Finite Group Databasebeta

← D5×#4714 #14437872

Subgroups — D5×#4714 #14437872

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
1D5×#875C211yesmaximal, characteristic
2D5×#869C211yesmaximal, characteristic, complemented
3#11750815C211yesmaximal, characteristic, complemented
4C5×#4714C211yesmaximal, characteristic, complemented
5C3×D5×#97C211yesmaximal, characteristic, complemented
6D5×#821C212yesmaximal
7#11748023C212yesmaximal, complemented
8#11748022C212yesmaximal, complemented
9D5×#816C212yesmaximal, complemented
10#11746914C211yesmaximal, characteristic, complemented
11#11746909C211yesmaximal, characteristic, complemented
12D5×#489—31nomaximal, Hall
13C2×D5×D12C2211yescharacteristic
14C2×D5×Dic6—21no—
15C2×D5×Dic6C2211yescharacteristic
16#91764C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C5×#875C2211yescharacteristic
19C5×#869C2211yescharacteristic, complemented
20C2×C3×C8×D5C2212yes—
21C3×C42×D5C2211yescharacteristic
22D5×(C2×D3)⋊C4—21no—
23D5×(C2×D3)⋊C4—21no—
24#91468—21no—
25#91468C2212yescomplemented
26D5×C4⋊Dic3—21no—
27D5×C4⋊Dic3C2212yes—
28#91376—21no—
29#91375C2211yescharacteristic
30#91373C2211yescharacteristic
31#91350—21no—
32#91350—21no—
33C3×C5×#97C2211yescharacteristic, complemented
34#91105C2212yes—
35#91100C2212yescomplemented
36C5×#821C2212yes—
37C5×#816C2212yescomplemented
38C3×#3947C2212yescomplemented
39C3×#3935C2211yescharacteristic, complemented
40#90975C2212yescomplemented
41#90973C2212yescomplemented
42#90969C2212yes—
43#90967C2212yes—
44C2×#4714—51nomaximal, Hall
45D5×C4⋊Q8—31no—
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×#97D311yescharacteristic, complemented
56C22×D3×D5—21no—
57C2×D60C2311yescharacteristic
58C2×Dic30—21no—
59C2×Dic30C2311yescharacteristic
60C2×C5×D12C2311yescharacteristic
61C2×C5×Dic6—21no—
62C2×C5×Dic6C2311yescharacteristic
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1204—22no—
67C2×#1204—21no—
68C2×#1203—21no—
69C2×D5×Dic3—22no—
70C2×D5×Dic3—21no—
71D5×D12—24no—
72D5×Dic6—24no—
73D5×Dic6—44no—
74C2×C3×C5×C8C2312yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80C5×(C2×D3)⋊C4—21no—
81C5×(C2×D3)⋊C4—21no—
82C5×C4⋊Dic3—21no—
83C5×C4⋊Dic3C2312yes—
84C3×C4×Dic5D411yescharacteristic
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5C2311yescharacteristic
87C2×C3×#168C2312yes—
88C3×C8×D5—24no—
89#6668—22no—
90#6668—22no—
91#6667—21no—
92#6667—21no—
93(C2×D3)⋊Dic5—21no—
94(C2×D3)⋊Dic5—21no—
95C2×#875—51no—
96C2×#869—51no—
97C2×C3×#97—51no—
98C2×#821—52no—
99C2×#816—52no—
100#4714—51no—
101#4714—51no—
102#4714—51no—
103#4714—52no—
104#4714—52no—
105#4714D511yescharacteristic, direct product factor
106C2×Q8×D5—31no—
107C2×Q8×D5—61no—
108C2×D4×D5—31no—
109C5×C4⋊Q8—31no—
110C5×#124—31no—
111#4093—31no—
112#4090—61no—
113#4082—31no—
114C2×C8×D5C2×D312yes—
115D5×C4⋊C4—32no—
116D5×C4⋊C4—61no—
117#4034—32no—
118#4034—61no—
119#4031—61no—
120#4031—61no—
121D5×C22⋊C4—61no—
122D5×C22⋊C4—61no—
123#4021—31no—
124C42×D5C2×D311yescharacteristic
125#4015—31no—
126C5×#103—32no—
127C5×#102—32no—
128C5×#97C2×D311yescharacteristic, complemented
129#3967—32no—
130#3964—32no—
131#3953—32no—
132#3948—32no—
133#3947C2×D312yescomplemented
134#3942—32no—
135#3941—32no—
136#3935C2×D311yescharacteristic, complemented
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—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—21no—
148C2×Dic15—22no—
149D60—22no—
150Dic30—22no—
151Dic30—42no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—22no—
154C5×D12—22no—
155C5×Dic6—22no—
156C5×Dic6—42no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D411yescharacteristic
159C2×C3×Dic5C2×D411yescharacteristic
160C3×C4×D5—22no—
161C3×C4×D5—22no—
162C3×C4×D5#4114yes—
163#1204—44no—
164#1204—42no—
165#1203—42no—
166D5×Dic3—42no—
167D5×Dic3—44no—
168C3×C5×C8—22no—
169C3×#168—22no—
170C22×D12—51no—
171C22×Dic6—51no—
172C22×Dic6—101no—
173C22×C3×C8—52no—
174C2×C3×C42—51no—
175C2×(C2×D3)⋊C4—101no—
176C2×(C2×D3)⋊C4—101no—
177C2×C4⋊Dic3—52no—
178C2×C4⋊Dic3—101no—
179#875—51no—
180#875—51no—
181#875—51no—
182#875—101no—
183#875—101no—
184#875C2×D511yescharacteristic
185#869—51no—
186#869—52no—
187#869—101no—
188#869—101no—
189#869C2×D511yescharacteristic, complemented
190C3×#97—52no—
191C3×#97—51no—
192C3×#97C2×D511yescharacteristic, complemented
193#821—52no—
194#821—52no—
195#821—52no—
196#821C2×D512yes—
197#816—52no—
198#816—52no—
199#816—52no—
200#816C2×D512yescomplemented
201C23×D5—61no—
202C2×C5×Q8—31no—
203C2×C5×Q8—61no—
204C2×C5×D4—31no—
205C2×C22⋊D5—61no—
206Q8×D5—64no—
207Q8×D5—124no—
208D4×D5—64no—
209C2×D20—31no—
210C2×C4×D5—61no—
211C2×C4×D5—62no—
212C2×C4×D5D1211yescharacteristic
213C2×C4×D5D1211yescharacteristic
214C2×C4×D5C22×D311yescharacteristic
215C2×Dic10—31no—
216C2×Dic10—61no—
217C2×Dic10—61no—
218C2×Dic10—62no—
219C2×C5×C8C22×D312yes—
220C5×C4⋊C4—32no—
221C5×C4⋊C4—61no—
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—32no—
232C4⋊Dic5—61no—
233#683—62no—
234#683—62no—
235C4×Dic5D1211yescharacteristic
236C4×Dic5D1211yescharacteristic
237C4×Dic5C22×D311yescharacteristic
238C2×#168C22×D312yes—
239C8×D5—24no—
240C2×C4⋊Q8—151no—
241C2×#124—151no—
242#489—31no—
243#489—152no—
244#489—152no—
245#489—151no—
246#489—151no—
247#489—151no—
248C2×#103—152no—
249C2×#102—152no—
250C2×#97—51no—
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×C5C2×#4112yes—
265Dic15—41no—
266Dic15—42no—
267C3×Dic5—21no—
268C3×Dic5—21no—
269C3×Dic5#12412yes—
270C5×Dic3—41no—
271C5×Dic3—42no—
272C23×D3—101no—
273C22×C3×C4—51no—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×Dic3—102no—
277C22×Dic3—101no—
278C2×D12—51no—
279C2×D12—104no—
280C2×D12—101no—
281C2×D12C22×D511yescharacteristic
282C2×Dic6—21no—
283C2×Dic6—51no—
284C2×Dic6—104no—
285C2×Dic6—102no—
286C2×Dic6—101no—
287C2×Dic6—101no—
288C2×Dic6—204no—
289C2×Dic6C22×D511yescharacteristic
290C2×C3×C8—52no—
291C2×C3×C8—104no—
292C2×C3×C8C22×D512yes—
293C3×C42—51no—
294C3×C42—51no—
295C3×C42—51no—
296C3×C42C22×D511yescharacteristic
297(C2×D3)⋊C4—21no—
298(C2×D3)⋊C4—21no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301(C2×D3)⋊C4—101no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—101no—
304(C2×D3)⋊C4—101no—
305C4⋊Dic3—21no—
306C4⋊Dic3—52no—
307C4⋊Dic3—102no—
308C4⋊Dic3—102no—
309C4⋊Dic3—101no—
310C4⋊Dic3C22×D512yes—
311C23×C5—61no—
312C22×D5—61no—
313C22×D5—122no—
314C22×D5—122no—
315C22×D5—122no—
316C22×D5C2×D1211yescharacteristic
317C5×Q8—62no—
318C5×Q8—122no—
319C5×D4—62no—
320C2×C4×C5—62no—
321C2×C4×C5—61no—
322C2×C4×C5C2×D1211yescharacteristic
323C2×C4×C5C2×D1211yescharacteristic
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—122no—
326C2×Dic5—62no—
327C2×Dic5—61no—
328C2×Dic5C2×D1211yescharacteristic
329C2×Dic5C2×D1211yescharacteristic
330C2×Dic5C2×D1211yescharacteristic
331D20—62no—
332C4×D5—22no—
333C4×D5—22no—
334C4×D5—122no—
335C4×D5—124no—
336C4×D5#23514yes—
337Dic10—62no—
338Dic10—124no—
339Dic10—122no—
340Dic10—122no—
341C5×C8—22no—
342#168—22no—
343C22×Q8—151no—
344C22×Q8—301no—
345C22×D4—151no—
346C22×C8—52no—
347C4⋊Q8—31no—
348C4⋊Q8—152no—
349C4⋊Q8—151no—
350C4⋊Q8—301no—
351C4⋊Q8—301no—
352#124—31no—
353#124—151no—
354#124—151no—
355#124—151no—
356#124—301no—
357#124—301no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—301no—
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—52no—
372#97—51no—
373#97D3×D511yescharacteristic, complemented
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—
386C2×C3×C4—51no—
387C2×C3×C4—54no—
388C2×C3×C4—51no—
389C2×C3×C4—51no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4D4×D511yescharacteristic
393C2×C3×C4D4×D511yescharacteristic
394C2×C3×C4C23×D511yescharacteristic
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—102no—
398C2×Dic3—101no—
399C2×Dic3—202no—
400C2×Dic3—204no—
401D12—22no—
402D12—102no—
403D12—202no—
404Dic6—22no—
405Dic6—42no—
406Dic6—102no—
407Dic6—202no—
408Dic6—204no—
409Dic6—202no—
410C3×C8—22no—
411C3×C8—102no—
412C22×C5—121no—
413C22×C5—121no—
414C22×C5—121no—
415C22×C5C22×D1211yescharacteristic
416C2×D5—121no—
417C2×D5—121no—
418C2×D5—121no—
419C2×D5—244no—
420C2×D5#87512yes—
421C2×D5#90812yes—
422C2×D5#90912yes—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—121no—
426C4×C5—122no—
427C4×C5C2×#23512yes—
428Dic5—21no—
429Dic5—21no—
430Dic5—121no—
431Dic5—122no—
432Dic5#87512yes—
433C24—301no—
434C2×Q8—31no—
435C2×Q8—61no—
436C2×Q8—151no—
437C2×Q8—301no—
438C2×Q8—302no—
439C2×Q8—304no—
440C2×Q8—301no—
441C2×Q8—604no—
442C2×D4—31no—
443C2×D4—151no—
444C2×D4—304no—
445C2×D4—301no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—301no—
450C22×C4—302no—
451C2×C8—52no—
452C2×C8—104no—
453C2×C8C2×D3×D512yes—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—152no—
457C4⋊C4—302no—
458C4⋊C4—302no—
459C4⋊C4—301no—
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—52no—
487C3×C4—101no—
488C3×C4—101no—
489C3×C4D5×#4112yes—
490Dic3—42no—
491Dic3—41no—
492Dic3—202no—
493Dic3—201no—
494C2×C5—241no—
495C2×C5C2×#87511yescharacteristic
496C2×C5C2×#90811yescharacteristic
497C2×C5C2×#90911yescharacteristic
498D5—241no—
499D5#471414yesdirect product factor
500C23—51no—
501C23—61no—
502C23—301no—
503C23—602no—
504C23—602no—
505C23—602no—
506Q8—62no—
507Q8—122no—
508Q8—302no—
509Q8—602no—
510Q8—602no—
511Q8—604no—
512D4—62no—
513D4—302no—
514D4—602no—
515C2×C4—51no—
516C2×C4—54no—
517C2×C4—51no—
518C2×C4—51no—
519C2×C4—61no—
520C2×C4—62no—
521C2×C4—102no—
522C2×C4—102no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—602no—
526C2×C4—604no—
527C2×C4D5×D1211yescharacteristic
528C2×C4D5×D1211yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—22no—
531C8—102no—
532C2×C3—54no—
533C2×C3D5×#12411yescharacteristic
534C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
535C2×C3D5×#13711yescharacteristic
536D3—81no—
537D3—401no—
538C5C2×#471411yescharacteristic, complemented, Sylow
539C22—52no—
540C22—52no—
541C22—52no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—601no—
546C22—601no—
547C22—601no—
548C22—1204no—
549C22C2×D5×D1211yescharacteristic
550C4—21no—
551C4—21no—
552C4—52no—
553C4—101no—
554C4—101no—
555C4—121no—
556C4—122no—
557C4—601no—
558C4—602no—
559C4D5×#23512yes—
560C3D5×#48911yescharacteristic, complemented, Sylow
561C2—54no—
562C2—241no—
563C2—1201no—
564C2D5×#87511yescharacteristic
565C2D5×#90811yescharacteristic
566C2D5×#90911yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
hypercenter#97D3×D5
hypocenterC3×C5C2×#489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. D5×#869C2semidirect
3. #11750815C2semidirect
4. C5×#4714C2semidirect
5. C3×D5×#97C2semidirect
7. #11748023C2semidirect
8. #11748022C2semidirect
9. D5×#816C2semidirect
10. #11746914C2semidirect
11. #11746909C2semidirect
17. #91758C22semidirect
19. C5×#869C22semidirect
25. #91468C22semidirect
33. C3×C5×#97C22semidirect
35. #91100C22semidirect
37. C5×#816C22semidirect
38. C3×#3947C22semidirect
39. C3×#3935C22semidirect
40. #90975C22semidirect
41. #90973C22semidirect
55. D5×#97D3semidirect
105. #4714D5direct (N × H)
128. C5×#97C2×D3semidirect
133. #3947C2×D3semidirect
136. #3935C2×D3semidirect
189. #869C2×D5semidirect
192. C3×#97C2×D5semidirect
200. #816C2×D5semidirect
373. #97D3×D5semidirect
378. C3×D5#489semidirect
472. C3×C5C2×#489semidirect
499. D5#4714direct (N × H)
538. C5C2×#4714semidirect
560. C3D5×#489semidirect

Maximal subgroups

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

subgroupindex
D5×#8752
D5×#8692
#117508152
C5×#47142
C3×D5×#972
D5×#8212
#117480232
#117480222
D5×#8162
#117469142
#117469092
D5×#4893
C2×#47145