Finite Group Databasebeta

← D5×#5020 #14430030

Subgroups — D5×#5020 #14430030

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic
2D5×#869C211yesmaximal, characteristic
3#11751121C211yesmaximal, characteristic, complemented
4C5×#5020C211yesmaximal, characteristic, complemented
5#11749348C212yesmaximal, complemented
6D5×#835C212yesmaximal
7D5×#808C212yesmaximal
8#11747411C212yesmaximal, complemented
9D5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
10#11746943C211yesmaximal, characteristic, complemented
11#11746918C211yesmaximal, characteristic, complemented
12D5×#475—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×D5×Dic6—21no—
15C3×C4×C5×Q8C2211yescharacteristic
16#91758C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×Q8×Dic5C2211yescharacteristic
19C3×D5×C4⋊C4—21no—
20C3×D5×C4⋊C4C2211yescharacteristic
21C3×#4033—21no—
22C3×#4033C2211yescharacteristic
23C3×C42×D5—21no—
24C3×C42×D5C2211yescharacteristic
25C3×C4×Dic10—21no—
26C3×C4×Dic10C2211yescharacteristic
27#91468—21no—
28#91468C2212yes—
29D5×C4⋊Dic3—21no—
30D5×C4⋊Dic3C2212yes—
31#91376—21no—
32C2×D5×C3⋊C8C2212yes—
33#91119C2212yes—
34#91092C2212yes—
35C4⋊(C3⋊#168)C2211yescharacteristic
36C5×#835C2212yes—
37C5×#808C2212yes—
38C5×C4⋊(C3⋊C8)C2211yescharacteristic
39#90987C2212yes—
40#90986C2212yes—
41#90982C2212yes—
42#90971C2212yes—
43#90970C2212yes—
44C2×#5020—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46C4×Q8×D5D311yescharacteristic
47C5×#475—31no—
48#65383—31no—
49#65309—31no—
50D5×#106—32no—
51#65143—32no—
52#65140—31no—
53D5×C4⋊C8—31no—
54D5×#103—32no—
55#65080—32no—
56C2×C3×C5×Q8C2311yescharacteristic
57C2×Dic30—21no—
58C2×C5×Dic6—21no—
59C3×Q8×D5—22no—
60C3×Q8×D5Q814yescomplemented
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5D411yescharacteristic
65C2×C3×C4×D5C2311yescharacteristic
66C2×C3×Dic10—21no—
67C2×C3×Dic10C2311yescharacteristic
68C2×#1204—22no—
69C2×D5×Dic3—22no—
70D5×Dic6—44no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C42×C5—21no—
74C3×C42×C5C2311yescharacteristic
75C4⋊Dic15—21no—
76C4⋊Dic15C2312yes—
77C2×C3⋊#168C2312yes—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2312yes—
80C2×C5×C3⋊C8C2312yes—
81C3×C4⋊Dic5—21no—
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—21no—
84C3×#683—21no—
85C3×#683—21no—
86C3×C4×Dic5—21no—
87C3×C4×Dic5—21no—
88C3×C4×Dic5—21no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92#6668—22no—
93#6668—22no—
94D5×C3⋊C8—24no—
95C2×C3×C4×Q8—51no—
96C2×#869—51no—
97C2×#835—52no—
98#5020—51no—
99#5020—51no—
100#5020—52no—
101#5020—52no—
102#5020—51no—
103#5020D511yescharacteristic, direct product factor
104C2×#808—52no—
105C2×C4⋊(C3⋊C8)—51no—
106C2×Q8×D5—61no—
107C2×Q8×D5C2×D311yescharacteristic
108C5×C4⋊Q8—31no—
109C4×C5×Q8C2×D311yescharacteristic
110Q8×Dic5C2×D311yescharacteristic
111#4090—61no—
112C2×C8×D5—32no—
113D5×C4⋊C4—21no—
114D5×C4⋊C4—32no—
115D5×C4⋊C4—61no—
116D5×C4⋊C4C2×D311yescharacteristic
117#4034—32no—
118#4034—61no—
119#4033—21no—
120#4033C2×D311yescharacteristic
121C42×D5—21no—
122C42×D5C2×D311yescharacteristic
123#4015—31no—
124C4×Dic10—21no—
125C4×Dic10C2×D311yescharacteristic
126C5×#106—32no—
127C5×C4⋊C8—31no—
128C5×#103—32no—
129#3967—32no—
130#3949—32no—
131#3948—32no—
132#3946—32no—
133#3942—32no—
134#3940—32no—
135#3940—32no—
136C4⋊#168—31no—
137C2×#475—151noSylow
138C22×C3×D5C2×D411yescharacteristic
139C3×C5×Q8—21no—
140C3×C5×Q8C2×Q812yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147Dic30—42no—
148C2×C5×Dic3—22no—
149C5×Dic6—42no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5C2×D411yescharacteristic
153C2×C3×Dic5C2×D411yescharacteristic
154C2×C3×Dic5C2×D411yescharacteristic
155C3×C4×D5—24no—
156C3×C4×D5—22no—
157C3×C4×D5—42no—
158C3×C4×D5SD1614yes—
159C3×C4×D5C2×Q812yes—
160C3×C4×D5#4112yes—
161C3×Dic10—21no—
162C3×Dic10—24no—
163C3×Dic10C2×Q812yescomplemented
164#1204—44no—
165D5×Dic3—44no—
166C3⋊#168—22no—
167C5×C3⋊C8—22no—
168C22×C3×Q8—51no—
169C22×Dic6—101no—
170C3×C4×Q8—51no—
171C3×C4×Q8—51no—
172C3×C4×Q8—51no—
173C3×C4×Q8—101no—
174C3×C4×Q8—101no—
175C3×C4×Q8C2×D511yescharacteristic
176C2×C3×C4⋊C4—51no—
177C2×C3×C4⋊C4—101no—
178C2×C3×C42—51no—
179C2×C3×C42—101no—
180C2×C4⋊Dic3—52no—
181C2×C4⋊Dic3—101no—
182C22×C3⋊C8—52no—
183#869—51no—
184#869—52no—
185#869—101no—
186#869—101no—
187#869C2×D511yescharacteristic
188#835—52no—
189#835—52no—
190#835—52no—
191#835C2×D512yes—
192#808—52no—
193#808—52no—
194#808—52no—
195#808C2×D512yes—
196C4⋊(C3⋊C8)—51no—
197C4⋊(C3⋊C8)—52no—
198C4⋊(C3⋊C8)C2×D511yescharacteristic
199C2×C5×Q8—61no—
200C2×C5×Q8C22×D311yescharacteristic
201Q8×D5—22no—
202Q8×D5—124no—
203Q8×D5Dic614yescomplemented
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5—62no—
207C2×C4×D5#6711yescharacteristic
208C2×C4×D5#6711yescharacteristic
209C2×C4×D5C22×D311yescharacteristic
210C2×Dic10—21no—
211C2×Dic10—61no—
212C2×Dic10—62no—
213C2×Dic10C22×D311yescharacteristic
214C2×C5×C8—32no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—32no—
217C5×C4⋊C4—61no—
218C5×C4⋊C4C22×D311yescharacteristic
219C42×C5—21no—
220C42×C5C22×D311yescharacteristic
221C4⋊Dic5—21no—
222C4⋊Dic5—32no—
223C4⋊Dic5—61no—
224C4⋊Dic5C22×D311yescharacteristic
225#683—21no—
226#683—21no—
227#683—21no—
228#683—62no—
229#683—62no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5#6711yescharacteristic
234C4×Dic5#6711yescharacteristic
235C4×Dic5C22×D311yescharacteristic
236C2×#168—32no—
237C8×D5—64no—
238C2×C4⋊Q8—151no—
239C2×C4×Q8—51no—
240#475—31no—
241#475—152no—
242#475—151no—
243#475—152no—
244#475—151no—
245#475—151no—
246C2×#106—152no—
247C2×C4⋊C8—151no—
248C2×#103—152no—
249C22×C3×C5C22×D411yescharacteristic
250C2×C3×D5C22⋊Q812yes—
251C2×C3×D5C2×SD1612yes—
252C2×C3×D5#13712yes—
253C3×C4×C5—22no—
254C3×C4×C5—21no—
255C3×C4×C5—41no—
256C3×C4×C5C2×SD1612yes—
257C3×C4×C5C22×Q811yescharacteristic
258C3×C4×C5C2×#4111yescharacteristic
259Dic15—42no—
260C3×Dic5—22no—
261C3×Dic5—21no—
262C3×Dic5—41no—
263C3×Dic5C22⋊Q812yes—
264C3×Dic5C2×SD1612yes—
265C5×Dic3—42no—
266C2×C3×Q8—54no—
267C2×C3×Q8—51no—
268C2×C3×Q8—101no—
269C2×C3×Q8—102no—
270C2×C3×Q8C22×D511yescharacteristic
271C22×C3×C4—51no—
272C22×C3×C4—51no—
273C22×C3×C4—51no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C22×Dic3—102no—
277C2×Dic6—21no—
278C2×Dic6—102no—
279C2×Dic6—101no—
280C2×Dic6—204no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—51no—
283C3×C4⋊C4—101no—
284C3×C4⋊C4—101no—
285C3×C4⋊C4—101no—
286C3×C4⋊C4—101no—
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C42—21no—
289C3×C42—51no—
290C3×C42—51no—
291C3×C42—51no—
292C3×C42—101no—
293C3×C42—101no—
294C3×C42—101no—
295C3×C42C22×D511yescharacteristic
296C4⋊Dic3—21no—
297C4⋊Dic3—52no—
298C4⋊Dic3—102no—
299C4⋊Dic3—102no—
300C4⋊Dic3—101no—
301C4⋊Dic3C22×D512yes—
302C2×C3⋊C8—52no—
303C2×C3⋊C8—104no—
304C2×C3⋊C8C22×D512yes—
305C22×D5C2×#6711yescharacteristic
306C5×Q8—21no—
307C5×Q8—122no—
308C5×Q8C2×Dic612yescomplemented
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—62no—
312C2×C4×C5C2×#6711yescharacteristic
313C2×C4×C5C2×#6711yescharacteristic
314C2×C4×C5C23×D311yescharacteristic
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—62no—
318C2×Dic5C2×#6711yescharacteristic
319C2×Dic5C2×#6711yescharacteristic
320C2×Dic5C2×#6711yescharacteristic
321C4×D5—24no—
322C4×D5—22no—
323C4×D5—42no—
324C4×D5—124no—
325C4×D5#21514yes—
326C4×D5C2×Dic612yes—
327C4×D5#23512yes—
328Dic10—21no—
329Dic10—24no—
330Dic10—122no—
331Dic10—124no—
332Dic10C2×Dic612yescomplemented
333C5×C8—62no—
334#168—62no—
335C22×Q8—51no—
336C22×Q8—301no—
337C22×C8—152no—
338C4⋊Q8—31no—
339C4⋊Q8—152no—
340C4⋊Q8—151no—
341C4⋊Q8—301no—
342C4⋊Q8—301no—
343C4×Q8—51no—
344C4×Q8—51no—
345C4×Q8—51no—
346C4×Q8—101no—
347C4×Q8—101no—
348C4×Q8D3×D511yescharacteristic
349C2×C4⋊C4—51no—
350C2×C4⋊C4—101no—
351C2×C4⋊C4—152no—
352C2×C4⋊C4—301no—
353C2×C42—51no—
354C2×C42—101no—
355#106—32no—
356#106—152no—
357#106—152no—
358#106—152no—
359C4⋊C8—31no—
360C4⋊C8—152no—
361C4⋊C8—151no—
362#103—32no—
363#103—152no—
364#103—152no—
365#103—152no—
366C2×C3×C5C2×C22⋊Q811yescharacteristic
367C2×C3×C5C22×SD1611yescharacteristic
368C2×C3×C5C2×#13711yescharacteristic
369C3×D5#47514yescomplemented
370C23×C3—51no—
371C3×Q8—21no—
372C3×Q8—52no—
373C3×Q8—104no—
374C3×Q8—101no—
375C3×Q8Q8×D512yescomplemented
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—51no—
379C2×C3×C4—51no—
380C2×C3×C4—52no—
381C2×C3×C4—52no—
382C2×C3×C4—54no—
383C2×C3×C4—51no—
384C2×C3×C4—102no—
385C2×C3×C4—104no—
386C2×C3×C4—101no—
387C2×C3×C4—101no—
388C2×C3×C4—202no—
389C2×C3×C4D4×D511yescharacteristic
390C2×C3×C4D4×D511yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392C2×Dic3—22no—
393C2×Dic3—102no—
394C2×Dic3—204no—
395Dic6—42no—
396Dic6—204no—
397Dic6—202no—
398C3⋊C8—22no—
399C3⋊C8—102no—
400C22×C5C22×#6711yescharacteristic
401C2×D5#92412yes—
402C2×D5C2×#21512yes—
403C2×D5#95112yes—
404C4×C5—22no—
405C4×C5—21no—
406C4×C5—41no—
407C4×C5—122no—
408C4×C5C2×#21512yes—
409C4×C5C22×Dic611yescharacteristic
410C4×C5C2×#23511yescharacteristic
411Dic5—22no—
412Dic5—21no—
413Dic5—41no—
414Dic5—122no—
415Dic5#92412yes—
416Dic5C2×#21512yes—
417C2×Q8—54no—
418C2×Q8—51no—
419C2×Q8—61no—
420C2×Q8—101no—
421C2×Q8—102no—
422C2×Q8—302no—
423C2×Q8—301no—
424C2×Q8—604no—
425C2×Q8C2×D3×D511yescharacteristic
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—302no—
432C2×C8—32no—
433C2×C8—152no—
434C2×C8—304no—
435C4⋊C4—21no—
436C4⋊C4—32no—
437C4⋊C4—51no—
438C4⋊C4—61no—
439C4⋊C4—101no—
440C4⋊C4—101no—
441C4⋊C4—101no—
442C4⋊C4—101no—
443C4⋊C4—152no—
444C4⋊C4—302no—
445C4⋊C4—302no—
446C4⋊C4—301no—
447C4⋊C4C2×D3×D511yescharacteristic
448C42—21no—
449C42—51no—
450C42—51no—
451C42—51no—
452C42—101no—
453C42—101no—
454C42—101no—
455C42C2×D3×D511yescharacteristic
456C3×C5C2×#47511yescharacteristic, complemented, Hall
457C22×C3—52no—
458C22×C3—52no—
459C22×C3—52no—
460C22×C3C2×D4×D511yescharacteristic
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—41no—
464C3×C4—52no—
465C3×C4—52no—
466C3×C4—101no—
467C3×C4—102no—
468C3×C4—201no—
469C3×C4D5×SD1612yes—
470C3×C4C2×Q8×D511yescharacteristic
471C3×C4D5×#4111yescharacteristic
472Dic3—42no—
473Dic3—202no—
474C2×C5C2×#92411yescharacteristic
475C2×C5C22×#21511yescharacteristic
476C2×C5C2×#95111yescharacteristic
477D5#502014yesdirect product factor
478C23—51no—
479Q8—21no—
480Q8—52no—
481Q8—104no—
482Q8—101no—
483Q8—122no—
484Q8—604no—
485Q8—602no—
486Q8D5×Dic612yescomplemented
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—51no—
490C2×C4—51no—
491C2×C4—52no—
492C2×C4—54no—
493C2×C4—52no—
494C2×C4—51no—
495C2×C4—62no—
496C2×C4—102no—
497C2×C4—104no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—202no—
501C2×C4—302no—
502C2×C4—604no—
503C2×C4D5×#6711yescharacteristic
504C2×C4D5×#6711yescharacteristic
505C2×C4C22×D3×D511yescharacteristic
506C8—62no—
507C8—302no—
508C2×C3—54no—
509C2×C3D5×C22⋊Q811yescharacteristic
510C2×C3C2×D5×SD1611yescharacteristic
511C2×C3D5×#13711yescharacteristic
512C5C2×#502011yescharacteristic, complemented, Sylow
513C22—52no—
514C22—52no—
515C22—52no—
516C22C2×D5×#6711yescharacteristic
517C4—22no—
518C4—21no—
519C4—41no—
520C4—52no—
521C4—52no—
522C4—102no—
523C4—101no—
524C4—122no—
525C4—201no—
526C4—602no—
527C4D5×#21512yes—
528C4C2×D5×Dic611yescharacteristic
529C4D5×#23511yescharacteristic
530C3D5×#47511yescharacteristic, complemented, Sylow
531C2—54no—
532C2D5×#92411yescharacteristic
533C2C2×D5×#21511yescharacteristic
534C2D5×#95111yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#475
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #11751121C2semidirect
4. C5×#5020C2semidirect
5. #11749348C2semidirect
8. #11747411C2semidirect
10. #11746943C2semidirect
11. #11746918C2semidirect
60. C3×Q8×D5Q8semidirect
103. #5020D5direct (N × H)
140. C3×C5×Q8C2×Q8semidirect
163. C3×Dic10C2×Q8semidirect
203. Q8×D5Dic6semidirect
308. C5×Q8C2×Dic6semidirect
332. Dic10C2×Dic6semidirect
369. C3×D5#475semidirect
375. C3×Q8Q8×D5semidirect
456. C3×C5C2×#475semidirect
477. D5#5020direct (N × H)
486. Q8D5×Dic6semidirect
512. C5C2×#5020semidirect
530. C3D5×#475semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
D5×#8692
#117511212
C5×#50202
#117493482
D5×#8352
D5×#8082
#117474112
D5×C4⋊(C3⋊C8)2
#117469432
#117469182
D5×#4753
C2×#50205