Finite Group Databasebeta

← C5×D5×#99 #13102004

Subgroups — C5×D5×#99 #13102004

Order 1600.

472 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 106 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
2C5×D5×C22⋊C4C212yesmaximal, complemented
3C52×#99C211yesmaximal, characteristic, complemented
4C5×#3966C211yesmaximal, characteristic, complemented
5C5×#3938C212yesmaximal, complemented
6C23×C5×D5C411yescharacteristic, complemented
7C23×C5×D5C2211yescharacteristic
8C2×C52×D4C2211yescharacteristic
9C2×C5×C22⋊D5C411yescharacteristic, complemented
10C2×C5×C22⋊D5C2211yescharacteristic
11C5×D4×D5—22no—
12C5×D4×D5—22no—
13C2×C5×D20C411yescharacteristic, complemented
14C2×C4×C5×D5—22no—
15C2×C4×C5×D5C411yescharacteristic, complemented
16C52×C22⋊C4C2212yescomplemented
17C5×C22⋊Dic5C2212yescomplemented
18C5×#685—22no—
19C2×C5×#99—51nomaximal
20D5×#99C511yesmaximal, characteristic, direct product factor
21C23×C52C2×C411yescharacteristic, complemented
22C23×C52C2311yescharacteristic
23C22×C5×D5—21no—
24C22×C5×D5—21no—
25C22×C5×D5—42no—
26C22×C5×D5—42no—
27C22×C5×D5C2×C411yescharacteristic
28C22×C5×D5C2×C411yescharacteristic
29C22×C5×D5C2×C411yescharacteristic, complemented
30C22×C5×D5D412yes—
31C22×C5×D5D412yes—
32C52×D4—22no—
33C2×C4×C52—22no—
34C2×C4×C52C2×C411yescharacteristic, complemented
35C5×C22⋊D5—22no—
36C5×C22⋊D5—22no—
37C2×C5×Dic5—22no—
38C2×C5×Dic5C2×C411yescharacteristic, complemented
39C5×D20—22no—
40C4×C5×D5—21no—
41C4×C5×D5—21no—
42C4×C5×D5—44no—
43C22×C5×D4—51no—
44C2×D4×D5C2×C511yescharacteristic
45C2×C5×C22⋊C4—52no—
46D5×C22⋊C4C2×C512yescomplemented
47C5×#99—22no—
48C5×#99—51no—
49C5×#99—52no—
50C5×#99D511yescharacteristic, direct product factor
51C5×#99C2×C511yescharacteristic, complemented
52#3966C2×C511yescharacteristic, complemented
53#3938C2×C512yescomplemented
54C22×C52—21no—
55C22×C52—41no—
56C22×C52—41no—
57C22×C52C22×C411yescharacteristic
58C22×C52C2×D412yes—
59C2×C5×D5—24no—
60C2×C5×D5—22no—
61C2×C5×D5—21no—
62C2×C5×D5—41no—
63C2×C5×D5—42no—
64C2×C5×D5—41no—
65C2×C5×D5—42no—
66C2×C5×D5—42no—
67C2×C5×D5C22⋊C411yescharacteristic
68C2×C5×D5C22⋊C412yes—
69C2×C5×D5C22⋊C411yescharacteristic
70C4×C52—21no—
71C4×C52—42no—
72C5×Dic5—21no—
73C5×Dic5—42no—
74C24×C5—51no—
75C24×C5—51no—
76C23×D5C4×C511yescharacteristic, complemented
77C23×D5C22×C511yescharacteristic
78C2×C5×D4—22no—
79C2×C5×D4—51no—
80C2×C5×D4—51no—
81C2×C5×D4—51no—
82C2×C5×D4—102no—
83C2×C5×D4—102no—
84C2×C5×D4C2×D511yescharacteristic
85C2×C5×D4C22×C511yescharacteristic
86C22×C4×C5—51no—
87C22×C4×C5—102no—
88C2×C22⋊D5C4×C511yescharacteristic, complemented
89C2×C22⋊D5C22×C511yescharacteristic
90D4×D5—22no—
91D4×D5—22no—
92C2×D20C4×C511yescharacteristic, complemented
93C2×C4×D5—22no—
94C2×C4×D5C4×C511yescharacteristic, complemented
95C5×C22⋊C4—24no—
96C5×C22⋊C4—52no—
97C5×C22⋊C4—102no—
98C5×C22⋊C4C2×D512yescomplemented
99C5×C22⋊C4C22×C512yescomplemented
100C22⋊Dic5C22×C512yescomplemented
101#685—22no—
102C2×#99—51noSylow
103C2×C52—22no—
104C2×C52—21no—
105C2×C52—41no—
106C2×C52C2×C22⋊C411yescharacteristic
107C5×D5—21no—
108C5×D5—22no—
109C5×D5—41no—
110C5×D5#9912yesdirect product factor
111C23×C5—22no—
112C23×C5—22no—
113C23×C5—51no—
114C23×C5—52no—
115C23×C5—51no—
116C23×C5—52no—
117C23×C5—51no—
118C23×C5—101no—
119C23×C5—101no—
120C23×C5—202no—
121C23×C5—202no—
122C23×C5C4×D511yescharacteristic, complemented
123C23×C5C2×C4×C511yescharacteristic, complemented
124C23×C5C22×D511yescharacteristic
125C23×C5C23×C511yescharacteristic
126C22×D5—21no—
127C22×D5—21no—
128C22×D5—42no—
129C22×D5—42no—
130C22×D5C2×C4×C511yescharacteristic
131C22×D5C2×C4×C511yescharacteristic
132C22×D5C2×C4×C511yescharacteristic, complemented
133C22×D5C5×D412yes—
134C22×D5C5×D412yes—
135C5×D4—22no—
136C5×D4—22no—
137C5×D4—44no—
138C5×D4—102no—
139C5×D4—102no—
140C5×D4—102no—
141C2×C4×C5—22no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—44no—
145C2×C4×C5—51no—
146C2×C4×C5—101no—
147C2×C4×C5—101no—
148C2×C4×C5—102no—
149C2×C4×C5—204no—
150C2×C4×C5C4×D511yescharacteristic, complemented
151C2×C4×C5C2×C4×C511yescharacteristic, complemented
152C22⋊D5—22no—
153C22⋊D5—22no—
154C2×Dic5—22no—
155C2×Dic5C2×C4×C511yescharacteristic, complemented
156D20—22no—
157C4×D5—21no—
158C4×D5—21no—
159C4×D5—44no—
160C22×D4—51no—
161C2×C22⋊C4—52no—
162#99—51no—
163#99—52no—
164#99C5×D511yescharacteristic, direct product factor
165C52C2×#9911yescharacteristic, complemented, Sylow
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—22no—
169C22×C5—24no—
170C22×C5—42no—
171C22×C5—41no—
172C22×C5—41no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—51no—
176C22×C5—51no—
177C22×C5—52no—
178C22×C5—82no—
179C22×C5—82no—
180C22×C5—104no—
181C22×C5—102no—
182C22×C5—101no—
183C22×C5—202no—
184C22×C5—201no—
185C22×C5—201no—
186C22×C5—202no—
187C22×C5—202no—
188C22×C5C2×C4×D511yescharacteristic
189C22×C5D4×D512yes—
190C22×C5C22×C4×C511yescharacteristic
191C22×C5C2×C5×D412yes—
192C2×D5—24no—
193C2×D5—22no—
194C2×D5—21no—
195C2×D5—41no—
196C2×D5—42no—
197C2×D5—42no—
198C2×D5—42no—
199C2×D5—41no—
200C2×D5C5×C22⋊C411yescharacteristic
201C2×D5C5×C22⋊C412yes—
202C2×D5C5×C22⋊C411yescharacteristic
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—42no—
206C4×C5—42no—
207C4×C5—42no—
208C4×C5—84no—
209C4×C5—101no—
210C4×C5—202no—
211Dic5—21no—
212Dic5—42no—
213C24—51no—
214C24—51no—
215C2×D4—51no—
216C2×D4—51no—
217C2×D4—51no—
218C2×D4—102no—
219C2×D4—102no—
220C2×D4C2×C5×D511yescharacteristic
221C22×C4—51no—
222C22×C4—102no—
223C22⋊C4—52no—
224C22⋊C4—102no—
225C22⋊C4C2×C5×D512yescomplemented
226C2×C5—22no—
227C2×C5—21no—
228C2×C5—22no—
229C2×C5—21no—
230C2×C5—22no—
231C2×C5—44no—
232C2×C5—42no—
233C2×C5—41no—
234C2×C5—41no—
235C2×C5—52no—
236C2×C5—82no—
237C2×C5—101no—
238C2×C5—102no—
239C2×C5—201no—
240C2×C5D5×C22⋊C411yescharacteristic
241C2×C5C2×C5×C22⋊C411yescharacteristic
242D5—21no—
243D5—22no—
244D5—41no—
245D5C5×#9912yesdirect product factor
246C23—51no—
247C23—52no—
248C23—51no—
249C23—52no—
250C23—51no—
251C23—101no—
252C23—101no—
253C23—202no—
254C23—202no—
255C23C4×C5×D511yescharacteristic, complemented
256C23C22×C5×D511yescharacteristic
257D4—22no—
258D4—102no—
259D4—102no—
260D4—102no—
261C2×C4—22no—
262C2×C4—51no—
263C2×C4—101no—
264C2×C4—101no—
265C2×C4—102no—
266C2×C4—204no—
267C2×C4C4×C5×D511yescharacteristic, complemented
268C5—22no—
269C5D5×#9911yescharacteristic, direct product factor
270C5C2×C5×#9911yescharacteristic, complemented
271C22—21no—
272C22—41no—
273C22—41no—
274C22—51no—
275C22—51no—
276C22—52no—
277C22—104no—
278C22—102no—
279C22—101no—
280C22—202no—
281C22—201no—
282C22—201no—
283C22—202no—
284C22—202no—
285C22C2×C4×C5×D511yescharacteristic
286C22C5×D4×D512yes—
287C4—21no—
288C4—42no—
289C4—101no—
290C4—202no—
291C2—22no—
292C2—21no—
293C2—41no—
294C2—52no—
295C2—101no—
296C2—102no—
297C2—201no—
298C2C5×D5×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C5D5×C22⋊C4
commutatorC22×C5C22×C4×C5
FrattiniC23C22×C5×D5
FittingC52×#99C2
socleC2×C52C2×C22⋊C4
prime radicalC2×C5×D4×D5C2
cosocleC23×C5C23×C5
hypercenterC5×#99D5
hypocenterC5C2×C5×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C5×#99

Complements

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

NH ≅ G/Ntype
2. C5×D5×C22⋊C4C2semidirect
3. C52×#99C2semidirect
4. C5×#3966C2semidirect
5. C5×#3938C2semidirect
6. C23×C5×D5C4semidirect
9. C2×C5×C22⋊D5C4semidirect
13. C2×C5×D20C4semidirect
15. C2×C4×C5×D5C4semidirect
16. C52×C22⋊C4C22semidirect
17. C5×C22⋊Dic5C22semidirect
20. D5×#99C5direct (N × H)
21. C23×C52C2×C4semidirect
29. C22×C5×D5C2×C4semidirect
34. C2×C4×C52C2×C4semidirect
38. C2×C5×Dic5C2×C4semidirect
46. D5×C22⋊C4C2×C5semidirect
50. C5×#99D5direct (N × H)
51. C5×#99C2×C5semidirect
52. #3966C2×C5semidirect
53. #3938C2×C5semidirect
76. C23×D5C4×C5semidirect
88. C2×C22⋊D5C4×C5semidirect
92. C2×D20C4×C5semidirect
94. C2×C4×D5C4×C5semidirect
98. C5×C22⋊C4C2×D5semidirect
99. C5×C22⋊C4C22×C5semidirect
100. C22⋊Dic5C22×C5semidirect
110. C5×D5#99direct (N × H)
122. C23×C5C4×D5semidirect
123. C23×C5C2×C4×C5semidirect
132. C22×D5C2×C4×C5semidirect
150. C2×C4×C5C4×D5semidirect
151. C2×C4×C5C2×C4×C5semidirect
155. C2×Dic5C2×C4×C5semidirect
164. #99C5×D5direct (N × H)
165. C52C2×#99semidirect
225. C22⋊C4C2×C5×D5semidirect
245. D5C5×#99direct (N × H)
255. C23C4×C5×D5semidirect
267. C2×C4C4×C5×D5semidirect
269. C5D5×#99direct (N × H)
270. C5C2×C5×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×D52
C5×D5×C22⋊C42
C52×#992
C5×#39662
C5×#39382
C2×C5×#995
D5×#995