Finite Group Databasebeta

← D5×#4021 #13105090

Subgroups — D5×#4021 #13105090

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×D5×D20C211yesmaximal, characteristic
2C2×D5×Dic10C211yesmaximal, characteristic, complemented
3#11717195C211yesmaximal, characteristic, complemented
4C5×#4021C211yesmaximal, characteristic, complemented
5C42×C5×D5C211yesmaximal, characteristic, complemented
6D5×#685C214yesmaximal, complemented
7#11716982C211yesmaximal, characteristic, complemented
8#11716979C211yesmaximal, characteristic, complemented
9#11716970C214yesmaximal, complemented
10C22×D52C2212yes—
11C2×C4⋊(C5⋊D5)C2211yescharacteristic
12C2×#6045C2211yescharacteristic, complemented
13C2×C5×D20C2211yescharacteristic
14C2×C4×C5×D5C2212yes—
15C2×C4×C5×D5C2211yescharacteristic
16C2×C5×Dic10C2211yescharacteristic, complemented
17C2×#6039C2212yescomplemented
18C2×#6038C2212yes—
19C2×D5×Dic5C2212yes—
20D5×D20—24no—
21D5×Dic10—24no—
22C42×C52C2211yescharacteristic, complemented
23#87808C2214yescomplemented
24C5×#685C2214yescomplemented
25C4×C5×Dic5C2212yescomplemented
26C4×C5×Dic5C2211yescharacteristic, complemented
27#87779C2214yescomplemented
28#87778C2214yescomplemented
29D5×#124—51nomaximal
30C2×#4021—51nomaximal
31C22×C5⋊D5C2312yes—
32C22×C5×D5C2312yes—
33C22×C5×D5C2311yescharacteristic
34C2×D52—24no—
35C2×D52—28no—
36C2×C4×C52C2312yes—
37C2×C4×C52C2311yescharacteristic
38C2×#1039C2312yes—
39C4⋊(C5⋊D5)—22no—
40#6045—22no—
41C2×C5×Dic5C2312yes—
42C2×C5×Dic5C2312yes—
43C2×C5×Dic5C2311yescharacteristic
44C5×D20—22no—
45C4×C5×D5—24no—
46C4×C5×D5D414yes—
47C5×Dic10—22no—
48#6039—24no—
49#6038—24no—
50D5×Dic5—24no—
51C2×Q8×D5—51no—
52C2×D4×D5—51no—
53C22×D20—51no—
54C22×Dic10—51no—
55C5×#124—51no—
56C2×C42×C5—51no—
57#4093—51no—
58#4082—51no—
59C2×#685—54no—
60#4031—54no—
61D5×C22⋊C4—54no—
62#4021—51no—
63#4021—51no—
64#4021—51no—
65#4021—51no—
66#4021—54no—
67#4021—102no—
68#4021D511yescharacteristic, direct product factor
69C42×D5D511yescharacteristic, complemented
70C22×C52C2411yescharacteristic
71C2×C5⋊D5—22no—
72C2×C5⋊D5—24no—
73C2×C5×D5—22no—
74C2×C5×D5—24no—
75C2×C5×D5C2×D412yes—
76C2×C5×D5#4114yes—
77D52—48no—
78C4×C52—22no—
79C4×C52C2×D412yes—
80#1039—22no—
81C5×Dic5—22no—
82C5×Dic5—22no—
83C5×Dic5C2×D412yes—
84C23×D5—52no—
85C23×D5—52no—
86C2×C5×Q8—51no—
87C2×C5×D4—51no—
88C22×C4×C5—51no—
89C22×C4×C5—52no—
90C2×C22⋊D5—52no—
91C22×Dic5—52no—
92Q8×D5—104no—
93D4×D5—104no—
94C2×D20—52no—
95C2×D20—51no—
96C2×D20—51no—
97C2×D20—102no—
98C2×D20—104no—
99C2×D20C2×D511yescharacteristic
100C2×C4×D5—52no—
101C2×C4×D5C2×D512yes—
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—22no—
112C42×C5—52no—
113C42×C5—51no—
114C42×C5C2×D511yescharacteristic, complemented
115C42×C5C2×D511yescharacteristic, complemented
116C22⋊Dic5—54no—
117#685—54no—
118#685—54no—
119#685—54no—
120#685—54no—
121#685—54no—
122#685—108no—
123#685C2×D514yescomplemented
124C4×Dic5C2×D512yescomplemented
125C4×Dic5C2×D511yescharacteristic, complemented
126C2×#124—251noSylow
127C2×C52C22×D411yescharacteristic
128C2×C52C2×#4112yes—
129C5⋊D5—42no—
130C5×D5—42no—
131C5×D5#12414yescomplemented
132C23×C5—51no—
133C23×C5—52no—
134C22×D5—52no—
135C22×D5—52no—
136C22×D5—104no—
137C22×D5—104no—
138C22×D5—108no—
139C22×D5—104no—
140C22×D5—108no—
141C22×D5C22×D512yes—
142C22×D5C22×D511yescharacteristic
143C5×Q8—102no—
144C5×D4—102no—
145C2×C4×C5—22no—
146C2×C4×C5—24no—
147C2×C4×C5—51no—
148C2×C4×C5—54no—
149C2×C4×C5—52no—
150C2×C4×C5—52no—
151C2×C4×C5—104no—
152C2×C4×C5C22×D512yes—
153C2×C4×C5C22×D512yes—
154C2×C4×C5C22×D511yescharacteristic
155C2×C4×C5C22×D511yescharacteristic
156C22⋊D5—104no—
157C2×Dic5—52no—
158C2×Dic5—52no—
159C2×Dic5—104no—
160C2×Dic5—104no—
161C2×Dic5C22×D512yes—
162C2×Dic5C22×D512yes—
163C2×Dic5C22×D511yescharacteristic
164D20—22no—
165D20—104no—
166D20—102no—
167D20—102no—
168D20—204no—
169C4×D5—24no—
170C4×D5—104no—
171C4×D5D2014yes—
172Dic10—22no—
173Dic10—104no—
174Dic10—102no—
175Dic10—102no—
176Dic10—104no—
177Dic10—204no—
178C22×Q8—251no—
179C22×D4—251no—
180#124—51no—
181#124—254no—
182#124—251no—
183#124—251no—
184#124—251no—
185C2×C22⋊C4—254no—
186C2×C42—51no—
187C52C2×#12411yescharacteristic, complemented, Sylow
188C22×C5—22no—
189C22×C5—52no—
190C22×C5—54no—
191C22×C5—102no—
192C22×C5—104no—
193C22×C5C23×D511yescharacteristic
194C22×C5C23×D511yescharacteristic
195C2×D5—22no—
196C2×D5—24no—
197C2×D5—102no—
198C2×D5—104no—
199C2×D5—102no—
200C2×D5—104no—
201C2×D5—204no—
202C2×D5—208no—
203C2×D5—208no—
204C2×D5—208no—
205C2×D5C2×D2012yes—
206C2×D5#70914yes—
207C4×C5—22no—
208C4×C5—22no—
209C4×C5—24no—
210C4×C5—44no—
211C4×C5—52no—
212C4×C5—102no—
213C4×C5—102no—
214C4×C5C2×D2012yes—
215C4×C5D4×D512yes—
216Dic5—22no—
217Dic5—22no—
218Dic5—102no—
219Dic5—102no—
220Dic5—204no—
221Dic5C2×D2012yes—
222C24—252no—
223C2×Q8—51no—
224C2×Q8—252no—
225C2×Q8—251no—
226C2×Q8—504no—
227C2×D4—51no—
228C2×D4—252no—
229C2×D4—251no—
230C2×D4—504no—
231C22×C4—51no—
232C22×C4—52no—
233C22×C4—252no—
234C22⋊C4—54no—
235C22⋊C4—254no—
236C22⋊C4—254no—
237C22⋊C4—254no—
238C42—52no—
239C42—51no—
240C42D5211yescharacteristic, complemented
241C2×C5—22no—
242C2×C5—24no—
243C2×C5—54no—
244C2×C5—202no—
245C2×C5C22×D2011yescharacteristic
246C2×C5C2×#70912yes—
247C2×C5C2×D4×D511yescharacteristic
248C2×C5D5×#4112yes—
249D5—42no—
250D5—202no—
251D5—202no—
252D5—404no—
253D5#402114yesdirect product factor
254C23—51no—
255C23—52no—
256C23—252no—
257C23—504no—
258C23—508no—
259Q8—102no—
260Q8—504no—
261Q8—502no—
262D4—102no—
263D4—504no—
264D4—502no—
265C2×C4—51no—
266C2×C4—54no—
267C2×C4—52no—
268C2×C4—52no—
269C2×C4—104no—
270C2×C4—252no—
271C2×C4—504no—
272C2×C4C2×D5212yes—
273C2×C4C2×D5211yescharacteristic
274C5—22no—
275C5C2×#402111yescharacteristic, complemented
276C5D5×#12411yescharacteristic, complemented
277C22—52no—
278C22—54no—
279C22—102no—
280C22—104no—
281C22—502no—
282C22—504no—
283C22—1008no—
284C22C22×D5211yescharacteristic
285C4—22no—
286C4—52no—
287C4—102no—
288C4—102no—
289C4—502no—
290C4D5×D2012yes—
291C2—54no—
292C2—202no—
293C2—1002no—
294C2C2×D5×D2011yescharacteristic
295C2D5×#70912yes—
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC42×C52C22
prime radicalC2×D5×D20C2
hypercenterC42D52
hypocenterC52C2×#124
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×D5×Dic10C2semidirect
3. #11717195C2semidirect
4. C5×#4021C2semidirect
5. C42×C5×D5C2semidirect
6. D5×#685C2semidirect
7. #11716982C2semidirect
8. #11716979C2semidirect
9. #11716970C2semidirect
12. C2×#6045C22semidirect
16. C2×C5×Dic10C22semidirect
17. C2×#6039C22semidirect
22. C42×C52C22semidirect
23. #87808C22semidirect
24. C5×#685C22semidirect
25. C4×C5×Dic5C22semidirect
26. C4×C5×Dic5C22semidirect
27. #87779C22semidirect
28. #87778C22semidirect
68. #4021D5direct (N × H)
69. C42×D5D5semidirect
109. C2×Dic10C2×D5semidirect
114. C42×C5C2×D5semidirect
115. C42×C5C2×D5semidirect
123. #685C2×D5semidirect
124. C4×Dic5C2×D5semidirect
125. C4×Dic5C2×D5semidirect
131. C5×D5#124semidirect
187. C52C2×#124semidirect
240. C42D52semidirect
253. D5#4021direct (N × H)
275. C5C2×#4021semidirect
276. C5D5×#124semidirect

Maximal subgroups

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

subgroupindex
C2×D5×D202
C2×D5×Dic102
#117171952
C5×#40212
C42×C5×D52
D5×#6852
#117169822
#117169792
#117169702
D5×#1245
C2×#40215