Finite Group Databasebeta

← D5×#4025 #13105153

Subgroups — D5×#4025 #13105153

Order 1600.

552 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11717199C211yesmaximal, characteristic, complemented
2C5×D5×C22⋊C4C211yesmaximal, characteristic
3C5×#4025C211yesmaximal, characteristic, complemented
4D5×C22⋊Dic5C211yesmaximal, characteristic
5D5×C22⋊Dic5C211yesmaximal, characteristic
6#11717074C211yesmaximal, characteristic, complemented
7#11717074C211yesmaximal, characteristic, complemented
8D5×C4⋊Dic5C211yesmaximal, characteristic, complemented
9D5×#683C211yesmaximal, characteristic, complemented
10D5×#683C211yesmaximal, characteristic, complemented
11C4×D5×Dic5C211yesmaximal, characteristic, complemented
12#11716980C211yesmaximal, characteristic, complemented
13#11716978C211yesmaximal, characteristic, complemented
14#11716977C211yesmaximal, characteristic, complemented
15#11716976C211yesmaximal, characteristic, complemented
16C23×C5×D5C2211yescharacteristic
17C2×C4×C5×D5C2211yescharacteristic
18C2×C4×C5×D5C2211yescharacteristic
19C2×D5×Dic5C2211yescharacteristic
20C2×D5×Dic5C2211yescharacteristic
21C2×D5×Dic5C2211yescharacteristic
22C2×D5×Dic5C2211yescharacteristic
23C52×C22⋊C4C2211yescharacteristic
24C22⋊#1039C2211yescharacteristic
25C22⋊#1039C2211yescharacteristic
26C4⋊#1039C2211yescharacteristic, complemented
27#87806C2211yescharacteristic, complemented
28#87806C2211yescharacteristic, complemented
29C4×#1039C2211yescharacteristic, complemented
30C5×C22⋊Dic5C2211yescharacteristic
31C5×C22⋊Dic5C2211yescharacteristic
32C5×C22⋊Dic5C2211yescharacteristic
33C5×#685C2211yescharacteristic
34C5×#685C2211yescharacteristic
35C5×C4⋊Dic5C2211yescharacteristic, complemented
36C5×#683C2211yescharacteristic, complemented
37C5×#683C2211yescharacteristic, complemented
38C4×C5×Dic5C2211yescharacteristic, complemented
39#87781C2211yescharacteristic, complemented
40#87781C2211yescharacteristic, complemented
41#87780C2211yescharacteristic, complemented
42#87780C2211yescharacteristic, complemented
43#87780C2211yescharacteristic, complemented
44#87780C2211yescharacteristic, complemented
45#87778C2211yescharacteristic
46#87778C2211yescharacteristic
47#87778C2211yescharacteristic
48#87778C2211yescharacteristic
49Dic52C2211yescharacteristic, complemented
50Dic52C2211yescharacteristic, complemented
51D5×#126—51nomaximal
52C2×#4025—51nomaximal
53C23×C52C2311yescharacteristic
54C22×C5×D5—22no—
55C22×C5×D5—22no—
56C22×C5×D5—22no—
57C22×C5×D5C2311yescharacteristic
58C22×C5×D5C2311yescharacteristic
59C2×C4×C52C2311yescharacteristic
60C2×C4×C52C2311yescharacteristic
61C2×#1039C2311yescharacteristic
62C2×#1039C2311yescharacteristic
63C2×#1039C2311yescharacteristic
64C2×#1039C2311yescharacteristic
65C2×C5×Dic5C2311yescharacteristic
66C2×C5×Dic5C2311yescharacteristic
67C2×C5×Dic5C2311yescharacteristic
68C2×C5×Dic5C2311yescharacteristic
69C2×C5×Dic5C2311yescharacteristic
70C2×C5×Dic5C2311yescharacteristic
71C4×C5×D5—22no—
72C4×C5×D5—22no—
73D5×Dic5—22no—
74D5×Dic5—22no—
75D5×Dic5—22no—
76D5×Dic5—22no—
77C5×#126—51no—
78C2×C5×C22⋊C4—51no—
79C2×C22⋊Dic5—51no—
80C2×C22⋊Dic5—51no—
81C2×C4⋊Dic5—51no—
82C2×#683—51no—
83C2×#683—51no—
84C2×C4×Dic5—51no—
85#4044—51no—
86#4044—51no—
87#4044—51no—
88D5×C4⋊C4—51no—
89D5×C4⋊C4—51no—
90D5×C4⋊C4—51no—
91D5×C22⋊C4—51no—
92D5×C22⋊C4—51no—
93D5×C22⋊C4D511yescharacteristic
94#4025—51no—
95#4025—51no—
96#4025—51no—
97#4025—51no—
98#4025—51no—
99#4025—51no—
100#4025—51no—
101#4025—51no—
102#4025—51no—
103#4025—51no—
104#4025—102no—
105#4025D511yescharacteristic, direct product factor
106#4022—51no—
107C42×D5—51no—
108C22×C52—21no—
109C22×C52—21no—
110C22×C52—21no—
111C22×C52C2411yescharacteristic
112C2×C5×D5—21no—
113C2×C5×D5—21no—
114C2×C5×D5—21no—
115C2×C5×D5—44no—
116C2×C5×D5#4112yes—
117C2×C5×D5#4112yes—
118C2×C5×D5#4112yes—
119C4×C52—21no—
120C4×C52—21no—
121#1039—21no—
122#1039—21no—
123#1039—21no—
124#1039—21no—
125C5×Dic5—21no—
126C5×Dic5—21no—
127C5×Dic5—21no—
128C5×Dic5—21no—
129C5×Dic5—21no—
130C5×Dic5—21no—
131C24×C5—51no—
132C23×D5C2×D511yescharacteristic
133C22×C4×C5—51no—
134C22×C4×C5—51no—
135C22×Dic5—51no—
136C22×Dic5—51no—
137C22×Dic5—51no—
138C22×Dic5—51no—
139C2×C4×D5—51no—
140C2×C4×D5—51no—
141C2×C4×D5—51no—
142C2×C4×D5—51no—
143C2×C4×D5C2×D511yescharacteristic
144C2×C4×D5C2×D511yescharacteristic
145C5×C4⋊C4—51no—
146C5×C4⋊C4—51no—
147C5×C4⋊C4—51no—
148C5×C22⋊C4—22no—
149C5×C22⋊C4—51no—
150C5×C22⋊C4—51no—
151C5×C22⋊C4—51no—
152C5×C22⋊C4—51no—
153C5×C22⋊C4—51no—
154C5×C22⋊C4C2×D511yescharacteristic
155C5×C22⋊C4C2×D511yescharacteristic
156C42×C5—51no—
157C22⋊Dic5—51no—
158C22⋊Dic5—51no—
159C22⋊Dic5—51no—
160C22⋊Dic5—51no—
161C22⋊Dic5—51no—
162C22⋊Dic5—51no—
163C22⋊Dic5—51no—
164C22⋊Dic5—51no—
165C22⋊Dic5—102no—
166C22⋊Dic5—102no—
167C22⋊Dic5C2×D511yescharacteristic
168C22⋊Dic5C2×D511yescharacteristic
169C22⋊Dic5C2×D511yescharacteristic
170#685—51no—
171#685—51no—
172#685—51no—
173#685—51no—
174#685C2×D511yescharacteristic
175#685C2×D511yescharacteristic
176C4⋊Dic5—51no—
177C4⋊Dic5—51no—
178C4⋊Dic5—51no—
179C4⋊Dic5—51no—
180C4⋊Dic5—51no—
181C4⋊Dic5—51no—
182C4⋊Dic5—102no—
183C4⋊Dic5C2×D511yescharacteristic, complemented
184#683—51no—
185#683—51no—
186#683—51no—
187#683—51no—
188#683—51no—
189#683—51no—
190#683—51no—
191#683—51no—
192#683—51no—
193#683—51no—
194#683—51no—
195#683—51no—
196#683—102no—
197#683—102no—
198#683C2×D511yescharacteristic, complemented
199#683C2×D511yescharacteristic, complemented
200C4×Dic5—51no—
201C4×Dic5—51no—
202C4×Dic5—51no—
203C4×Dic5—51no—
204C4×Dic5—51no—
205C4×Dic5—51no—
206C4×Dic5—102no—
207C4×Dic5C2×D511yescharacteristic, complemented
208C2×#126—251noSylow
209C2×C52—41no—
210C2×C52C2×#4111yescharacteristic
211C2×C52C2×#4111yescharacteristic
212C2×C52C2×#4111yescharacteristic
213C5×D5—41no—
214C5×D5#12614yescomplemented
215C23×C5—22no—
216C23×C5—51no—
217C23×C5—51no—
218C23×C5—102no—
219C23×C5—102no—
220C23×C5—102no—
221C23×C5C22×D511yescharacteristic
222C23×C5C22×D511yescharacteristic
223C22×D5—22no—
224C22×D5—22no—
225C22×D5—22no—
226C22×D5C22×D511yescharacteristic
227C22×D5C22×D511yescharacteristic
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—51no—
231C2×C4×C5—51no—
232C2×C4×C5—51no—
233C2×C4×C5—51no—
234C2×C4×C5—51no—
235C2×C4×C5—51no—
236C2×C4×C5—102no—
237C2×C4×C5—102no—
238C2×C4×C5C22×D511yescharacteristic
239C2×C4×C5C22×D511yescharacteristic
240C2×C4×C5C22×D511yescharacteristic
241C2×C4×C5C22×D511yescharacteristic
242C2×Dic5—51no—
243C2×Dic5—51no—
244C2×Dic5—51no—
245C2×Dic5—51no—
246C2×Dic5—51no—
247C2×Dic5—51no—
248C2×Dic5—51no—
249C2×Dic5—51no—
250C2×Dic5—102no—
251C2×Dic5—102no—
252C2×Dic5—102no—
253C2×Dic5—102no—
254C2×Dic5—102no—
255C2×Dic5—102no—
256C2×Dic5—102no—
257C2×Dic5—102no—
258C2×Dic5C22×D511yescharacteristic
259C2×Dic5C22×D511yescharacteristic
260C2×Dic5C22×D511yescharacteristic
261C2×Dic5C22×D511yescharacteristic
262C2×Dic5C22×D511yescharacteristic
263C2×Dic5C22×D511yescharacteristic
264C4×D5—22no—
265C4×D5—22no—
266C4×D5—102no—
267C4×D5—102no—
268C4×D5—102no—
269C4×D5—102no—
270#126—51no—
271#126—251no—
272#126—251no—
273#126—251no—
274#126—251no—
275#126—251no—
276#126—251no—
277#126—251no—
278C2×C4⋊C4—251no—
279C2×C4⋊C4—251no—
280C2×C4⋊C4—251no—
281C2×C22⋊C4—51no—
282C2×C22⋊C4—251no—
283C2×C22⋊C4—251no—
284C2×C42—251no—
285C52C2×#12611yescharacteristic, complemented, Sylow
286C22×C5—21no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—22no—
293C22×C5—42no—
294C22×C5—42no—
295C22×C5—42no—
296C22×C5—52no—
297C22×C5—52no—
298C22×C5—52no—
299C22×C5—101no—
300C22×C5—101no—
301C22×C5—101no—
302C22×C5—204no—
303C22×C5C23×D511yescharacteristic
304C22×C5C23×D511yescharacteristic
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—21no—
308C2×D5—44no—
309C2×D5#70912yes—
310C2×D5#71112yes—
311C2×D5#71112yes—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—42no—
317C4×C5—42no—
318C4×C5—101no—
319C4×C5—101no—
320C4×C5—101no—
321C4×C5—101no—
322C4×C5—101no—
323C4×C5—101no—
324Dic5—21no—
325Dic5—21no—
326Dic5—21no—
327Dic5—21no—
328Dic5—21no—
329Dic5—21no—
330Dic5—101no—
331Dic5—101no—
332Dic5—101no—
333Dic5—101no—
334Dic5—101no—
335Dic5—101no—
336Dic5—101no—
337Dic5—101no—
338Dic5—202no—
339Dic5—202no—
340Dic5—202no—
341Dic5—202no—
342C24—51no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—251no—
346C22×C4—251no—
347C22×C4—251no—
348C22×C4—251no—
349C4⋊C4—51no—
350C4⋊C4—51no—
351C4⋊C4—51no—
352C4⋊C4—251no—
353C4⋊C4—251no—
354C4⋊C4—251no—
355C4⋊C4—251no—
356C4⋊C4—251no—
357C4⋊C4—251no—
358C4⋊C4—251no—
359C4⋊C4—251no—
360C4⋊C4—251no—
361C22⋊C4—51no—
362C22⋊C4—51no—
363C22⋊C4—51no—
364C22⋊C4—51no—
365C22⋊C4—51no—
366C22⋊C4—251no—
367C22⋊C4—251no—
368C22⋊C4—251no—
369C22⋊C4—251no—
370C22⋊C4—251no—
371C22⋊C4—251no—
372C22⋊C4D5211yescharacteristic
373C42—51no—
374C42—251no—
375C42—251no—
376C42—251no—
377C2×C5—22no—
378C2×C5—22no—
379C2×C5—22no—
380C2×C5—41no—
381C2×C5—41no—
382C2×C5—54no—
383C2×C5—82no—
384C2×C5—201no—
385C2×C5C2×#70911yescharacteristic
386C2×C5C2×#71111yescharacteristic
387C2×C5C2×#71111yescharacteristic
388C2×C5D5×#4111yescharacteristic
389C2×C5D5×#4111yescharacteristic
390C2×C5D5×#4111yescharacteristic
391D5—41no—
392D5#402514yesdirect product factor
393C23—51no—
394C23—51no—
395C23—102no—
396C23—102no—
397C23—102no—
398C23C2×D5211yescharacteristic
399C2×C4—51no—
400C2×C4—51no—
401C2×C4—51no—
402C2×C4—51no—
403C2×C4—51no—
404C2×C4—51no—
405C2×C4—102no—
406C2×C4—102no—
407C2×C4—251no—
408C2×C4—251no—
409C2×C4—251no—
410C2×C4—251no—
411C2×C4—502no—
412C2×C4—502no—
413C2×C4—502no—
414C2×C4—502no—
415C2×C4C2×D5211yescharacteristic
416C2×C4C2×D5211yescharacteristic
417C5—22no—
418C5C2×#402511yescharacteristic, complemented
419C5D5×#12611yescharacteristic, complemented
420C22—21no—
421C22—21no—
422C22—21no—
423C22—52no—
424C22—52no—
425C22—52no—
426C22—101no—
427C22—101no—
428C22—101no—
429C22—204no—
430C22C22×D5211yescharacteristic
431C4—21no—
432C4—21no—
433C4—101no—
434C4—101no—
435C4—101no—
436C4—101no—
437C4—101no—
438C4—101no—
439C4—501no—
440C4—501no—
441C4—501no—
442C4—501no—
443C2—41no—
444C2—54no—
445C2—201no—
446C2D5×#70911yescharacteristic
447C2D5×#71111yescharacteristic
448C2D5×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
prime radicalC23×C5×D5C22
hypercenterC22⋊C4D52
hypocenterC52C2×#126
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11717199C2semidirect
3. C5×#4025C2semidirect
6. #11717074C2semidirect
7. #11717074C2semidirect
8. D5×C4⋊Dic5C2semidirect
9. D5×#683C2semidirect
10. D5×#683C2semidirect
11. C4×D5×Dic5C2semidirect
12. #11716980C2semidirect
13. #11716978C2semidirect
14. #11716977C2semidirect
15. #11716976C2semidirect
26. C4⋊#1039C22semidirect
27. #87806C22semidirect
28. #87806C22semidirect
29. C4×#1039C22semidirect
35. C5×C4⋊Dic5C22semidirect
36. C5×#683C22semidirect
37. C5×#683C22semidirect
38. C4×C5×Dic5C22semidirect
39. #87781C22semidirect
40. #87781C22semidirect
41. #87780C22semidirect
42. #87780C22semidirect
43. #87780C22semidirect
44. #87780C22semidirect
49. Dic52C22semidirect
50. Dic52C22semidirect
105. #4025D5direct (N × H)
183. C4⋊Dic5C2×D5semidirect
198. #683C2×D5semidirect
199. #683C2×D5semidirect
207. C4×Dic5C2×D5semidirect
214. C5×D5#126semidirect
285. C52C2×#126semidirect
392. D5#4025direct (N × H)
418. C5C2×#4025semidirect
419. C5D5×#126semidirect

Maximal subgroups

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

subgroupindex
#117171992
C5×D5×C22⋊C42
C5×#40252
D5×C22⋊Dic52
#117170742
D5×C4⋊Dic52
D5×#6832
C4×D5×Dic52
#117169802
#117169782
#117169772
#117169762
D5×#1265
C2×#40255