Finite Group Databasebeta

← #123×D25 #13098979

Subgroups — #123×D25 #13098979

Order 1600.

513 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 513 conjugacy classes of subgroups — too many to draw. Only its 133 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×D4×D25C211yesmaximal, characteristic
2C22×C4×D25C211yesmaximal, characteristic, complemented
3C25×#123C211yesmaximal, characteristic, complemented
4#11716497C211yesmaximal, characteristic, complemented
5#11716491C211yesmaximal, characteristic, complemented
6#11716456C212yesmaximal, complemented
7C4⋊C4×D25C212yesmaximal, complemented
8#11716448C211yesmaximal, characteristic, complemented
9#11716445C212yesmaximal, complemented
10C22⋊C4×D25C211yesmaximal, characteristic, complemented
11C22⋊C4×D25C212yesmaximal, complemented
12C23×D25C2211yescharacteristic
13C23×D25C2211yescharacteristic
14C2×D4×C25C2211yescharacteristic
15C22×C4×C25C2211yescharacteristic, complemented
16C2×C22⋊D25C2211yescharacteristic
17C2×C22⋊D25C2211yescharacteristic
18C22×Dic25C2211yescharacteristic, complemented
19D4×D25—24no—
20C2×D100C2211yescharacteristic
21C2×C4×D25—24no—
22C2×C4×D25C2212yes—
23C2×C4×D25C2212yes—
24C2×C4×D25C2211yescharacteristic
25C2×C4×D25C2212yescomplemented
26C4⋊C4×C25C2212yescomplemented
27C22⋊C4×C25C2212yescomplemented
28C22⋊C4×C25C2211yescharacteristic, complemented
29C22⋊Dic25C2212yescomplemented
30C22⋊Dic25C2211yescharacteristic, complemented
31#87720C2212yescomplemented
32#87720C2212yescomplemented
33#87720C2212yescomplemented
34C4⋊Dic25C2212yescomplemented
35#87718C2212yescomplemented
36#87718C2212yescomplemented
37D5×#123—51nomaximal
38C23×C25C2311yescharacteristic
39C23×C25C2311yescharacteristic
40C22×D25—24no—
41C22×D25—22no—
42C22×D25—24no—
43C22×D25D414yes—
44C22×D25C2311yescharacteristic
45C22×D25C2311yescharacteristic
46C22×D25C2311yescharacteristic
47D4×C25—22no—
48C2×C4×C25—22no—
49C2×C4×C25C2311yescharacteristic
50C2×C4×C25C2312yes—
51C2×C4×C25C2312yes—
52C22⋊D25—22no—
53C22⋊D25—22no—
54C2×Dic25—22no—
55C2×Dic25C2311yescharacteristic
56C2×Dic25C2312yes—
57C2×Dic25C2312yes—
58D100—22no—
59C4×D25—24no—
60C4×D25—24no—
61C4×D25—22no—
62C4×D25—24no—
63C2×D4×D5—51no—
64C22×C4×D5—51no—
65C5×#123D511yescharacteristic
66#4081—51no—
67#4075—51no—
68#4040—52no—
69D5×C4⋊C4—52no—
70#4032—51no—
71#4029—52no—
72D5×C22⋊C4—51no—
73D5×C22⋊C4—52no—
74C22×C25—22no—
75C22×C25—21no—
76C22×C25—22no—
77C22×C25C2×D412yes—
78C22×C25C2411yescharacteristic
79C2×D25—22no—
80C2×D25—28no—
81C2×D25—21no—
82C2×D25—22no—
83C2×D25—44no—
84C2×D25C2×D412yes—
85C2×D25C2×D412yes—
86C2×D25#4114yes—
87C4×C25—22no—
88C4×C25—21no—
89C4×C25—22no—
90Dic25—22no—
91Dic25—21no—
92Dic25—22no—
93C23×D5—51no—
94C23×D5—51no—
95C2×C5×D4C2×D511yescharacteristic
96C22×C4×C5C2×D511yescharacteristic
97C2×C22⋊D5—51no—
98C2×C22⋊D5—51no—
99C22×Dic5—51no—
100D4×D5—104no—
101C2×D20—51no—
102C2×C4×D5—52no—
103C2×C4×D5—52no—
104C2×C4×D5—51no—
105C2×C4×D5—52no—
106C2×C4×D5—104no—
107C5×C4⋊C4C2×D512yes—
108C5×C22⋊C4C2×D512yes—
109C5×C22⋊C4C2×D511yescharacteristic
110C22⋊Dic5—52no—
111C22⋊Dic5—51no—
112#685—52no—
113#685—52no—
114#685—52no—
115C4⋊Dic5—52no—
116#683—52no—
117#683—52no—
118C2×#123—251noSylow
119C2×C25—22no—
120C2×C25—41no—
121C2×C25C22×D411yescharacteristic
122C2×C25C2×#4112yes—
123D25—22no—
124D25—41no—
125D25#12314yesdirect product factor
126C23×C5C22×D511yescharacteristic
127C23×C5C22×D511yescharacteristic
128C22×D5—51no—
129C22×D5—54no—
130C22×D5—51no—
131C22×D5—51no—
132C22×D5—104no—
133C22×D5—102no—
134C22×D5—104no—
135C5×D4—22no—
136C2×C4×C5—22no—
137C2×C4×C5C22×D511yescharacteristic
138C2×C4×C5C22×D512yes—
139C2×C4×C5C22×D512yes—
140C22⋊D5—102no—
141C22⋊D5—102no—
142C2×Dic5—51no—
143C2×Dic5—52no—
144C2×Dic5—52no—
145C2×Dic5—102no—
146D20—102no—
147C4×D5—104no—
148C4×D5—104no—
149C4×D5—104no—
150C4×D5—102no—
151C22×D4—251no—
152C23×C4—251no—
153#123—251no—
154#123—251no—
155#123—252no—
156#123—252no—
157#123—251no—
158#123D2511yescharacteristic, direct product factor
159C2×C4⋊C4—252no—
160C2×C22⋊C4—251no—
161C2×C22⋊C4—252no—
162C25C2×#12311yescharacteristic, complemented, Sylow
163C22×C5—22no—
164C22×C5—21no—
165C22×C5—22no—
166C22×C5D4×D512yes—
167C22×C5C23×D511yescharacteristic
168C2×D5—52no—
169C2×D5—54no—
170C2×D5—52no—
171C2×D5—108no—
172C2×D5—102no—
173C2×D5—101no—
174C2×D5—102no—
175C2×D5—204no—
176C4×C5—22no—
177C4×C5—21no—
178C4×C5—22no—
179Dic5—102no—
180Dic5—101no—
181Dic5—102no—
182C24—251no—
183C24—251no—
184C2×D4—251no—
185C2×D4—251no—
186C2×D4—251no—
187C2×D4—504no—
188C2×D4C2×D2511yescharacteristic
189C22×C4—251no—
190C22×C4—252no—
191C22×C4—252no—
192C22×C4—251no—
193C22×C4—252no—
194C22×C4—504no—
195C22×C4C2×D2511yescharacteristic, complemented
196C4⋊C4—252no—
197C4⋊C4—252no—
198C4⋊C4—252no—
199C4⋊C4C2×D2512yescomplemented
200C22⋊C4—251no—
201C22⋊C4—252no—
202C22⋊C4—252no—
203C22⋊C4—252no—
204C22⋊C4—252no—
205C22⋊C4C2×D2511yescharacteristic, complemented
206C22⋊C4C2×D2512yescomplemented
207C2×C5—22no—
208C2×C5—41no—
209C2×C5C2×D4×D511yescharacteristic
210C2×C5D5×#4112yes—
211D5—54no—
212D5—102no—
213D5—201no—
214C23—251no—
215C23—254no—
216C23—251no—
217C23—251no—
218C23—504no—
219C23—502no—
220C23—504no—
221C23C22×D2511yescharacteristic
222C23C22×D2511yescharacteristic
223D4—22no—
224D4—502no—
225D4—502no—
226D4—502no—
227C2×C4—22no—
228C2×C4—252no—
229C2×C4—252no—
230C2×C4—251no—
231C2×C4—504no—
232C2×C4—504no—
233C2×C4—502no—
234C2×C4—504no—
235C2×C4—502no—
236C2×C4C22×D2512yes—
237C2×C4C22×D2512yes—
238C2×C4C22×D2511yescharacteristic
239C5D5×#12311yescharacteristic
240C22—22no—
241C22—21no—
242C22—22no—
243C22—252no—
244C22—254no—
245C22—252no—
246C22—508no—
247C22—502no—
248C22—501no—
249C22—502no—
250C22—1004no—
251C22D4×D2512yes—
252C22C23×D2511yescharacteristic
253C4—22no—
254C4—21no—
255C4—22no—
256C4—502no—
257C4—501no—
258C4—502no—
259C2—22no—
260C2—41no—
261C2—254no—
262C2—502no—
263C2—1001no—
264C2C2×D4×D2511yescharacteristic
265C2#41×D2512yes—
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#123C2
prime radicalC2×D4×D25C2
hypercenter#123D25
hypocenterC25C2×#123
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×D25C2semidirect
3. C25×#123C2semidirect
4. #11716497C2semidirect
5. #11716491C2semidirect
6. #11716456C2semidirect
7. C4⋊C4×D25C2semidirect
8. #11716448C2semidirect
9. #11716445C2semidirect
10. C22⋊C4×D25C2semidirect
11. C22⋊C4×D25C2semidirect
15. C22×C4×C25C22semidirect
18. C22×Dic25C22semidirect
25. C2×C4×D25C22semidirect
26. C4⋊C4×C25C22semidirect
27. C22⋊C4×C25C22semidirect
28. C22⋊C4×C25C22semidirect
29. C22⋊Dic25C22semidirect
30. C22⋊Dic25C22semidirect
31. #87720C22semidirect
32. #87720C22semidirect
33. #87720C22semidirect
34. C4⋊Dic25C22semidirect
35. #87718C22semidirect
36. #87718C22semidirect
125. D25#123direct (N × H)
158. #123D25direct (N × H)
162. C25C2×#123semidirect
195. C22×C4C2×D25semidirect
199. C4⋊C4C2×D25semidirect
205. C22⋊C4C2×D25semidirect
206. C22⋊C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D252
C22×C4×D252
C25×#1232
#117164972
#117164912
#117164562
C4⋊C4×D252
#117164482
#117164452
C22⋊C4×D252
D5×#1235