Finite Group Databasebeta

← D5×#5058 #14438985

Subgroups — D5×#5058 #14438985

Order 1920.

1336 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×#124C211yesmaximal, characteristic, complemented
2C2×D5×#215C212yesmaximal, complemented
3C2×D5×#213C212yesmaximal, complemented
4D5×#874C211yesmaximal, characteristic, complemented
5#11751159C211yesmaximal, characteristic, complemented
6C5×#5058C211yesmaximal, characteristic, complemented
7#11749340C212yesmaximal, complemented
8#11749094C212yesmaximal, complemented
9#11747042C211yesmaximal, characteristic, complemented
10#11747036C211yesmaximal, characteristic, complemented
11D5×#803C211yesmaximal, characteristic, complemented
12D5×#496—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×C3×D4×D5C2211yescharacteristic
15C2×D5×D12—22no—
16C2×D5×D12C2212yes—
17C3×C5×#124C2211yescharacteristic, complemented
18C2×#6717C2212yescomplemented
19C2×#6715C2212yescomplemented
20#91763C2211yescharacteristic, complemented
21C2×C5×#215C2212yescomplemented
22C2×C5×#213C2212yescomplemented
23C5×#874C2211yescharacteristic, complemented
24C3×#4093C2211yescharacteristic, complemented
25C3×#4082C2211yescharacteristic, complemented
26C3×#4031—22no—
27C3×D5×C22⋊C4—22no—
28C3×#4021C2211yescharacteristic, complemented
29C3×C42×D5C2211yescharacteristic
30D5×#215—28no—
31D5×#213—28no—
32#91451—22no—
33#91451C2212yescomplemented
34C2×#6658C2212yescomplemented
35C2×#6656C2212yescomplemented
36C2×#6653C2212yescomplemented
37C2×#6652C2212yescomplemented
38C2×D5×C3⋊C8C2212yes—
39#91087C2211yescharacteristic, complemented
40C5×#803C2211yescharacteristic, complemented
41#90952C2212yescomplemented
42C2×#5058—51nomaximal, Hall
43C2×D5×SD16—32no—
44C2×D5×D8—32no—
45D5×#127—31no—
46D5×#124D311yescharacteristic, complemented
47C5×#496—31no—
48#65465—32no—
49#65443—32no—
50#65363—31no—
51#65347—31no—
52#65001—31no—
53D5×#97—31no—
54C23×C3×D5—21no—
55C22×D3×D5—22no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C2×D60—22no—
59C2×D60C2312yes—
60C2×C5×D12—22no—
61C2×C5×D12C2312yes—
62C2×C3×C22⋊D5—21no—
63C3×Q8×D5—24no—
64C3×D4×D5—24no—
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5D412yes—
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×Dic10—21no—
70C2×C3×Dic10C2311yescharacteristic
71C2×#1203—22no—
72C2×#1203—24no—
73D5×D12—24no—
74D5×D12—24no—
75D5×D12—48no—
76C3×C5×C22⋊C4—22no—
77C3×C42×C5C2311yescharacteristic
78#6717—24no—
79#6715—24no—
80C2×C3⋊#168C2312yes—
81C5×#215—24no—
82C5×#213—24no—
83C2×C5×C3⋊C8C2312yes—
84C3×C22⋊Dic5—22no—
85C3×#685—22no—
86C3×#685—22no—
87C3×C4×Dic5D412yes—
88C3×C4×Dic5C2311yescharacteristic
89#6658—24no—
90#6656—24no—
91#6653—24no—
92#6652—24no—
93D5×C3⋊C8D418yescomplemented
94C2×C3×#124—51no—
95C22×#215—52no—
96C22×#213—52no—
97C2×#874—51no—
98#5058—51no—
99#5058—52no—
100#5058—52no—
101#5058—51no—
102#5058—51no—
103#5058D511yescharacteristic, direct product factor
104C2×#803—51no—
105C2×Q8×D5C2×D311yescharacteristic
106C2×D4×D5—32no—
107C2×D4×D5—62no—
108C2×D4×D5C2×D311yescharacteristic
109C2×C5×SD16—32no—
110C2×C5×D8—32no—
111C5×#127—31no—
112C5×#124C2×D311yescharacteristic, complemented
113#4093C2×D311yescharacteristic, complemented
114C2×#688—32no—
115#4086—32no—
116#4086—62no—
117#4082C2×D311yescharacteristic, complemented
118C2×#687—32no—
119C2×#686—32no—
120C2×#686—32no—
121D5×SD16—68no—
122D5×D8—68no—
123C2×D40—32no—
124C2×#677—32no—
125C2×C8×D5—32no—
126#4031—22no—
127D5×C22⋊C4—22no—
128#4021C2×D311yescharacteristic, complemented
129#4020—31no—
130C42×D5C2×D311yescharacteristic
131C5×#97—31no—
132#3947—32no—
133#3935—31no—
134C2×#496—151noSylow
135C23×C3×C5—21no—
136C22×D15—22no—
137C22×C5×D3—22no—
138C22×C3×D5—21no—
139C22×C3×D5—42no—
140C22×C3×D5—44no—
141C22×C3×D5C2×D411yescharacteristic
142C2×D3×D5—44no—
143C2×D3×D5—48no—
144C3×C5×Q8—22no—
145C3×C5×D4—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149D60—22no—
150D60—22no—
151D60—44no—
152C5×D12—22no—
153C5×D12—22no—
154C5×D12—44no—
155C3×C22⋊D5—42no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5C2×D412yes—
158C2×C3×Dic5C2×D411yescharacteristic
159C3×D20—22no—
160C3×C4×D5—24no—
161C3×C4×D5—42no—
162C3×C4×D5C2×D414yes—
163C3×Dic10—22no—
164C3×Dic10—42no—
165#1203—48no—
166#1203—44no—
167C3⋊#168C2×D414yescomplemented
168C5×C3⋊C8C2×D414yescomplemented
169C22×C3×Q8—51no—
170C22×C3×D4—51no—
171C22×D12—52no—
172C22×D12—102no—
173C3×#124—51no—
174C3×#124—51no—
175C3×#124—51no—
176C3×#124—102no—
177C3×#124C2×D511yescharacteristic, complemented
178C2×C3×C22⋊C4—102no—
179C2×C3×C42—51no—
180C2×#215—52no—
181C2×#215—52no—
182C2×#215—52no—
183C2×#215—108no—
184C2×#215C2×D512yescomplemented
185C2×#213—52no—
186C2×#213—52no—
187C2×#213—52no—
188C2×#213—108no—
189C2×#213C2×D512yescomplemented
190C22×C3⋊C8—52no—
191#874—52no—
192#874—51no—
193#874—102no—
194#874C2×D511yescharacteristic, complemented
195#803—51no—
196#803—52no—
197#803C2×D511yescharacteristic, complemented
198C23×D5—21no—
199C23×D5—62no—
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—32no—
202C2×C5×D4—62no—
203C2×C5×D4C22×D311yescharacteristic
204C2×C22⋊D5—21no—
205C2×C22⋊D5—62no—
206C2×C22⋊D5—64no—
207Q8×D5—24no—
208D4×D5—24no—
209D4×D5—64no—
210D4×D5—64no—
211D4×D5—128no—
212C2×D20—32no—
213C2×D20—62no—
214C2×D20C22×D311yescharacteristic
215C2×C4×D5—21no—
216C2×C4×D5#6712yes—
217C2×C4×D5C22×D311yescharacteristic
218C2×Dic10—21no—
219C2×Dic10C22×D311yescharacteristic
220C5×SD16—64no—
221C5×D8—64no—
222C2×C5×C8—32no—
223C5×C22⋊C4—22no—
224C42×C5C22×D311yescharacteristic
225C22⋊Dic5—22no—
226#688—64no—
227#687—64no—
228#686—64no—
229#686—64no—
230#685—22no—
231#685—22no—
232C4×Dic5#6712yes—
233C4×Dic5C22×D311yescharacteristic
234C2×#168—32no—
235D40—64no—
236#677—64no—
237C8×D5—38no—
238C22×SD16—152no—
239C22×D8—152no—
240C2×#127—151no—
241C2×#124—51no—
242#496—31no—
243#496—151no—
244#496—151no—
245#496—152no—
246#496—152no—
247#496—151no—
248C2×#97—151no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—42no—
253C2×D15—44no—
254C2×C5×D3—42no—
255C2×C5×D3—44no—
256C2×C3×D5—41no—
257C2×C3×D5—42no—
258C2×C3×D5—84no—
259C2×C3×D5#12712yes—
260C2×C3×D5AGL(1,ℤ/8)14yes—
261D3×D5—88no—
262C3×C4×C5—22no—
263C3×C4×C5—41no—
264C3×C4×C5C22×D412yes—
265C3×Dic5—22no—
266C3×Dic5—41no—
267C3×Dic5#12712yes—
268C24×C3—101no—
269C23×D3—102no—
270C2×C3×Q8—51no—
271C2×C3×Q8—101no—
272C2×C3×Q8—104no—
273C2×C3×Q8C22×D511yescharacteristic
274C2×C3×D4—51no—
275C2×C3×D4—104no—
276C2×C3×D4—101no—
277C2×C3×D4C22×D511yescharacteristic
278C22×C3×C4—51no—
279C22×C3×C4—52no—
280C22×C3×C4—101no—
281C2×D12—22no—
282C2×D12—52no—
283C2×D12—104no—
284C2×D12—104no—
285C2×D12—104no—
286C2×D12—102no—
287C2×D12—102no—
288C2×D12—208no—
289C2×D12C22×D512yes—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—102no—
292C3×C22⋊C4—102no—
293C3×C22⋊C4—102no—
294C3×C42—52no—
295C3×C42—51no—
296C3×C42C22×D511yescharacteristic
297#215—24no—
298#215—104no—
299#215—104no—
300#215—104no—
301#213—24no—
302#213—104no—
303#213—104no—
304#213—104no—
305C2×C3⋊C8—52no—
306C2×C3⋊C8—58no—
307C2×C3⋊C8C22×D512yes—
308C23×C5—21no—
309C23×C5—62no—
310C22×D5—21no—
311C22×D5—42no—
312C22×D5—44no—
313C22×D5—62no—
314C22×D5—124no—
315C22×D5—128no—
316C22×D5C2×#6711yescharacteristic
317C5×Q8—22no—
318C5×D4—22no—
319C5×D4—62no—
320C5×D4—62no—
321C5×D4—124no—
322C2×C4×C5—21no—
323C2×C4×C5C2×#6712yes—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—42no—
326C22⋊D5—128no—
327C22⋊D5—124no—
328C2×Dic5—21no—
329C2×Dic5C2×#6712yes—
330C2×Dic5C2×#6711yescharacteristic
331D20—22no—
332D20—62no—
333D20—62no—
334D20—124no—
335C4×D5—24no—
336C4×D5—42no—
337C4×D5D3×D414yes—
338Dic10—22no—
339Dic10—42no—
340C5×C8—34no—
341#168—34no—
342C22×Q8—51no—
343C22×D4—51no—
344C22×D4—152no—
345C22×D4—302no—
346C2×SD16—32no—
347C2×SD16—152no—
348C2×SD16—152no—
349C2×SD16—152no—
350C2×SD16—308no—
351C2×D8—32no—
352C2×D8—152no—
353C2×D8—152no—
354C2×D8—152no—
355C2×D8—308no—
356C22×C8—152no—
357#127—31no—
358#127—152no—
359#127—151no—
360#127—302no—
361#124—51no—
362#124—51no—
363#124—51no—
364#124—102no—
365#124D3×D511yescharacteristic, complemented
366C2×C22⋊C4—102no—
367C2×C42—51no—
368#97—31no—
369#97—152no—
370#97—151no—
371C2×C3×C5—81no—
372C2×C3×C5C2×#12711yescharacteristic
373C2×C3×C5C2×AGL(1,ℤ/8)12yes—
374D15—82no—
375C3×D5—81no—
376C3×D5#49614yescomplemented
377C5×D3—82no—
378C23×C3—21no—
379C23×C3—51no—
380C23×C3—101no—
381C23×C3—202no—
382C23×C3—204no—
383C22×D3—22no—
384C22×D3—102no—
385C22×D3—204no—
386C22×D3—208no—
387C3×Q8—22no—
388C3×Q8—102no—
389C3×Q8—202no—
390C3×D4—22no—
391C3×D4—102no—
392C3×D4—202no—
393C2×C3×C4—21no—
394C2×C3×C4—51no—
395C2×C3×C4—54no—
396C2×C3×C4—52no—
397C2×C3×C4—104no—
398C2×C3×C4—101no—
399C2×C3×C4—202no—
400C2×C3×C4D4×D512yes—
401C2×C3×C4C23×D511yescharacteristic
402D12—22no—
403D12—22no—
404D12—44no—
405D12—102no—
406D12—102no—
407D12—204no—
408D12—204no—
409D12—208no—
410C3⋊C8—54no—
411C3⋊C8D4×D514yescomplemented
412C22×C5—41no—
413C22×C5—42no—
414C22×C5—122no—
415C22×C5—124no—
416C22×C5C22×#6711yescharacteristic
417C2×D5—41no—
418C2×D5—42no—
419C2×D5—84no—
420C2×D5—122no—
421C2×D5—124no—
422C2×D5—248no—
423C2×D5#94012yes—
424C2×D5#94914yes—
425C4×C5—22no—
426C4×C5—41no—
427C4×C5C2×D3×D412yes—
428Dic5—22no—
429Dic5—41no—
430Dic5#94012yes—
431C24—101no—
432C24—302no—
433C2×Q8—51no—
434C2×Q8—101no—
435C2×Q8—104no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—32no—
438C2×D4—51no—
439C2×D4—62no—
440C2×D4—104no—
441C2×D4—101no—
442C2×D4—152no—
443C2×D4—304no—
444C2×D4—304no—
445C2×D4—304no—
446C2×D4—302no—
447C2×D4—302no—
448C2×D4—608no—
449C2×D4C2×D3×D511yescharacteristic
450C22×C4—51no—
451C22×C4—52no—
452C22×C4—101no—
453SD16—64no—
454SD16—304no—
455SD16—304no—
456SD16—304no—
457D8—64no—
458D8—304no—
459D8—304no—
460D8—304no—
461C2×C8—32no—
462C2×C8—158no—
463C2×C8—152no—
464C22⋊C4—22no—
465C22⋊C4—102no—
466C22⋊C4—102no—
467C22⋊C4—102no—
468C42—52no—
469C42—51no—
470C42C2×D3×D511yescharacteristic
471C3×C5C2×#49611yescharacteristic, complemented, Hall
472C22×C3—41no—
473C22×C3—42no—
474C22×C3—52no—
475C22×C3—54no—
476C22×C3—201no—
477C22×C3—202no—
478C22×C3—404no—
479C22×C3C2×D4×D511yescharacteristic
480C2×D3—42no—
481C2×D3—44no—
482C2×D3—202no—
483C2×D3—204no—
484C2×D3—408no—
485C3×C4—22no—
486C3×C4—41no—
487C3×C4—52no—
488C3×C4—102no—
489C3×C4—201no—
490C3×C4C2×D4×D512yes—
491C2×C5—81no—
492C2×C5—242no—
493C2×C5C2×#94011yescharacteristic
494C2×C5C2×#94912yes—
495D5—81no—
496D5—242no—
497D5#505814yesdirect product factor
498C23—21no—
499C23—51no—
500C23—62no—
501C23—101no—
502C23—202no—
503C23—204no—
504C23—302no—
505C23—604no—
506C23—608no—
507Q8—22no—
508Q8—102no—
509Q8—202no—
510D4—22no—
511D4—62no—
512D4—62no—
513D4—102no—
514D4—124no—
515D4—202no—
516D4—302no—
517D4—302no—
518D4—604no—
519D4—604no—
520D4—608no—
521C2×C4—21no—
522C2×C4—51no—
523C2×C4—54no—
524C2×C4—52no—
525C2×C4—104no—
526C2×C4—101no—
527C2×C4—202no—
528C2×C4D5×#6712yes—
529C2×C4C22×D3×D511yescharacteristic
530C8—34no—
531C8—154no—
532C2×C3—54no—
533C2×C3—81no—
534C2×C3—401no—
535C2×C3D5×#12711yescharacteristic
536C2×C3D5×AGL(1,ℤ/8)12yes—
537D3—82no—
538D3—402no—
539C5C2×#505811yescharacteristic, complemented, Sylow
540C22—41no—
541C22—42no—
542C22—52no—
543C22—54no—
544C22—122no—
545C22—124no—
546C22—201no—
547C22—202no—
548C22—404no—
549C22—602no—
550C22—604no—
551C22—1208no—
552C22C2×D5×#6711yescharacteristic
553C4—22no—
554C4—41no—
555C4—52no—
556C4—102no—
557C4—201no—
558C4D3×D4×D512yes—
559C3D5×#49611yescharacteristic, complemented, Sylow
560C2—54no—
561C2—81no—
562C2—242no—
563C2—401no—
564C2—1202no—
565C2D5×#94011yescharacteristic
566C2D5×#94912yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5C2×#496
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×D5×#124C2semidirect
2. C2×D5×#215C2semidirect
3. C2×D5×#213C2semidirect
4. D5×#874C2semidirect
5. #11751159C2semidirect
6. C5×#5058C2semidirect
7. #11749340C2semidirect
8. #11749094C2semidirect
9. #11747042C2semidirect
10. #11747036C2semidirect
11. D5×#803C2semidirect
17. C3×C5×#124C22semidirect
18. C2×#6717C22semidirect
19. C2×#6715C22semidirect
20. #91763C22semidirect
21. C2×C5×#215C22semidirect
22. C2×C5×#213C22semidirect
23. C5×#874C22semidirect
24. C3×#4093C22semidirect
25. C3×#4082C22semidirect
28. C3×#4021C22semidirect
33. #91451C22semidirect
34. C2×#6658C22semidirect
35. C2×#6656C22semidirect
36. C2×#6653C22semidirect
37. C2×#6652C22semidirect
39. #91087C22semidirect
40. C5×#803C22semidirect
41. #90952C22semidirect
46. D5×#124D3semidirect
93. D5×C3⋊C8D4semidirect
103. #5058D5direct (N × H)
112. C5×#124C2×D3semidirect
113. #4093C2×D3semidirect
117. #4082C2×D3semidirect
128. #4021C2×D3semidirect
167. C3⋊#168C2×D4semidirect
168. C5×C3⋊C8C2×D4semidirect
177. C3×#124C2×D5semidirect
184. C2×#215C2×D5semidirect
189. C2×#213C2×D5semidirect
194. #874C2×D5semidirect
197. #803C2×D5semidirect
365. #124D3×D5semidirect
376. C3×D5#496semidirect
411. C3⋊C8D4×D5semidirect
471. C3×C5C2×#496semidirect
497. D5#5058direct (N × H)
539. C5C2×#5058semidirect
559. C3D5×#496semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1242
C2×D5×#2152
C2×D5×#2132
D5×#8742
#117511592
C5×#50582
#117493402
#117490942
#117470422
#117470362
D5×#8032
D5×#4963
C2×#50585