Finite Group Databasebeta

← D5×#5570 #14484534

Subgroups — D5×#5570 #14484534

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756329C211yesmaximal, characteristic, complemented
2C5×#5570C211yesmaximal, characteristic, complemented
3C3×C4×Q8×D5C211yesmaximal, characteristic
4#11755267C212yesmaximal, complemented
5Q8×D5×Dic3C212yesmaximal
6D5×#890C216yesmaximal
7#11753315C216yesmaximal, complemented
8D5×#869C213yesmaximal
9C4×D5×Dic6C213yesmaximal
10#11752477C213yesmaximal, complemented
11#11752476C213yesmaximal, complemented
12D5×#557—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×D5×Dic6C2213yes—
15C3×C4×C5×Q8C2211yescharacteristic
16Q8×Dic15C2212yes—
17#91779C2216yes—
18#91758C2213yes—
19C4×Dic30C2213yes—
20C5×Q8×Dic3C2212yes—
21C5×#890C2216yes—
22C5×#869C2213yes—
23C4×C5×Dic6C2213yes—
24C3×Q8×Dic5C2211yescharacteristic
25C3×D5×C4⋊C4C2213yes—
26C3×#4033C2213yes—
27C3×C42×D5C2213yes—
28C3×C4×Dic10C2213yes—
29#91468C2216yes—
30#91468C2216yes—
31C4×#1204C2216yes—
32D5×C4⋊Dic3C2216yes—
33D5×C4⋊Dic3C2216yes—
34D5×C4⋊Dic3C2211yescharacteristic
35D5×Dic3⋊C4C2216yes—
36C4×D5×Dic3C2216yes—
37#91384C2216yes—
38#91381C2216yes—
39#91376C2216yes—
40#91335C22112yes—
41#91334C22112yes—
42#91333C2213yes—
43Dic5×Dic6C2213yes—
44#91331C2216yes—
45Dic3×Dic10C2216yes—
46#91323C2216yes—
47C2×#5570—51nomaximal, Hall
48C5×#557—31no—
49D5×C4⋊Q8—33no—
50#66055—33no—
51D5×#125—36no—
52#66019—36no—
53C4×Q8×D5—33no—
54C4×Q8×D5—32no—
55C4×Q8×D5D311yescharacteristic
56#65904—31no—
57#65903—32no—
58#65901—33no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×Dic30C2313yes—
61C2×C5×Dic6C2313yes—
62C3×Q8×D5Q818yescomplemented
63C2×C3×C4×D5C2313yes—
64C2×C3×C4×D5C2313yes—
65C2×C3×C4×D5C2311yescharacteristic
66C2×C3×Dic10C2313yes—
67C2×#1204C2316yes—
68C2×D5×Dic3C2312yes—
69C2×D5×Dic3C2316yes—
70D5×Dic6—212no—
71C3×C5×C4⋊C4C2313yes—
72C3×C42×C5C2313yes—
73C4⋊Dic15C2316yes—
74C4⋊Dic15C2316yes—
75C4⋊Dic15C2311yescharacteristic
76#6712C2316yes—
77C4×Dic15C2316yes—
78C5×C4⋊Dic3C2311yescharacteristic
79C5×C4⋊Dic3C2316yes—
80C5×C4⋊Dic3C2316yes—
81C5×Dic3⋊C4C2316yes—
82C4×C5×Dic3C2316yes—
83C3×C4⋊Dic5C2313yes—
84C3×#683C2316yes—
85C3×C4×Dic5C2313yes—
86C3×C4×Dic5C2313yes—
87C3×C4×Dic5C2313yes—
88Dic3⋊Dic5C2316yes—
89#6669C2316yes—
90#6668C2312yes—
91#6668C23112yes—
92#6668C23112yes—
93Dic3×Dic5C2316yes—
94Dic3×Dic5C2316yes—
95C2×C3×C4×Q8—51no—
96C2×Q8×Dic3—52no—
97#5570—51no—
98#5570—52no—
99#5570—56no—
100#5570—53no—
101#5570—53no—
102#5570D511yescharacteristic, direct product factor
103C2×#890—56no—
104C2×#869—53no—
105C2×C4×Dic6—53no—
106C2×Q8×D5—33no—
107C2×Q8×D5C2×D311yescharacteristic
108C5×C4⋊Q8—33no—
109C5×#125—36no—
110C4×C5×Q8—32no—
111C4×C5×Q8—33no—
112C4×C5×Q8C2×D311yescharacteristic
113Q8×Dic5—32no—
114Q8×Dic5—33no—
115Q8×Dic5C2×D311yescharacteristic
116#4090—36no—
117D5×C4⋊C4—36no—
118D5×C4⋊C4—36no—
119D5×C4⋊C4—36no—
120D5×C4⋊C4—31no—
121D5×C4⋊C4C2×D313yes—
122#4036—36no—
123#4036—36no—
124#4035—312no—
125#4035—312no—
126#4034—36no—
127#4034—36no—
128#4033—36no—
129#4033—33no—
130#4033—36no—
131#4033C2×D313yes—
132C42×D5—36no—
133C42×D5C2×D313yes—
134#4016—36no—
135#4015—33no—
136C4×Dic10—36no—
137C4×Dic10—33no—
138C4×Dic10—36no—
139C4×Dic10C2×D313yes—
140C2×#557—151noSylow
141C22×C3×D5C2411yescharacteristic
142C3×C5×Q8C2×Q814yescomplemented
143C2×C3×C4×C5C2413yes—
144C2×C3×C4×C5C2413yes—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15C2412yes—
147C2×Dic15C2416yes—
148Dic30—26no—
149C2×C5×Dic3C2412yes—
150C2×C5×Dic3C2416yes—
151C5×Dic6—26no—
152C2×C3×Dic5C2413yes—
153C2×C3×Dic5C2413yes—
154C2×C3×Dic5C2411yescharacteristic
155C3×C4×D5—26no—
156C3×C4×D5C2×Q8112yes—
157C3×C4×D5#4114yes—
158C3×Dic10C2×Q8112yescomplemented
159#1204—212no—
160D5×Dic3—212no—
161D5×Dic3—24no—
162C22×C3×Q8—51no—
163C22×Dic6—53no—
164C3×C4×Q8—51no—
165C3×C4×Q8—53no—
166C3×C4×Q8—53no—
167C3×C4×Q8C2×D511yescharacteristic
168C2×C3×C4⋊C4—53no—
169C2×C3×C42—53no—
170Q8×Dic3—52no—
171Q8×Dic3—56no—
172Q8×Dic3—56no—
173Q8×Dic3C2×D512yes—
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3—56no—
176C2×C4⋊Dic3—56no—
177C2×Dic3⋊C4—56no—
178C2×C4×Dic3—56no—
179#890—56no—
180#890—512no—
181#890—56no—
182#890—512no—
183#890—56no—
184#890C2×D516yes—
185#869—56no—
186#869—53no—
187#869—56no—
188#869—56no—
189#869C2×D513yes—
190C4×Dic6—53no—
191C4×Dic6—53no—
192C4×Dic6—53no—
193C4×Dic6—56no—
194C4×Dic6—56no—
195C4×Dic6C2×D513yes—
196C2×C5×Q8—33no—
197C2×C5×Q8C22×D311yescharacteristic
198Q8×D5—612no—
199Q8×D5Dic618yescomplemented
200C2×C4×D5—36no—
201C2×C4×D5—32no—
202C2×C4×D5C22×D313yes—
203C2×C4×D5C22×D313yes—
204C2×C4×D5C22×D311yescharacteristic
205C2×Dic10—33no—
206C2×Dic10—36no—
207C2×Dic10C22×D313yes—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—36no—
210C5×C4⋊C4—36no—
211C5×C4⋊C4—36no—
212C5×C4⋊C4C22×D313yes—
213C42×C5—36no—
214C42×C5C22×D313yes—
215C4⋊Dic5—31no—
216C4⋊Dic5—36no—
217C4⋊Dic5—36no—
218C4⋊Dic5—36no—
219C4⋊Dic5C22×D313yes—
220#683—36no—
221#683—32no—
222#683—312no—
223#683—312no—
224#683—36no—
225#683C22×D316yes—
226C4×Dic5—36no—
227C4×Dic5—36no—
228C4×Dic5—36no—
229C4×Dic5C22×D313yes—
230C4×Dic5C22×D313yes—
231C4×Dic5C22×D313yes—
232#557—31no—
233#557—153no—
234#557—152no—
235#557—156no—
236#557—153no—
237#557—151no—
238C2×C4⋊Q8—153no—
239C2×#125—156no—
240C2×C4×Q8—51no—
241C2×C4×Q8—153no—
242C2×C4×Q8—152no—
243C22×C3×C5C2511yescharacteristic
244C2×C3×D5C22×Q812yes—
245C2×C3×D5C2×#4112yes—
246C2×C3×D52−1+412yes—
247C3×C4×C5—23no—
248C3×C4×C5C22×Q816yes—
249C3×C4×C5C2×#4112yes—
250Dic15—26no—
251Dic15—22no—
252C3×Dic5—23no—
253C3×Dic5C22×Q816yes—
254C3×Dic5C2×#4112yes—
255C5×Dic3—26no—
256C5×Dic3—22no—
257C2×C3×Q8—58no—
258C2×C3×Q8—53no—
259C2×C3×Q8C22×D511yescharacteristic
260C22×C3×C4—53no—
261C22×C3×C4—51no—
262C22×C3×C4—53no—
263C22×Dic3—52no—
264C22×Dic3—56no—
265C2×Dic6—53no—
266C2×Dic6—56no—
267C2×Dic6—1012no—
268C2×Dic6C22×D513yes—
269C3×C4⋊C4—56no—
270C3×C4⋊C4—53no—
271C3×C4⋊C4C22×D513yes—
272C3×C42—53no—
273C3×C42—53no—
274C3×C42—53no—
275C3×C42C22×D513yes—
276C4⋊Dic3—51no—
277C4⋊Dic3—56no—
278C4⋊Dic3—56no—
279C4⋊Dic3—52no—
280C4⋊Dic3—512no—
281C4⋊Dic3—512no—
282C4⋊Dic3C22×D511yescharacteristic
283C4⋊Dic3C22×D516yes—
284C4⋊Dic3C22×D516yes—
285Dic3⋊C4—56no—
286Dic3⋊C4—56no—
287Dic3⋊C4—56no—
288Dic3⋊C4C22×D516yes—
289C4×Dic3—56no—
290C4×Dic3—56no—
291C4×Dic3—56no—
292C4×Dic3C22×D516yes—
293C22×D5C23×D311yescharacteristic
294C5×Q8—66no—
295C5×Q8C2×Dic614yescomplemented
296C2×C4×C5—32no—
297C2×C4×C5—36no—
298C2×C4×C5C23×D313yes—
299C2×C4×C5C23×D313yes—
300C2×C4×C5C23×D311yescharacteristic
301C2×Dic5—32no—
302C2×Dic5—36no—
303C2×Dic5C23×D313yes—
304C2×Dic5C23×D313yes—
305C2×Dic5C23×D311yescharacteristic
306C4×D5—26no—
307C4×D5—612no—
308C4×D5—64no—
309C4×D5C2×Dic6112yes—
310C4×D5#23914yes—
311Dic10—66no—
312Dic10—612no—
313Dic10C2×Dic6112yescomplemented
314C22×Q8—51no—
315C22×Q8—153no—
316C4⋊Q8—33no—
317C4⋊Q8—156no—
318C4⋊Q8—156no—
319C4⋊Q8—156no—
320C4⋊Q8—153no—
321#125—36no—
322#125—156no—
323#125—1512no—
324#125—1512no—
325#125—156no—
326#125—156no—
327C4×Q8—32no—
328C4×Q8—33no—
329C4×Q8—51no—
330C4×Q8—53no—
331C4×Q8—53no—
332C4×Q8—156no—
333C4×Q8—156no—
334C4×Q8—153no—
335C4×Q8—156no—
336C4×Q8—153no—
337C4×Q8—156no—
338C4×Q8—152no—
339C4×Q8—153no—
340C4×Q8D3×D511yescharacteristic
341C2×C4⋊C4—53no—
342C2×C4⋊C4—151no—
343C2×C4⋊C4—156no—
344C2×C4⋊C4—156no—
345C2×C4⋊C4—156no—
346C2×C42—53no—
347C2×C42—156no—
348C2×C3×C5C23×Q811yescharacteristic
349C2×C3×C5C22×#4111yescharacteristic
350C2×C3×C5C2×2−1+411yescharacteristic
351C3×D5#55714yescomplemented
352C23×C3—51no—
353C3×Q8—512no—
354C3×Q8Q8×D514yescomplemented
355C2×C3×C4—53no—
356C2×C3×C4—51no—
357C2×C3×C4—512no—
358C2×C3×C4—54no—
359C2×C3×C4—53no—
360C2×C3×C4—106no—
361C2×C3×C4C23×D513yes—
362C2×C3×C4C23×D513yes—
363C2×C3×C4C23×D511yescharacteristic
364C2×Dic3—52no—
365C2×Dic3—56no—
366C2×Dic3—1012no—
367C2×Dic3—104no—
368C2×Dic3C23×D512yes—
369C2×Dic3C23×D516yes—
370Dic6—26no—
371Dic6—1012no—
372Dic6—106no—
373C22×C5C24×D311yescharacteristic
374C2×D5C22×Dic612yes—
375C2×D5C2×#23912yes—
376C2×D5#101012yes—
377C4×C5—23no—
378C4×C5—66no—
379C4×C5—62no—
380C4×C5C22×Dic616yes—
381C4×C5C2×#23912yes—
382Dic5—23no—
383Dic5—66no—
384Dic5—62no—
385Dic5C22×Dic616yes—
386Dic5C2×#23912yes—
387C2×Q8—33no—
388C2×Q8—58no—
389C2×Q8—53no—
390C2×Q8—156no—
391C2×Q8—153no—
392C2×Q8—3012no—
393C2×Q8C2×D3×D511yescharacteristic
394C22×C4—51no—
395C22×C4—53no—
396C22×C4—53no—
397C22×C4—152no—
398C22×C4—156no—
399C4⋊C4—31no—
400C4⋊C4—36no—
401C4⋊C4—36no—
402C4⋊C4—36no—
403C4⋊C4—56no—
404C4⋊C4—53no—
405C4⋊C4—152no—
406C4⋊C4—156no—
407C4⋊C4—156no—
408C4⋊C4—1512no—
409C4⋊C4—1512no—
410C4⋊C4—151no—
411C4⋊C4—156no—
412C4⋊C4—156no—
413C4⋊C4—156no—
414C4⋊C4C2×D3×D513yes—
415C42—36no—
416C42—53no—
417C42—53no—
418C42—53no—
419C42—156no—
420C42—156no—
421C42—156no—
422C42C2×D3×D513yes—
423C3×C5C2×#55711yescharacteristic, complemented, Hall
424C22×C3—52no—
425C22×C3—52no—
426C22×C3—52no—
427C22×C3C24×D511yescharacteristic
428C3×C4—23no—
429C3×C4—56no—
430C3×C4—52no—
431C3×C4—103no—
432C3×C4C2×Q8×D516yes—
433C3×C4D5×#4112yes—
434Dic3—26no—
435Dic3—22no—
436Dic3—106no—
437Dic3—102no—
438C2×C5C23×Dic611yescharacteristic
439C2×C5C22×#23911yescharacteristic
440C2×C5C2×#101011yescharacteristic
441D5#557014yesdirect product factor
442C23—51no—
443Q8—512no—
444Q8—66no—
445Q8—3012no—
446Q8—306no—
447Q8D5×Dic614yescomplemented
448C2×C4—32no—
449C2×C4—36no—
450C2×C4—51no—
451C2×C4—53no—
452C2×C4—512no—
453C2×C4—54no—
454C2×C4—53no—
455C2×C4—106no—
456C2×C4—152no—
457C2×C4—156no—
458C2×C4—3012no—
459C2×C4—304no—
460C2×C4C22×D3×D513yes—
461C2×C4C22×D3×D513yes—
462C2×C4C22×D3×D511yescharacteristic
463C2×C3—54no—
464C2×C3C22×Q8×D511yescharacteristic
465C2×C3C2×D5×#4111yescharacteristic
466C2×C3D5×2−1+411yescharacteristic
467C5C2×#557011yescharacteristic, complemented, Sylow
468C22—52no—
469C22—52no—
470C22—52no—
471C22C23×D3×D511yescharacteristic
472C4—23no—
473C4—56no—
474C4—52no—
475C4—66no—
476C4—62no—
477C4—103no—
478C4—306no—
479C4—302no—
480C4C2×D5×Dic616yes—
481C4D5×#23912yes—
482C3D5×#55711yescharacteristic, complemented, Sylow
483C2—54no—
484C2C22×D5×Dic611yescharacteristic
485C2C2×D5×#23911yescharacteristic
486C2D5×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC22×C3×D5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#557
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756329C2semidirect
2. C5×#5570C2semidirect
4. #11755267C2semidirect
7. #11753315C2semidirect
10. #11752477C2semidirect
11. #11752476C2semidirect
62. C3×Q8×D5Q8semidirect
102. #5570D5direct (N × H)
142. C3×C5×Q8C2×Q8semidirect
158. C3×Dic10C2×Q8semidirect
199. Q8×D5Dic6semidirect
295. C5×Q8C2×Dic6semidirect
313. Dic10C2×Dic6semidirect
351. C3×D5#557semidirect
354. C3×Q8Q8×D5semidirect
423. C3×C5C2×#557semidirect
441. D5#5570direct (N × H)
447. Q8D5×Dic6semidirect
467. C5C2×#5570semidirect
482. C3D5×#557semidirect

Maximal subgroups

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

subgroupindex
#117563292
C5×#55702
C3×C4×Q8×D52
#117552672
Q8×D5×Dic32
D5×#8902
#117533152
D5×#8692
C4×D5×Dic62
#117524772
#117524762
D5×#5573
C2×#55705