Finite Group Databasebeta

← C2×#10607960 #12268816

Subgroups — C2×#10607960 #12268816

Order 1280.

3070 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic, complemented
2C22×C4×D20C211yesmaximal, characteristic
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×#65280C212yesmaximal
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65276C211yesmaximal, characteristic, complemented
7C2×#65276C211yesmaximal, characteristic, complemented
8C2×#65270C212yesmaximal, complemented
9C2×#65217C211yesmaximal, characteristic, complemented
10#10607960C2116yesmaximal, direct product factor
11C2×#64964C212yesmaximal, complemented
12C2×#64958C212yesmaximal, complemented
13C23×D20C2211yescharacteristic
14C23×C4×D5C2211yescharacteristic
15C23×C4×D5C2211yescharacteristic
16C22×C5×C4⋊C4C2212yes—
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×#685C2212yes—
22C22×#685C2211yescharacteristic
23C22×#685C2212yes—
24C22×#685C2212yes—
25C22×#685C2212yes—
26C22×C4⋊Dic5C2211yescharacteristic
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×#683C2212yes—
30C22×C4×Dic5C2212yes—
31C2×#4038—28no—
32C2×#4038C2218yescomplemented
33C2×C4×D20—28no—
34C2×C4×D20C2218yes—
35C5×#389C2218yescomplemented
36C2×C5×#95C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C2×#3963C2212yes—
41#65280C22116yes—
42#65276C2218yescomplemented
43#65276C2218yescomplemented
44#65276C2218yescomplemented
45#65270C22116yescomplemented
46#65217C2218yescomplemented
47#64964C22116yescomplemented
48#64958C22116yescomplemented
49C2×#2485—51nomaximal, Sylow
50C24×D5C2311yescharacteristic
51C24×D5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2312yes—
54C23×C4×C5C2312yes—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×Dic5C2312yes—
58C23×Dic5C2312yes—
59C23×Dic5C2311yescharacteristic
60C23×Dic5C2311yescharacteristic
61C22×D20—24no—
62C22×D20—24no—
63C22×D20—24no—
64C22×D20C2314yes—
65C22×C4×D5—24no—
66C22×C4×D5—24no—
67C22×C4×D5—24no—
68C22×C4×D5—24no—
69C22×C4×D5—24no—
70C22×C4×D5D418yes—
71C22×C4×D5C2314yes—
72C22×C4×D5C2314yes—
73C2×C5×C4⋊C4—24no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—28no—
76C2×C5×C4⋊C4C2318yes—
77C2×C5×C4⋊C4C2314yes—
78C2×C5×C4⋊C4C2314yes—
79C2×C42×C5—24no—
80C2×C42×C5C2314yes—
81C2×#685—24no—
82C2×#685—28no—
83C2×#685—28no—
84C2×#685—24no—
85C2×#685—44no—
86C2×#685—44no—
87C2×#685C2318yes—
88C2×#685C2318yes—
89C2×#685C2314yes—
90C2×#685C2314yes—
91C2×#685C2318yes—
92C2×#685C2318yes—
93C2×C4⋊Dic5—24no—
94C2×C4⋊Dic5—24no—
95C2×C4⋊Dic5—24no—
96C2×C4⋊Dic5C2314yes—
97C2×C4⋊Dic5C2314yes—
98C2×C4⋊Dic5C2314yes—
99C2×#683—44no—
100C2×#683C2318yes—
101C2×C4×Dic5—28no—
102C2×C4×Dic5C2318yes—
103#4038—232no—
104C4×D20—232no—
105C5×#95C2318yes—
106#3963C2318yes—
107#3963C2318yes—
108#3963C2318yes—
109#3963C2318yes—
110C22×C4×D4—51no—
111C22×#117—51no—
112#2485—516no—
113C2×#397—52no—
114C2×#394—52no—
115C2×#389—51no—
116C2×#389D511yescharacteristic, complemented
117C2×#388—52no—
118C2×#387—52no—
119C2×#380—51no—
120C2×#380—51no—
121C2×#380—51no—
122C24×C5C2411yescharacteristic
123C23×D5—22no—
124C23×D5—22no—
125C23×D5—22no—
126C23×D5—22no—
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×D5C2×D414yes—
136C23×D5#4114yes—
137C23×D5C2412yes—
138C23×D5C2412yes—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—24no—
143C22×C4×C5—24no—
144C22×C4×C5—24no—
145C22×C4×C5—24no—
146C22×C4×C5—24no—
147C22×C4×C5—22no—
148C22×C4×C5—24no—
149C22×C4×C5—22no—
150C22×C4×C5C2×D414yes—
151C22×C4×C5#4114yes—
152C22×C4×C5#4114yes—
153C22×C4×C5#4114yes—
154C22×C4×C5C2412yes—
155C22×C4×C5C2414yes—
156C22×C4×C5C2414yes—
157C22×C4×C5C2412yes—
158C22×C4×C5C2412yes—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—24no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—24no—
166C22×Dic5—24no—
167C22×Dic5—24no—
168C22×Dic5—24no—
169C22×Dic5—24no—
170C22×Dic5C2×D414yes—
171C22×Dic5C2412yes—
172C22×Dic5C2414yes—
173C22×Dic5C2414yes—
174C22×Dic5C2412yes—
175C2×D20—232no—
176C2×D20—28no—
177C2×D20—28no—
178C2×D20—28no—
179C2×C4×D5—232no—
180C2×C4×D5—28no—
181C2×C4×D5—28no—
182C2×C4×D5—28no—
183C2×C4×D5—28no—
184C2×C4×D5—28no—
185C2×C4×D5—416no—
186C2×C4×D5C2×D4116yes—
187C5×C4⋊C4—28no—
188C5×C4⋊C4—28no—
189C5×C4⋊C4—216no—
190C42×C5—28no—
191#685—28no—
192#685—216no—
193#685—216no—
194#685—28no—
195#685—48no—
196#685—48no—
197C4⋊Dic5—28no—
198C4⋊Dic5—28no—
199C4⋊Dic5—28no—
200#683—48no—
201C4×Dic5—216no—
202C23×D4—51no—
203C24×C4—51no—
204C24×C4—51no—
205C2×C4×D4—58no—
206C2×C4×D4—108no—
207C2×#117—58no—
208C2×#117—108no—
209C22×C4⋊C4—51no—
210C22×C4⋊C4—51no—
211C22×C4⋊C4—51no—
212C22×C4⋊C4—52no—
213C22×C4⋊C4C2×D512yes—
214C22×C4⋊C4C2×D511yescharacteristic
215C22×C4⋊C4C2×D511yescharacteristic
216C22×C22⋊C4—52no—
217C22×C22⋊C4—52no—
218C22×C22⋊C4—51no—
219C22×C22⋊C4—51no—
220C22×C22⋊C4—52no—
221C22×C22⋊C4—52no—
222C22×C42—52no—
223C22×C42C2×D511yescharacteristic
224#397—516no—
225#394—516no—
226#389—58no—
227#389C2×D518yescomplemented
228#388—516no—
229#387—516no—
230#380—58no—
231#380—58no—
232#380—58no—
233C2×#95—52no—
234C2×#95—52no—
235C2×#95—52no—
236C2×#95—52no—
237C2×#95C2×D512yes—
238C23×C5C22×D412yes—
239C23×C5C2×#4112yes—
240C23×C5C2×#4112yes—
241C23×C5C2×#4112yes—
242C23×C5C2×#4112yes—
243C23×C5H(5,𝔽2)12yes—
244C23×C52−1+412yes—
245C23×C5C2511yescharacteristic
246C22×D5—28no—
247C22×D5—28no—
248C22×D5—28no—
249C22×D5—28no—
250C22×D5—28no—
251C22×D5—28no—
252C22×D5—22no—
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—22no—
259C22×D5—22no—
260C22×D5—22no—
261C22×D5—22no—
262C22×D5—22no—
263C22×D5—22no—
264C22×D5—44no—
265C22×D5—44no—
266C22×D5—44no—
267C22×D5—44no—
268C22×D5—44no—
269C22×D5—44no—
270C22×D5—44no—
271C22×D5—44no—
272C22×D5C22×D414yes—
273C22×D5C2×#4114yes—
274C2×C4×C5—28no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—24no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—24no—
282C2×C4×C5—24no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—22no—
286C2×C4×C5—48no—
287C2×C4×C5—44no—
288C2×C4×C5—48no—
289C2×C4×C5#123116yes—
290C2×C4×C5C22×D414yes—
291C2×C4×C5C2×#4114yes—
292C2×C4×C5C2×#4114yes—
293C2×C4×C5C2×#4114yes—
294C2×Dic5—28no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—24no—
298C2×Dic5—22no—
299C2×Dic5—24no—
300C2×Dic5—24no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—24no—
304C2×Dic5—24no—
305C2×Dic5—24no—
306C2×Dic5—44no—
307C2×Dic5—48no—
308C2×Dic5—48no—
309C2×Dic5C22×D414yes—
310D20—232no—
311C4×D5—232no—
312C4×D5—416no—
313C25—51no—
314C25—51no—
315C22×D4—54no—
316C22×D4—104no—
317C22×D4—104no—
318C22×D4—104no—
319C23×C4—51no—
320C23×C4—58no—
321C23×C4—54no—
322C23×C4—52no—
323C23×C4—52no—
324C23×C4—51no—
325C23×C4—54no—
326C23×C4—104no—
327C23×C4—104no—
328C23×C4—104no—
329C23×C4—104no—
330C23×C4—104no—
331C23×C4C22×D511yescharacteristic
332C23×C4C22×D512yes—
333C23×C4C22×D512yes—
334C23×C4C22×D511yescharacteristic
335C23×C4C22×D511yescharacteristic
336C4×D4—1032no—
337#117—1032no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—54no—
342C2×C4⋊C4—54no—
343C2×C4⋊C4—54no—
344C2×C4⋊C4—58no—
345C2×C4⋊C4—104no—
346C2×C4⋊C4—104no—
347C2×C4⋊C4—104no—
348C2×C4⋊C4—204no—
349C2×C4⋊C4C22×D514yes—
350C2×C4⋊C4C22×D514yes—
351C2×C4⋊C4C22×D518yes—
352C2×C22⋊C4—58no—
353C2×C22⋊C4—54no—
354C2×C22⋊C4—54no—
355C2×C22⋊C4—58no—
356C2×C22⋊C4—58no—
357C2×C22⋊C4—58no—
358C2×C22⋊C4—104no—
359C2×C22⋊C4—108no—
360C2×C22⋊C4—104no—
361C2×C22⋊C4—108no—
362C2×C22⋊C4—204no—
363C2×C22⋊C4—204no—
364C2×C42—24no—
365C2×C42—58no—
366C2×C42—108no—
367C2×C42C22×D514yes—
368#95—58no—
369#95—58no—
370#95—58no—
371#95—58no—
372#95C22×D518yes—
373C22×C5C2×#12314yes—
374C22×C5#52514yes—
375C22×C5#53714yes—
376C22×C5#55214yes—
377C22×C5#55314yes—
378C22×C5#55514yes—
379C22×C5#55614yes—
380C22×C5C23×D411yescharacteristic
381C22×C5C22×#4111yescharacteristic
382C22×C5C22×#4111yescharacteristic
383C22×C5C22×#4111yescharacteristic
384C22×C5C22×#4111yescharacteristic
385C22×C5C2×H(5,𝔽2)11yescharacteristic
386C22×C5C2×2−1+411yescharacteristic
387C2×D5—24no—
388C2×D5—24no—
389C2×D5—24no—
390C2×D5—24no—
391C2×D5—24no—
392C2×D5—24no—
393C2×D5—42no—
394C2×D5—42no—
395C2×D5—42no—
396C2×D5—42no—
397C2×D5—42no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—416no—
402C2×D5—416no—
403C4×C5—24no—
404C4×C5—44no—
405C4×C5—42no—
406C4×C5—44no—
407C4×C5C2×#12318yes—
408Dic5—24no—
409Dic5—42no—
410Dic5—44no—
411Dic5—44no—
412C24—54no—
413C24—54no—
414C24—52no—
415C24—52no—
416C24—102no—
417C24—102no—
418C24—102no—
419C24—102no—
420C24—102no—
421C24—102no—
422C24—102no—
423C24—102no—
424C24—102no—
425C24—102no—
426C24—102no—
427C24—102no—
428C24C23×D511yescharacteristic
429C2×D4—108no—
430C2×D4—108no—
431C2×D4—1032no—
432C2×D4—108no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—54no—
445C22×C4—52no—
446C22×C4—516no—
447C22×C4—52no—
448C22×C4—54no—
449C22×C4—54no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—108no—
453C22×C4—108no—
454C22×C4—1032no—
455C22×C4—102no—
456C22×C4—104no—
457C22×C4—102no—
458C22×C4—104no—
459C22×C4—102no—
460C22×C4—104no—
461C22×C4—104no—
462C22×C4—104no—
463C22×C4—104no—
464C22×C4—108no—
465C22×C4—108no—
466C22×C4—108no—
467C22×C4—2016no—
468C22×C4#70914yes—
469C22×C4D4×D514yes—
470C22×C4#71114yes—
471C22×C4#71314yes—
472C22×C4C23×D514yes—
473C22×C4C23×D514yes—
474C22×C4C23×D512yes—
475C22×C4C23×D512yes—
476C22×C4C23×D512yes—
477C4⋊C4—28no—
478C4⋊C4—28no—
479C4⋊C4—216no—
480C4⋊C4—108no—
481C4⋊C4—108no—
482C4⋊C4—108no—
483C4⋊C4—208no—
484C22⋊C4—108no—
485C22⋊C4—1016no—
486C22⋊C4—108no—
487C22⋊C4—1016no—
488C22⋊C4—208no—
489C22⋊C4—208no—
490C42—28no—
491C42—1016no—
492C2×C5#248518yescomplemented
493C2×C5C22×#12311yescharacteristic
494C2×C5C2×#52511yescharacteristic
495C2×C5C2×#53711yescharacteristic
496C2×C5C2×#55211yescharacteristic
497C2×C5C2×#55311yescharacteristic
498C2×C5C2×#55511yescharacteristic
499C2×C5C2×#55611yescharacteristic
500D5—44no—
501D5—44no—
502C23—54no—
503C23—54no—
504C23—108no—
505C23—108no—
506C23—108no—
507C23—108no—
508C23—108no—
509C23—102no—
510C23—102no—
511C23—102no—
512C23—102no—
513C23—102no—
514C23—102no—
515C23—102no—
516C23—102no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—102no—
521C23—108no—
522C23—204no—
523C23—204no—
524C23—204no—
525C23—204no—
526C23—204no—
527C23—204no—
528C23—204no—
529C23—204no—
530C23C2×#70912yes—
531C23C2×D4×D512yes—
532C23C2×#71112yes—
533C23C2×#71312yes—
534C23#414712yes—
535C23D5×#4112yes—
536C23#414912yes—
537C23C24×D511yescharacteristic
538D4—1032no—
539C2×C4—28no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—48no—
552C2×C4—48no—
553C2×C4—44no—
554C2×C4—54no—
555C2×C4—108no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—1032no—
559C2×C4—102no—
560C2×C4—104no—
561C2×C4—102no—
562C2×C4—104no—
563C2×C4—102no—
564C2×C4—104no—
565C2×C4—104no—
566C2×C4—104no—
567C2×C4—104no—
568C2×C4—204no—
569C2×C4—208no—
570C2×C4—208no—
571C2×C4—2016no—
572C2×C4#4040116yes—
573C2×C4C2×#70914yes—
574C2×C4C2×D4×D514yes—
575C2×C4C2×#71114yes—
576C2×C4C2×#71314yes—
577C5C2×#248511yescharacteristic, complemented, Sylow
578C22—104no—
579C22—104no—
580C22—104no—
581C22—104no—
582C22—104no—
583C22—104no—
584C22—202no—
585C22—202no—
586C22—202no—
587C22—202no—
588C22—2016no—
589C22—2016no—
590C22—202no—
591C22—202no—
592C22—202no—
593C22—202no—
594C22C2×#404014yes—
595C22#6589714yes—
596C22#6591514yes—
597C22#6594014yes—
598C22#6596314yes—
599C22#6602914yes—
600C22#6606614yes—
601C22C22×#70911yescharacteristic
602C22C22×D4×D511yescharacteristic
603C22C22×#71111yescharacteristic
604C22C22×#71311yescharacteristic
605C22C2×#414711yescharacteristic
606C22C2×D5×#4111yescharacteristic
607C22C2×#414911yescharacteristic
608C4—24no—
609C4—42no—
610C4—44no—
611C4—44no—
612C4—104no—
613C4—202no—
614C4—204no—
615C4—204no—
616C4C2×#404018yes—
617C2—204no—
618C2—204no—
619C2#1060796018yesdirect product factor
620C2C22×#404011yescharacteristic
621C2C2×#6589711yescharacteristic
622C2C2×#6591511yescharacteristic
623C2C2×#6594011yescharacteristic
624C2C2×#6596311yescharacteristic
625C2C2×#6602911yescharacteristic
626C2C2×#6606611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#389D5
hypocenterC5C2×#2485
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#4038C2semidirect
3. C2×C5×#389C2semidirect
5. C2×#65276C2semidirect
6. C2×#65276C2semidirect
7. C2×#65276C2semidirect
8. C2×#65270C2semidirect
9. C2×#65217C2semidirect
10. #10607960C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64958C2semidirect
32. C2×#4038C22semidirect
35. C5×#389C22semidirect
42. #65276C22semidirect
43. #65276C22semidirect
44. #65276C22semidirect
45. #65270C22semidirect
46. #65217C22semidirect
47. #64964C22semidirect
48. #64958C22semidirect
116. C2×#389D5semidirect
227. #389C2×D5semidirect
492. C2×C5#2485semidirect
577. C5C2×#2485semidirect
619. C2#10607960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40382
C22×C4×D202
C2×C5×#3892
C2×#652802
C2×#652762
C2×#652702
C2×#652172
#106079602
C2×#649642
C2×#649582
C2×#24855