Finite Group Databasebeta

← D5×#5120 #14412445

Subgroups — D5×#5120 #14412445

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C2×C3×D5×M16C211yesmaximal, characteristic
3D5×#926C211yesmaximal, characteristic
4#11751221C211yesmaximal, characteristic, complemented
5C5×#5120C211yesmaximal, characteristic, complemented
6#11748417C211yesmaximal, characteristic, complemented
7#11748409C211yesmaximal, characteristic, complemented
8#11748122C214yesmaximal, complemented
9D5×#816C214yesmaximal, complemented
10D5×#419—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1204—21no—
15C22×D5×Dic3—21no—
16C2×D5×Dic6—21no—
17C2×D5×Dic6—21no—
18C2×D5×Dic6—24no—
19C2×D5×Dic6C418yescomplemented
20C2×D5×Dic6C2212yes—
21C2×D5×Dic6C2212yes—
22C2×C3×C5×M16C2211yescharacteristic
23#91815C2211yescharacteristic
24C5×#926C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26C3×D5×M16—24no—
27C2×C3×#676C2212yes—
28C2×C3×C8×D5C2212yes—
29D5×#217—21no—
30#91528—21no—
31D5×C4⋊Dic3C2212yes—
32C4×D5×Dic3—21no—
33#91358C2212yes—
34#91357—21no—
35#91100C2214yescomplemented
36C5×#816C2214yescomplemented
37#90975C2214yescomplemented
38#90973C2214yescomplemented
39C2×#5120—51nomaximal, Hall
40C22×Q8×D5—31no—
41C2×D5×M16D311yescharacteristic
42D5×#117—31no—
43C5×#419—31no—
44#65514—31no—
45#65409—31no—
46#65293—31no—
47#65091—34no—
48D5×#103—34no—
49C23×C3×D5D411yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×Dic15—21no—
52C2×Dic30—21no—
53C2×Dic30—22no—
54C2×Dic30C2×C414yescomplemented
55C2×Dic30C2312yes—
56C22×C5×Dic3—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—22no—
59C2×C5×Dic6C2×C414yescomplemented
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5D411yescharacteristic
62C2×C3×C4×D5C2×C414yes—
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5D414yes—
66C2×C3×C4×D5C2311yescharacteristic
67C2×C3×C4×D5C2311yescharacteristic
68C2×#1204—28no—
69C2×#1204—22no—
70C2×#1204—22no—
71C2×D5×Dic3—28no—
72C2×D5×Dic3—22no—
73C2×D5×Dic3—22no—
74C2×D5×Dic3—22no—
75D5×Dic6—28no—
76D5×Dic6—28no—
77D5×Dic6—24no—
78D5×Dic6—24no—
79D5×Dic6C2×C418yes—
80D5×Dic6C2×C418yescomplemented
81C3×C5×M16—22no—
82C2×C3×C5×C8C2312yes—
83#6719—21no—
84C4⋊Dic15C2312yes—
85C4×Dic15—21no—
86C5×#217—21no—
87C5×C4⋊Dic3C2312yes—
88C4×C5×Dic3—21no—
89C3×#681—22no—
90C2×C3×#168C2312yes—
91C3×#676—24no—
92C3×C8×D5—24no—
93#6668—22no—
94#6665—22no—
95Dic3×Dic5—22no—
96C23×Dic6—51no—
97C22×C3×M16—51no—
98C2×#926—51no—
99#5120—51no—
100#5120—51no—
101#5120—51no—
102#5120—54no—
103#5120D511yescharacteristic, direct product factor
104C2×#816—54no—
105C22×C5×Q8—31no—
106C2×Q8×D5—38no—
107C2×Q8×D5—32no—
108C2×Q8×D5—32no—
109C2×Q8×D5—61no—
110C2×Q8×D5—61no—
111C2×Q8×D5—64no—
112C22×C4×D5—61no—
113C22×C4×D5C2×D311yescharacteristic
114C22×Dic10—31no—
115C22×Dic10—61no—
116C2×C5×M16C2×D311yescharacteristic
117C5×#117—31no—
118#4072—31no—
119C2×#681C2×D311yescharacteristic
120D5×M16—24no—
121C2×#676C2×D312yes—
122C2×C8×D5C2×D312yes—
123#4038—32no—
124D5×C4⋊C4—32no—
125D5×C22⋊C4—61no—
126#4023—61no—
127#4018—61no—
128C42×D5—61no—
129C5×#103—34no—
130#3967—34no—
131#3948—34no—
132#3942—34no—
133C2×#419—151noSylow
134C23×C3×C5C2×D411yescharacteristic
135C22×C3×D5—24no—
136C22×C3×D5C22⋊C414yes—
137C22×C3×D5C2×D411yescharacteristic
138C22×C3×D5C2×D411yescharacteristic
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—24no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146Dic30—24no—
147Dic30—22no—
148Dic30C22×C414yes—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C5×Dic6—24no—
153C5×Dic6—22no—
154C5×Dic6C22×C414yes—
155C2×C3×Dic5C22⋊C414yes—
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C3×C4×D5C22⋊C414yes—
159C3×C4×D5C22⋊C414yes—
160C3×C4×D5C22×C412yes—
161C3×C4×D5C22×C412yes—
162C3×C4×D5C2×D412yes—
163C3×C4×D5C2×D412yes—
164#1204—28no—
165#1204—28no—
166D5×Dic3—28no—
167D5×Dic3—28no—
168D5×Dic3—44no—
169C3×C5×C8—22no—
170C3×#168—22no—
171C23×C3×C4—51no—
172C23×Dic3—101no—
173C22×Dic6—51no—
174C22×Dic6—58no—
175C22×Dic6—52no—
176C22×Dic6—52no—
177C22×Dic6—101no—
178C22×Dic6—101no—
179C22×Dic6—104no—
180C22×Dic6—101no—
181C22×Dic6C2×D511yescharacteristic
182C2×C3×M16—51no—
183C2×C3×M16—52no—
184C2×C3×M16—104no—
185C2×C3×M16C2×D511yescharacteristic
186C22×C3×C8—52no—
187C2×#217—101no—
188#926—51no—
189#926—52no—
190#926—101no—
191#926—101no—
192#926C2×D511yescharacteristic
193C2×C4⋊Dic3—52no—
194C2×C4×Dic3—101no—
195#816—54no—
196#816—54no—
197#816—54no—
198#816C2×D514yescomplemented
199C23×D5D1211yescharacteristic
200C2×C5×Q8—34no—
201C2×C5×Q8—32no—
202C2×C5×Q8—61no—
203C2×C5×Q8—62no—
204C22×C4×C5—61no—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—61no—
207C22×Dic5D1211yescharacteristic
208Q8×D5—38no—
209Q8×D5—38no—
210Q8×D5—68no—
211Q8×D5—68no—
212Q8×D5—64no—
213Q8×D5—64no—
214C2×C4×D5—68no—
215C2×C4×D5—62no—
216C2×C4×D5—62no—
217C2×C4×D5—62no—
218C2×C4×D5C4×D314yes—
219C2×C4×D5D1211yescharacteristic
220C2×C4×D5D1211yescharacteristic
221C2×C4×D5#6714yes—
222C2×C4×D5C22×D311yescharacteristic
223C2×C4×D5C22×D311yescharacteristic
224C2×Dic10—34no—
225C2×Dic10—32no—
226C2×Dic10—61no—
227C2×Dic10—62no—
228C2×Dic10—68no—
229C2×Dic10—62no—
230C2×Dic10—62no—
231C5×M16—22no—
232C2×C5×C8C22×D312yes—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236C22⋊Dic5—61no—
237#685—62no—
238C4⋊Dic5—32no—
239#683—62no—
240C4×Dic5—61no—
241C4×Dic5—62no—
242#681—22no—
243C2×#168C22×D312yes—
244#676—24no—
245C8×D5—24no—
246C23×Q8—151no—
247C22×M16—51no—
248C2×#117—151no—
249#419—31no—
250#419—154no—
251#419—151no—
252#419—151no—
253#419—151no—
254C2×#103—154no—
255C22×C3×C5—22no—
256C22×C3×C5C2×C22⋊C412yes—
257C22×C3×C5C22×D411yescharacteristic
258C2×C3×D5—22no—
259C2×C3×D5—28no—
260C2×C3×D5C2×C22⋊C412yes—
261C2×C3×D5C2×C22⋊C412yes—
262C2×C3×D5#13714yes—
263C3×C4×C5C2×C22⋊C412yes—
264C3×C4×C5C23×C411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—24no—
267Dic15—42no—
268C3×Dic5C2×C22⋊C412yes—
269C3×Dic5C2×C22⋊C412yes—
270C5×Dic3—24no—
271C5×Dic3—42no—
272C24×C3—51no—
273C22×C3×C4—51no—
274C22×C3×C4—54no—
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—54no—
278C22×C3×C4—51no—
279C22×C3×C4—51no—
280C22×C3×C4C22×D511yescharacteristic
281C22×Dic3—21no—
282C22×Dic3—102no—
283C22×Dic3—102no—
284C22×Dic3—108no—
285C22×Dic3—102no—
286C22×Dic3—101no—
287C2×Dic6—21no—
288C2×Dic6—22no—
289C2×Dic6—54no—
290C2×Dic6—52no—
291C2×Dic6—58no—
292C2×Dic6—58no—
293C2×Dic6—104no—
294C2×Dic6—104no—
295C2×Dic6—108no—
296C2×Dic6—108no—
297C2×Dic6—102no—
298C2×Dic6—102no—
299C2×Dic6—108no—
300C2×Dic6—101no—
301C2×Dic6—102no—
302C2×Dic6C4×D514yescomplemented
303C2×Dic6C22×D512yes—
304C3×M16—22no—
305C3×M16—104no—
306C3×M16—102no—
307C2×C3×C8—52no—
308C2×C3×C8—104no—
309C2×C3×C8C22×D512yes—
310#217—21no—
311#217—102no—
312#217—101no—
313C4⋊Dic3—52no—
314C4⋊Dic3—102no—
315C4⋊Dic3C22×D512yes—
316C4×Dic3—21no—
317C4×Dic3—102no—
318C4×Dic3—101no—
319C23×C5C2×D1211yescharacteristic
320C22×D5—24no—
321C22×D5(C2×D3)⋊C414yes—
322C22×D5C2×D1211yescharacteristic
323C22×D5C2×D1211yescharacteristic
324C5×Q8—34no—
325C5×Q8—64no—
326C5×Q8—62no—
327C2×C4×C5—64no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5C2×C4×D312yes—
331C2×C4×C5C2×D1211yescharacteristic
332C2×C4×C5C2×#6712yes—
333C2×C4×C5C23×D311yescharacteristic
334C2×Dic5—64no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5(C2×D3)⋊C414yes—
338C2×Dic5C2×D1211yescharacteristic
339C2×Dic5C2×D1211yescharacteristic
340C4×D5—68no—
341C4×D5—68no—
342C4×D5—124no—
343C4×D5(C2×D3)⋊C414yes—
344C4×D5(C2×D3)⋊C414yes—
345C4×D5C2×C4×D312yes—
346C4×D5C2×C4×D312yes—
347C4×D5C2×#6712yes—
348C4×D5C2×#6712yes—
349Dic10—34no—
350Dic10—64no—
351Dic10—62no—
352Dic10—68no—
353Dic10—68no—
354C5×C8—22no—
355#168—22no—
356C22×Q8—31no—
357C22×Q8—152no—
358C22×Q8—152no—
359C22×Q8—158no—
360C22×Q8—151no—
361C22×Q8—301no—
362C22×Q8—301no—
363C22×Q8—301no—
364C22×Q8—304no—
365C23×C4—51no—
366C23×C4—301no—
367C2×M16—51no—
368C2×M16—52no—
369C2×M16—104no—
370C2×M16D3×D511yescharacteristic
371C22×C8—52no—
372#117—31no—
373#117—152no—
374#117—151no—
375#117—301no—
376#117—301no—
377C2×C4⋊C4—152no—
378C2×C22⋊C4—301no—
379C2×C42—301no—
380#103—34no—
381#103—154no—
382#103—154no—
383#103—154no—
384C2×C3×C5—22no—
385C2×C3×C5C22×C22⋊C411yescharacteristic
386C2×C3×C5C2×#13712yes—
387C3×D5—22no—
388C3×D5#41914yescomplemented
389C23×C3—51no—
390C23×C3—51no—
391C23×C3—54no—
392C23×C3—104no—
393C23×C3D4×D511yescharacteristic
394C2×C3×C4—51no—
395C2×C3×C4—51no—
396C2×C3×C4—54no—
397C2×C3×C4—52no—
398C2×C3×C4—52no—
399C2×C3×C4—52no—
400C2×C3×C4—52no—
401C2×C3×C4—54no—
402C2×C3×C4—54no—
403C2×C3×C4C2×C4×D512yes—
404C2×C3×C4D4×D511yescharacteristic
405C2×C3×C4D4×D512yes—
406C2×C3×C4C23×D511yescharacteristic
407C2×Dic3—22no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—108no—
411C2×Dic3—108no—
412C2×Dic3—102no—
413C2×Dic3—104no—
414C2×Dic3—102no—
415C2×Dic3—204no—
416Dic6—22no—
417Dic6—24no—
418Dic6—54no—
419Dic6—108no—
420Dic6—108no—
421Dic6—102no—
422Dic6—104no—
423Dic6C2×C4×D514yes—
424C3×C8—22no—
425C3×C8—102no—
426C22×C5—22no—
427C22×C5C2×(C2×D3)⋊C412yes—
428C22×C5C22×D1211yescharacteristic
429C2×D5—22no—
430C2×D5—28no—
431C2×D5#90914yes—
432C2×D5C2×(C2×D3)⋊C412yes—
433C2×D5C2×(C2×D3)⋊C412yes—
434C4×C5—64no—
435C4×C5—122no—
436C4×C5C2×(C2×D3)⋊C412yes—
437C4×C5C22×C4×D311yescharacteristic
438C4×C5C22×#6711yescharacteristic
439Dic5—64no—
440Dic5—122no—
441Dic5C2×(C2×D3)⋊C412yes—
442Dic5C2×(C2×D3)⋊C412yes—
443C24—51no—
444C2×Q8—34no—
445C2×Q8—32no—
446C2×Q8—61no—
447C2×Q8—62no—
448C2×Q8—158no—
449C2×Q8—158no—
450C2×Q8—154no—
451C2×Q8—152no—
452C2×Q8—308no—
453C2×Q8—302no—
454C2×Q8—302no—
455C2×Q8—308no—
456C2×Q8—308no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—301no—
460C2×Q8—302no—
461C22×C4—51no—
462C22×C4—54no—
463C22×C4—51no—
464C22×C4—51no—
465C22×C4—54no—
466C22×C4—51no—
467C22×C4—51no—
468C22×C4—61no—
469C22×C4—308no—
470C22×C4—302no—
471C22×C4—302no—
472C22×C4—302no—
473C22×C4—301no—
474C22×C4C2×D3×D511yescharacteristic
475M16—22no—
476M16—104no—
477M16—102no—
478C2×C8—52no—
479C2×C8—104no—
480C2×C8C2×D3×D512yes—
481C4⋊C4—32no—
482C4⋊C4—152no—
483C4⋊C4—302no—
484C22⋊C4—61no—
485C22⋊C4—302no—
486C22⋊C4—301no—
487C42—61no—
488C42—302no—
489C42—301no—
490C3×C5C2×#41911yescharacteristic, complemented, Hall
491C22×C3—22no—
492C22×C3—52no—
493C22×C3—54no—
494C22×C3—52no—
495C22×C3—108no—
496C22×C3—102no—
497C22×C3D5×C22⋊C412yes—
498C22×C3C2×D4×D511yescharacteristic
499C3×C4—52no—
500C3×C4—52no—
501C3×C4D5×C22⋊C412yes—
502C3×C4C22×C4×D511yescharacteristic
503C3×C4C2×D4×D511yescharacteristic
504Dic3—24no—
505Dic3—42no—
506Dic3—104no—
507Dic3—202no—
508C2×C5—22no—
509C2×C5C2×#90912yes—
510C2×C5C22×(C2×D3)⋊C411yescharacteristic
511D5—22no—
512D5#512014yesdirect product factor
513C23—51no—
514C23—54no—
515C23—51no—
516C23—104no—
517C23D5×D1211yescharacteristic
518Q8—34no—
519Q8—64no—
520Q8—62no—
521Q8—154no—
522Q8—308no—
523Q8—308no—
524Q8—304no—
525Q8—302no—
526C2×C4—54no—
527C2×C4—51no—
528C2×C4—51no—
529C2×C4—54no—
530C2×C4—54no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—52no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—308no—
539C2×C4—308no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—604no—
544C2×C4C4×D3×D512yes—
545C2×C4D5×D1211yescharacteristic
546C2×C4D5×#6712yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—22no—
549C8—102no—
550C2×C3—22no—
551C2×C3—54no—
552C2×C3—102no—
553C2×C3C2×D5×C22⋊C411yescharacteristic
554C2×C3D5×#13712yes—
555C5C2×#512011yescharacteristic, complemented, Sylow
556C22—22no—
557C22—54no—
558C22—52no—
559C22—52no—
560C22—108no—
561C22—102no—
562C22D5×(C2×D3)⋊C412yes—
563C22C2×D5×D1211yescharacteristic
564C4—52no—
565C4—52no—
566C4—64no—
567C4—122no—
568C4—304no—
569C4—602no—
570C4D5×(C2×D3)⋊C412yes—
571C4C2×C4×D3×D511yescharacteristic
572C4C2×D5×#6711yescharacteristic
573C3D5×#41911yescharacteristic, complemented, Sylow
574C2—22no—
575C2—54no—
576C2—102no—
577C2D5×#90912yes—
578C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5C2×#419
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11751221C2semidirect
5. C5×#5120C2semidirect
6. #11748417C2semidirect
7. #11748409C2semidirect
8. #11748122C2semidirect
9. D5×#816C2semidirect
19. C2×D5×Dic6C4semidirect
35. #91100C22semidirect
36. C5×#816C22semidirect
37. #90975C22semidirect
38. #90973C22semidirect
54. C2×Dic30C2×C4semidirect
59. C2×C5×Dic6C2×C4semidirect
80. D5×Dic6C2×C4semidirect
103. #5120D5direct (N × H)
198. #816C2×D5semidirect
302. C2×Dic6C4×D5semidirect
388. C3×D5#419semidirect
490. C3×C5C2×#419semidirect
512. D5#5120direct (N × H)
555. C5C2×#5120semidirect
573. C3D5×#419semidirect

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×C3×D5×M162
D5×#9262
#117512212
C5×#51202
#117484172
#117484092
#117481222
D5×#8162
D5×#4193
C2×#51205