Finite Group Databasebeta

← C2×D5×#501 #12968906

Subgroups — C2×D5×#501 #12968906

Order 1280.

2142 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×D5×#125C211yesmaximal, characteristic
3C2×C5×#501C211yesmaximal, characteristic, complemented
4C2×#65369C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6D5×#501C2116yesmaximal, direct product factor
7C2×D5×#107C212yesmaximal
8C2×#65165C212yesmaximal, complemented
9C2×D5×#106C212yesmaximal
10C2×#65145C212yesmaximal, complemented
11C2×D5×#97C211yesmaximal, characteristic
12C2×#64991C211yesmaximal, characteristic, complemented
13C22×Q8×D5—21no—
14C2×C5×C4⋊Q8C2211yescharacteristic
15C2×C5×#125C2211yescharacteristic
16C2×#4090—21no—
17C22×C8×D5C2212yes—
18D5×C4⋊Q8—24no—
19D5×C4⋊Q8C2218yes—
20D5×#125—24no—
21D5×#125C2218yes—
22C2×D5×C4⋊C4—21no—
23C2×D5×C4⋊C4—21no—
24C2×D5×C4⋊C4—21no—
25C2×D5×C4⋊C4C2211yescharacteristic
26C2×D5×C4⋊C4C2211yescharacteristic
27C2×D5×C4⋊C4C2212yes—
28C2×#4036C2211yescharacteristic
29C2×#4036C2211yescharacteristic
30C2×#4035—21no—
31C2×#4035—21no—
32C2×#4034—21no—
33C2×#4034C2212yes—
34C2×C42×D5C2211yescharacteristic
35C2×#4016C2211yescharacteristic
36C2×#4015C2211yescharacteristic
37C5×#501C2218yescomplemented
38C2×C5×#107C2212yes—
39C2×C5×#106C2212yes—
40C2×C5×#97C2211yescharacteristic
41C2×#3950C2212yes—
42C2×#3949C2212yes—
43C2×#3947C2212yes—
44#65369C2218yescomplemented
45#65354C2218yescomplemented
46C2×#3940C2212yes—
47C2×#3940C2212yes—
48C2×#3939C2212yes—
49C2×#3939C2212yes—
50C2×#3935C2211yescharacteristic
51D5×#107C22116yes—
52#65165C22116yescomplemented
53D5×#106C22116yes—
54#65145C22116yescomplemented
55D5×#97C2218yes—
56#64991C2218yescomplemented
57C22×#501—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C2×Q8×D5—28no—
60C2×Q8×D5—48no—
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5—22no—
64C22×C4×D5D411yescharacteristic
65C22×C4×D5D411yescharacteristic
66C22×C4×D5C2311yescharacteristic
67C22×Dic10—21no—
68C22×Dic10—22no—
69C22×C5×C8C2312yes—
70C5×C4⋊Q8—22no—
71C5×C4⋊Q8C2314yes—
72C5×#125—22no—
73C5×#125C2314yes—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4C2312yes—
78C2×C5×C4⋊C4C2311yescharacteristic
79C2×C5×C4⋊C4C2311yescharacteristic
80C2×C42×C5C2311yescharacteristic
81#4090—28no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5C2312yes—
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×#683—21no—
89C2×#683—21no—
90C2×#683—22no—
91C2×#683—22no—
92C2×#683—21no—
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×C4×Dic5D411yescharacteristic
97C2×C4×Dic5D411yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99C22×#168C2312yes—
100C2×C8×D5Q8116yescomplemented
101C2×C8×D5C2318yes—
102D5×C4⋊C4—24no—
103D5×C4⋊C4—28no—
104D5×C4⋊C4—28no—
105D5×C4⋊C4—28no—
106D5×C4⋊C4—22no—
107D5×C4⋊C4—22no—
108D5×C4⋊C4C2318yes—
109D5×C4⋊C4C2314yes—
110D5×C4⋊C4C2314yes—
111#4036—22no—
112#4036—22no—
113#4036C2314yes—
114#4036C2314yes—
115#4035—28no—
116#4035—28no—
117#4034—24no—
118#4034—28no—
119#4034C2318yes—
120C42×D5D414yes—
121C42×D5C2314yes—
122#4016—22no—
123#4016C2314yes—
124#4015—22no—
125#4015C2314yes—
126C5×#107C2318yes—
127C5×#106C2318yes—
128C5×#97C2314yes—
129#3950C2318yes—
130#3949C2318yes—
131#3947C2318yes—
132#3940C2318yes—
133#3940C2318yes—
134#3939C2318yes—
135#3939C2318yes—
136#3935C2314yes—
137C22×C4⋊Q8—51no—
138C22×#125—51no—
139C2×#501—516no—
140C2×#501—52no—
141C2×#501—52no—
142C2×#501—51no—
143C2×#501—51no—
144C2×#501—51no—
145C2×#501D511yescharacteristic, direct product factor
146C22×#107—52no—
147C22×#106—52no—
148C22×#97—51no—
149C23×D5C2×D411yescharacteristic
150C2×C5×Q8—24no—
151C2×C5×Q8—44no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2411yescharacteristic
158C22×Dic5—22no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C22×Dic5C2×D411yescharacteristic
164Q8×D5—432no—
165C2×C4×D5—24no—
166C2×C4×D5—24no—
167C2×C4×D5—28no—
168C2×C4×D5—24no—
169C2×C4×D5—24no—
170C2×C4×D5—44no—
171C2×C4×D5—48no—
172C2×C4×D5—44no—
173C2×C4×D5C2×D414yes—
174C2×C4×D5C2×D414yes—
175C2×C4×D5C2×D412yes—
176C2×C4×D5C2×Q818yes—
177C2×C4×D5C2412yes—
178C2×Dic10—24no—
179C2×Dic10—28no—
180C2×Dic10—48no—
181C2×Dic10—44no—
182C2×C5×C8C2×Q818yescomplemented
183C2×C5×C8C2414yes—
184C5×C4⋊C4—24no—
185C5×C4⋊C4—24no—
186C5×C4⋊C4—24no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4C2412yes—
191C5×C4⋊C4C2412yes—
192C5×C4⋊C4C2414yes—
193C42×C5C2×D412yes—
194C42×C5C2412yes—
195C4⋊Dic5—22no—
196C4⋊Dic5—24no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—24no—
200C4⋊Dic5—24no—
201C4⋊Dic5C2412yes—
202C4⋊Dic5C2414yes—
203C4⋊Dic5C2412yes—
204#683—24no—
205#683—24no—
206#683—28no—
207#683—28no—
208#683—24no—
209#683—24no—
210#683—24no—
211#683—24no—
212C4×Dic5C2×D412yes—
213C4×Dic5C2×D414yes—
214C4×Dic5C2×D414yes—
215C4×Dic5C2412yes—
216C2×#168C2×Q818yescomplemented
217C2×#168C2414yes—
218C8×D5C2×Q8132yescomplemented
219C23×Q8—101no—
220C23×C8—52no—
221C2×C4⋊Q8—58no—
222C2×C4⋊Q8—52no—
223C2×C4⋊Q8—51no—
224C2×C4⋊Q8—101no—
225C2×C4⋊Q8—104no—
226C2×C4⋊Q8—101no—
227C2×C4⋊Q8C2×D511yescharacteristic
228C2×#125—58no—
229C2×#125—51no—
230C2×#125—51no—
231C2×#125—51no—
232C2×#125—101no—
233C2×#125—101no—
234C2×#125—104no—
235C2×#125C2×D511yescharacteristic
236C22×C4⋊C4—51no—
237C22×C4⋊C4—52no—
238C22×C4⋊C4—51no—
239C22×C4⋊C4—101no—
240C22×C4⋊C4—101no—
241C22×C4⋊C4—101no—
242C22×C42—51no—
243#501—58no—
244#501—58no—
245#501—516no—
246#501—516no—
247#501—58no—
248#501C2×D518yesdirect product factor
249C2×#107—52no—
250C2×#107—52no—
251C2×#107—52no—
252C2×#107—516no—
253C2×#107C2×D512yes—
254C2×#106—52no—
255C2×#106—52no—
256C2×#106—52no—
257C2×#106—516no—
258C2×#106C2×D512yes—
259C2×#97—52no—
260C2×#97—51no—
261C2×#97—58no—
262C2×#97C2×D511yescharacteristic
263C23×C5C22×D411yescharacteristic
264C22×D5C4⋊Q814yes—
265C22×D5AGL(1,ℤ/8)14yes—
266C22×D5#13714yes—
267C22×D5C22×D412yes—
268C5×Q8—48no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—24no—
274C2×C4×C5—44no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5C22×D412yes—
278C2×C4×C5C22×D412yes—
279C2×C4×C5C22×D411yescharacteristic
280C2×C4×C5C22×Q814yes—
281C2×C4×C5C2511yescharacteristic
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—24no—
287C2×Dic5—44no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5C4⋊Q814yes—
291C2×Dic5C22×D412yes—
292C2×Dic5C22×D412yes—
293C2×Dic5C22×D412yes—
294C4×D5—28no—
295C4×D5—28no—
296C4×D5—48no—
297C4×D5—416no—
298C4×D5—48no—
299C4×D5C4⋊Q818yes—
300C4×D5C22×Q818yes—
301Dic10—416no—
302Dic10—48no—
303C5×C8C22×Q818yescomplemented
304#168C22×Q818yescomplemented
305C22×Q8—21no—
306C22×Q8—102no—
307C22×Q8—108no—
308C22×Q8—101no—
309C22×Q8—208no—
310C23×C4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—101no—
314C23×C4—101no—
315C23×C4—102no—
316C22×C8—52no—
317C22×C8—516no—
318C22×C8—58no—
319C22×C8C22×D512yes—
320C4⋊Q8—22no—
321C4⋊Q8—58no—
322C4⋊Q8—54no—
323C4⋊Q8—108no—
324C4⋊Q8—104no—
325C4⋊Q8—108no—
326C4⋊Q8—102no—
327C4⋊Q8C22×D514yes—
328#125—22no—
329#125—54no—
330#125—54no—
331#125—54no—
332#125—108no—
333#125—108no—
334#125—102no—
335#125—102no—
336#125—102no—
337#125C22×D514yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—54no—
345C2×C4⋊C4—54no—
346C2×C4⋊C4—58no—
347C2×C4⋊C4—102no—
348C2×C4⋊C4—102no—
349C2×C4⋊C4—104no—
350C2×C4⋊C4—108no—
351C2×C4⋊C4—108no—
352C2×C4⋊C4—108no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4—102no—
356C2×C4⋊C4—101no—
357C2×C4⋊C4—101no—
358C2×C4⋊C4—101no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4—102no—
361C2×C4⋊C4—101no—
362C2×C4⋊C4—101no—
363C2×C4⋊C4—101no—
364C2×C4⋊C4C22×D511yescharacteristic
365C2×C4⋊C4C22×D511yescharacteristic
366C2×C4⋊C4C22×D512yes—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42—51no—
370C2×C42—54no—
371C2×C42—54no—
372C2×C42C22×D511yescharacteristic
373#107—58no—
374#107—58no—
375#107—58no—
376#107C22×D518yes—
377#106—58no—
378#106—58no—
379#106—58no—
380#106C22×D518yes—
381#97—58no—
382#97—54no—
383#97C22×D514yes—
384C22×C5C2×C4⋊Q812yes—
385C22×C5C2×AGL(1,ℤ/8)12yes—
386C22×C5C2×#13712yes—
387C22×C5C23×D411yescharacteristic
388C2×D5#501116yesdirect product factor
389C2×D5C2×C4⋊Q814yes—
390C2×D5C2×AGL(1,ℤ/8)14yes—
391C2×D5C2×#13714yes—
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—44no—
395C4×C5—42no—
396C4×C5—42no—
397C4×C5C2×C4⋊Q812yes—
398C4×C5C23×Q812yes—
399Dic5—22no—
400Dic5—22no—
401Dic5—44no—
402Dic5—42no—
403Dic5—42no—
404Dic5C2×C4⋊Q814yes—
405C24—51no—
406C2×Q8—24no—
407C2×Q8—44no—
408C2×Q8—108no—
409C2×Q8—104no—
410C2×Q8—204no—
411C2×Q8—208no—
412C2×Q8—2032no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—51no—
417C22×C4—52no—
418C22×C4—58no—
419C22×C4—52no—
420C22×C4—51no—
421C22×C4—51no—
422C22×C4—54no—
423C22×C4—54no—
424C22×C4—104no—
425C22×C4—104no—
426C22×C4—104no—
427C22×C4—104no—
428C22×C4—108no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—102no—
432C22×C4—208no—
433C22×C4—204no—
434C22×C4—204no—
435C22×C4D4×D511yescharacteristic
436C22×C4D4×D511yescharacteristic
437C22×C4C23×D511yescharacteristic
438C2×C8—58no—
439C2×C8—54no—
440C2×C8—532no—
441C2×C8Q8×D518yescomplemented
442C2×C8C23×D514yes—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—52no—
450C4⋊C4—54no—
451C4⋊C4—52no—
452C4⋊C4—104no—
453C4⋊C4—104no—
454C4⋊C4—108no—
455C4⋊C4—104no—
456C4⋊C4—104no—
457C4⋊C4—104no—
458C4⋊C4—104no—
459C4⋊C4—108no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—102no—
463C4⋊C4—104no—
464C4⋊C4—104no—
465C4⋊C4—104no—
466C4⋊C4C23×D512yes—
467C4⋊C4C23×D514yes—
468C4⋊C4C23×D512yes—
469C42—54no—
470C42—54no—
471C42—52no—
472C42—52no—
473C42D4×D512yes—
474C42C23×D512yes—
475C2×C5C2×#50114yescomplemented
476C2×C5C22×C4⋊Q811yescharacteristic
477C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
478C2×C5C22×#13711yescharacteristic
479D5C2×#50118yesdirect product factor
480C23—54no—
481C23—54no—
482C23—54no—
483C23—52no—
484C23C2×D4×D511yescharacteristic
485Q8—48no—
486Q8—208no—
487Q8—2016no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—54no—
497C2×C4—52no—
498C2×C4—58no—
499C2×C4—58no—
500C2×C4—52no—
501C2×C4—52no—
502C2×C4—108no—
503C2×C4—108no—
504C2×C4—102no—
505C2×C4—102no—
506C2×C4—102no—
507C2×C4—102no—
508C2×C4—104no—
509C2×C4—2016no—
510C2×C4—208no—
511C2×C4—208no—
512C2×C4—204no—
513C2×C4—202no—
514C2×C4—202no—
515C2×C4C2×D4×D512yes—
516C2×C4C2×D4×D512yes—
517C2×C4C2×D4×D511yescharacteristic
518C2×C4C2×Q8×D514yes—
519C2×C4C24×D511yescharacteristic
520C8—58no—
521C8C2×Q8×D518yescomplemented
522C5C22×#50111yescharacteristic, complemented, Sylow
523C22—516no—
524C22—54no—
525C22—54no—
526C22—54no—
527C22D5×C4⋊Q812yes—
528C22D5×AGL(1,ℤ/8)12yes—
529C22D5×#13712yes—
530C22C22×D4×D511yescharacteristic
531C4—22no—
532C4—22no—
533C4—44no—
534C4—42no—
535C4—42no—
536C4—54no—
537C4—102no—
538C4—102no—
539C4—204no—
540C4—202no—
541C4—202no—
542C4D5×C4⋊Q812yes—
543C4C22×Q8×D512yes—
544C2—58no—
545C2D5×#50114yesdirect product factor
546C2C2×D5×C4⋊Q811yescharacteristic
547C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
548C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#501C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#501D5
hypocenterC5C22×#501
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×C5×#501C2semidirect
4. C2×#65369C2semidirect
5. C2×#65354C2semidirect
6. D5×#501C2direct (N × H)
8. C2×#65165C2semidirect
10. C2×#65145C2semidirect
12. C2×#64991C2semidirect
37. C5×#501C22semidirect
44. #65369C22semidirect
45. #65354C22semidirect
52. #65165C22semidirect
54. #65145C22semidirect
56. #64991C22semidirect
100. C2×C8×D5Q8semidirect
145. C2×#501D5direct (N × H)
182. C2×C5×C8C2×Q8semidirect
216. C2×#168C2×Q8semidirect
218. C8×D5C2×Q8semidirect
248. #501C2×D5direct (N × H)
303. C5×C8C22×Q8semidirect
304. #168C22×Q8semidirect
388. C2×D5#501direct (N × H)
441. C2×C8Q8×D5semidirect
475. C2×C5C2×#501semidirect
479. D5C2×#501direct (N × H)
521. C8C2×Q8×D5semidirect
522. C5C22×#501semidirect
545. C2D5×#501direct (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×D5×#1252
C2×C5×#5012
C2×#653692
C2×#653542
D5×#5012
C2×D5×#1072
C2×#651652
C2×D5×#1062
C2×#651452
C2×D5×#972
C2×#649912
C22×#5015