Finite Group Databasebeta

← D5×#4082 #13106201

Subgroups — D5×#4082 #13106201

Order 1600.

736 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D4×D5C211yesmaximal, characteristic
2C2×D5×Dic10C211yesmaximal, characteristic, complemented
3#11717256C211yesmaximal, characteristic, complemented
4C5×#4082C211yesmaximal, characteristic, complemented
5D5×C22⋊Dic5C214yesmaximal, complemented
6#11717077C214yesmaximal, complemented
7C4×D5×Dic5C211yesmaximal, characteristic, complemented
8#11716981C211yesmaximal, characteristic, complemented
9#11716979C211yesmaximal, characteristic, complemented
10C23×C5×D5C2212yes—
11C2×C52×D4C2211yescharacteristic
12C2×#6045C2211yescharacteristic, complemented
13C2×C5×C22⋊D5C2212yes—
14C5×D4×D5—24no—
15C2×C5×D20C2211yescharacteristic
16C2×C4×C5×D5C2211yescharacteristic
17C2×C5×Dic10C2211yescharacteristic, complemented
18C2×#6039C2212yescomplemented
19C2×D5×Dic5C2212yes—
20C2×D5×Dic5C2212yes—
21D5×Dic10—24no—
22C22⋊#1039C2214yescomplemented
23C4×#1039C2211yescharacteristic, complemented
24C5×C22⋊Dic5C2214yescomplemented
25C4×C5×Dic5C2211yescharacteristic, complemented
26#87778C2214yescomplemented
27#87778C2214yescomplemented
28Dic52C2212yescomplemented
29C2×#4082—51nomaximal
30D5×#124—51nomaximal
31C23×C52C2312yes—
32C22×C5×D5—24no—
33C22×C5×D5—28no—
34C22×C5×D5C2312yes—
35C22×C5×D5C2311yescharacteristic
36C52×D4—22no—
37C2×C4×C52C2311yescharacteristic
38C2×#1039C2312yes—
39C2×#1039C2312yes—
40#6045—22no—
41C5×C22⋊D5—24no—
42C2×C5×Dic5C2312yes—
43C2×C5×Dic5C2312yes—
44C2×C5×Dic5C2311yescharacteristic
45C5×D20—22no—
46C4×C5×D5D414yes—
47C5×Dic10—22no—
48#6039—24no—
49D5×Dic5—24no—
50D5×Dic5—24no—
51C22×C5×D4—51no—
52C2×Q8×D5—51no—
53C2×D4×D5D511yescharacteristic
54C22×Dic10—51no—
55C5×#124—51no—
56C2×C22⋊Dic5—54no—
57#4093—51no—
58#4082—51no—
59#4082—51no—
60#4082—51no—
61#4082—54no—
62#4082—51no—
63#4082—102no—
64#4082D511yescharacteristic, direct product factor
65C2×C4×Dic5—51no—
66#4031—54no—
67D5×C22⋊C4—54no—
68#4021—51no—
69C42×D5—51no—
70C22×C52—22no—
71C22×C52—24no—
72C22×C52C2411yescharacteristic
73C2×C5×D5—22no—
74C2×C5×D5—24no—
75C2×C5×D5—48no—
76C2×C5×D5C2×D412yes—
77C2×C5×D5#4114yes—
78C4×C52C2×D412yes—
79#1039—22no—
80#1039—22no—
81C5×Dic5—22no—
82C5×Dic5—22no—
83C5×Dic5C2×D412yes—
84C24×C5—52no—
85C23×D5C2×D512yes—
86C2×C5×Q8—51no—
87C2×C5×D4—22no—
88C2×C5×D4—52no—
89C2×C5×D4—51no—
90C2×C5×D4—104no—
91C2×C5×D4C2×D511yescharacteristic
92C2×C5×D4C2×D511yescharacteristic
93C22×C4×C5—51no—
94C2×C22⋊D5C2×D512yes—
95C22×Dic5—52no—
96C22×Dic5—52no—
97Q8×D5—104no—
98D4×D5—24no—
99C2×D20C2×D511yescharacteristic
100C2×C4×D5—52no—
101C2×C4×D5—52no—
102C2×C4×D5C2×D511yescharacteristic
103C2×Dic10—51no—
104C2×Dic10—51no—
105C2×Dic10—52no—
106C2×Dic10—52no—
107C2×Dic10—102no—
108C2×Dic10—104no—
109C2×Dic10C2×D511yescharacteristic, complemented
110C5×C22⋊C4—54no—
111C42×C5—51no—
112C22⋊Dic5—54no—
113C22⋊Dic5—54no—
114C22⋊Dic5—54no—
115C22⋊Dic5—54no—
116C22⋊Dic5—108no—
117C22⋊Dic5C2×D514yescomplemented
118#685—54no—
119#685—54no—
120C4×Dic5—51no—
121C4×Dic5—51no—
122C4×Dic5—52no—
123C4×Dic5—52no—
124C4×Dic5—102no—
125C4×Dic5C2×D511yescharacteristic, complemented
126C2×#124—251noSylow
127C2×C52—42no—
128C2×C52C22×D411yescharacteristic
129C2×C52C2×#4112yes—
130C5×D5—42no—
131C5×D5#12414yescomplemented
132C23×C5—24no—
133C23×C5—51no—
134C23×C5—52no—
135C23×C5—104no—
136C23×C5—108no—
137C23×C5C22×D512yes—
138C23×C5C22×D512yes—
139C22×D5—28no—
140C22×D5—24no—
141C22×D5C22×D512yes—
142C22×D5C22×D511yescharacteristic
143C5×Q8—102no—
144C5×D4—22no—
145C5×D4—22no—
146C5×D4—44no—
147C5×D4—104no—
148C5×D4—102no—
149C2×C4×C5—22no—
150C2×C4×C5—51no—
151C2×C4×C5—54no—
152C2×C4×C5—52no—
153C2×C4×C5—52no—
154C2×C4×C5C22×D511yescharacteristic
155C2×C4×C5C22×D511yescharacteristic
156C22⋊D5—24no—
157C2×Dic5—52no—
158C2×Dic5—52no—
159C2×Dic5—52no—
160C2×Dic5—52no—
161C2×Dic5—104no—
162C2×Dic5—104no—
163C2×Dic5—104no—
164C2×Dic5—104no—
165C2×Dic5C22×D512yes—
166C2×Dic5C22×D512yes—
167C2×Dic5C22×D511yescharacteristic
168D20—22no—
169C4×D5—104no—
170C4×D5—104no—
171C4×D5C22⋊D514yes—
172Dic10—22no—
173Dic10—104no—
174Dic10—102no—
175Dic10—102no—
176Dic10—104no—
177Dic10—204no—
178C22×Q8—251no—
179C22×D4—51no—
180#124—51no—
181#124—251no—
182#124—254no—
183#124—251no—
184#124—251no—
185C2×C22⋊C4—254no—
186C2×C42—251no—
187C52C2×#12411yescharacteristic, complemented, Sylow
188C22×C5—22no—
189C22×C5—24no—
190C22×C5—24no—
191C22×C5—22no—
192C22×C5—22no—
193C22×C5—44no—
194C22×C5—48no—
195C22×C5—52no—
196C22×C5—54no—
197C22×C5—102no—
198C22×C5—104no—
199C22×C5—208no—
200C22×C5C23×D511yescharacteristic
201C22×C5C23×D511yescharacteristic
202C2×D5—24no—
203C2×D5—22no—
204C2×D5—48no—
205C2×D5#71114yes—
206C2×D5C2×C22⋊D512yes—
207C4×C5—24no—
208C4×C5—52no—
209C4×C5—102no—
210C4×C5—102no—
211C4×C5D4×D512yes—
212C4×C5C2×C22⋊D512yes—
213Dic5—22no—
214Dic5—22no—
215Dic5—102no—
216Dic5—102no—
217Dic5—102no—
218Dic5—102no—
219Dic5—204no—
220Dic5—204no—
221Dic5C2×C22⋊D512yes—
222C24—52no—
223C2×Q8—51no—
224C2×Q8—252no—
225C2×Q8—251no—
226C2×Q8—504no—
227C2×D4—52no—
228C2×D4—51no—
229C2×D4—104no—
230C2×D4D5211yescharacteristic
231C22×C4—51no—
232C22×C4—252no—
233C22×C4—252no—
234C22⋊C4—54no—
235C22⋊C4—254no—
236C22⋊C4—254no—
237C22⋊C4—254no—
238C42—51no—
239C42—252no—
240C42—251no—
241C2×C5—24no—
242C2×C5—22no—
243C2×C5—42no—
244C2×C5—42no—
245C2×C5—54no—
246C2×C5—84no—
247C2×C5—202no—
248C2×C5C2×D4×D511yescharacteristic
249C2×C5C2×#71112yes—
250C2×C5D5×#4112yes—
251C2×C5C22×C22⋊D511yescharacteristic
252D5—42no—
253D5#408214yesdirect product factor
254C23—51no—
255C23—52no—
256C23—104no—
257C23—108no—
258C23C2×D5212yes—
259Q8—102no—
260Q8—504no—
261Q8—502no—
262D4—22no—
263D4—104no—
264D4—102no—
265C2×C4—51no—
266C2×C4—54no—
267C2×C4—52no—
268C2×C4—52no—
269C2×C4—252no—
270C2×C4—252no—
271C2×C4—504no—
272C2×C4—504no—
273C2×C4C2×D5211yescharacteristic
274C5—22no—
275C5D5×#12411yescharacteristic, complemented
276C5C2×#408211yescharacteristic, complemented
277C22—24no—
278C22—22no—
279C22—54no—
280C22—52no—
281C22—104no—
282C22—102no—
283C22—208no—
284C22C22×D5211yescharacteristic
285C4—52no—
286C4—102no—
287C4—102no—
288C4—502no—
289C4—502no—
290C4D5×C22⋊D512yes—
291C2—42no—
292C2—54no—
293C2—202no—
294C2D5×#71112yes—
295C2C2×D5×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC2×C52×D4C22
prime radicalC2×C5×D4×D5C2
hypercenterC2×D4D52
hypocenterC52C2×#124
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×D5×Dic10C2semidirect
3. #11717256C2semidirect
4. C5×#4082C2semidirect
5. D5×C22⋊Dic5C2semidirect
6. #11717077C2semidirect
7. C4×D5×Dic5C2semidirect
8. #11716981C2semidirect
9. #11716979C2semidirect
12. C2×#6045C22semidirect
17. C2×C5×Dic10C22semidirect
18. C2×#6039C22semidirect
22. C22⋊#1039C22semidirect
23. C4×#1039C22semidirect
24. C5×C22⋊Dic5C22semidirect
25. C4×C5×Dic5C22semidirect
26. #87778C22semidirect
27. #87778C22semidirect
28. Dic52C22semidirect
64. #4082D5direct (N × H)
109. C2×Dic10C2×D5semidirect
117. C22⋊Dic5C2×D5semidirect
125. C4×Dic5C2×D5semidirect
131. C5×D5#124semidirect
187. C52C2×#124semidirect
253. D5#4082direct (N × H)
275. C5D5×#124semidirect
276. C5C2×#4082semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×D52
C2×D5×Dic102
#117172562
C5×#40822
D5×C22⋊Dic52
#117170772
C4×D5×Dic52
#117169812
#117169792
C2×#40825
D5×#1245