Finite Group Databasebeta

← D5×#5713 #14484723

Subgroups — D5×#5713 #14484723

Order 1920.

2480 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756472C211yesmaximal, characteristic, complemented
2C5×#5713C211yesmaximal, characteristic, complemented
3C3×D5×#127C211yesmaximal, characteristic
4#11754863C214yesmaximal, complemented
5#11754862C214yesmaximal, complemented
6#11754861C214yesmaximal, complemented
7D5×#936C214yesmaximal, complemented
8D5×#935C214yesmaximal, complemented
9D4×D5×Dic3C214yesmaximal, complemented
10#11752636C212yesmaximal, complemented
11C4×D5×Dic6C212yesmaximal, complemented
12D5×#559—31nomaximal, Hall
13C2×C3×D4×D5C2214yes—
14C2×C3×D4×D5C2212yes—
15C22×D5×Dic3C2214yes—
16C2×D5×Dic6C2212yes—
17C3×C5×#127C2211yescharacteristic
18#91825C2214yescomplemented
19#91824C2214yescomplemented
20D4×Dic15C2214yescomplemented
21C4×Dic30C2212yescomplemented
22C5×#936C2214yescomplemented
23C5×#935C2214yescomplemented
24C5×D4×Dic3C2214yescomplemented
25C4×C5×Dic6C2212yescomplemented
26C3×#4086C2214yes—
27C3×#4086C2212yes—
28C3×#4020C2211yescharacteristic
29C3×C42×D5C2211yescharacteristic
30#91559C2218yescomplemented
31Dic3×C22⋊D5C2218yescomplemented
32#91548C2218yescomplemented
33D5×#217C2218yes—
34D5×#217C2214yes—
35#91537C2214yescomplemented
36#91536C2214yescomplemented
37#91534C2218yescomplemented
38#91534C2218yescomplemented
39C4×#1204C2214yescomplemented
40#91434C2214yescomplemented
41Dic3×D20C2214yescomplemented
42D5×C4⋊Dic3C2212yes—
43#91407C2218yescomplemented
44D5×Dic3⋊C4C2214yes—
45C4×D5×Dic3C2214yes—
46#91368C2214yescomplemented
47#91364C2214yescomplemented
48#91333C2212yescomplemented
49Dic5×Dic6C2212yescomplemented
50#91323C2214yescomplemented
51C2×#5713—51nomaximal, Hall
52C5×#559—31no—
53D5×#127D311yescharacteristic
54#66047—31no—
55#66015—34no—
56D5×#124—34no—
57#65998—34no—
58D5×#123—34no—
59#65919—32no—
60C4×Q8×D5—32no—
61#65893—34no—
62C4×D4×D5—34no—
63C23×C3×D5C2314yes—
64C2×C3×C5×D4C2314yes—
65C2×C3×C5×D4C2312yes—
66C22×Dic15C2314yes—
67C2×Dic30C2312yes—
68C22×C5×Dic3C2314yes—
69C2×C5×Dic6C2312yes—
70C2×C3×C22⋊D5C2318yes—
71C2×C3×C22⋊D5C2314yes—
72C3×D4×D5—216no—
73C3×D4×D5—44no—
74C2×C3×D20C2314yes—
75C2×C3×D20C2312yes—
76C2×C3×C4×D5C2311yescharacteristic
77C2×C3×C4×D5C2312yes—
78C2×#1204C2314yes—
79C2×D5×Dic3—48no—
80C2×D5×Dic3C2314yes—
81C2×D5×Dic3C2314yes—
82C2×D5×Dic3C2318yes—
83D5×Dic6—28no—
84C3×C42×C5C2311yescharacteristic
85#6719C2314yes—
86#6719C2318yes—
87C4⋊Dic15C2312yes—
88#6712C2314yes—
89C4×Dic15C2314yes—
90C5×#217C2318yes—
91C5×#217C2314yes—
92C5×C4⋊Dic3C2312yes—
93C5×Dic3⋊C4C2314yes—
94C4×C5×Dic3C2314yes—
95C3×C4×Dic5C2312yes—
96C3×C4×Dic5C2311yescharacteristic
97Dic3⋊Dic5C2314yes—
98#6669C2314yes—
99#6668C2314yes—
100#6665C2318yes—
101#6665C2318yes—
102#6665C2318yes—
103Dic3×Dic5C2314yes—
104Dic3×Dic5C2314yes—
105C2×C3×#127—51no—
106C2×#936—54no—
107C2×#935—54no—
108C2×D4×Dic3—54no—
109#5713—51no—
110#5713—54no—
111#5713—54no—
112#5713—54no—
113#5713—52no—
114#5713D511yescharacteristic, direct product factor
115C2×C4×Dic6—52no—
116C2×Q8×D5—32no—
117C2×D4×D5C2×D314yes—
118C2×D4×D5C2×D312yes—
119C22×C4×D5—34no—
120C5×#127C2×D311yescharacteristic
121C5×#124—34no—
122C5×#123—34no—
123C4×C5×Q8—32no—
124C4×C5×D4—34no—
125#4093—34no—
126Q8×Dic5—32no—
127#4086C2×D314yes—
128#4086C2×D312yes—
129#4082—34no—
130#4081—34no—
131D4×Dic5—34no—
132#4075—34no—
133C4×C22⋊D5—38no—
134#4040—38no—
135#4039—34no—
136D5×C4⋊C4—34no—
137D5×C4⋊C4—32no—
138#4033—32no—
139#4033—34no—
140#4032—34no—
141#4031—38no—
142#4031—38no—
143#4029—38no—
144#4027—38no—
145D5×C22⋊C4—38no—
146D5×C22⋊C4—34no—
147#4021—34no—
148#4020C2×D311yescharacteristic
149C4×D20—34no—
150C42×D5—34no—
151C42×D5C2×D311yescharacteristic
152C4×Dic10—32no—
153C4×Dic10—34no—
154C2×#559—151noSylow
155C23×C3×C5C2414yes—
156C22×C3×D5—216no—
157C22×C3×D5—28no—
158C22×C3×D5C2414yes—
159C22×C3×D5C2411yescharacteristic
160C3×C5×D4—28no—
161C3×C5×D4—42no—
162C2×C3×C4×C5C2411yescharacteristic
163C2×C3×C4×C5C2412yes—
164C2×Dic15—44no—
165C2×Dic15C2414yes—
166C2×Dic15C2414yes—
167Dic30—24no—
168C2×C5×Dic3—44no—
169C2×C5×Dic3C2414yes—
170C2×C5×Dic3C2414yes—
171C5×Dic6—24no—
172C3×C22⋊D5—216no—
173C3×C22⋊D5—44no—
174C2×C3×Dic5C2411yescharacteristic
175C2×C3×Dic5C2412yes—
176C3×D20—28no—
177C3×D20—42no—
178C3×C4×D5—22no—
179C3×C4×D5#4118yes—
180#1204—28no—
181D5×Dic3—28no—
182D5×Dic3—28no—
183D5×Dic3—48no—
184C22×C3×D4—54no—
185C22×C3×D4—52no—
186C23×Dic3—54no—
187C22×Dic6—52no—
188C3×#127—52no—
189C3×#127—54no—
190C3×#127—51no—
191C3×#127C2×D511yescharacteristic
192C2×C3×C42—51no—
193C2×#217—58no—
194C2×#217—54no—
195#936—54no—
196#936—54no—
197#936—58no—
198#936—58no—
199#936—54no—
200#936C2×D514yescomplemented
201#935—54no—
202#935—54no—
203#935—54no—
204#935—58no—
205#935—58no—
206#935C2×D514yescomplemented
207D4×Dic3—54no—
208D4×Dic3—58no—
209D4×Dic3—58no—
210D4×Dic3—54no—
211D4×Dic3—54no—
212D4×Dic3C2×D514yescomplemented
213C2×C4⋊Dic3—52no—
214C2×Dic3⋊C4—54no—
215C2×C4×Dic3—54no—
216C4×Dic6—52no—
217C4×Dic6—52no—
218C4×Dic6—52no—
219C4×Dic6—54no—
220C4×Dic6—54no—
221C4×Dic6C2×D512yescomplemented
222C23×D5C22×D314yes—
223C2×C5×Q8—32no—
224C2×C5×D4C22×D314yes—
225C2×C5×D4C22×D312yes—
226C22×C4×C5—34no—
227C2×C22⋊D5C22×D318yes—
228C2×C22⋊D5C22×D314yes—
229C22×Dic5—34no—
230Q8×D5—68no—
231D4×D5—216no—
232D4×D5—44no—
233C2×D20C22×D314yes—
234C2×D20C22×D312yes—
235C2×C4×D5—34no—
236C2×C4×D5—34no—
237C2×C4×D5—38no—
238C2×C4×D5—128no—
239C2×C4×D5C22×D311yescharacteristic
240C2×C4×D5C22×D312yes—
241C2×Dic10—32no—
242C2×Dic10—34no—
243C5×C4⋊C4—32no—
244C5×C4⋊C4—34no—
245C5×C22⋊C4—38no—
246C5×C22⋊C4—34no—
247C42×C5—34no—
248C42×C5C22×D311yescharacteristic
249C22⋊Dic5—38no—
250C22⋊Dic5—34no—
251#685—38no—
252#685—38no—
253#685—38no—
254C4⋊Dic5—32no—
255C4⋊Dic5—34no—
256#683—34no—
257#683—34no—
258#683—34no—
259C4×Dic5—34no—
260C4×Dic5—34no—
261C4×Dic5—34no—
262C4×Dic5C22×D312yes—
263C4×Dic5C22×D311yescharacteristic
264#559—31no—
265#559—154no—
266#559—152no—
267#559—154no—
268#559—154no—
269#559—151no—
270C2×#127—51no—
271C2×#124—154no—
272C2×#123—154no—
273C2×C4×Q8—152no—
274C2×C4×D4—154no—
275C22×C3×C5—28no—
276C22×C3×C5—24no—
277C22×C3×C5C2511yescharacteristic
278C2×C3×D5—28no—
279C2×C3×D5—24no—
280C2×C3×D5—416no—
281C2×C3×D5C2×#4114yes—
282C2×C3×D5H(5,𝔽2)12yes—
283C3×C4×C5—21no—
284C3×C4×C5C2×#4114yes—
285Dic15—24no—
286Dic15—24no—
287C3×Dic5—21no—
288C3×Dic5C2×#4114yes—
289C5×Dic3—24no—
290C5×Dic3—24no—
291C24×C3—54no—
292C2×C3×D4—58no—
293C2×C3×D4—54no—
294C2×C3×D4—54no—
295C2×C3×D4—52no—
296C2×C3×D4—1016no—
297C2×C3×D4—204no—
298C2×C3×D4C22×D514yes—
299C2×C3×D4C22×D512yes—
300C22×C3×C4—52no—
301C22×C3×C4—51no—
302C22×Dic3—54no—
303C22×Dic3—54no—
304C22×Dic3—54no—
305C22×Dic3—58no—
306C22×Dic3—208no—
307C22×Dic3C22×D514yes—
308C2×Dic6—52no—
309C2×Dic6—54no—
310C2×Dic6—108no—
311C2×Dic6C22×D512yes—
312C3×C42—51no—
313C3×C42—52no—
314C3×C42C22×D511yescharacteristic
315#217—58no—
316#217—54no—
317#217—58no—
318#217—58no—
319#217—58no—
320#217C22×D518yes—
321#217C22×D514yes—
322C4⋊Dic3—52no—
323C4⋊Dic3—54no—
324C4⋊Dic3C22×D512yes—
325Dic3⋊C4—54no—
326Dic3⋊C4—54no—
327Dic3⋊C4—54no—
328Dic3⋊C4C22×D514yes—
329C4×Dic3—54no—
330C4×Dic3—54no—
331C4×Dic3—54no—
332C4×Dic3C22×D514yes—
333C23×C5C23×D314yes—
334C22×D5—216no—
335C22×D5—28no—
336C22×D5C23×D314yes—
337C22×D5C23×D311yescharacteristic
338C5×Q8—64no—
339C5×D4—28no—
340C5×D4—42no—
341C2×C4×C5—34no—
342C2×C4×C5—34no—
343C2×C4×C5—124no—
344C2×C4×C5C23×D311yescharacteristic
345C2×C4×C5C23×D312yes—
346C22⋊D5—216no—
347C22⋊D5—44no—
348C2×Dic5—34no—
349C2×Dic5—34no—
350C2×Dic5—124no—
351C2×Dic5C23×D311yescharacteristic
352C2×Dic5C23×D312yes—
353D20—28no—
354D20—42no—
355C4×D5—22no—
356C4×D5—68no—
357C4×D5—68no—
358C4×D5—128no—
359C4×D5#23718yes—
360Dic10—64no—
361Dic10—68no—
362C22×Q8—152no—
363C22×D4—54no—
364C22×D4—52no—
365C23×C4—154no—
366#127—52no—
367#127—54no—
368#127—51no—
369#127D3×D511yescharacteristic
370#124—34no—
371#124—154no—
372#124—158no—
373#124—158no—
374#124—154no—
375#124—154no—
376#123—34no—
377#123—158no—
378#123—154no—
379#123—158no—
380#123—154no—
381#123—154no—
382C4×Q8—32no—
383C4×Q8—154no—
384C4×Q8—152no—
385C4×Q8—154no—
386C4×Q8—152no—
387C4×Q8—152no—
388C4×D4—34no—
389C4×D4—154no—
390C4×D4—158no—
391C4×D4—154no—
392C4×D4—158no—
393C4×D4—154no—
394C2×C4⋊C4—152no—
395C2×C4⋊C4—154no—
396C2×C22⋊C4—158no—
397C2×C22⋊C4—154no—
398C2×C42—51no—
399C2×C42—154no—
400C2×C3×C5—44no—
401C2×C3×C5C22×#4112yes—
402C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
403C3×D5—44no—
404C3×D5#55914yescomplemented
405C23×C3—51no—
406C23×C3—54no—
407C23×C3—108no—
408C23×C3—1016no—
409C23×C3C23×D514yes—
410C3×D4—28no—
411C3×D4—42no—
412C3×D4—1016no—
413C3×D4—108no—
414C3×D4—202no—
415C3×D4—204no—
416C2×C3×C4—52no—
417C2×C3×C4—58no—
418C2×C3×C4—51no—
419C2×C3×C4—102no—
420C2×C3×C4C23×D511yescharacteristic
421C2×C3×C4C23×D512yes—
422C2×Dic3—44no—
423C2×Dic3—54no—
424C2×Dic3—54no—
425C2×Dic3—108no—
426C2×Dic3—108no—
427C2×Dic3—208no—
428C2×Dic3—204no—
429C2×Dic3C23×D514yes—
430C2×Dic3C23×D514yes—
431Dic6—24no—
432Dic6—108no—
433Dic6—104no—
434C22×C5—28no—
435C22×C5—24no—
436C22×C5C24×D311yescharacteristic
437C2×D5—28no—
438C2×D5—24no—
439C2×D5—416no—
440C2×D5C2×#23714yes—
441C2×D5#100412yes—
442C4×C5—21no—
443C4×C5—64no—
444C4×C5—64no—
445C4×C5C2×#23714yes—
446Dic5—21no—
447Dic5—64no—
448Dic5—64no—
449Dic5C2×#23714yes—
450C24—54no—
451C2×Q8—32no—
452C2×Q8—154no—
453C2×Q8—152no—
454C2×Q8—308no—
455C2×D4—58no—
456C2×D4—54no—
457C2×D4—54no—
458C2×D4—52no—
459C2×D4—1016no—
460C2×D4—204no—
461C2×D4C2×D3×D514yes—
462C2×D4C2×D3×D512yes—
463C22×C4—34no—
464C22×C4—52no—
465C22×C4—51no—
466C22×C4—154no—
467C22×C4—154no—
468C22×C4—158no—
469C22×C4—154no—
470C22×C4—608no—
471C4⋊C4—32no—
472C4⋊C4—34no—
473C4⋊C4—154no—
474C4⋊C4—154no—
475C4⋊C4—154no—
476C4⋊C4—152no—
477C4⋊C4—154no—
478C22⋊C4—38no—
479C22⋊C4—34no—
480C22⋊C4—158no—
481C22⋊C4—158no—
482C22⋊C4—158no—
483C22⋊C4—158no—
484C22⋊C4—154no—
485C42—34no—
486C42—51no—
487C42—52no—
488C42—154no—
489C42—154no—
490C42—154no—
491C42C2×D3×D511yescharacteristic
492C3×C5C2×#55911yescharacteristic, complemented, Hall
493C22×C3—28no—
494C22×C3—24no—
495C22×C3—54no—
496C22×C3—52no—
497C22×C3—108no—
498C22×C3—104no—
499C22×C3—2016no—
500C22×C3C24×D511yescharacteristic
501C3×C4—21no—
502C3×C4—54no—
503C3×C4—101no—
504C3×C4D5×#4114yes—
505Dic3—24no—
506Dic3—24no—
507Dic3—104no—
508Dic3—104no—
509C2×C5—44no—
510C2×C5C22×#23712yes—
511C2×C5C2×#100411yescharacteristic
512D5—44no—
513D5#571314yesdirect product factor
514C23—51no—
515C23—54no—
516C23—108no—
517C23—1016no—
518C23C22×D3×D514yes—
519Q8—64no—
520Q8—308no—
521Q8—304no—
522D4—28no—
523D4—42no—
524D4—1016no—
525D4—108no—
526D4—202no—
527D4—204no—
528C2×C4—34no—
529C2×C4—34no—
530C2×C4—52no—
531C2×C4—58no—
532C2×C4—51no—
533C2×C4—102no—
534C2×C4—124no—
535C2×C4—154no—
536C2×C4—154no—
537C2×C4—308no—
538C2×C4—308no—
539C2×C4—608no—
540C2×C4—604no—
541C2×C4C22×D3×D511yescharacteristic
542C2×C4C22×D3×D512yes—
543C2×C3—44no—
544C2×C3—54no—
545C2×C3—204no—
546C2×C3C2×D5×#4112yes—
547C2×C3D5×H(5,𝔽2)11yescharacteristic
548C5C2×#571311yescharacteristic, complemented, Sylow
549C22—28no—
550C22—24no—
551C22—54no—
552C22—52no—
553C22—108no—
554C22—104no—
555C22—2016no—
556C22C23×D3×D511yescharacteristic
557C4—21no—
558C4—54no—
559C4—64no—
560C4—64no—
561C4—101no—
562C4—304no—
563C4—304no—
564C4D5×#23714yes—
565C3D5×#55911yescharacteristic, complemented, Sylow
566C2—44no—
567C2—54no—
568C2—204no—
569C2C2×D5×#23712yes—
570C2D5×#100411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#127C22
prime radicalC3×D5×#127C2
hypercenter#127D3×D5
hypocenterC3×C5C2×#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11756472C2semidirect
2. C5×#5713C2semidirect
4. #11754863C2semidirect
5. #11754862C2semidirect
6. #11754861C2semidirect
7. D5×#936C2semidirect
8. D5×#935C2semidirect
9. D4×D5×Dic3C2semidirect
10. #11752636C2semidirect
11. C4×D5×Dic6C2semidirect
18. #91825C22semidirect
19. #91824C22semidirect
20. D4×Dic15C22semidirect
21. C4×Dic30C22semidirect
22. C5×#936C22semidirect
23. C5×#935C22semidirect
24. C5×D4×Dic3C22semidirect
25. C4×C5×Dic6C22semidirect
30. #91559C22semidirect
31. Dic3×C22⋊D5C22semidirect
32. #91548C22semidirect
35. #91537C22semidirect
36. #91536C22semidirect
37. #91534C22semidirect
38. #91534C22semidirect
39. C4×#1204C22semidirect
40. #91434C22semidirect
41. Dic3×D20C22semidirect
43. #91407C22semidirect
46. #91368C22semidirect
47. #91364C22semidirect
48. #91333C22semidirect
49. Dic5×Dic6C22semidirect
50. #91323C22semidirect
114. #5713D5direct (N × H)
200. #936C2×D5semidirect
206. #935C2×D5semidirect
212. D4×Dic3C2×D5semidirect
221. C4×Dic6C2×D5semidirect
404. C3×D5#559semidirect
492. C3×C5C2×#559semidirect
513. D5#5713direct (N × H)
548. C5C2×#5713semidirect
565. C3D5×#559semidirect

Maximal subgroups

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

subgroupindex
#117564722
C5×#57132
C3×D5×#1272
#117548632
#117548622
#117548612
D5×#9362
D5×#9352
D4×D5×Dic32
#117526362
C4×D5×Dic62
D5×#5593
C2×#57135