Finite Group Databasebeta

← C2×D5×#477 #12966779

Subgroups — C2×D5×#477 #12966779

Order 1280.

2358 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×C4×Q8×D5C211yesmaximal, characteristic
3C2×C5×#477C211yesmaximal, characteristic, complemented
4C2×#65380C211yesmaximal, characteristic, complemented
5C2×#65310C211yesmaximal, characteristic, complemented
6D5×#477C2116yesmaximal, direct product factor
7C2×#65164C212yesmaximal, complemented
8C2×D5×#107C212yesmaximal
9C2×#65139C211yesmaximal, characteristic, complemented
10C2×D5×C4⋊C8C211yesmaximal, characteristic
11C2×D5×#103C212yesmaximal
12C2×#65083C212yesmaximal, complemented
13C22×Q8×D5—21no—
14C22×Q8×D5C2211yescharacteristic
15C2×C5×C4⋊Q8C2211yescharacteristic
16C2×C4×C5×Q8C2211yescharacteristic
17C2×Q8×Dic5C2211yescharacteristic
18C2×#4090—21no—
19C22×C8×D5C2212yes—
20D5×C4⋊Q8—24no—
21D5×C4⋊Q8C2218yes—
22C4×Q8×D5—24no—
23C4×Q8×D5C2218yes—
24C2×D5×C4⋊C4—21no—
25C2×D5×C4⋊C4—21no—
26C2×D5×C4⋊C4C2212yes—
27C2×D5×C4⋊C4C2211yescharacteristic
28C2×#4034—21no—
29C2×#4034C2212yes—
30C2×#4033—21no—
31C2×#4033C2211yescharacteristic
32C2×C42×D5—21no—
33C2×C42×D5C2211yescharacteristic
34C2×#4015C2211yescharacteristic
35C2×C4×Dic10—21no—
36C2×C4×Dic10C2211yescharacteristic
37C5×#477C2218yescomplemented
38C2×C5×#107C2212yes—
39C2×C5×C4⋊C8C2211yescharacteristic
40C2×C5×#103C2212yes—
41C2×#3967C2212yes—
42C2×#3950C2212yes—
43C2×#3948C2212yes—
44C2×#3946C2212yes—
45#65380C2218yescomplemented
46#65310C2218yescomplemented
47C2×#3942C2212yes—
48C2×#3939C2212yes—
49C2×#3939C2212yes—
50C2×C4⋊#168C2211yescharacteristic
51D5×#107C22116yes—
52#65164C22116yescomplemented
53#65139C2218yescomplemented
54D5×C4⋊C8C2218yes—
55D5×#103C22116yes—
56#65083C22116yescomplemented
57C22×#477—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C5×Q8C2311yescharacteristic
60C2×Q8×D5—22no—
61C2×Q8×D5—28no—
62C2×Q8×D5—24no—
63C2×Q8×D5—48no—
64C2×Q8×D5Q818yescomplemented
65C2×Q8×D5C2314yes—
66C22×C4×D5—21no—
67C22×C4×D5—21no—
68C22×C4×D5—22no—
69C22×C4×D5D411yescharacteristic
70C22×C4×D5D411yescharacteristic
71C22×C4×D5C2311yescharacteristic
72C22×Dic10—21no—
73C22×Dic10—21no—
74C22×Dic10—22no—
75C22×Dic10C2311yescharacteristic
76C22×C5×C8C2312yes—
77C5×C4⋊Q8—22no—
78C5×C4⋊Q8C2314yes—
79C4×C5×Q8—22no—
80C4×C5×Q8C2314yes—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4C2311yescharacteristic
84C2×C5×C4⋊C4C2312yes—
85C2×C42×C5—21no—
86C2×C42×C5C2311yescharacteristic
87Q8×Dic5—22no—
88Q8×Dic5C2314yes—
89#4090—28no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2312yes—
94C2×#683—21no—
95C2×#683—21no—
96C2×#683—21no—
97C2×#683—22no—
98C2×#683—22no—
99C2×C4×Dic5—21no—
100C2×C4×Dic5—21no—
101C2×C4×Dic5—21no—
102C2×C4×Dic5D411yescharacteristic
103C2×C4×Dic5D411yescharacteristic
104C2×C4×Dic5C2311yescharacteristic
105C22×#168C2312yes—
106C2×C8×D5—28no—
107C2×C8×D5C2318yes—
108D5×C4⋊C4—24no—
109D5×C4⋊C4—28no—
110D5×C4⋊C4—28no—
111D5×C4⋊C4—22no—
112D5×C4⋊C4C2318yes—
113D5×C4⋊C4C2314yes—
114#4034—24no—
115#4034—28no—
116#4034C2318yes—
117#4033—28no—
118#4033—22no—
119#4033C2314yes—
120C42×D5—28no—
121C42×D5D414yes—
122C42×D5C2314yes—
123#4015—22no—
124#4015C2314yes—
125C4×Dic10—22no—
126C4×Dic10—28no—
127C4×Dic10C2314yes—
128C5×#107C2318yes—
129C5×C4⋊C8C2314yes—
130C5×#103C2318yes—
131#3967C2318yes—
132#3950C2318yes—
133#3948C2318yes—
134#3946C2318yes—
135#3942C2318yes—
136#3939C2318yes—
137#3939C2318yes—
138C4⋊#168C2314yes—
139C22×C4⋊Q8—51no—
140C22×C4×Q8—51no—
141C2×#477—516no—
142C2×#477—52no—
143C2×#477—51no—
144C2×#477—52no—
145C2×#477—51no—
146C2×#477—51no—
147C2×#477D511yescharacteristic, direct product factor
148C22×#107—52no—
149C22×C4⋊C8—51no—
150C22×#103—52no—
151C23×D5C2×D411yescharacteristic
152C2×C5×Q8—21no—
153C2×C5×Q8—24no—
154C2×C5×Q8—22no—
155C2×C5×Q8—44no—
156C2×C5×Q8C2×Q814yescomplemented
157C2×C5×Q8C2412yes—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2411yescharacteristic
164C22×Dic5—21no—
165C22×Dic5—22no—
166C22×Dic5—21no—
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C22×Dic5C2×D411yescharacteristic
170Q8×D5—216no—
171Q8×D5—28no—
172Q8×D5—432no—
173Q8×D5C2×Q8116yescomplemented
174C2×C4×D5—28no—
175C2×C4×D5—24no—
176C2×C4×D5—24no—
177C2×C4×D5—28no—
178C2×C4×D5—24no—
179C2×C4×D5—44no—
180C2×C4×D5—48no—
181C2×C4×D5Q1618yes—
182C2×C4×D5C2×D414yes—
183C2×C4×D5C2×D412yes—
184C2×C4×D5C2×D414yes—
185C2×C4×D5C2×Q814yes—
186C2×C4×D5#4114yes—
187C2×C4×D5C2412yes—
188C2×Dic10—21no—
189C2×Dic10—22no—
190C2×Dic10—28no—
191C2×Dic10—24no—
192C2×Dic10—24no—
193C2×Dic10—28no—
194C2×Dic10—48no—
195C2×Dic10—44no—
196C2×Dic10C2×Q814yescomplemented
197C2×Dic10C2412yes—
198C2×C5×C8—24no—
199C2×C5×C8C2414yes—
200C5×C4⋊C4—24no—
201C5×C4⋊C4—24no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4C2412yes—
205C5×C4⋊C4C2414yes—
206C42×C5—24no—
207C42×C5C2×D412yes—
208C42×C5C2412yes—
209C4⋊Dic5—21no—
210C4⋊Dic5—22no—
211C4⋊Dic5—24no—
212C4⋊Dic5—24no—
213C4⋊Dic5C2412yes—
214C4⋊Dic5C2414yes—
215#683—24no—
216#683—24no—
217#683—24no—
218#683—28no—
219#683—28no—
220C4×Dic5—24no—
221C4×Dic5—24no—
222C4×Dic5—24no—
223C4×Dic5C2×D414yes—
224C4×Dic5C2×D412yes—
225C4×Dic5C2×D414yes—
226C4×Dic5C2412yes—
227C2×#168—24no—
228C2×#168C2414yes—
229C8×D5—216no—
230C23×Q8—51no—
231C23×Q8—101no—
232C23×C8—52no—
233C2×C4⋊Q8—58no—
234C2×C4⋊Q8—52no—
235C2×C4⋊Q8—51no—
236C2×C4⋊Q8—101no—
237C2×C4⋊Q8—104no—
238C2×C4⋊Q8—101no—
239C2×C4⋊Q8C2×D511yescharacteristic
240C2×C4×Q8—51no—
241C2×C4×Q8—58no—
242C2×C4×Q8—51no—
243C2×C4×Q8—51no—
244C2×C4×Q8—101no—
245C2×C4×Q8—101no—
246C2×C4×Q8—104no—
247C2×C4×Q8C2×D511yescharacteristic
248C22×C4⋊C4—52no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—101no—
251C22×C4⋊C4—101no—
252C22×C42—51no—
253C22×C42—101no—
254#477—58no—
255#477—58no—
256#477—516no—
257#477—58no—
258#477—516no—
259#477C2×D518yesdirect product factor
260C2×#107—52no—
261C2×#107—52no—
262C2×#107—52no—
263C2×#107—516no—
264C2×#107C2×D512yes—
265C2×C4⋊C8—52no—
266C2×C4⋊C8—51no—
267C2×C4⋊C8—58no—
268C2×C4⋊C8C2×D511yescharacteristic
269C2×#103—52no—
270C2×#103—52no—
271C2×#103—52no—
272C2×#103—516no—
273C2×#103C2×D512yes—
274C23×C5C22×D411yescharacteristic
275C22×D5C22⋊Q814yes—
276C22×D5C2×Q1614yes—
277C22×D5AGL(1,ℤ/8)14yes—
278C22×D5C22×D412yes—
279C5×Q8—24no—
280C5×Q8—22no—
281C5×Q8—48no—
282C5×Q8C22×Q814yescomplemented
283C2×C4×C5—24no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—24no—
288C2×C4×C5—44no—
289C2×C4×C5—42no—
290C2×C4×C5C2×Q1614yes—
291C2×C4×C5C22×D412yes—
292C2×C4×C5C22×D411yescharacteristic
293C2×C4×C5C22×D412yes—
294C2×C4×C5C22×Q812yes—
295C2×C4×C5C2×#4112yes—
296C2×C4×C5C2511yescharacteristic
297C2×Dic5—24no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—24no—
302C2×Dic5—44no—
303C2×Dic5—42no—
304C2×Dic5C22⋊Q814yes—
305C2×Dic5C2×Q1614yes—
306C2×Dic5C22×D412yes—
307C2×Dic5C22×D412yes—
308C2×Dic5C22×D412yes—
309C4×D5—216no—
310C4×D5—28no—
311C4×D5—48no—
312C4×D5—416no—
313C4×D5C22⋊Q818yes—
314C4×D5C2×Q16116yes—
315C4×D5C22×Q814yes—
316C4×D5C2×#4114yes—
317Dic10—24no—
318Dic10—22no—
319Dic10—216no—
320Dic10—416no—
321Dic10—48no—
322Dic10C22×Q814yescomplemented
323C5×C8—24no—
324#168—24no—
325C22×Q8—21no—
326C22×Q8—58no—
327C22×Q8—54no—
328C22×Q8—51no—
329C22×Q8—101no—
330C22×Q8—102no—
331C22×Q8—102no—
332C22×Q8—104no—
333C22×Q8—108no—
334C22×Q8—101no—
335C22×Q8—208no—
336C22×Q8C22×D511yescharacteristic
337C23×C4—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—101no—
341C23×C4—102no—
342C23×C4—101no—
343C22×C8—52no—
344C22×C8—58no—
345C22×C8—108no—
346C22×C8C22×D512yes—
347C4⋊Q8—22no—
348C4⋊Q8—58no—
349C4⋊Q8—54no—
350C4⋊Q8—108no—
351C4⋊Q8—104no—
352C4⋊Q8—108no—
353C4⋊Q8—102no—
354C4⋊Q8C22×D514yes—
355C4×Q8—22no—
356C4×Q8—54no—
357C4×Q8—54no—
358C4×Q8—54no—
359C4×Q8—108no—
360C4×Q8—108no—
361C4×Q8—102no—
362C4×Q8—102no—
363C4×Q8—102no—
364C4×Q8C22×D514yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—52no—
369C2×C4⋊C4—54no—
370C2×C4⋊C4—58no—
371C2×C4⋊C4—102no—
372C2×C4⋊C4—104no—
373C2×C4⋊C4—108no—
374C2×C4⋊C4—108no—
375C2×C4⋊C4—101no—
376C2×C4⋊C4—102no—
377C2×C4⋊C4—101no—
378C2×C4⋊C4—101no—
379C2×C4⋊C4—102no—
380C2×C4⋊C4—101no—
381C2×C4⋊C4—101no—
382C2×C4⋊C4C22×D511yescharacteristic
383C2×C4⋊C4C22×D512yes—
384C2×C42—21no—
385C2×C42—51no—
386C2×C42—51no—
387C2×C42—51no—
388C2×C42—54no—
389C2×C42—54no—
390C2×C42—108no—
391C2×C42—101no—
392C2×C42—101no—
393C2×C42—101no—
394C2×C42C22×D511yescharacteristic
395#107—58no—
396#107—58no—
397#107—58no—
398#107C22×D518yes—
399C4⋊C8—58no—
400C4⋊C8—54no—
401C4⋊C8C22×D514yes—
402#103—58no—
403#103—58no—
404#103—58no—
405#103C22×D518yes—
406C22×C5C2×C22⋊Q812yes—
407C22×C5C22×Q1612yes—
408C22×C5C2×AGL(1,ℤ/8)12yes—
409C22×C5C23×D411yescharacteristic
410C2×D5#477116yesdirect product factor
411C2×D5C2×C22⋊Q814yes—
412C2×D5C22×Q1614yes—
413C2×D5C2×AGL(1,ℤ/8)14yes—
414C4×C5—24no—
415C4×C5—22no—
416C4×C5—44no—
417C4×C5—42no—
418C4×C5C2×C22⋊Q812yes—
419C4×C5C22×Q1614yes—
420C4×C5C23×Q811yescharacteristic
421C4×C5C22×#4111yescharacteristic
422Dic5—24no—
423Dic5—22no—
424Dic5—44no—
425Dic5—42no—
426Dic5C2×C22⋊Q814yes—
427Dic5C22×Q1614yes—
428C24—51no—
429C2×Q8—21no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—44no—
433C2×Q8—516no—
434C2×Q8—54no—
435C2×Q8—52no—
436C2×Q8—104no—
437C2×Q8—108no—
438C2×Q8—108no—
439C2×Q8—1016no—
440C2×Q8—108no—
441C2×Q8—101no—
442C2×Q8—104no—
443C2×Q8—102no—
444C2×Q8—204no—
445C2×Q8—208no—
446C2×Q8—2032no—
447C2×Q8Q8×D514yescomplemented
448C2×Q8C23×D512yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—51no—
453C22×C4—51no—
454C22×C4—54no—
455C22×C4—52no—
456C22×C4—54no—
457C22×C4—54no—
458C22×C4—52no—
459C22×C4—58no—
460C22×C4—51no—
461C22×C4—54no—
462C22×C4—104no—
463C22×C4—104no—
464C22×C4—108no—
465C22×C4—104no—
466C22×C4—108no—
467C22×C4—101no—
468C22×C4—101no—
469C22×C4—102no—
470C22×C4—208no—
471C22×C4—204no—
472C22×C4D4×D511yescharacteristic
473C22×C4D4×D511yescharacteristic
474C22×C4C23×D511yescharacteristic
475C2×C8—24no—
476C2×C8—54no—
477C2×C8—1016no—
478C2×C8—104no—
479C2×C8C23×D514yes—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—54no—
485C4⋊C4—52no—
486C4⋊C4—104no—
487C4⋊C4—108no—
488C4⋊C4—104no—
489C4⋊C4—104no—
490C4⋊C4—108no—
491C4⋊C4—101no—
492C4⋊C4—102no—
493C4⋊C4—104no—
494C4⋊C4—104no—
495C4⋊C4C23×D514yes—
496C4⋊C4C23×D512yes—
497C42—24no—
498C42—54no—
499C42—52no—
500C42—54no—
501C42—52no—
502C42—104no—
503C42—104no—
504C42—104no—
505C42D4×D512yes—
506C42C23×D512yes—
507C2×C5C2×#47714yescomplemented
508C2×C5C22×C22⋊Q811yescharacteristic
509C2×C5C23×Q1611yescharacteristic
510C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
511D5C2×#47718yesdirect product factor
512C23—54no—
513C23—54no—
514C23—54no—
515C23—52no—
516C23C2×D4×D511yescharacteristic
517Q8—24no—
518Q8—22no—
519Q8—48no—
520Q8—54no—
521Q8—1016no—
522Q8—104no—
523Q8—102no—
524Q8—208no—
525Q8—2016no—
526Q8C2×Q8×D514yescomplemented
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—54no—
535C2×C4—54no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—516no—
539C2×C4—58no—
540C2×C4—54no—
541C2×C4—54no—
542C2×C4—52no—
543C2×C4—108no—
544C2×C4—1016no—
545C2×C4—102no—
546C2×C4—104no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—104no—
550C2×C4—2016no—
551C2×C4—208no—
552C2×C4—204no—
553C2×C4—202no—
554C2×C4D5×Q1614yes—
555C2×C4C2×D4×D512yes—
556C2×C4C2×D4×D512yes—
557C2×C4C2×D4×D511yescharacteristic
558C2×C4C2×Q8×D512yes—
559C2×C4D5×#4112yes—
560C2×C4C24×D511yescharacteristic
561C8—24no—
562C8—104no—
563C5C22×#47711yescharacteristic, complemented, Sylow
564C22—54no—
565C22—516no—
566C22—54no—
567C22—54no—
568C22D5×C22⋊Q812yes—
569C22C2×D5×Q1612yes—
570C22D5×AGL(1,ℤ/8)12yes—
571C22C22×D4×D511yescharacteristic
572C4—24no—
573C4—22no—
574C4—44no—
575C4—42no—
576C4—54no—
577C4—54no—
578C4—104no—
579C4—102no—
580C4—204no—
581C4—202no—
582C4D5×C22⋊Q812yes—
583C4C2×D5×Q1614yes—
584C4C22×Q8×D511yescharacteristic
585C4C2×D5×#4111yescharacteristic
586C2—58no—
587C2D5×#47714yesdirect product factor
588C2C2×D5×C22⋊Q811yescharacteristic
589C2C22×D5×Q1611yescharacteristic
590C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#477C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#477D5
hypocenterC5C22×#477
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. C2×C5×#477C2semidirect
4. C2×#65380C2semidirect
5. C2×#65310C2semidirect
6. D5×#477C2direct (N × H)
7. C2×#65164C2semidirect
9. C2×#65139C2semidirect
12. C2×#65083C2semidirect
37. C5×#477C22semidirect
45. #65380C22semidirect
46. #65310C22semidirect
52. #65164C22semidirect
53. #65139C22semidirect
56. #65083C22semidirect
64. C2×Q8×D5Q8semidirect
147. C2×#477D5direct (N × H)
156. C2×C5×Q8C2×Q8semidirect
173. Q8×D5C2×Q8semidirect
196. C2×Dic10C2×Q8semidirect
259. #477C2×D5direct (N × H)
282. C5×Q8C22×Q8semidirect
322. Dic10C22×Q8semidirect
410. C2×D5#477direct (N × H)
447. C2×Q8Q8×D5semidirect
507. C2×C5C2×#477semidirect
511. D5C2×#477direct (N × H)
526. Q8C2×Q8×D5semidirect
563. C5C22×#477semidirect
587. C2D5×#477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×C4×Q8×D52
C2×C5×#4772
C2×#653802
C2×#653102
D5×#4772
C2×#651642
C2×D5×#1072
C2×#651392
C2×D5×C4⋊C82
C2×D5×#1032
C2×#650832
C22×#4775