Finite Group Databasebeta

← C2×#10605643 #12268469

Subgroups — C2×#10605643 #12268469

Order 1280.

3374 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C5×#380C211yesmaximal, characteristic, complemented
4C2×#65501C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65274C211yesmaximal, characteristic, complemented
7C2×#65262C211yesmaximal, characteristic, complemented
8C2×#65245C212yesmaximal
9C2×#65238C212yesmaximal, complemented
10#10605643C2116yesmaximal, direct product factor
11C2×#64957C212yesmaximal, complemented
12C2×#64947C212yesmaximal, complemented
13C24×C4×C5C2211yescharacteristic
14C23×C22⋊D5C2211yescharacteristic
15C23×C4×D5C2211yescharacteristic
16C23×C4×D5C2212yes—
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2212yes—
20C22×C22⋊Dic5C2211yescharacteristic
21C22×C22⋊Dic5C2212yes—
22C2×C4×C22⋊D5—28no—
23C2×C4×C22⋊D5C2218yes—
24C22×#685C2211yescharacteristic
25C22×#685C2212yes—
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2212yes—
29C22×#683C2212yes—
30C22×#683C2211yescharacteristic
31C22×#683C2212yes—
32C22×C4×Dic5C2211yescharacteristic
33C2×D5×C4⋊C4—28no—
34C2×D5×C4⋊C4C2218yescomplemented
35C5×#380C2218yescomplemented
36C2×C5×#95C2212yes—
37#65501C2218yescomplemented
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C2×#3963C2212yes—
41C2×#3963C2212yes—
42#65276C2218yescomplemented
43#65274C2218yescomplemented
44#65262C2218yescomplemented
45#65245C22116yes—
46#65238C22116yescomplemented
47#64957C22116yescomplemented
48#64947C22116yescomplemented
49C2×#2487—51nomaximal, Sylow
50C25×C5C2311yescharacteristic
51C24×D5C2311yescharacteristic
52C23×C4×C5—24no—
53C23×C4×C5—24no—
54C23×C4×C5—24no—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2312yes—
57C23×C4×C5C2312yes—
58C23×C4×C5C2314yes—
59C23×C4×C5C2311yescharacteristic
60C22×C22⋊D5—24no—
61C22×C22⋊D5—24no—
62C22×C22⋊D5Q818yes—
63C22×C22⋊D5C2314yes—
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2312yes—
66C23×Dic5C2312yes—
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C22×C4×D5—24no—
70C22×C4×D5—24no—
71C22×C4×D5—28no—
72C22×C4×D5—44no—
73C22×C4×D5—44no—
74C22×C4×D5D418yes—
75C22×C4×D5C2314yes—
76C22×C4×D5C2318yes—
77C2×C5×C4⋊C4—24no—
78C2×C5×C4⋊C4—24no—
79C2×C5×C4⋊C4C2314yes—
80C2×C5×C4⋊C4C2314yes—
81C2×C5×C22⋊C4—44no—
82C2×C5×C22⋊C4C2318yes—
83C2×C22⋊Dic5—24no—
84C2×C22⋊Dic5—44no—
85C2×C22⋊Dic5C2314yes—
86C2×C22⋊Dic5C2318yes—
87C4×C22⋊D5—232no—
88C2×#685—24no—
89C2×#685—28no—
90C2×#685C2314yes—
91C2×#685C2318yes—
92C2×C4⋊Dic5—24no—
93C2×C4⋊Dic5—24no—
94C2×C4⋊Dic5—44no—
95C2×C4⋊Dic5C2314yes—
96C2×C4⋊Dic5C2314yes—
97C2×C4⋊Dic5C2318yes—
98C2×#683—28no—
99C2×#683—24no—
100C2×#683—44no—
101C2×#683C2318yes—
102C2×#683C2314yes—
103C2×#683C2318yes—
104C2×C4×Dic5—24no—
105C2×C4×Dic5C2314yes—
106D5×C4⋊C4—232no—
107C5×#95C2318yes—
108#3963C2318yes—
109#3963C2318yes—
110#3963C2318yes—
111#3963C2318yes—
112C22×C4×D4—51no—
113C23×C4⋊C4—51no—
114#2487—516no—
115C2×#400—52no—
116C2×#399—52no—
117C2×#389—51no—
118C2×#389—51no—
119C2×#386—52no—
120C2×#385—52no—
121C2×#380—51no—
122C2×#380—51no—
123C2×#380D511yescharacteristic, complemented
124C24×C5—22no—
125C24×C5—22no—
126C24×C5—22no—
127C24×C5—22no—
128C24×C5—22no—
129C24×C5—22no—
130C24×C5C2×Q814yes—
131C24×C5C2412yes—
132C24×C5C2411yescharacteristic
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5C2×D414yes—
138C23×D5C2×Q814yes—
139C23×D5#4114yes—
140C23×D5C2412yes—
141C22×C4×C5—24no—
142C22×C4×C5—22no—
143C22×C4×C5—24no—
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—28no—
151C22×C4×C5—28no—
152C22×C4×C5—28no—
153C22×C4×C5—416no—
154C22×C4×C5C2×D414yes—
155C22×C4×C5#4114yes—
156C22×C4×C5#4114yes—
157C22×C4×C5C2414yes—
158C22×C4×C5C2414yes—
159C22×C4×C5C2412yes—
160C22×C4×C5C2412yes—
161C2×C22⋊D5—232no—
162C2×C22⋊D5—28no—
163C2×C22⋊D5—28no—
164C2×C22⋊D5C2×Q8116yes—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—24no—
171C22×Dic5—24no—
172C22×Dic5—24no—
173C22×Dic5—24no—
174C22×Dic5—24no—
175C22×Dic5—24no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5C2×D414yes—
179C22×Dic5C2×Q814yes—
180C22×Dic5C2414yes—
181C22×Dic5C2414yes—
182C22×Dic5C2412yes—
183C22×Dic5C2412yes—
184C22×Dic5C2412yes—
185C2×C4×D5—232no—
186C2×C4×D5—28no—
187C2×C4×D5—28no—
188C2×C4×D5—216no—
189C2×C4×D5—48no—
190C2×C4×D5—48no—
191C2×C4×D5—432no—
192C2×C4×D5C2×D4116yes—
193C5×C4⋊C4—28no—
194C5×C4⋊C4—28no—
195C5×C22⋊C4—48no—
196C22⋊Dic5—28no—
197C22⋊Dic5—48no—
198#685—28no—
199#685—216no—
200C4⋊Dic5—28no—
201C4⋊Dic5—28no—
202C4⋊Dic5—48no—
203#683—216no—
204#683—28no—
205#683—48no—
206C4×Dic5—28no—
207C23×D4—51no—
208C24×C4—51no—
209C24×C4—52no—
210C24×C4C2×D511yescharacteristic
211C2×C4×D4—58no—
212C2×C4×D4—108no—
213C22×C4⋊C4—52no—
214C22×C4⋊C4—51no—
215C22×C4⋊C4—51no—
216C22×C4⋊C4—51no—
217C22×C4⋊C4—52no—
218C22×C4⋊C4—52no—
219C22×C4⋊C4—58no—
220C22×C4⋊C4—108no—
221C22×C4⋊C4C2×D511yescharacteristic
222C22×C4⋊C4C2×D511yescharacteristic
223C22×C22⋊C4—51no—
224C22×C22⋊C4—51no—
225C22×C22⋊C4—52no—
226C22×C22⋊C4—52no—
227C22×C22⋊C4C2×D512yes—
228C22×C42—51no—
229#400—516no—
230#399—516no—
231#389—58no—
232#389—58no—
233#386—516no—
234#385—516no—
235#380—58no—
236#380—58no—
237#380C2×D518yescomplemented
238C2×#95—52no—
239C2×#95—52no—
240C2×#95—52no—
241C2×#95—52no—
242C2×#95C2×D512yes—
243C23×C5—28no—
244C23×C5—28no—
245C23×C5—28no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—22no—
249C23×C5—22no—
250C23×C5—22no—
251C23×C5—22no—
252C23×C5—44no—
253C23×C5—44no—
254C23×C5—44no—
255C23×C5—44no—
256C23×C5C22×D412yes—
257C23×C5C22×Q814yes—
258C23×C5C22×Q812yes—
259C23×C5C2×#4112yes—
260C23×C5C2×#4112yes—
261C23×C5C2×#4112yes—
262C23×C5H(5,𝔽2)12yes—
263C23×C5H(5,𝔽2)12yes—
264C23×C5C2511yescharacteristic
265C22×D5—28no—
266C22×D5—28no—
267C22×D5—28no—
268C22×D5—28no—
269C22×D5—28no—
270C22×D5—28no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—22no—
275C22×D5C22⋊Q8116yes—
276C22×D5C22×D414yes—
277C22×D5C22×Q814yes—
278C22×D5C2×#4114yes—
279C2×C4×C5—22no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—24no—
288C2×C4×C5—44no—
289C2×C4×C5—48no—
290C2×C4×C5—48no—
291C2×C4×C5—416no—
292C2×C4×C5#123116yes—
293C2×C4×C5C22×D414yes—
294C2×C4×C5C2×#4114yes—
295C2×C4×C5C2×#4114yes—
296C22⋊D5—232no—
297C2×Dic5—28no—
298C2×Dic5—28no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—24no—
305C2×Dic5—24no—
306C2×Dic5—24no—
307C2×Dic5—22no—
308C2×Dic5—24no—
309C2×Dic5—22no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—48no—
313C2×Dic5—44no—
314C2×Dic5—48no—
315C2×Dic5C22×D414yes—
316C2×Dic5C22×Q814yes—
317C4×D5—232no—
318C4×D5—432no—
319C25—51no—
320C25C22×D511yescharacteristic
321C22×D4—58no—
322C22×D4—54no—
323C22×D4—104no—
324C22×D4—104no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—51no—
329C23×C4—51no—
330C23×C4—58no—
331C23×C4—54no—
332C23×C4—51no—
333C23×C4—52no—
334C23×C4—52no—
335C23×C4—58no—
336C23×C4—108no—
337C23×C4—104no—
338C23×C4—104no—
339C23×C4—204no—
340C23×C4—204no—
341C23×C4C22×D514yes—
342C23×C4C22×D512yes—
343C23×C4C22×D511yescharacteristic
344C23×C4C22×D512yes—
345C23×C4C22×D511yescharacteristic
346C4×D4—1032no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—54no—
350C2×C4⋊C4—58no—
351C2×C4⋊C4—54no—
352C2×C4⋊C4—54no—
353C2×C4⋊C4—58no—
354C2×C4⋊C4—58no—
355C2×C4⋊C4—1032no—
356C2×C4⋊C4—108no—
357C2×C4⋊C4—104no—
358C2×C4⋊C4—104no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—204no—
361C2×C4⋊C4—204no—
362C2×C4⋊C4C22×D514yes—
363C2×C4⋊C4C22×D514yes—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—54no—
366C2×C22⋊C4—54no—
367C2×C22⋊C4—58no—
368C2×C22⋊C4—58no—
369C2×C22⋊C4—104no—
370C2×C22⋊C4—108no—
371C2×C22⋊C4—104no—
372C2×C22⋊C4—204no—
373C2×C22⋊C4C22×D518yes—
374C2×C42—54no—
375C2×C42—104no—
376#95—58no—
377#95—58no—
378#95—58no—
379#95—58no—
380#95C22×D518yes—
381C22×C5—24no—
382C22×C5—24no—
383C22×C5—24no—
384C22×C5—42no—
385C22×C5—42no—
386C22×C5—42no—
387C22×C5—42no—
388C22×C5—416no—
389C22×C5C2×C22⋊Q814yes—
390C22×C5C2×#12314yes—
391C22×C5#53514yes—
392C22×C5#55314yes—
393C22×C5#55314yes—
394C22×C5#55414yes—
395C22×C5#55414yes—
396C22×C5C23×D411yescharacteristic
397C22×C5C23×Q811yescharacteristic
398C22×C5C22×#4111yescharacteristic
399C22×C5C22×#4111yescharacteristic
400C22×C5C22×#4111yescharacteristic
401C22×C5C2×H(5,𝔽2)11yescharacteristic
402C22×C5C2×H(5,𝔽2)11yescharacteristic
403C2×D5—24no—
404C2×D5—24no—
405C2×D5—24no—
406C2×D5—24no—
407C2×D5—24no—
408C2×D5—24no—
409C2×D5—232no—
410C2×D5C2×C22⋊Q818yes—
411C4×C5—42no—
412C4×C5—44no—
413C4×C5—44no—
414C4×C5C2×#12318yes—
415Dic5—24no—
416Dic5—24no—
417Dic5—44no—
418Dic5—42no—
419Dic5—44no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—54no—
427C24—54no—
428C24—54no—
429C24—52no—
430C24—102no—
431C24—102no—
432C24—102no—
433C24—102no—
434C24Q8×D514yes—
435C24C23×D512yes—
436C24C23×D511yescharacteristic
437C2×D4—516no—
438C2×D4—108no—
439C2×D4—1032no—
440C2×D4—108no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—416no—
454C22×C4—54no—
455C22×C4—54no—
456C22×C4—52no—
457C22×C4—52no—
458C22×C4—516no—
459C22×C4—54no—
460C22×C4—54no—
461C22×C4—52no—
462C22×C4—1016no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—108no—
468C22×C4—108no—
469C22×C4—1032no—
470C22×C4—104no—
471C22×C4—102no—
472C22×C4—104no—
473C22×C4—102no—
474C22×C4—104no—
475C22×C4—104no—
476C22×C4—104no—
477C22×C4—104no—
478C22×C4—102no—
479C22×C4—208no—
480C22×C4—208no—
481C22×C4—2032no—
482C22×C4#70914yes—
483C22×C4D4×D514yes—
484C22×C4#71114yes—
485C22×C4C23×D512yes—
486C22×C4C23×D514yes—
487C22×C4C23×D514yes—
488C22×C4C23×D512yes—
489C4⋊C4—28no—
490C4⋊C4—28no—
491C4⋊C4—1016no—
492C4⋊C4—108no—
493C4⋊C4—108no—
494C4⋊C4—108no—
495C4⋊C4—208no—
496C4⋊C4—208no—
497C22⋊C4—48no—
498C22⋊C4—108no—
499C22⋊C4—1016no—
500C22⋊C4—108no—
501C22⋊C4—208no—
502C42—108no—
503C2×C5—44no—
504C2×C5#248718yescomplemented
505C2×C5C22×C22⋊Q811yescharacteristic
506C2×C5C22×#12311yescharacteristic
507C2×C5C2×#53511yescharacteristic
508C2×C5C2×#55311yescharacteristic
509C2×C5C2×#55311yescharacteristic
510C2×C5C2×#55411yescharacteristic
511C2×C5C2×#55411yescharacteristic
512D5—28no—
513C23—28no—
514C23—28no—
515C23—28no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—516no—
527C23—54no—
528C23—54no—
529C23—54no—
530C23—108no—
531C23—108no—
532C23—108no—
533C23—108no—
534C23—108no—
535C23—108no—
536C23—102no—
537C23—102no—
538C23—102no—
539C23—102no—
540C23C2×#70912yes—
541C23C2×D4×D512yes—
542C23C2×#71112yes—
543C23#414412yes—
544C23C2×Q8×D514yes—
545C23C2×Q8×D512yes—
546C23D5×#4112yes—
547C23#414912yes—
548C23C24×D511yescharacteristic
549D4—1032no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—44no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4—416no—
563C2×C4—54no—
564C2×C4—54no—
565C2×C4—108no—
566C2×C4—108no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—102no—
571C2×C4—1032no—
572C2×C4—104no—
573C2×C4—102no—
574C2×C4—104no—
575C2×C4—102no—
576C2×C4—104no—
577C2×C4—104no—
578C2×C4—104no—
579C2×C4—104no—
580C2×C4—102no—
581C2×C4—2032no—
582C2×C4—208no—
583C2×C4—208no—
584C2×C4—204no—
585C2×C4#4029116yes—
586C2×C4C2×#70914yes—
587C2×C4C2×D4×D514yes—
588C2×C4C2×#71114yes—
589C5C2×#248711yescharacteristic, complemented, Sylow
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—416no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—58no—
599C22—104no—
600C22—104no—
601C22—104no—
602C22—1032no—
603C22—104no—
604C22—104no—
605C22—104no—
606C22C2×#402914yes—
607C22#6584514yes—
608C22#6586414yes—
609C22#6594114yes—
610C22#6594814yes—
611C22D5×C22⋊Q814yes—
612C22#6596914yes—
613C22C22×#70911yescharacteristic
614C22C22×D4×D511yescharacteristic
615C22C22×#71111yescharacteristic
616C22C2×#414411yescharacteristic
617C22C22×Q8×D511yescharacteristic
618C22C2×D5×#4111yescharacteristic
619C22C2×#414911yescharacteristic
620C4—44no—
621C4—44no—
622C4—42no—
623C4—104no—
624C4—104no—
625C4—204no—
626C4—204no—
627C4—202no—
628C4C2×#402918yes—
629C2—44no—
630C2—108no—
631C2#1060564318yesdirect product factor
632C2C22×#402911yescharacteristic
633C2C2×#6584511yescharacteristic
634C2C2×#6586411yescharacteristic
635C2C2×#6594111yescharacteristic
636C2C2×#6594811yescharacteristic
637C2C2×#6596911yescharacteristic
638C2C2×D5×C22⋊Q811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#380C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#380D5
hypocenterC5C2×#2487
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×D5×C4⋊C4C2semidirect
3. C2×C5×#380C2semidirect
4. C2×#65501C2semidirect
5. C2×#65276C2semidirect
6. C2×#65274C2semidirect
7. C2×#65262C2semidirect
9. C2×#65238C2semidirect
10. #10605643C2direct (N × H)
11. C2×#64957C2semidirect
12. C2×#64947C2semidirect
34. C2×D5×C4⋊C4C22semidirect
35. C5×#380C22semidirect
37. #65501C22semidirect
42. #65276C22semidirect
43. #65274C22semidirect
44. #65262C22semidirect
46. #65238C22semidirect
47. #64957C22semidirect
48. #64947C22semidirect
123. C2×#380D5semidirect
237. #380C2×D5semidirect
504. C2×C5#2487semidirect
589. C5C2×#2487semidirect
631. C2#10605643direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×D5×C4⋊C42
C2×C5×#3802
C2×#655012
C2×#652762
C2×#652742
C2×#652622
C2×#652452
C2×#652382
#106056432
C2×#649572
C2×#649472
C2×#24875