Finite Group Databasebeta

← D5×#5483 #14481712

Subgroups — D5×#5483 #14481712

Order 1920.

2592 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756242C211yesmaximal, characteristic, complemented
2C5×#5483C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4#11755432C212yesmaximal, complemented
5C2×D5×#217C212yesmaximal
6#11754468C214yesmaximal, complemented
7D5×#924C214yesmaximal, complemented
8#11753044C218yesmaximal, complemented
9D5×#878C218yesmaximal, complemented
10D5×#543—31nomaximal, Hall
11C24×C3×D5C2211yescharacteristic
12C22×C3×C4×D5C2212yes—
13C22×D5×Dic3C2214yes—
14C2×D5×Dic6C2214yescomplemented
15C2×C3×C5×C22⋊C4C2211yescharacteristic
16C2×#6719C2212yes—
17#91813C2214yescomplemented
18#91767C2218yescomplemented
19C2×C5×#217C2212yes—
20C5×#924C2214yescomplemented
21C5×#878C2218yescomplemented
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×#685C2212yes—
24C3×D5×C22⋊C4C2214yes—
25C3×D5×C22⋊C4C2214yes—
26#91576C2218yescomplemented
27#91575C2218yescomplemented
28#91574C2218yescomplemented
29D5×#217C2214yes—
30D5×#217C2214yes—
31D5×#217C2214yes—
32D5×#217C2214yes—
33C2×#6665C2214yes—
34#91431C2218yescomplemented
35#91430C2218yescomplemented
36#91422C2218yescomplemented
37#91421C2218yescomplemented
38D5×C4⋊Dic3C2214yescomplemented
39D5×Dic3⋊C4C2218yescomplemented
40#91360C2214yescomplemented
41#91359C2214yescomplemented
42#91349C2218yescomplemented
43C2×#5483—51nomaximal, Hall
44C5×#543—31no—
45#65968—34no—
46#65968—38no—
47D5×C22⋊Q8—38no—
48D5×C22⋊Q8—34no—
49C2×D5×C22⋊C4—32no—
50C2×D5×C22⋊C4D311yescharacteristic
51#65817—31no—
52#65817—32no—
53C24×C3×C5C2311yescharacteristic
54C23×C3×D5—44no—
55C23×C3×D5Q818yescomplemented
56C23×C3×D5C2312yes—
57C23×C3×D5C2311yescharacteristic
58C23×C3×D5C2312yes—
59C23×C3×D5C2311yescharacteristic
60C22×C3×C4×C5C2312yes—
61C22×Dic15C2314yes—
62C2×Dic30C2314yescomplemented
63C22×C5×Dic3C2314yes—
64C2×C5×Dic6C2314yescomplemented
65C22×C3×Dic5C2312yes—
66C2×C3×C4×D5—44no—
67C2×C3×C4×D5C2314yes—
68C2×C3×C4×D5C2314yes—
69C2×#1204C2318yescomplemented
70C2×D5×Dic3—48no—
71C2×D5×Dic3C2318yes—
72C2×D5×Dic3C2318yes—
73D5×Dic6—48no—
74C3×C5×C22⋊C4C2314yes—
75#6719C2314yes—
76#6719C2314yes—
77C4⋊Dic15C2314yescomplemented
78#6712C2318yescomplemented
79C5×#217C2314yes—
80C5×#217C2314yes—
81C5×C4⋊Dic3C2314yescomplemented
82C5×Dic3⋊C4C2318yescomplemented
83C3×C22⋊Dic5C2314yes—
84C3×#685C2318yes—
85Dic3⋊Dic5C2318yescomplemented
86#6669C2318yescomplemented
87#6668C2318yescomplemented
88#6665C2318yes—
89#6665C2318yes—
90C22×C3×C22⋊C4—51no—
91C22×#217—52no—
92C2×#924—54no—
93#5483—51no—
94#5483—52no—
95#5483—54no—
96#5483—58no—
97#5483D511yescharacteristic, direct product factor
98C2×#878—58no—
99C24×D5C2×D311yescharacteristic
100C2×Q8×D5—34no—
101C22×C4×D5—34no—
102C22×C4×D5C2×D312yes—
103C5×C22⋊Q8—34no—
104C5×C22⋊Q8—38no—
105C2×C5×C22⋊C4—32no—
106C2×C5×C22⋊C4C2×D311yescharacteristic
107C2×C22⋊Dic5—32no—
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4092—34no—
110#4092—38no—
111C2×#685—34no—
112C2×#685C2×D312yes—
113#4070—34no—
114#4070—38no—
115#4043—34no—
116#4043—38no—
117#4042—38no—
118#4042—38no—
119#4042—38no—
120D5×C4⋊C4—38no—
121D5×C4⋊C4—34no—
122D5×C22⋊C4—34no—
123D5×C22⋊C4—34no—
124D5×C22⋊C4—34no—
125D5×C22⋊C4—34no—
126D5×C22⋊C4C2×D314yes—
127D5×C22⋊C4C2×D314yes—
128#4024—38no—
129#4024—38no—
130#4024—38no—
131C2×#543—151noSylow
132C23×C3×C5—42no—
133C23×C3×C5C2×Q814yescomplemented
134C23×C3×C5C2412yes—
135C23×C3×C5C2411yescharacteristic
136C22×C3×D5—28no—
137C22×C3×D5—24no—
138C22×C3×D5—416no—
139C22×C3×D5—42no—
140C22×C3×D5—44no—
141C22×C3×D5C2×Q818yes—
142C22×C3×D5C2×Q814yes—
143C22×C3×D5C2×Q818yescomplemented
144C22×C3×D5C2×Q814yescomplemented
145C22×C3×D5C2411yescharacteristic
146C22×C3×D5C2412yes—
147C22×C3×D5C2411yescharacteristic
148C2×C3×C4×C5—42no—
149C2×C3×C4×C5C2414yes—
150C2×Dic15—44no—
151C2×Dic15C2418yes—
152Dic30—44no—
153C2×C5×Dic3—44no—
154C2×C5×Dic3C2418yes—
155C5×Dic6—44no—
156C2×C3×Dic5—42no—
157C2×C3×Dic5C2414yes—
158C3×C4×D5—28no—
159C3×C4×D5—44no—
160#1204—48no—
161D5×Dic3—216no—
162D5×Dic3—48no—
163C25×C3—51no—
164C23×C3×C4—52no—
165C23×Dic3—54no—
166C22×Dic6—54no—
167C2×C3×C22⋊C4—51no—
168C2×C3×C22⋊C4—52no—
169C2×C3×C22⋊C4—54no—
170C2×C3×C22⋊C4—54no—
171C2×C3×C22⋊C4C2×D511yescharacteristic
172C2×#217—52no—
173C2×#217—54no—
174C2×#217—54no—
175C2×#217—54no—
176C2×#217—54no—
177C2×#217—54no—
178C2×#217C2×D512yes—
179C2×C4⋊Dic3—54no—
180#924—54no—
181#924—54no—
182#924—58no—
183#924—54no—
184#924—58no—
185#924C2×D514yescomplemented
186C2×Dic3⋊C4—58no—
187#878—58no—
188#878—58no—
189#878—58no—
190#878—58no—
191#878—58no—
192#878—58no—
193#878—58no—
194#878C2×D518yescomplemented
195C24×C5C22×D311yescharacteristic
196C23×D5—44no—
197C23×D5Dic618yescomplemented
198C23×D5C22×D312yes—
199C23×D5C22×D311yescharacteristic
200C23×D5C22×D311yescharacteristic
201C23×D5C22×D312yes—
202C2×C5×Q8—34no—
203C22×C4×C5—34no—
204C22×C4×C5C22×D312yes—
205C22×Dic5—34no—
206C22×Dic5C22×D312yes—
207Q8×D5—128no—
208C2×C4×D5—38no—
209C2×C4×D5—38no—
210C2×C4×D5—44no—
211C2×C4×D5—128no—
212C2×C4×D5C22×D314yes—
213C2×C4×D5C22×D314yes—
214C2×Dic10—34no—
215C2×Dic10—38no—
216C5×C4⋊C4—38no—
217C5×C4⋊C4—34no—
218C5×C22⋊C4—34no—
219C5×C22⋊C4—34no—
220C5×C22⋊C4C22×D314yes—
221C22⋊Dic5—34no—
222C22⋊Dic5—34no—
223C22⋊Dic5C22×D314yes—
224#685—38no—
225#685—38no—
226#685C22×D318yes—
227C4⋊Dic5—34no—
228C4⋊Dic5—38no—
229#683—38no—
230#683—38no—
231#683—38no—
232#543—31no—
233#543—152no—
234#543—154no—
235#543—158no—
236#543—151no—
237C2×C22⋊Q8—158no—
238C2×C22⋊Q8—154no—
239C22×C22⋊C4—51no—
240C22×C22⋊C4—152no—
241C22×C3×C5—22no—
242C22×C3×C5—24no—
243C22×C3×C5—44no—
244C22×C3×C5C22×Q814yes—
245C22×C3×C5C22×Q812yes—
246C22×C3×C5C2511yescharacteristic
247C2×C3×D5—24no—
248C2×C3×D5—22no—
249C2×C3×D5—216no—
250C2×C3×D5—28no—
251C2×C3×D5—44no—
252C2×C3×D5—48no—
253C2×C3×D5C22×Q812yes—
254C2×C3×D5C22×Q814yes—
255C2×C3×D5C22×Q812yes—
256C2×C3×D5H(5,𝔽2)14yes—
257C3×C4×C5—24no—
258Dic15—28no—
259C3×Dic5—24no—
260C5×Dic3—28no—
261C24×C3—51no—
262C24×C3—52no—
263C24×C3—58no—
264C24×C3—52no—
265C24×C3—51no—
266C24×C3—204no—
267C24×C3C22×D511yescharacteristic
268C22×C3×C4—52no—
269C22×C3×C4—54no—
270C22×C3×C4—54no—
271C22×C3×C4—204no—
272C22×C3×C4C22×D512yes—
273C22×Dic3—54no—
274C22×Dic3—58no—
275C22×Dic3—58no—
276C22×Dic3—208no—
277C22×Dic3C22×D514yes—
278C2×Dic6—54no—
279C2×Dic6—58no—
280C2×Dic6—208no—
281C2×Dic6C22×D514yescomplemented
282C3×C22⋊C4—54no—
283C3×C22⋊C4—58no—
284C3×C22⋊C4C22×D514yes—
285#217—54no—
286#217—54no—
287#217—58no—
288#217—58no—
289#217C22×D514yes—
290#217C22×D514yes—
291C4⋊Dic3—54no—
292C4⋊Dic3—58no—
293C4⋊Dic3C22×D514yescomplemented
294Dic3⋊C4—58no—
295Dic3⋊C4—58no—
296Dic3⋊C4—58no—
297Dic3⋊C4C22×D518yescomplemented
298C23×C5—42no—
299C23×C5C2×Dic614yescomplemented
300C23×C5C23×D311yescharacteristic
301C23×C5C23×D312yes—
302C22×D5—24no—
303C22×D5—28no—
304C22×D5—416no—
305C22×D5—44no—
306C22×D5—42no—
307C22×D5C2×Dic618yes—
308C22×D5C2×Dic614yes—
309C22×D5C2×Dic614yescomplemented
310C22×D5C2×Dic618yescomplemented
311C22×D5C23×D311yescharacteristic
312C22×D5C23×D312yes—
313C22×D5C23×D311yescharacteristic
314C5×Q8—124no—
315C2×C4×C5—38no—
316C2×C4×C5—42no—
317C2×C4×C5—124no—
318C2×C4×C5C23×D314yes—
319C2×Dic5—38no—
320C2×Dic5—42no—
321C2×Dic5—124no—
322C2×Dic5C23×D314yes—
323C4×D5—28no—
324C4×D5—44no—
325C4×D5—616no—
326C4×D5—128no—
327Dic10—128no—
328Dic10—124no—
329C25—51no—
330C22×Q8—154no—
331C23×C4—52no—
332C23×C4—154no—
333C22⋊Q8—34no—
334C22⋊Q8—38no—
335C22⋊Q8—158no—
336C22⋊Q8—158no—
337C22⋊Q8—158no—
338C22⋊Q8—158no—
339C22⋊Q8—158no—
340C22⋊Q8—158no—
341C22⋊Q8—158no—
342C22⋊Q8—158no—
343C22⋊Q8—154no—
344C22⋊Q8—154no—
345C22⋊Q8—154no—
346C22⋊Q8—158no—
347C2×C4⋊C4—158no—
348C2×C4⋊C4—154no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—52no—
352C2×C22⋊C4—54no—
353C2×C22⋊C4—54no—
354C2×C22⋊C4—154no—
355C2×C22⋊C4—154no—
356C2×C22⋊C4—154no—
357C2×C22⋊C4—154no—
358C2×C22⋊C4—154no—
359C2×C22⋊C4—152no—
360C2×C22⋊C4D3×D511yescharacteristic
361C2×C3×C5—22no—
362C2×C3×C5—24no—
363C2×C3×C5C23×Q811yescharacteristic
364C2×C3×C5C2×H(5,𝔽2)12yes—
365C3×D5—24no—
366C3×D5—22no—
367C3×D5#54314yescomplemented
368C23×C3—42no—
369C23×C3—51no—
370C23×C3—54no—
371C23×C3—58no—
372C23×C3—51no—
373C23×C3—52no—
374C23×C3—58no—
375C23×C3—54no—
376C23×C3—108no—
377C23×C3—104no—
378C23×C3—204no—
379C23×C3—202no—
380C23×C3—2016no—
381C23×C3Q8×D514yescomplemented
382C23×C3C23×D511yescharacteristic
383C23×C3C23×D512yes—
384C2×C3×C4—42no—
385C2×C3×C4—54no—
386C2×C3×C4—108no—
387C2×C3×C4—204no—
388C2×C3×C4—202no—
389C2×C3×C4C23×D514yes—
390C2×Dic3—44no—
391C2×Dic3—58no—
392C2×Dic3—1016no—
393C2×Dic3—208no—
394C2×Dic3—204no—
395C2×Dic3C23×D518yes—
396Dic6—44no—
397Dic6—208no—
398Dic6—204no—
399C22×C5—22no—
400C22×C5—24no—
401C22×C5—44no—
402C22×C5C22×Dic612yes—
403C22×C5C22×Dic614yes—
404C22×C5C24×D311yescharacteristic
405C2×D5—22no—
406C2×D5—24no—
407C2×D5—28no—
408C2×D5—216no—
409C2×D5—48no—
410C2×D5—44no—
411C2×D5C22×Dic612yes—
412C2×D5C22×Dic614yes—
413C2×D5C22×Dic612yes—
414C2×D5#100414yes—
415C4×C5—24no—
416C4×C5—68no—
417Dic5—24no—
418Dic5—68no—
419C24—52no—
420C24—51no—
421C24—58no—
422C24—51no—
423C24—52no—
424C24—204no—
425C24C2×D3×D511yescharacteristic
426C2×Q8—34no—
427C2×Q8—158no—
428C2×Q8—154no—
429C2×Q8—608no—
430C22×C4—34no—
431C22×C4—52no—
432C22×C4—54no—
433C22×C4—54no—
434C22×C4—158no—
435C22×C4—158no—
436C22×C4—154no—
437C22×C4—204no—
438C22×C4—608no—
439C22×C4C2×D3×D512yes—
440C4⋊C4—38no—
441C4⋊C4—34no—
442C4⋊C4—158no—
443C4⋊C4—158no—
444C4⋊C4—158no—
445C4⋊C4—158no—
446C4⋊C4—154no—
447C22⋊C4—34no—
448C22⋊C4—34no—
449C22⋊C4—54no—
450C22⋊C4—58no—
451C22⋊C4—158no—
452C22⋊C4—158no—
453C22⋊C4—154no—
454C22⋊C4—154no—
455C22⋊C4C2×D3×D514yes—
456C3×C5C2×#54311yescharacteristic, complemented, Hall
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—44no—
460C22×C3—52no—
461C22×C3—54no—
462C22×C3—52no—
463C22×C3—54no—
464C22×C3—1016no—
465C22×C3—108no—
466C22×C3—104no—
467C22×C3—102no—
468C22×C3—208no—
469C22×C3—204no—
470C22×C3C2×Q8×D512yes—
471C22×C3C2×Q8×D514yes—
472C22×C3C24×D511yescharacteristic
473C3×C4—24no—
474C3×C4—104no—
475Dic3—28no—
476Dic3—108no—
477C2×C5—22no—
478C2×C5—24no—
479C2×C5C23×Dic611yescharacteristic
480C2×C5C2×#100412yes—
481D5—22no—
482D5—24no—
483D5#548314yesdirect product factor
484C23—42no—
485C23—51no—
486C23—58no—
487C23—54no—
488C23—52no—
489C23—51no—
490C23—54no—
491C23—58no—
492C23—104no—
493C23—108no—
494C23—202no—
495C23—204no—
496C23—2016no—
497C23D5×Dic614yescomplemented
498C23C22×D3×D511yescharacteristic
499C23C22×D3×D512yes—
500Q8—124no—
501Q8—604no—
502Q8—608no—
503C2×C4—38no—
504C2×C4—42no—
505C2×C4—54no—
506C2×C4—108no—
507C2×C4—124no—
508C2×C4—158no—
509C2×C4—204no—
510C2×C4—202no—
511C2×C4—3016no—
512C2×C4—608no—
513C2×C4—604no—
514C2×C4C22×D3×D514yes—
515C2×C3—24no—
516C2×C3—22no—
517C2×C3—54no—
518C2×C3—104no—
519C2×C3—102no—
520C2×C3C22×Q8×D511yescharacteristic
521C2×C3D5×H(5,𝔽2)12yes—
522C5C2×#548311yescharacteristic, complemented, Sylow
523C22—22no—
524C22—24no—
525C22—44no—
526C22—52no—
527C22—54no—
528C22—54no—
529C22—52no—
530C22—108no—
531C22—1016no—
532C22—102no—
533C22—104no—
534C22—204no—
535C22—208no—
536C22C2×D5×Dic612yes—
537C22C2×D5×Dic614yes—
538C22C23×D3×D511yescharacteristic
539C4—24no—
540C4—68no—
541C4—104no—
542C4—308no—
543C3D5×#54311yescharacteristic, complemented, Sylow
544C2—22no—
545C2—24no—
546C2—54no—
547C2—102no—
548C2—104no—
549C2C22×D5×Dic611yescharacteristic
550C2D5×#100412yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×C22⋊C4C22
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#543
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11756242C2semidirect
2. C5×#5483C2semidirect
4. #11755432C2semidirect
6. #11754468C2semidirect
7. D5×#924C2semidirect
8. #11753044C2semidirect
9. D5×#878C2semidirect
14. C2×D5×Dic6C22semidirect
17. #91813C22semidirect
18. #91767C22semidirect
20. C5×#924C22semidirect
21. C5×#878C22semidirect
26. #91576C22semidirect
27. #91575C22semidirect
28. #91574C22semidirect
34. #91431C22semidirect
35. #91430C22semidirect
36. #91422C22semidirect
37. #91421C22semidirect
38. D5×C4⋊Dic3C22semidirect
39. D5×Dic3⋊C4C22semidirect
40. #91360C22semidirect
41. #91359C22semidirect
42. #91349C22semidirect
55. C23×C3×D5Q8semidirect
62. C2×Dic30C23semidirect
64. C2×C5×Dic6C23semidirect
69. C2×#1204C23semidirect
77. C4⋊Dic15C23semidirect
78. #6712C23semidirect
81. C5×C4⋊Dic3C23semidirect
82. C5×Dic3⋊C4C23semidirect
85. Dic3⋊Dic5C23semidirect
86. #6669C23semidirect
87. #6668C23semidirect
97. #5483D5direct (N × H)
133. C23×C3×C5C2×Q8semidirect
143. C22×C3×D5C2×Q8semidirect
144. C22×C3×D5C2×Q8semidirect
185. #924C2×D5semidirect
194. #878C2×D5semidirect
197. C23×D5Dic6semidirect
281. C2×Dic6C22×D5semidirect
293. C4⋊Dic3C22×D5semidirect
297. Dic3⋊C4C22×D5semidirect
299. C23×C5C2×Dic6semidirect
309. C22×D5C2×Dic6semidirect
310. C22×D5C2×Dic6semidirect
367. C3×D5#543semidirect
381. C23×C3Q8×D5semidirect
456. C3×C5C2×#543semidirect
483. D5#5483direct (N × H)
497. C23D5×Dic6semidirect
522. C5C2×#5483semidirect
543. C3D5×#543semidirect

Maximal subgroups

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

subgroupindex
#117562422
C5×#54832
C2×C3×D5×C22⋊C42
#117554322
C2×D5×#2172
#117544682
D5×#9242
#117530442
D5×#8782
D5×#5433
C2×#54835