23×D5C2412yes—
142C23×D5C2412yes—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—24no—
147C22×C4×C5—24no—
148C22×C4×C5—24no—
149C22×C4×C5—24no—
150C22×C4×C5—24no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—24no—
154C22×C4×C5C2×D414yes—
155C22×C4×C5C2×D414yes—
156C22×C4×C5#4114yes—
157C22×C4×C5#4114yes—
158C22×C4×C5C2412yes—
159C22×C4×C5C2414yes—
160C22×C4×C5C2414yes—
161C22×C4×C5C2412yes—
162C22×C4×C5C2412yes—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—24no—
166C22×Dic5—24no—
167C22×Dic5—22no—
168C22×Dic5—24no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—24no—
172C22×Dic5—24no—
173C22×Dic5—24no—
174C22×Dic5C2×D414yes—
175C22×Dic5C2412yes—
176C22×Dic5C2414yes—
177C22×Dic5C2414yes—
178C22×Dic5C2412yes—
179C2×D20—232no—
180C2×D20—28no—
181C2×D20—28no—
182C2×D20C2×D4116yes—
183C2×C4×D5—232no—
184C2×C4×D5—28no—
185C2×C4×D5—28no—
186C2×C4×D5—216no—
187C2×C4×D5—216no—
188C2×C4×D5—216no—
189C2×C4×D5—28no—
190C2×C4×D5—28no—
191C2×C4×D5—28no—
192C2×C4×D5—432no—
193C2×C4×D5—416no—
194C2×C4×D5C2×D4116yes—
195C5×C4⋊C4—28no—
196C5×C4⋊C4—216no—
197C5×C4⋊C4—28no—
198C42×C5—28no—
199#685—28no—
200#685—216no—
201#685—216no—
202#685—216no—
203#685—28no—
204C4⋊Dic5—28no—
205C4⋊Dic5—28no—
206C4⋊Dic5—28no—
207#683—216no—
208#683—216no—
209C23×D4—51no—
210C24×C4—51no—
211C24×C4—52no—
212C24×C4—51no—
213C2×#123—516no—
214C2×#123—1016no—
215C2×C4×D4—58no—
216C2×C4×D4—108no—
217C22×C4⋊C4—52no—
218C22×C4⋊C4—52no—
219C22×C4⋊C4—51no—
220C22×C4⋊C4—51no—
221C22×C4⋊C4—51no—
222C22×C4⋊C4—58no—
223C22×C4⋊C4—108no—
224C22×C4⋊C4C2×D512yes—
225C22×C4⋊C4C2×D511yescharacteristic
226C22×C4⋊C4C2×D511yescharacteristic
227C22×C22⋊C4—51no—
228C22×C22⋊C4—52no—
229C22×C22⋊C4—52no—
230C22×C22⋊C4—51no—
231C22×C22⋊C4—52no—
232C22×C42C2×D511yescharacteristic
233#398—516no—
234#397—516no—
235#389—58no—
236#389C2×D518yescomplemented
237#381—516no—
238#380—58no—
239#380—58no—
240#380—58no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95C2×D512yes—
246C23×C5C22×D412yes—
247C23×C5C22×D412yes—
248C23×C5C2×#4112yes—
249C23×C5C2×#4112yes—
250C23×C5C2×#4112yes—
251C23×C52−1+412yes—
252C23×C52−1+412yes—
253C23×C5C2511yescharacteristic
254C22×D5—28no—
255C22×D5—28no—
256C22×D5—28no—
257C22×D5—28no—
258C22×D5—28no—
259C22×D5—28no—
260C22×D5—22no—
261C22×D5—22no—
262C22×D5—22no—
263C22×D5—22no—
264C22×D5—28no—
265C22×D5—28no—
266C22×D5—28no—
267C22×D5—22no—
268C22×D5—22no—
269C22×D5—22no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—44no—
274C22×D5—44no—
275C22×D5—44no—
276C22×D5—44no—
277C22×D5#121116yes—
278C22×D5C22×D414yes—
279C22×D5C22×D414yes—
280C22×D5C22×D414yes—
281C22×D5C2×#4114yes—
282C2×C4×C5—28no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—22no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—24no—
290C2×C4×C5—24no—
291C2×C4×C5—22no—
292C2×C4×C5—22no—
293C2×C4×C5—24no—
294C2×C4×C5—48no—
295C2×C4×C5—44no—
296C2×C4×C5—48no—
297C2×C4×C5#123116yescomplemented
298C2×C4×C5C22×D414yes—
299C2×C4×C5C22×D414yes—
300C2×C4×C5C2×#4114yes—
301C2×C4×C5C2×#4114yes—
302C2×Dic5—28no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—24no—
306C2×Dic5—24no—
307C2×Dic5—24no—
308C2×Dic5—22no—
309C2×Dic5—24no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—24no—
313C2×Dic5—24no—
314C2×Dic5—48no—
315C2×Dic5—44no—
316C2×Dic5—48no—
317C2×Dic5C22×D414yes—
318D20—232no—
319C4×D5—232no—
320C4×D5—432no—
321C4×D5—416no—
322C25—51no—
323C25—51no—
324C22×D4—58no—
325C22×D4—54no—
326C22×D4—104no—
327C22×D4—104no—
328C23×C4—51no—
329C23×C4—58no—
330C23×C4—54no—
331C23×C4—52no—
332C23×C4—52no—
333C23×C4—51no—
334C23×C4—58no—
335C23×C4—54no—
336C23×C4—108no—
337C23×C4—108no—
338C23×C4—108no—
339C23×C4—104no—
340C23×C4—104no—
341C23×C4—104no—
342C23×C4—104no—
343C23×C4—104no—
344C23×C4C22×D512yes—
345C23×C4C22×D511yescharacteristic
346C23×C4C22×D512yes—
347C23×C4C22×D511yescharacteristic
348C23×C4C22×D511yescharacteristic
349#123—1064no—
350C4×D4—1032no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—54no—
355C2×C4⋊C4—58no—
356C2×C4⋊C4—54no—
357C2×C4⋊C4—58no—
358C2×C4⋊C4—54no—
359C2×C4⋊C4—1032no—
360C2×C4⋊C4—108no—
361C2×C4⋊C4—104no—
362C2×C4⋊C4—104no—
363C2×C4⋊C4—108no—
364C2×C4⋊C4—104no—
365C2×C4⋊C4C22×D514yes—
366C2×C4⋊C4C22×D518yes—
367C2×C4⋊C4C22×D514yes—
368C2×C22⋊C4—54no—
369C2×C22⋊C4—54no—
370C2×C22⋊C4—58no—
371C2×C22⋊C4—58no—
372C2×C22⋊C4—58no—
373C2×C22⋊C4—104no—
374C2×C22⋊C4—104no—
375C2×C22⋊C4—108no—
376C2×C22⋊C4—108no—
377C2×C22⋊C4—108no—
378C2×C42—24no—
379C2×C42C22×D514yes—
380#95—58no—
381#95—58no—
382#95—58no—
383#95—58no—
384#95C22×D518yes—
385C22×C5C2×#12114yes—
386C22×C5C2×#12314yes—
387C22×C5#53614yes—
388C22×C5#54714yes—
389C22×C5#54714yes—
390C22×C5#55214yes—
391C22×C5#55214yes—
392C22×C5C23×D411yescharacteristic
393C22×C5C23×D411yescharacteristic
394C22×C5C22×#4111yescharacteristic
395C22×C5C22×#4111yescharacteristic
396C22×C5C22×#4111yescharacteristic
397C22×C5C2×2−1+411yescharacteristic
398C22×C5C2×2−1+411yescharacteristic
399C2×D5—24no—
400C2×D5—24no—
401C2×D5—24no—
402C2×D5—24no—
403C2×D5—24no—
404C2×D5—24no—
405C2×D5—232no—
406C2×D5—24no—
407C2×D5—24no—
408C2×D5—24no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—42no—
412C2×D5—42no—
413C2×D5—416no—
414C2×D5C2×#12118yes—
415C4×C5—24no—
416C4×C5—44no—
417C4×C5—42no—
418C4×C5—44no—
419C4×C5C2×#12318yescomplemented
420Dic5—24no—
421Dic5—44no—
422Dic5—42no—
423Dic5—44no—
424C24—54no—
425C24—54no—
426C24—54no—
427C24—52no—
428C24—54no—
429C24—52no—
430C24—102no—
431C24—102no—
432C24—102no—
433C24—102no—
434C24—102no—
435C24—102no—
436C24—102no—
437C24—102no—
438C24—102no—
439C24—102no—
440C24C23×D511yescharacteristic
441C2×D4—516no—
442C2×D4—108no—
443C2×D4—1032no—
444C2×D4—108no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—54no—
457C22×C4—52no—
458C22×C4—516no—
459C22×C4—52no—
460C22×C4—54no—
461C22×C4—54no—
462C22×C4—1016no—
463C22×C4—1016no—
464C22×C4—1016no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—108no—
468C22×C4—108no—
469C22×C4—1032no—
470C22×C4—102no—
471C22×C4—104no—
472C22×C4—102no—
473C22×C4—104no—
474C22×C4—104no—
475C22×C4—104no—
476C22×C4—102no—
477C22×C4—104no—
478C22×C4—104no—
479C22×C4—108no—
480C22×C4—108no—
481C22×C4—108no—
482C22×C4—2032no—
483C22×C4—2016no—
484C22×C4#70914yes—
485C22×C4D4×D514yes—
486C22×C4D4×D514yes—
487C22×C4#71314yes—
488C22×C4C23×D512yes—
489C22×C4C23×D514yes—
490C22×C4C23×D514yes—
491C22×C4C23×D512yes—
492C22×C4C23×D512yes—
493C4⋊C4—28no—
494C4⋊C4—28no—
495C4⋊C4—216no—
496C4⋊C4—1016no—
497C4⋊C4—108no—
498C4⋊C4—108no—
499C4⋊C4—1016no—
500C4⋊C4—108no—
501C22⋊C4—108no—
502C22⋊C4—108no—
503C22⋊C4—1016no—
504C22⋊C4—1016no—
505C22⋊C4—1016no—
506C42—28no—
507C2×C5#248618yescomplemented
508C2×C5C22×#12111yescharacteristic
509C2×C5C22×#12311yescharacteristic
510C2×C5C2×#53611yescharacteristic
511C2×C5C2×#54711yescharacteristic
512C2×C5C2×#54711yescharacteristic
513C2×C5C2×#55211yescharacteristic
514C2×C5C2×#55211yescharacteristic
515D5—28no—
516D5—44no—
517C23—516no—
518C23—54no—
519C23—54no—
520C23—54no—
521C23—54no—
522C23—108no—
523C23—108no—
524C23—108no—
525C23—108no—
526C23—108no—
527C23—102no—
528C23—102no—
529C23—102no—
530C23—102no—
531C23—108no—
532C23—108no—
533C23—108no—
534C23—108no—
535C23—102no—
536C23—102no—
537C23—102no—
538C23—102no—
539C23—102no—
540C23—102no—
541C23—204no—
542C23—204no—
543C23—204no—
544C23—204no—
545C23C2×#70912yes—
546C23C2×D4×D512yes—
547C23C2×D4×D512yes—
548C23C2×#71312yes—
549C23#414712yes—
550C23D5×#4112yes—
551C23#415012yes—
552C23C24×D511yescharacteristic
553D4—1032no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—44no—
569C2×C4—54no—
570C2×C4—108no—
571C2×C4—102no—
572C2×C4—102no—
573C2×C4—1032no—
574C2×C4—102no—
575C2×C4—104no—
576C2×C4—102no—
577C2×C4—104no—
578C2×C4—104no—
579C2×C4—104no—
580C2×C4—102no—
581C2×C4—104no—
582C2×C4—104no—
583C2×C4—2032no—
584C2×C4—208no—
585C2×C4—204no—
586C2×C4—208no—
587C2×C4—2016no—
588C2×C4#4040116yescomplemented
589C2×C4C2×#70914yes—
590C2×C4C2×D4×D514yes—
591C2×C4C2×D4×D514yes—
592C2×C4C2×#71314yes—
593C5C2×#248611yescharacteristic, complemented, Sylow
594C22—58no—
595C22—104no—
596C22—104no—
597C22—104no—
598C22—104no—
599C22—1032no—
600C22—104no—
601C22—104no—
602C22—104no—
603C22—104no—
604C22—104no—
605C22—202no—
606C22—202no—
607C22—2016no—
608C22—202no—
609C22—202no—
610C22C2×#404014yes—
611C22#6588514yes—
612C22#6591514yes—
613C22D5×#12114yes—
614C22#6596214yes—
615C22#6602814yes—
616C22#6606014yes—
617C22C22×#70911yescharacteristic
618C22C22×D4×D511yescharacteristic
619C22C22×D4×D511yescharacteristic
620C22C22×#71311yescharacteristic
621C22C2×#414711yescharacteristic
622C22C2×D5×#4111yescharacteristic
623C22C2×#415011yescharacteristic
624C4—24no—
625C4—42no—
626C4—44no—
627C4—44no—
628C4—104no—
629C4—204no—
630C4—202no—
631C4—204no—
632C4C2×#404018yescomplemented
633C2—108no—
634C2—204no—
635C2#1060796218yesdirect product factor
636C2C22×#404011yescharacteristic
637C2C2×#6588511yescharacteristic
638C2C2×#6591511yescharacteristic
639C2C2×D5×#12111yescharacteristic
640C2C2×#6596211yescharacteristic
641C2C2×#6602811yescharacteristic
642C2C2×#6606011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#389D5
hypocenterC5C2×#2486
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×D5×C4⋊C4C2semidirect
4. C2×C5×#389C2semidirect
5. C2×#65276C2semidirect
6. C2×#65276C2semidirect
7. C2×#65276C2semidirect
8. C2×#65273C2semidirect
9. C2×#65217C2semidirect
10. #10607962C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64953C2semidirect
34. C2×D5×C4⋊C4C22semidirect
37. C5×#389C22semidirect
43. #65276C22semidirect
44. #65276C22semidirect
45. #65276C22semidirect
46. #65273C22semidirect
47. #65217C22semidirect
48. #64964C22semidirect
49. #64953C22semidirect
121. C2×#389D5semidirect
236. #389C2×D5semidirect
297. C2×C4×C5#123semidirect
419. C4×C5C2×#123semidirect
507. C2×C5#2486semidirect
588. C2×C4#4040semidirect
593. C5C2×#2486semidirect
632. C4C2×#4040semidirect
635. C2#10607962direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40402
C22×D5×C4⋊C42
C22×C4×D202
C2×C5×#3892
C2×#652762
C2×#652732
C2×#652172
#106079622
C2×#649642
C2×#649532
C2×#24865