Finite Group Databasebeta

← D5×#5089 #14437902

Subgroups — D5×#5089 #14437902

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
2D5×#875C211yesmaximal, characteristic
3#11751190C211yesmaximal, characteristic, complemented
4C5×#5089C211yesmaximal, characteristic, complemented
5D5×#810C212yesmaximal, complemented
6D5×#809C212yesmaximal
7#11747369C212yesmaximal, complemented
8#11747159C212yesmaximal, complemented
9D5×#803C211yesmaximal, characteristic, complemented
10#11746935C211yesmaximal, characteristic, complemented
11#11746904C211yesmaximal, characteristic, complemented
12D5×#489—31nomaximal, Hall
13C2×C3×Q8×D5—21no—
14C2×D5×D12C2211yescharacteristic
15C2×D5×Dic6C2211yescharacteristic
16C3×C5×C4⋊Q8C2211yescharacteristic, complemented
17#91764C2211yescharacteristic
18C5×#875C2211yescharacteristic
19C3×#4090—21no—
20C3×D5×C4⋊C4—21no—
21C3×D5×C4⋊C4C2212yes—
22C3×#4034—21no—
23C3×#4034C2212yescomplemented
24C3×C42×D5C2211yescharacteristic
25C3×#4015C2211yescharacteristic, complemented
26D5×(C2×D3)⋊C4—21no—
27D5×(C2×D3)⋊C4—21no—
28#91375C2211yescharacteristic
29#91373C2211yescharacteristic
30#91350—21no—
31#91350—21no—
32C2×D5×C3⋊C8C2212yes—
33#91094C2212yescomplemented
34#91093C2212yes—
35#91087C2211yescharacteristic, complemented
36C5×#810C2212yescomplemented
37C5×#809C2212yes—
38C5×#803C2211yescharacteristic, complemented
39#90974C2212yescomplemented
40#90972C2212yescomplemented
41#90968C2212yes—
42#90966C2212yes—
43#90952C2212yescomplemented
44C2×#5089—51nomaximal, Hall
45D5×C4⋊Q8D311yescharacteristic, complemented
46D5×#124—31no—
47C5×#489—31no—
48#65378—31no—
49#65344—31no—
50D5×#103—32no—
51#65084—32no—
52D5×#102—32no—
53#65054—32no—
54#65003—31no—
55D5×#97—31no—
56C22×D3×D5—21no—
57C2×C3×C5×Q8—21no—
58C2×D60C2311yescharacteristic
59C2×Dic30C2311yescharacteristic
60C2×C5×D12C2311yescharacteristic
61C2×C5×Dic6C2311yescharacteristic
62C3×Q8×D5—44no—
63C2×C3×C4×D5—22no—
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D411yescharacteristic
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×Dic10—21no—
68C2×C3×Dic10—22no—
69C2×#1204—21no—
70C2×#1203—21no—
71C2×D5×Dic3—21no—
72D5×D12—24no—
73D5×Dic6—24no—
74C3×C5×C4⋊C4—21no—
75C3×C5×C4⋊C4C2312yes—
76C3×C42×C5C2311yescharacteristic
77#6714—21no—
78#6714—21no—
79C2×C3⋊#168C2312yes—
80C5×(C2×D3)⋊C4—21no—
81C5×(C2×D3)⋊C4—21no—
82C2×C5×C3⋊C8C2312yes—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2312yes—
85C3×#683—22no—
86C3×#683—22no—
87C3×C4×Dic5D411yescharacteristic
88C3×C4×Dic5D411yescharacteristic
89C3×C4×Dic5C2311yescharacteristic
90#6667—21no—
91#6667—21no—
92(C2×D3)⋊Dic5—21no—
93(C2×D3)⋊Dic5—21no—
94D5×C3⋊C8—24no—
95C2×C3×C4⋊Q8—51no—
96C2×#875—51no—
97#5089—51no—
98#5089—51no—
99#5089—52no—
100#5089—52no—
101#5089—51no—
102#5089D511yescharacteristic, direct product factor
103C2×#810—52no—
104C2×#809—52no—
105C2×#803—51no—
106C2×Q8×D5—21no—
107C2×Q8×D5—31no—
108C2×D4×D5—31no—
109C5×C4⋊Q8C2×D311yescharacteristic, complemented
110C5×#124—31no—
111#4093—31no—
112#4090—21no—
113#4082—31no—
114C2×C8×D5—32no—
115D5×C4⋊C4—21no—
116D5×C4⋊C4C2×D312yes—
117#4034—21no—
118#4034C2×D312yescomplemented
119#4031—61no—
120#4031—61no—
121D5×C22⋊C4—61no—
122D5×C22⋊C4—61no—
123#4021—31no—
124C42×D5C2×D311yescharacteristic
125#4015C2×D311yescharacteristic, complemented
126C5×#103—32no—
127C5×#102—32no—
128C5×#97—31no—
129#3967—32no—
130#3964—32no—
131#3953—32no—
132#3948—32no—
133#3947—32no—
134#3942—32no—
135#3941—32no—
136#3935—31no—
137C2×#489—151noSylow
138C22×D15—21no—
139C22×C5×D3—21no—
140C22×C3×D5C2×D411yescharacteristic
141C2×D3×D5—42no—
142C2×D3×D5—42no—
143C2×D3×D5—42no—
144C3×C5×Q8—42no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2411yescharacteristic
149C2×Dic15—21no—
150D60—22no—
151Dic30—22no—
152C2×C5×Dic3—21no—
153C5×D12—22no—
154C5×Dic6—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C3×C4×D5—22no—
160C3×C4×D5—22no—
161C3×C4×D5—44no—
162C3×C4×D5#4114yes—
163C3×Dic10—44no—
164C3×Dic10—42no—
165#1204—42no—
166#1203—42no—
167D5×Dic3—42no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C22×C3×Q8—101no—
171C22×D12—51no—
172C22×Dic6—51no—
173C3×C4⋊Q8—52no—
174C3×C4⋊Q8—51no—
175C3×C4⋊Q8—101no—
176C3×C4⋊Q8—101no—
177C3×C4⋊Q8C2×D511yescharacteristic, complemented
178C2×C3×C4⋊C4—52no—
179C2×C3×C4⋊C4—101no—
180C2×C3×C42—51no—
181C2×(C2×D3)⋊C4—101no—
182C2×(C2×D3)⋊C4—101no—
183C22×C3⋊C8—52no—
184#875—51no—
185#875—51no—
186#875—51no—
187#875—101no—
188#875—101no—
189#875C2×D511yescharacteristic
190#810—52no—
191#810—52no—
192#810—52no—
193#810C2×D512yescomplemented
194#809—52no—
195#809—52no—
196#809—52no—
197#809C2×D512yes—
198#803—51no—
199#803—52no—
200#803C2×D511yescharacteristic, complemented
201C23×D5—61no—
202C2×C5×Q8—21no—
203C2×C5×Q8—31no—
204C2×C5×D4—31no—
205C2×C22⋊D5—61no—
206Q8×D5—44no—
207Q8×D5—64no—
208D4×D5—64no—
209C2×D20—31no—
210C2×C4×D5—22no—
211C2×C4×D5—61no—
212C2×C4×D5#6711yescharacteristic
213C2×C4×D5#6711yescharacteristic
214C2×C4×D5C22×D311yescharacteristic
215C2×Dic10—21no—
216C2×Dic10—22no—
217C2×Dic10—31no—
218C2×Dic10—61no—
219C2×C5×C8—32no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4C22×D312yes—
222C5×C22⋊C4—61no—
223C5×C22⋊C4—61no—
224C42×C5C22×D311yescharacteristic
225C22⋊Dic5—61no—
226C22⋊Dic5—61no—
227#685—61no—
228#685—61no—
229#685—61no—
230#685—61no—
231C4⋊Dic5—21no—
232C4⋊Dic5C22×D312yes—
233#683—22no—
234#683—22no—
235C4×Dic5#6711yescharacteristic
236C4×Dic5#6711yescharacteristic
237C4×Dic5C22×D311yescharacteristic
238C2×#168—32no—
239C8×D5—64no—
240C2×C4⋊Q8—51no—
241C2×#124—151no—
242#489—31no—
243#489—151no—
244#489—152no—
245#489—152no—
246#489—151no—
247#489—151no—
248C2×#103—152no—
249C2×#102—152no—
250C2×#97—151no—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—41no—
253C2×D15—41no—
254C2×D15—41no—
255C2×C5×D3—41no—
256C2×C5×D3—41no—
257C2×C5×D3—41no—
258C2×C3×D5#12412yes—
259C2×C3×D5AGL(1,ℤ/8)12yes—
260C2×C3×D5#13712yes—
261D3×D5—84no—
262C3×C4×C5—21no—
263C3×C4×C5—21no—
264C3×C4×C5—42no—
265C3×C4×C5C2×#4112yes—
266Dic15—41no—
267C3×Dic5—21no—
268C3×Dic5—21no—
269C3×Dic5—42no—
270C3×Dic5#12412yes—
271C5×Dic3—41no—
272C23×D3—101no—
273C2×C3×Q8—21no—
274C2×C3×Q8—102no—
275C2×C3×Q8—101no—
276C2×C3×Q8—204no—
277C22×C3×C4—51no—
278C22×C3×C4—51no—
279C22×C3×C4—51no—
280C22×C3×C4—102no—
281C22×Dic3—101no—
282C2×D12—51no—
283C2×D12—104no—
284C2×D12—101no—
285C2×D12C22×D511yescharacteristic
286C2×Dic6—51no—
287C2×Dic6—104no—
288C2×Dic6—101no—
289C2×Dic6C22×D511yescharacteristic
290C3×C4⋊C4—21no—
291C3×C4⋊C4—52no—
292C3×C4⋊C4—102no—
293C3×C4⋊C4—102no—
294C3×C4⋊C4—101no—
295C3×C4⋊C4C22×D512yes—
296C3×C42—51no—
297C3×C42—51no—
298C3×C42—51no—
299C3×C42C22×D511yescharacteristic
300(C2×D3)⋊C4—21no—
301(C2×D3)⋊C4—21no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—101no—
304(C2×D3)⋊C4—101no—
305(C2×D3)⋊C4—101no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—104no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—61no—
312C22×D5—61no—
313C22×D5—122no—
314C22×D5—122no—
315C22×D5—122no—
316C22×D5C2×#6711yescharacteristic
317C5×Q8—42no—
318C5×Q8—62no—
319C5×D4—62no—
320C2×C4×C5—22no—
321C2×C4×C5—61no—
322C2×C4×C5C2×#6711yescharacteristic
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—122no—
326C2×Dic5—22no—
327C2×Dic5—61no—
328C2×Dic5C2×#6711yescharacteristic
329C2×Dic5C2×#6711yescharacteristic
330C2×Dic5C2×#6711yescharacteristic
331D20—62no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—44no—
335C4×D5—122no—
336C4×D5#23914yes—
337Dic10—44no—
338Dic10—42no—
339Dic10—62no—
340Dic10—122no—
341C5×C8—62no—
342#168—62no—
343C22×Q8—101no—
344C22×Q8—151no—
345C22×D4—151no—
346C22×C8—152no—
347C4⋊Q8—52no—
348C4⋊Q8—51no—
349C4⋊Q8—101no—
350C4⋊Q8—101no—
351C4⋊Q8D3×D511yescharacteristic, complemented
352#124—31no—
353#124—151no—
354#124—151no—
355#124—151no—
356#124—301no—
357#124—301no—
358C2×C4⋊C4—52no—
359C2×C4⋊C4—101no—
360C2×C22⋊C4—301no—
361C2×C22⋊C4—301no—
362C2×C42—51no—
363#103—32no—
364#103—152no—
365#103—152no—
366#103—152no—
367#102—32no—
368#102—152no—
369#102—152no—
370#102—152no—
371#97—31no—
372#97—152no—
373#97—151no—
374C2×C3×C5C2×#12411yescharacteristic
375C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C3×C5C2×#13711yescharacteristic
377D15—81no—
378C3×D5#48914yescomplemented
379C5×D3—81no—
380C23×C3—51no—
381C22×D3—21no—
382C22×D3—101no—
383C22×D3—202no—
384C22×D3—202no—
385C22×D3—202no—
386C3×Q8—42no—
387C3×Q8—202no—
388C3×Q8—204no—
389C2×C3×C4—22no—
390C2×C3×C4—51no—
391C2×C3×C4—54no—
392C2×C3×C4—51no—
393C2×C3×C4—51no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4—102no—
397C2×C3×C4—204no—
398C2×C3×C4D4×D511yescharacteristic
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4C23×D511yescharacteristic
401C2×Dic3—21no—
402C2×Dic3—101no—
403C2×Dic3—202no—
404D12—22no—
405D12—102no—
406D12—202no—
407Dic6—22no—
408Dic6—102no—
409Dic6—202no—
410C3⋊C8—22no—
411C3⋊C8—102no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C22×#6711yescharacteristic
416C2×D5—121no—
417C2×D5—121no—
418C2×D5—121no—
419C2×D5—244no—
420C2×D5#93212yes—
421C2×D5#94212yes—
422C2×D5#94712yes—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—42no—
426C4×C5—121no—
427C4×C5C2×#23912yes—
428Dic5—21no—
429Dic5—21no—
430Dic5—42no—
431Dic5—121no—
432Dic5#94712yes—
433C24—301no—
434C2×Q8—21no—
435C2×Q8—31no—
436C2×Q8—102no—
437C2×Q8—101no—
438C2×Q8—151no—
439C2×Q8—204no—
440C2×Q8—301no—
441C2×Q8—304no—
442C2×D4—31no—
443C2×D4—151no—
444C2×D4—304no—
445C2×D4—301no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—102no—
450C22×C4—301no—
451C2×C8—32no—
452C2×C8—152no—
453C2×C8—304no—
454C4⋊C4—21no—
455C4⋊C4—52no—
456C4⋊C4—102no—
457C4⋊C4—102no—
458C4⋊C4—101no—
459C4⋊C4C2×D3×D512yes—
460C22⋊C4—61no—
461C22⋊C4—61no—
462C22⋊C4—301no—
463C22⋊C4—301no—
464C22⋊C4—301no—
465C22⋊C4—301no—
466C22⋊C4—301no—
467C22⋊C4—301no—
468C42—51no—
469C42—51no—
470C42—51no—
471C42C2×D3×D511yescharacteristic
472C3×C5C2×#48911yescharacteristic, complemented, Hall
473C22×C3—52no—
474C22×C3—52no—
475C22×C3—52no—
476C22×C3C2×D4×D511yescharacteristic
477C2×D3—41no—
478C2×D3—41no—
479C2×D3—41no—
480C2×D3—201no—
481C2×D3—201no—
482C2×D3—201no—
483C2×D3—404no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—42no—
487C3×C4—52no—
488C3×C4—101no—
489C3×C4—101no—
490C3×C4—202no—
491C3×C4D5×#4112yes—
492Dic3—41no—
493Dic3—201no—
494C2×C5—241no—
495C2×C5C2×#93211yescharacteristic
496C2×C5C2×#94211yescharacteristic
497C2×C5C2×#94711yescharacteristic
498D5—241no—
499D5#508914yesdirect product factor
500C23—51no—
501C23—61no—
502C23—301no—
503C23—602no—
504C23—602no—
505C23—602no—
506Q8—42no—
507Q8—62no—
508Q8—202no—
509Q8—204no—
510Q8—302no—
511Q8—602no—
512D4—62no—
513D4—302no—
514D4—602no—
515C2×C4—22no—
516C2×C4—51no—
517C2×C4—54no—
518C2×C4—51no—
519C2×C4—51no—
520C2×C4—61no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—204no—
525C2×C4—301no—
526C2×C4—602no—
527C2×C4D5×#6711yescharacteristic
528C2×C4D5×#6711yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—62no—
531C8—302no—
532C2×C3—54no—
533C2×C3D5×#12411yescharacteristic
534C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
535C2×C3D5×#13711yescharacteristic
536D3—81no—
537D3—401no—
538C5C2×#508911yescharacteristic, complemented, Sylow
539C22—52no—
540C22—52no—
541C22—52no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—601no—
546C22—601no—
547C22—601no—
548C22—1204no—
549C22C2×D5×#6711yescharacteristic
550C4—21no—
551C4—21no—
552C4—42no—
553C4—52no—
554C4—101no—
555C4—101no—
556C4—121no—
557C4—202no—
558C4—601no—
559C4D5×#23912yes—
560C3D5×#48911yescharacteristic, complemented, Sylow
561C2—54no—
562C2—241no—
563C2—1201no—
564C2D5×#93211yescharacteristic
565C2D5×#94211yescharacteristic
566C2D5×#94711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D5×C4⋊Q8C2semidirect
3. #11751190C2semidirect
4. C5×#5089C2semidirect
5. D5×#810C2semidirect
7. #11747369C2semidirect
8. #11747159C2semidirect
9. D5×#803C2semidirect
10. #11746935C2semidirect
11. #11746904C2semidirect
16. C3×C5×C4⋊Q8C22semidirect
23. C3×#4034C22semidirect
25. C3×#4015C22semidirect
33. #91094C22semidirect
35. #91087C22semidirect
36. C5×#810C22semidirect
38. C5×#803C22semidirect
39. #90974C22semidirect
40. #90972C22semidirect
43. #90952C22semidirect
45. D5×C4⋊Q8D3semidirect
102. #5089D5direct (N × H)
109. C5×C4⋊Q8C2×D3semidirect
118. #4034C2×D3semidirect
125. #4015C2×D3semidirect
177. C3×C4⋊Q8C2×D5semidirect
193. #810C2×D5semidirect
200. #803C2×D5semidirect
351. C4⋊Q8D3×D5semidirect
378. C3×D5#489semidirect
472. C3×C5C2×#489semidirect
499. D5#5089direct (N × H)
538. C5C2×#5089semidirect
560. C3D5×#489semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
D5×#8752
#117511902
C5×#50892
D5×#8102
D5×#8092
#117473692
#117471592
D5×#8032
#117469352
#117469042
D5×#4893
C2×#50895