Finite Group Databasebeta

← D5×#5081 #14439906

Subgroups — D5×#5081 #14439906

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C4⋊Q8C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic
3#11751182C211yesmaximal, characteristic, complemented
4C5×#5081C211yesmaximal, characteristic, complemented
5D5×#808C212yesmaximal
6D5×#807C212yesmaximal
7#11747158C212yesmaximal, complemented
8#11747157C212yesmaximal, complemented
9D5×#803C211yesmaximal, characteristic
10#11746969C211yesmaximal, characteristic, complemented
11#11746952C211yesmaximal, characteristic, complemented
12D5×#501—31nomaximal, Hall
13C2×C3×Q8×D5—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91759C2211yescharacteristic
16C5×#870C2211yescharacteristic
17C3×#4090—21no—
18C3×D5×C4⋊C4—21no—
19C3×D5×C4⋊C4C2212yes—
20C3×#4034—21no—
21C3×#4034C2212yes—
22C3×C42×D5C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24D5×C4⋊Dic3C2211yescharacteristic
25D5×C4⋊Dic3C2211yescharacteristic
26D5×Dic3⋊C4—21no—
27D5×Dic3⋊C4—21no—
28#91388C2211yescharacteristic
29#91388C2211yescharacteristic
30#91378—21no—
31#91378—21no—
32C2×D5×C3⋊C8C2212yes—
33#91092C2212yes—
34#91091C2212yes—
35#91087C2211yescharacteristic
36C5×#808C2212yes—
37C5×#807C2212yes—
38C5×#803C2211yescharacteristic
39#90990C2212yes—
40#90989C2212yes—
41#90987C2212yes—
42#90986C2212yes—
43#90952C2212yes—
44C2×#5081—51nomaximal, Hall
45D5×C4⋊Q8D311yescharacteristic
46D5×#125—31no—
47C5×#501—31no—
48#65369—31no—
49#65354—31no—
50D5×#107—32no—
51#65165—32no—
52D5×#106—32no—
53#65145—32no—
54D5×#97—31no—
55#64991—31no—
56C2×C3×C5×Q8—21no—
57C3×Q8×D5—44no—
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5D411yescharacteristic
60C2×C3×C4×D5D411yescharacteristic
61C2×C3×C4×D5C2311yescharacteristic
62C2×C3×Dic10—21no—
63C2×C3×Dic10—22no—
64C2×D5×Dic3—21no—
65C2×D5×Dic3—21no—
66C3×C5×C4⋊C4—21no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70C4⋊Dic15C2311yescharacteristic
71#6712—21no—
72#6712—21no—
73C2×C3⋊#168C2312yes—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×C4⋊Dic3C2311yescharacteristic
76C5×Dic3⋊C4—21no—
77C5×Dic3⋊C4—21no—
78C2×C5×C3⋊C8C2312yes—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×#683—22no—
82C3×#683—22no—
83C3×C4×Dic5D411yescharacteristic
84C3×C4×Dic5D411yescharacteristic
85C3×C4×Dic5C2311yescharacteristic
86Dic3⋊Dic5—21no—
87Dic3⋊Dic5—21no—
88#6669—21no—
89#6669—21no—
90#6668—21no—
91#6668—21no—
92D5×C3⋊C8Q818yescomplemented
93C2×C3×C4⋊Q8—51no—
94C2×#870—51no—
95#5081—51no—
96#5081—51no—
97#5081—52no—
98#5081—52no—
99#5081—51no—
100#5081D511yescharacteristic, direct product factor
101C2×#808—52no—
102C2×#807—52no—
103C2×#803—51no—
104C2×Q8×D5—21no—
105C5×C4⋊Q8C2×D311yescharacteristic
106C5×#125—31no—
107#4090—21no—
108C2×C8×D5—32no—
109D5×C4⋊C4—21no—
110D5×C4⋊C4—31no—
111D5×C4⋊C4—31no—
112D5×C4⋊C4—61no—
113D5×C4⋊C4—61no—
114D5×C4⋊C4C2×D312yes—
115#4036—31no—
116#4036—31no—
117#4035—61no—
118#4035—61no—
119#4034—21no—
120#4034C2×D312yes—
121C42×D5C2×D311yescharacteristic
122#4016—31no—
123#4015C2×D311yescharacteristic
124C5×#107—32no—
125C5×#106—32no—
126C5×#97—31no—
127#3950—32no—
128#3949—32no—
129#3947—32no—
130#3940—32no—
131#3940—32no—
132#3939—32no—
133#3939—32no—
134#3935—31no—
135C2×#501—151noSylow
136C22×C3×D5C2×D411yescharacteristic
137C3×C5×Q8—42no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C2×D411yescharacteristic
148C2×C3×Dic5C2×D411yescharacteristic
149C2×C3×Dic5C2×D411yescharacteristic
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152C3×C4×D5—44no—
153C3×C4×D5C2×Q814yes—
154C3×Dic10—44no—
155C3×Dic10—42no—
156D5×Dic3—42no—
157D5×Dic3—42no—
158C3⋊#168C2×Q814yescomplemented
159C5×C3⋊C8C2×Q814yescomplemented
160C22×C3×Q8—101no—
161C3×C4⋊Q8—52no—
162C3×C4⋊Q8—51no—
163C3×C4⋊Q8—101no—
164C3×C4⋊Q8—101no—
165C3×C4⋊Q8C2×D511yescharacteristic
166C2×C3×C4⋊C4—52no—
167C2×C3×C4⋊C4—101no—
168C2×C3×C42—51no—
169C2×C4⋊Dic3—51no—
170C2×C4⋊Dic3—51no—
171C2×Dic3⋊C4—101no—
172C2×Dic3⋊C4—101no—
173C22×C3⋊C8—52no—
174#870—51no—
175#870—51no—
176#870—51no—
177#870—101no—
178#870—101no—
179#870C2×D511yescharacteristic
180#808—52no—
181#808—52no—
182#808—52no—
183#808C2×D512yes—
184#807—52no—
185#807—52no—
186#807—52no—
187#807C2×D512yes—
188#803—51no—
189#803—52no—
190#803C2×D511yescharacteristic
191C2×C5×Q8—21no—
192Q8×D5—44no—
193C2×C4×D5—22no—
194C2×C4×D5—61no—
195C2×C4×D5—61no—
196C2×C4×D5#6711yescharacteristic
197C2×C4×D5#6711yescharacteristic
198C2×C4×D5C22×D311yescharacteristic
199C2×Dic10—21no—
200C2×Dic10—22no—
201C2×C5×C8—32no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—31no—
205C5×C4⋊C4—61no—
206C5×C4⋊C4—61no—
207C5×C4⋊C4C22×D312yes—
208C42×C5C22×D311yescharacteristic
209C4⋊Dic5—21no—
210C4⋊Dic5—31no—
211C4⋊Dic5—31no—
212C4⋊Dic5—61no—
213C4⋊Dic5—61no—
214C4⋊Dic5C22×D312yes—
215#683—22no—
216#683—22no—
217#683—61no—
218#683—61no—
219#683—61no—
220#683—61no—
221#683—61no—
222#683—61no—
223C4×Dic5#6711yescharacteristic
224C4×Dic5#6711yescharacteristic
225C4×Dic5C22×D311yescharacteristic
226C2×#168—32no—
227C8×D5—38no—
228C2×C4⋊Q8—51no—
229C2×#125—151no—
230#501—31no—
231#501—151no—
232#501—152no—
233#501—152no—
234#501—151no—
235#501—151no—
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—151no—
239C22×C3×C5C22×D411yescharacteristic
240C2×C3×D5C4⋊Q812yes—
241C2×C3×D5AGL(1,ℤ/8)12yes—
242C2×C3×D5#13712yes—
243C3×C4×C5—21no—
244C3×C4×C5—21no—
245C3×C4×C5—42no—
246C3×C4×C5C22×Q812yes—
247Dic15—41no—
248Dic15—41no—
249C3×Dic5—21no—
250C3×Dic5—21no—
251C3×Dic5—42no—
252C3×Dic5C4⋊Q812yes—
253C5×Dic3—41no—
254C5×Dic3—41no—
255C2×C3×Q8—21no—
256C2×C3×Q8—102no—
257C2×C3×Q8—101no—
258C2×C3×Q8—204no—
259C22×C3×C4—51no—
260C22×C3×C4—51no—
261C22×C3×C4—51no—
262C22×C3×C4—102no—
263C22×Dic3—101no—
264C22×Dic3—101no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—52no—
267C3×C4⋊C4—102no—
268C3×C4⋊C4—102no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4C22×D512yes—
271C3×C42—51no—
272C3×C42—51no—
273C3×C42—51no—
274C3×C42C22×D511yescharacteristic
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3—101no—
278C4⋊Dic3—101no—
279C4⋊Dic3C22×D511yescharacteristic
280C4⋊Dic3C22×D511yescharacteristic
281Dic3⋊C4—21no—
282Dic3⋊C4—21no—
283Dic3⋊C4—101no—
284Dic3⋊C4—101no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287Dic3⋊C4—101no—
288Dic3⋊C4—101no—
289C2×C3⋊C8—52no—
290C2×C3⋊C8—58no—
291C2×C3⋊C8C22×D512yes—
292C22×D5C2×#6711yescharacteristic
293C5×Q8—42no—
294C2×C4×C5—22no—
295C2×C4×C5—61no—
296C2×C4×C5—61no—
297C2×C4×C5C2×#6711yescharacteristic
298C2×C4×C5C2×#6711yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—22no—
301C2×Dic5—61no—
302C2×Dic5—61no—
303C2×Dic5C2×#6711yescharacteristic
304C2×Dic5C2×#6711yescharacteristic
305C2×Dic5C2×#6711yescharacteristic
306C4×D5—22no—
307C4×D5—22no—
308C4×D5—44no—
309C4×D5—122no—
310C4×D5—122no—
311C4×D5D3×Q814yes—
312Dic10—44no—
313Dic10—42no—
314C5×C8—34no—
315#168—34no—
316C22×Q8—101no—
317C22×C8—152no—
318C4⋊Q8—52no—
319C4⋊Q8—51no—
320C4⋊Q8—101no—
321C4⋊Q8—101no—
322C4⋊Q8D3×D511yescharacteristic
323#125—31no—
324#125—151no—
325#125—151no—
326#125—151no—
327#125—301no—
328#125—301no—
329C2×C4⋊C4—52no—
330C2×C4⋊C4—101no—
331C2×C4⋊C4—151no—
332C2×C4⋊C4—151no—
333C2×C4⋊C4—301no—
334C2×C4⋊C4—301no—
335C2×C42—51no—
336#107—32no—
337#107—152no—
338#107—152no—
339#107—152no—
340#106—32no—
341#106—152no—
342#106—152no—
343#106—152no—
344#97—31no—
345#97—152no—
346#97—151no—
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350C3×D5#50114yescomplemented
351C23×C3—51no—
352C3×Q8—42no—
353C3×Q8—202no—
354C3×Q8—204no—
355C2×C3×C4—22no—
356C2×C3×C4—51no—
357C2×C3×C4—54no—
358C2×C3×C4—51no—
359C2×C3×C4—51no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—204no—
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4D4×D511yescharacteristic
366C2×C3×C4C23×D511yescharacteristic
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—202no—
372C2×Dic3—202no—
373C3⋊C8—54no—
374C3⋊C8Q8×D514yescomplemented
375C22×C5C22×#6711yescharacteristic
376C2×D5#93212yes—
377C2×D5#94212yes—
378C2×D5#94412yes—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—42no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5C2×D3×Q812yes—
385Dic5—21no—
386Dic5—21no—
387Dic5—42no—
388Dic5—121no—
389Dic5—121no—
390Dic5#94412yes—
391C2×Q8—21no—
392C2×Q8—102no—
393C2×Q8—101no—
394C2×Q8—204no—
395C22×C4—51no—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—102no—
399C22×C4—301no—
400C22×C4—301no—
401C2×C8—32no—
402C2×C8—158no—
403C2×C8—152no—
404C4⋊C4—21no—
405C4⋊C4—31no—
406C4⋊C4—31no—
407C4⋊C4—52no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—102no—
411C4⋊C4—102no—
412C4⋊C4—101no—
413C4⋊C4—151no—
414C4⋊C4—151no—
415C4⋊C4—301no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C4⋊C4—301no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4C2×D3×D512yes—
424C42—51no—
425C42—51no—
426C42—51no—
427C42C2×D3×D511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3—52no—
430C22×C3—52no—
431C22×C3—52no—
432C22×C3C2×D4×D511yescharacteristic
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—42no—
436C3×C4—52no—
437C3×C4—101no—
438C3×C4—101no—
439C3×C4—202no—
440C3×C4C2×Q8×D512yes—
441Dic3—41no—
442Dic3—41no—
443Dic3—201no—
444Dic3—201no—
445C2×C5C2×#93211yescharacteristic
446C2×C5C2×#94211yescharacteristic
447C2×C5C2×#94411yescharacteristic
448D5#508114yesdirect product factor
449C23—51no—
450Q8—42no—
451Q8—202no—
452Q8—204no—
453C2×C4—22no—
454C2×C4—51no—
455C2×C4—54no—
456C2×C4—51no—
457C2×C4—51no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—102no—
463C2×C4—204no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—34no—
472C8—154no—
473C2×C3—54no—
474C2×C3D5×C4⋊Q811yescharacteristic
475C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
476C2×C3D5×#13711yescharacteristic
477C5C2×#508111yescharacteristic, complemented, Sylow
478C22—52no—
479C22—52no—
480C22—52no—
481C22C2×D5×#6711yescharacteristic
482C4—21no—
483C4—21no—
484C4—42no—
485C4—52no—
486C4—101no—
487C4—101no—
488C4—121no—
489C4—121no—
490C4—202no—
491C4—601no—
492C4—601no—
493C4D3×Q8×D512yes—
494C3D5×#50111yescharacteristic, complemented, Sylow
495C2—54no—
496C2D5×#93211yescharacteristic
497C2D5×#94211yescharacteristic
498C2D5×#94411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C3×D5C2×D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#501
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. #11751182C2semidirect
4. C5×#5081C2semidirect
7. #11747158C2semidirect
8. #11747157C2semidirect
10. #11746969C2semidirect
11. #11746952C2semidirect
92. D5×C3⋊C8Q8semidirect
100. #5081D5direct (N × H)
158. C3⋊#168C2×Q8semidirect
159. C5×C3⋊C8C2×Q8semidirect
350. C3×D5#501semidirect
374. C3⋊C8Q8×D5semidirect
428. C3×C5C2×#501semidirect
448. D5#5081direct (N × H)
477. C5C2×#5081semidirect
494. C3D5×#501semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
D5×#8702
#117511822
C5×#50812
D5×#8082
D5×#8072
#117471582
#117471572
D5×#8032
#117469692
#117469522
D5×#5013
C2×#50815