Finite Group Databasebeta

← C2×#10601063 #12100960

Subgroups — C2×#10601063 #12100960

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4092C211yesmaximal, characteristic
2C23×C8×D5C211yesmaximal, characteristic
3C22×C5×#103C211yesmaximal, characteristic, complemented
4C22×#3967C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic
6C2×#64771C211yesmaximal, characteristic, complemented
7C2×#64749C211yesmaximal, characteristic, complemented
8#10601063C218yesmaximal, direct product factor
9C23×C5×Q8C2211yescharacteristic
10C23×C4×D5C2211yescharacteristic
11C23×C5×C8C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C2×#4092—22no—
14C2×#4092—24no—
15C2×#4092C418yescomplemented
16C2×#4092C2214yes—
17C22×#685—21no—
18C22×#685—21no—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683—21no—
22C23×#168C2211yescharacteristic
23C22×C8×D5—24no—
24C22×C8×D5—24no—
25C22×C8×D5—24no—
26C22×C8×D5C2214yes—
27C2×C5×#103—24no—
28C2×C5×#103C2214yescomplemented
29C2×#3967—24no—
30C2×#3967C2214yescomplemented
31C2×#3963—21no—
32#65276—22no—
33#65276C2214yes—
34#64771C2214yescomplemented
35#64749C2214yescomplemented
36C2×#1892—51nomaximal, Sylow
37C24×D5D411yescharacteristic
38C22×C5×Q8—22no—
39C22×C5×Q8—21no—
40C22×C5×Q8—22no—
41C22×C5×Q8—22no—
42C22×C5×Q8—22no—
43C22×C5×Q8—22no—
44C22×C5×Q8C2×C414yes—
45C22×C5×Q8C2312yes—
46C23×C4×C5—21no—
47C23×C4×C5—21no—
48C23×C4×C5C2311yescharacteristic
49C23×Dic5—21no—
50C23×Dic5—21no—
51C23×Dic5D411yescharacteristic
52C22×C4×D5—22no—
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5C2×C414yes—
57C22×C4×D5D412yes—
58C22×C4×D5D414yes—
59C22×C4×D5C2312yes—
60C22×C5×C8—22no—
61C22×C5×C8—22no—
62C22×C5×C8D414yes—
63C22×C5×C8C2312yes—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—22no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4C2312yes—
68#4092—216no—
69#4092—28no—
70#4092C2×C4116yescomplemented
71C2×#685—28no—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—44no—
75C2×C4⋊Dic5—21no—
76C2×C4⋊Dic5—22no—
77C2×C4⋊Dic5—22no—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5C2×C414yes—
81C2×C4⋊Dic5C2312yes—
82C2×C4⋊Dic5C2312yes—
83C2×#683—28no—
84C2×#683—24no—
85C22×#168—22no—
86C22×#168—22no—
87C22×#168D414yes—
88C22×#168C2312yes—
89C2×C8×D5—232no—
90C2×C8×D5—28no—
91C2×C8×D5—28no—
92C2×C8×D5—28no—
93C5×#103—28no—
94#3967—28no—
95#3963—24no—
96C24×C8—51no—
97C22×C22⋊Q8—51no—
98C22×#103—51no—
99C22×#103D511yescharacteristic, complemented
100C2×#380—51no—
101#1892—58no—
102C2×#340—51no—
103C2×#340—51no—
104C24×C5C2×D411yescharacteristic
105C23×D5—22no—
106C23×D5—22no—
107C23×D5—22no—
108C23×D5—22no—
109C23×D5C22⋊C414yes—
110C23×D5SD1614yes—
111C23×D5Q1614yes—
112C23×D5C2×D412yes—
113C2×C5×Q8—24no—
114C2×C5×Q8—22no—
115C2×C5×Q8—28no—
116C2×C5×Q8—28no—
117C2×C5×Q8—22no—
118C2×C5×Q8—22no—
119C2×C5×Q8—22no—
120C2×C5×Q8—22no—
121C2×C5×Q8—44no—
122C2×C5×Q8—42no—
123C2×C5×Q8—42no—
124C2×C5×Q8—44no—
125C2×C5×Q8C22×C414yes—
126C22×C4×C5—24no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—42no—
130C22×C4×C5—42no—
131C22×C4×C5—42no—
132C22×C4×C5—42no—
133C22×C4×C5—42no—
134C22×C4×C5C22×C412yes—
135C22×C4×C5C2×D411yescharacteristic
136C22×C4×C5C2×D412yes—
137C22×C4×C5C2×D412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5#4112yes—
140C22×C4×C5#4112yes—
141C22×C4×C5C2411yescharacteristic
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—24no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—42no—
148C22×Dic5—42no—
149C22×Dic5—42no—
150C22×Dic5—42no—
151C22×Dic5—42no—
152C22×Dic5C22⋊C414yes—
153C22×Dic5C2×D412yes—
154C2×C4×D5—28no—
155C2×C4×D5—28no—
156C2×C4×D5—28no—
157C2×C4×D5—24no—
158C2×C4×D5—24no—
159C2×C4×D5—28no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5C22⋊C418yes—
165C2×C4×D5C22×C414yes—
166C2×C4×D5C2×D414yes—
167C2×C5×C8—28no—
168C2×C5×C8—22no—
169C2×C5×C8—22no—
170C2×C5×C8C2×D414yes—
171C5×C4⋊C4—22no—
172C5×C4⋊C4—22no—
173C5×C4⋊C4—42no—
174#685—216no—
175#685—48no—
176C4⋊Dic5—24no—
177C4⋊Dic5—22no—
178C4⋊Dic5—22no—
179C4⋊Dic5—22no—
180C4⋊Dic5—42no—
181C4⋊Dic5C22×C414yes—
182#683—216no—
183C2×#168—28no—
184C2×#168—22no—
185C2×#168—22no—
186C2×#168C2×D414yes—
187C8×D5—232no—
188C23×Q8C2×D511yescharacteristic
189C24×C4—51no—
190C23×C8—51no—
191C23×C8—54no—
192C23×C8—104no—
193C23×C8—104no—
194C23×C8—104no—
195C23×C8C2×D511yescharacteristic
196C2×C22⋊Q8—58no—
197C2×C22⋊Q8—54no—
198C2×C22⋊Q8—104no—
199C2×C22⋊Q8—102no—
200C22×C4⋊C4—51no—
201C22×C4⋊C4—51no—
202C22×C4⋊C4—101no—
203C22×C4⋊C4C2×D511yescharacteristic
204C22×C22⋊C4—101no—
205C22×C22⋊C4—101no—
206C2×#103—24no—
207C2×#103—54no—
208C2×#103—104no—
209C2×#103C2×D514yescomplemented
210#380—54no—
211#380—102no—
212C2×#95—101no—
213#340—54no—
214#340—54no—
215C23×C5C2×C22⋊C412yes—
216C23×C5#12112yes—
217C23×C5#12112yes—
218C23×C5C2×SD1612yes—
219C23×C5C2×Q1612yes—
220C23×C5#13512yes—
221C23×C5#13512yes—
222C23×C5C22×D411yescharacteristic
223C22×D5—22no—
224C22×D5—22no—
225C22×D5—22no—
226C22×D5—22no—
227C22×D5—28no—
228C22×D5—28no—
229C22×D5—28no—
230C22×D5—28no—
231C22×D5—28no—
232C22×D5—28no—
233C22×D5#103116yescomplemented
234C22×D5C2×C22⋊C414yes—
235C22×D5C2×SD1614yes—
236C22×D5C2×Q1614yes—
237C5×Q8—24no—
238C5×Q8—24no—
239C5×Q8—42no—
240C5×Q8—42no—
241C5×Q8—48no—
242C2×C4×C5—24no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—48no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—84no—
250C2×C4×C5C2×C22⋊C412yes—
251C2×C4×C5C4×D414yes—
252C2×C4×C5C4×D414yes—
253C2×C4×C5#12014yes—
254C2×C4×C5#12112yes—
255C2×C4×C5#12112yes—
256C2×C4×C5#12314yes—
257C2×C4×C5C23×C411yescharacteristic
258C2×C4×C5C22×D411yescharacteristic
259C2×C4×C5C22×D411yescharacteristic
260C2×C4×C5C22×D411yescharacteristic
261C2×C4×C5C2×#4111yescharacteristic
262C2×C4×C5C2×#4111yescharacteristic
263C2×Dic5—22no—
264C2×Dic5—22no—
265C2×Dic5—28no—
266C2×Dic5—24no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—48no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—84no—
274C2×Dic5C2×C22⋊C414yes—
275C4×D5—24no—
276C4×D5—24no—
277C4×D5—24no—
278C4×D5—24no—
279C4×D5—216no—
280C5×C8—24no—
281#168—24no—
282C25—51no—
283C22×Q8—21no—
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8C4×D514yes—
290C22×Q8C22×D512yes—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—51no—
294C23×C4—54no—
295C23×C4—54no—
296C23×C4—52no—
297C23×C4—52no—
298C23×C4—102no—
299C23×C4—102no—
300C23×C4—102no—
301C23×C4—102no—
302C23×C4—101no—
303C23×C4—101no—
304C23×C4C22×D511yescharacteristic
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—54no—
308C22×C8—52no—
309C22×C8—108no—
310C22×C8—108no—
311C22×C8—1032no—
312C22×C8—102no—
313C22×C8—102no—
314C22×C8—108no—
315C22×C8C22⋊D514yes—
316C22×C8C22×D512yes—
317C22⋊Q8—516no—
318C22⋊Q8—108no—
319C22⋊Q8—1016no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—54no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—52no—
326C2×C4⋊C4—104no—
327C2×C4⋊C4—108no—
328C2×C4⋊C4—102no—
329C2×C4⋊C4—101no—
330C2×C4⋊C4—102no—
331C2×C4⋊C4—102no—
332C2×C4⋊C4—101no—
333C2×C4⋊C4C22×D512yes—
334C2×C22⋊C4—104no—
335C2×C22⋊C4—108no—
336C2×C22⋊C4—104no—
337C2×C22⋊C4—204no—
338#103—28no—
339#103—108no—
340#95—104no—
341C22×C5#38614yes—
342C22×C5C2×#10314yes—
343C22×C5#41614yes—
344C22×C5#46514yes—
345C22×C5#46514yes—
346C22×C5#46714yes—
347C22×C5#46714yes—
348C22×C5C22×C22⋊C411yescharacteristic
349C22×C5C2×#12111yescharacteristic
350C22×C5C2×#12111yescharacteristic
351C22×C5C22×SD1611yescharacteristic
352C22×C5C22×Q1611yescharacteristic
353C22×C5C2×#13511yescharacteristic
354C22×C5C2×#13511yescharacteristic
355C2×D5—24no—
356C2×D5—232no—
357C2×D5—24no—
358C2×D5—24no—
359C2×D5—24no—
360C2×D5—24no—
361C2×D5—24no—
362C2×D5C2×#10318yescomplemented
363C4×C5—44no—
364C4×C5—82no—
365C4×C5#38614yes—
366C4×C5C2×C4×D411yescharacteristic
367C4×C5C2×C4×D411yescharacteristic
368C4×C5C2×#12011yescharacteristic
369C4×C5C2×#12311yescharacteristic
370Dic5—24no—
371Dic5—44no—
372Dic5—82no—
373C24—52no—
374C24—54no—
375C24—54no—
376C24—54no—
377C24—102no—
378C24—102no—
379C24—102no—
380C24—102no—
381C24D4×D511yescharacteristic
382C2×Q8—22no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—28no—
389C2×Q8—28no—
390C2×Q8—44no—
391C2×Q8—42no—
392C2×Q8—44no—
393C2×Q8—42no—
394C2×Q8C2×C4×D514yes—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—52no—
404C22×C4—54no—
405C22×C4—54no—
406C22×C4—54no—
407C22×C4—58no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—102no—
413C22×C4—102no—
414C22×C4—108no—
415C22×C4—108no—
416C22×C4—104no—
417C22×C4—108no—
418C22×C4—108no—
419C22×C4—104no—
420C22×C4—102no—
421C22×C4—104no—
422C22×C4—102no—
423C22×C4—202no—
424C22×C4—202no—
425C22×C4—202no—
426C22×C4—202no—
427C22×C4—202no—
428C22×C4C2×C4×D512yes—
429C22×C4#70912yes—
430C22×C4D4×D512yes—
431C22×C4D4×D512yes—
432C22×C4D4×D511yescharacteristic
433C22×C4#71112yes—
434C22×C4C2×C22⋊D512yes—
435C22×C4C23×D511yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—28no—
439C2×C8—54no—
440C2×C8—1032no—
441C2×C8—102no—
442C2×C8—102no—
443C2×C8—108no—
444C2×C8C2×C22⋊D514yes—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—54no—
449C4⋊C4—1016no—
450C4⋊C4—102no—
451C4⋊C4—104no—
452C4⋊C4—102no—
453C4⋊C4—102no—
454C4⋊C4—202no—
455C22⋊C4—1016no—
456C22⋊C4—208no—
457C2×C5#189218yescomplemented
458C2×C5C2×#38611yescharacteristic
459C2×C5C22×#10311yescharacteristic
460C2×C5C2×#41611yescharacteristic
461C2×C5C2×#46511yescharacteristic
462C2×C5C2×#46511yescharacteristic
463C2×C5C2×#46711yescharacteristic
464C2×C5C2×#46711yescharacteristic
465D5—28no—
466C23—54no—
467C23—54no—
468C23—54no—
469C23—516no—
470C23—102no—
471C23—102no—
472C23—102no—
473C23—108no—
474C23—108no—
475C23—108no—
476C23—102no—
477C23—108no—
478C23—108no—
479C23—108no—
480C23D5×C22⋊C412yes—
481C23#403012yes—
482C23D5×SD1612yes—
483C23#406212yes—
484C23D5×Q1612yes—
485C23#406512yes—
486C23#408412yes—
487C23C2×D4×D511yescharacteristic
488Q8—24no—
489Q8—24no—
490Q8—42no—
491Q8—42no—
492Q8—48no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—48no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—54no—
501C2×C4—84no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—108no—
505C2×C4—104no—
506C2×C4—104no—
507C2×C4—104no—
508C2×C4—104no—
509C2×C4—1016no—
510C2×C4—104no—
511C2×C4—202no—
512C2×C4—202no—
513C2×C4—208no—
514C2×C4—202no—
515C2×C4—202no—
516C2×C4—202no—
517C2×C4—404no—
518C2×C4D5×C22⋊C412yes—
519C2×C4#402714yes—
520C2×C4#402914yes—
521C2×C4#403012yes—
522C2×C4C4×C22⋊D514yes—
523C2×C4#408314yes—
524C2×C4#408412yes—
525C2×C4C22×C4×D511yescharacteristic
526C2×C4C2×#70911yescharacteristic
527C2×C4C2×D4×D511yescharacteristic
528C2×C4C2×D4×D511yescharacteristic
529C2×C4C2×#71111yescharacteristic
530C2×C4C22×C22⋊D511yescharacteristic
531C8—24no—
532C8—104no—
533C5C2×#189211yescharacteristic, complemented, Sylow
534C22—58no—
535C22—104no—
536C22—104no—
537C22—104no—
538C22—104no—
539C22—104no—
540C22—104no—
541C22—1032no—
542C22D5×#10314yes—
543C22#6509314yes—
544C22#6509614yes—
545C22#6510214yes—
546C22#6524514yes—
547C22#6546014yes—
548C22#6547714yes—
549C22C2×D5×C22⋊C411yescharacteristic
550C22C2×#403011yescharacteristic
551C22C2×D5×SD1611yescharacteristic
552C22C2×#406211yescharacteristic
553C22C2×D5×Q1611yescharacteristic
554C22C2×#406511yescharacteristic
555C22C2×#408411yescharacteristic
556C4—44no—
557C4—82no—
558C4—104no—
559C4—204no—
560C4—402no—
561C4#6524514yes—
562C4C2×#402711yescharacteristic
563C4C2×#402911yescharacteristic
564C4C2×C4×C22⋊D511yescharacteristic
565C4C2×#408311yescharacteristic
566C2—108no—
567C2#1060106318yesdirect product factor
568C2C2×D5×#10311yescharacteristic
569C2C2×#6509311yescharacteristic
570C2C2×#6509611yescharacteristic
571C2C2×#6510211yescharacteristic
572C2C2×#6524511yescharacteristic
573C2C2×#6546011yescharacteristic
574C2C2×#6547711yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC22×C5×#103C2
socleC24×C5C2×D4
prime radicalC24×D5D4
cosocleC22×C4×C5C24
hypercenterC22×#103D5
hypocenterC5C2×#1892
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C22×C5×#103C2semidirect
4. C22×#3967C2semidirect
6. C2×#64771C2semidirect
7. C2×#64749C2semidirect
8. #10601063C2direct (N × H)
15. C2×#4092C4semidirect
28. C2×C5×#103C22semidirect
30. C2×#3967C22semidirect
34. #64771C22semidirect
35. #64749C22semidirect
70. #4092C2×C4semidirect
99. C22×#103D5semidirect
209. C2×#103C2×D5semidirect
233. C22×D5#103semidirect
362. C2×D5C2×#103semidirect
457. C2×C5#1892semidirect
533. C5C2×#1892semidirect
567. C2#10601063direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40922
C23×C8×D52
C22×C5×#1032
C22×#39672
C2×#652762
C2×#647712
C2×#647492
#106010632
C2×#18925