Finite Group Databasebeta

← D5×#5055 #14437899

Subgroups — D5×#5055 #14437899

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×#124C211yesmaximal, characteristic
2D5×#869C211yesmaximal, characteristic, complemented
3#11751156C211yesmaximal, characteristic, complemented
4C5×#5055C211yesmaximal, characteristic, complemented
5#11749352C212yesmaximal, complemented
6D5×#835C212yesmaximal, complemented
7#11749105C212yesmaximal, complemented
8D5×#832C212yesmaximal
9D5×#803C211yesmaximal, characteristic, complemented
10#11746898C211yesmaximal, characteristic, complemented
11#11746893C211yesmaximal, characteristic, complemented
12D5×#489—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×C3×D4×D5C2211yescharacteristic
15C2×D5×Dic6—21no—
16C3×C5×#124C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C5×#869C2211yescharacteristic, complemented
19C3×#4093C2211yescharacteristic
20C3×#4082C2211yescharacteristic
21C3×#4031—21no—
22C3×#4031—21no—
23C3×D5×C22⋊C4—21no—
24C3×D5×C22⋊C4—21no—
25C3×#4021C2211yescharacteristic
26C3×C42×D5C2211yescharacteristic
27#91468—21no—
28#91468C2212yescomplemented
29D5×C4⋊Dic3—21no—
30D5×C4⋊Dic3C2212yes—
31#91376—21no—
32C2×D5×C3⋊C8C2212yes—
33#91119C2212yescomplemented
34#91116C2212yes—
35#91087C2211yescharacteristic, complemented
36C5×#835C2212yescomplemented
37C5×#832C2212yes—
38C5×#803C2211yescharacteristic, complemented
39#90971C2212yescomplemented
40#90970C2212yescomplemented
41#90965C2212yes—
42#90964C2212yes—
43#90952C2212yescomplemented
44C2×#5055—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46D5×#124D311yescharacteristic
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—
56C23×C3×D5—21no—
57C2×C3×C5×Q8C2311yescharacteristic
58C2×C3×C5×D4C2311yescharacteristic
59C2×Dic30—21no—
60C2×C5×Dic6—21no—
61C2×C3×C22⋊D5—21no—
62C3×Q8×D5—24no—
63C3×D4×D5—24no—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×C4×D5D411yescharacteristic
67C2×C3×C4×D5D411yescharacteristic
68C2×C3×C4×D5C2311yescharacteristic
69C2×C3×Dic10—21no—
70C2×C3×Dic10C2311yescharacteristic
71C2×#1204—22no—
72C2×D5×Dic3—22no—
73D5×Dic6—44no—
74C3×C5×C22⋊C4—21no—
75C3×C5×C22⋊C4—21no—
76C3×C42×C5C2311yescharacteristic
77C4⋊Dic15—21no—
78C4⋊Dic15C2312yes—
79C2×C3⋊#168C2312yes—
80C5×C4⋊Dic3—21no—
81C5×C4⋊Dic3C2312yes—
82C2×C5×C3⋊C8C2312yes—
83C3×C22⋊Dic5—21no—
84C3×C22⋊Dic5—21no—
85C3×#685—21no—
86C3×#685—21no—
87C3×#685—21no—
88C3×#685—21no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92#6668—22no—
93#6668—22no—
94D5×C3⋊C8—24no—
95C2×C3×#124—51no—
96C2×#869—51no—
97C2×#835—52no—
98C2×#832—52no—
99#5055—51no—
100#5055—51no—
101#5055—52no—
102#5055—52no—
103#5055—51no—
104#5055D511yescharacteristic, direct product factor
105C2×#803—51no—
106C2×Q8×D5—61no—
107C2×Q8×D5C2×D311yescharacteristic
108C2×D4×D5C2×D311yescharacteristic
109C5×C4⋊Q8—31no—
110C5×#124C2×D311yescharacteristic
111#4093C2×D311yescharacteristic
112#4090—61no—
113#4082C2×D311yescharacteristic
114C2×C8×D5—32no—
115D5×C4⋊C4—32no—
116D5×C4⋊C4—61no—
117#4034—32no—
118#4034—61no—
119#4031—21no—
120#4031—21no—
121D5×C22⋊C4—21no—
122D5×C22⋊C4—21no—
123#4021C2×D311yescharacteristic
124C42×D5C2×D311yescharacteristic
125#4015—31no—
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
138C23×C3×C5—21no—
139C22×C3×D5—21no—
140C22×C3×D5—42no—
141C22×C3×D5—42no—
142C22×C3×D5—42no—
143C22×C3×D5C2×D411yescharacteristic
144C3×C5×Q8—22no—
145C3×C5×D4—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150C2×Dic15—22no—
151Dic30—42no—
152C2×C5×Dic3—22no—
153C5×Dic6—42no—
154C3×C22⋊D5—42no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5C2×D411yescharacteristic
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C3×D20—22no—
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5—42no—
163C3×C4×D5#4114yes—
164C3×Dic10—22no—
165C3×Dic10—42no—
166#1204—44no—
167D5×Dic3—44no—
168C3⋊#168—22no—
169C5×C3⋊C8—22no—
170C22×C3×Q8—51no—
171C22×C3×D4—51no—
172C22×Dic6—101no—
173C3×#124—51no—
174C3×#124—51no—
175C3×#124—51no—
176C3×#124—101no—
177C3×#124—101no—
178C3×#124C2×D511yescharacteristic
179C2×C3×C22⋊C4—101no—
180C2×C3×C22⋊C4—101no—
181C2×C3×C42—51no—
182C2×C4⋊Dic3—52no—
183C2×C4⋊Dic3—101no—
184C22×C3⋊C8—52no—
185#869—51no—
186#869—52no—
187#869—101no—
188#869—101no—
189#869C2×D511yescharacteristic, complemented
190#835—52no—
191#835—52no—
192#835—52no—
193#835C2×D512yescomplemented
194#832—52no—
195#832—52no—
196#832—52no—
197#832C2×D512yes—
198#803—51no—
199#803—52no—
200#803C2×D511yescharacteristic, complemented
201C23×D5—21no—
202C2×C5×Q8—61no—
203C2×C5×Q8C22×D311yescharacteristic
204C2×C5×D4C22×D311yescharacteristic
205C2×C22⋊D5—21no—
206Q8×D5—24no—
207Q8×D5—124no—
208D4×D5—24no—
209C2×D20C22×D311yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—62no—
212C2×C4×D5#6711yescharacteristic
213C2×C4×D5#6711yescharacteristic
214C2×C4×D5C22×D311yescharacteristic
215C2×Dic10—21no—
216C2×Dic10—61no—
217C2×Dic10—62no—
218C2×Dic10C22×D311yescharacteristic
219C2×C5×C8—32no—
220C5×C4⋊C4—32no—
221C5×C4⋊C4—61no—
222C5×C22⋊C4—21no—
223C5×C22⋊C4—21no—
224C42×C5C22×D311yescharacteristic
225C22⋊Dic5—21no—
226C22⋊Dic5—21no—
227#685—21no—
228#685—21no—
229#685—21no—
230#685—21no—
231C4⋊Dic5—32no—
232C4⋊Dic5—61no—
233#683—62no—
234#683—62no—
235C4×Dic5#6711yescharacteristic
236C4×Dic5#6711yescharacteristic
237C4×Dic5C22×D311yescharacteristic
238C2×#168—32no—
239C8×D5—64no—
240C2×C4⋊Q8—151no—
241C2×#124—51no—
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×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5—41no—
254C22×C3×C5C22×D411yescharacteristic
255C2×C3×D5—41no—
256C2×C3×D5—41no—
257C2×C3×D5—41no—
258C2×C3×D5—84no—
259C2×C3×D5#12412yes—
260C2×C3×D5AGL(1,ℤ/8)12yes—
261C2×C3×D5#13712yes—
262C3×C4×C5—21no—
263C3×C4×C5—21no—
264C3×C4×C5—41no—
265C3×C4×C5C2×#4112yes—
266Dic15—42no—
267C3×Dic5—21no—
268C3×Dic5—21no—
269C3×Dic5—41no—
270C3×Dic5#12412yes—
271C5×Dic3—42no—
272C24×C3—101no—
273C2×C3×Q8—51no—
274C2×C3×Q8—101no—
275C2×C3×Q8—104no—
276C2×C3×Q8C22×D511yescharacteristic
277C2×C3×D4—51no—
278C2×C3×D4—104no—
279C2×C3×D4—101no—
280C2×C3×D4C22×D511yescharacteristic
281C22×C3×C4—51no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—101no—
285C22×Dic3—102no—
286C2×Dic6—21no—
287C2×Dic6—102no—
288C2×Dic6—101no—
289C2×Dic6—204no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—101no—
293C3×C22⋊C4—101no—
294C3×C22⋊C4—101no—
295C3×C22⋊C4—101no—
296C3×C22⋊C4—101no—
297C3×C22⋊C4—101no—
298C3×C42—51no—
299C3×C42—51no—
300C3×C42—51no—
301C3×C42C22×D511yescharacteristic
302C4⋊Dic3—21no—
303C4⋊Dic3—52no—
304C4⋊Dic3—102no—
305C4⋊Dic3—102no—
306C4⋊Dic3—101no—
307C4⋊Dic3C22×D512yes—
308C2×C3⋊C8—52no—
309C2×C3⋊C8—104no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—21no—
312C22×D5—21no—
313C22×D5—42no—
314C22×D5—42no—
315C22×D5—42no—
316C22×D5C2×#6711yescharacteristic
317C5×Q8—22no—
318C5×Q8—122no—
319C5×D4—22no—
320C2×C4×C5—21no—
321C2×C4×C5—62no—
322C2×C4×C5C2×#6711yescharacteristic
323C2×C4×C5C2×#6711yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—42no—
326C2×Dic5—21no—
327C2×Dic5—62no—
328C2×Dic5C2×#6711yescharacteristic
329C2×Dic5C2×#6711yescharacteristic
330C2×Dic5C2×#6711yescharacteristic
331D20—22no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—42no—
335C4×D5—124no—
336C4×D5#23714yes—
337Dic10—22no—
338Dic10—42no—
339Dic10—124no—
340Dic10—122no—
341C5×C8—62no—
342#168—62no—
343C22×Q8—51no—
344C22×Q8—301no—
345C22×D4—51no—
346C22×C8—152no—
347C4⋊Q8—31no—
348C4⋊Q8—152no—
349C4⋊Q8—151no—
350C4⋊Q8—301no—
351C4⋊Q8—301no—
352#124—51no—
353#124—51no—
354#124—51no—
355#124—101no—
356#124—101no—
357#124D3×D511yescharacteristic
358C2×C4⋊C4—152no—
359C2×C4⋊C4—301no—
360C2×C22⋊C4—101no—
361C2×C22⋊C4—101no—
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×C5—81no—
375C2×C3×C5C2×#12411yescharacteristic
376C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
377C2×C3×C5C2×#13711yescharacteristic
378C3×D5—81no—
379C3×D5#48914yescomplemented
380C23×C3—21no—
381C23×C3—51no—
382C23×C3—101no—
383C23×C3—202no—
384C23×C3—202no—
385C23×C3—202no—
386C3×Q8—22no—
387C3×Q8—102no—
388C3×Q8—202no—
389C3×D4—22no—
390C3×D4—102no—
391C3×D4—202no—
392C2×C3×C4—21no—
393C2×C3×C4—51no—
394C2×C3×C4—54no—
395C2×C3×C4—51no—
396C2×C3×C4—51no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—101no—
400C2×C3×C4—202no—
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C23×D511yescharacteristic
404C2×Dic3—22no—
405C2×Dic3—102no—
406C2×Dic3—204no—
407Dic6—42no—
408Dic6—204no—
409Dic6—202no—
410C3⋊C8—22no—
411C3⋊C8—102no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5C22×#6711yescharacteristic
416C2×D5—41no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—84no—
420C2×D5#93612yes—
421C2×D5#94912yes—
422C2×D5#95112yes—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—41no—
426C4×C5—122no—
427C4×C5C2×#23712yes—
428Dic5—21no—
429Dic5—21no—
430Dic5—41no—
431Dic5—122no—
432Dic5#93612yes—
433C24—101no—
434C2×Q8—51no—
435C2×Q8—61no—
436C2×Q8—101no—
437C2×Q8—104no—
438C2×Q8—302no—
439C2×Q8—301no—
440C2×Q8—604no—
441C2×Q8C2×D3×D511yescharacteristic
442C2×D4—51no—
443C2×D4—104no—
444C2×D4—101no—
445C2×D4C2×D3×D511yescharacteristic
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—101no—
450C22×C4—302no—
451C2×C8—32no—
452C2×C8—152no—
453C2×C8—304no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—152no—
457C4⋊C4—302no—
458C4⋊C4—302no—
459C4⋊C4—301no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—101no—
463C22⋊C4—101no—
464C22⋊C4—101no—
465C22⋊C4—101no—
466C22⋊C4—101no—
467C22⋊C4—101no—
468C42—51no—
469C42—51no—
470C42—51no—
471C42C2×D3×D511yescharacteristic
472C3×C5C2×#48911yescharacteristic, complemented, Hall
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—52no—
477C22×C3—52no—
478C22×C3—52no—
479C22×C3—201no—
480C22×C3—201no—
481C22×C3—201no—
482C22×C3—404no—
483C22×C3C2×D4×D511yescharacteristic
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—41no—
487C3×C4—52no—
488C3×C4—101no—
489C3×C4—101no—
490C3×C4—201no—
491C3×C4D5×#4112yes—
492Dic3—42no—
493Dic3—202no—
494C2×C5—81no—
495C2×C5C2×#93611yescharacteristic
496C2×C5C2×#94911yescharacteristic
497C2×C5C2×#95111yescharacteristic
498D5—81no—
499D5#505514yesdirect product factor
500C23—21no—
501C23—51no—
502C23—101no—
503C23—202no—
504C23—202no—
505C23—202no—
506Q8—22no—
507Q8—102no—
508Q8—122no—
509Q8—202no—
510Q8—602no—
511Q8—604no—
512D4—22no—
513D4—102no—
514D4—202no—
515C2×C4—21no—
516C2×C4—51no—
517C2×C4—54no—
518C2×C4—51no—
519C2×C4—51no—
520C2×C4—62no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—101no—
524C2×C4—202no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4D5×#6711yescharacteristic
528C2×C4D5×#6711yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—62no—
531C8—302no—
532C2×C3—54no—
533C2×C3—81no—
534C2×C3—401no—
535C2×C3D5×#12411yescharacteristic
536C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
537C2×C3D5×#13711yescharacteristic
538C5C2×#505511yescharacteristic, complemented, Sylow
539C22—41no—
540C22—41no—
541C22—41no—
542C22—52no—
543C22—52no—
544C22—52no—
545C22—201no—
546C22—201no—
547C22—201no—
548C22—404no—
549C22C2×D5×#6711yescharacteristic
550C4—21no—
551C4—21no—
552C4—41no—
553C4—52no—
554C4—101no—
555C4—101no—
556C4—122no—
557C4—201no—
558C4—602no—
559C4D5×#23712yes—
560C3D5×#48911yescharacteristic, complemented, Sylow
561C2—54no—
562C2—81no—
563C2—401no—
564C2D5×#93611yescharacteristic
565C2D5×#94911yescharacteristic
566C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
hypercenter#124D3×D5
hypocenterC3×C5C2×#489
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
2. D5×#869C2semidirect
3. #11751156C2semidirect
4. C5×#5055C2semidirect
5. #11749352C2semidirect
6. D5×#835C2semidirect
7. #11749105C2semidirect
9. D5×#803C2semidirect
10. #11746898C2semidirect
11. #11746893C2semidirect
17. #91758C22semidirect
18. C5×#869C22semidirect
28. #91468C22semidirect
33. #91119C22semidirect
35. #91087C22semidirect
36. C5×#835C22semidirect
38. C5×#803C22semidirect
39. #90971C22semidirect
40. #90970C22semidirect
43. #90952C22semidirect
104. #5055D5direct (N × H)
189. #869C2×D5semidirect
193. #835C2×D5semidirect
200. #803C2×D5semidirect
379. C3×D5#489semidirect
472. C3×C5C2×#489semidirect
499. D5#5055direct (N × H)
538. C5C2×#5055semidirect
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×#1242
D5×#8692
#117511562
C5×#50552
#117493522
D5×#8352
#117491052
D5×#8322
D5×#8032
#117468982
#117468932
D5×#4893
C2×#50555