Finite Group Databasebeta

← #13098914

Subgroups — #13098914

Order 1600.

642 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C22×C22⋊D25C212yesmaximal, complemented
2C2×D4×D25C212yesmaximal, complemented
3C25×#120C211yesmaximal, characteristic, complemented
4#11716502C211yesmaximal, characteristic, complemented
5#11716501C212yesmaximal, complemented
6#11716499C211yesmaximal, characteristic, complemented
7#11716446C212yesmaximal, complemented
8#11716444C212yesmaximal, complemented
9#11716443C212yesmaximal, complemented
10C24×C25C2211yescharacteristic, complemented
11C23×D25C2212yescomplemented
12C23×D25C2211yescharacteristic, complemented
13C2×D4×C25C2212yescomplemented
14C2×D4×C25C2211yescharacteristic, complemented
15C2×C22⋊D25—28no—
16C2×C22⋊D25C2212yes—
17C2×C22⋊D25C2212yescomplemented
18C2×C22⋊D25C2212yescomplemented
19C2×C22⋊D25C2212yescomplemented
20C2×C22⋊D25C2212yescomplemented
21C22×Dic25C2212yescomplemented
22D4×D25—28no—
23C2×D100C2212yescomplemented
24C2×D100C2211yescharacteristic, complemented
25C2×C4×D25C2212yescomplemented
26C22⋊C4×C25C2212yescomplemented
27C22⋊C4×C25C2211yescharacteristic, complemented
28C22⋊Dic25C2211yescharacteristic, complemented
29#87720C2212yescomplemented
30#87720C2212yescomplemented
31#87718C2212yescomplemented
32C4×Dic25C2211yescharacteristic, complemented
33#65924—51nomaximal
34C23×C25—24no—
35C23×C25—41no—
36C23×C25C2311yescharacteristic
37C23×C25C2311yescharacteristic
38C23×C25C2312yes—
39C22×D25—24no—
40C22×D25—24no—
41C22×D25—24no—
42C22×D25—41no—
43C22×D25—42no—
44C22×D25C2312yes—
45C22×D25C2312yes—
46D4×C25—24no—
47D4×C25—41no—
48C2×C4×C25C2311yescharacteristic
49C2×C4×C25C2312yes—
50C22⋊D25—24no—
51C22⋊D25—24no—
52C22⋊D25—24no—
53C22⋊D25—24no—
54C22⋊D25D418yescomplemented
55C2×Dic25—24no—
56C2×Dic25C2312yes—
57C2×Dic25C2312yes—
58D100—24no—
59D100—41no—
60C4×D25—24no—
61C22×C22⋊D5—52no—
62C2×D4×D5—52no—
63C5×#120D511yescharacteristic
64#4086—51no—
65#4085—52no—
66#4083—51no—
67#4030—52no—
68#4028—52no—
69#4027—52no—
70C22×C25—22no—
71C22×C25—22no—
72C22×C25—22no—
73C22×C25—22no—
74C22×C25—21no—
75C22×C25—21no—
76C22×C25—44no—
77C22×C25C2×D414yescomplemented
78C22×C25C2411yescharacteristic
79C2×D25—22no—
80C2×D25—22no—
81C2×D25—22no—
82C2×D25—22no—
83C2×D25—22no—
84C2×D25—44no—
85C2×D25—48no—
86C2×D25C2×D414yescomplemented
87C4×C25—22no—
88C4×C25—21no—
89Dic25—22no—
90Dic25C2×D414yescomplemented
91C24×C5C2×D511yescharacteristic
92C23×D5—51no—
93C23×D5—52no—
94C2×C5×D4C2×D512yes—
95C2×C5×D4C2×D511yescharacteristic
96C2×C22⋊D5—52no—
97C2×C22⋊D5—52no—
98C2×C22⋊D5—52no—
99C2×C22⋊D5—52no—
100C2×C22⋊D5—52no—
101C2×C22⋊D5—108no—
102C22×Dic5—52no—
103D4×D5—108no—
104C2×D20—52no—
105C2×D20—51no—
106C2×C4×D5—52no—
107C5×C22⋊C4C2×D512yes—
108C5×C22⋊C4C2×D511yescharacteristic
109C22⋊Dic5—51no—
110#685—52no—
111#685—52no—
112#683—52no—
113C4×Dic5—51no—
114D42—251noSylow
115C2×C25—24no—
116C2×C25—41no—
117C2×C25—41no—
118C2×C25C22×D412yes—
119C2×C25H(5,𝔽2)11yescharacteristic
120D25—24no—
121D25—42no—
122C23×C5—24no—
123C23×C5—41no—
124C23×C5C22×D511yescharacteristic
125C23×C5C22×D511yescharacteristic
126C23×C5C22×D512yes—
127C22×D5—52no—
128C22×D5—52no—
129C22×D5—104no—
130C22×D5—104no—
131C22×D5—104no—
132C22×D5—201no—
133C22×D5—202no—
134C5×D4—24no—
135C5×D4—41no—
136C2×C4×C5C22×D511yescharacteristic
137C2×C4×C5C22×D512yes—
138C22⋊D5—58no—
139C22⋊D5—104no—
140C22⋊D5—104no—
141C22⋊D5—104no—
142C22⋊D5—104no—
143C2×Dic5—52no—
144C2×Dic5—52no—
145C2×Dic5—104no—
146D20—104no—
147D20—201no—
148C4×D5—104no—
149C22×D4—252no—
150C22×D4—252no—
151#127—251no—
152#121—252no—
153#121—252no—
154#120—251no—
155#120—252no—
156#120D2511yescharacteristic, complemented
157C4×D4—252no—
158C25D4211yescharacteristic, complemented, Sylow
159C22×C5—22no—
160C22×C5—22no—
161C22×C5—22no—
162C22×C5—22no—
163C22×C5—21no—
164C22×C5—21no—
165C22×C5—44no—
166C22×C5D4×D514yes—
167C22×C5C23×D511yescharacteristic
168C2×D5—54no—
169C2×D5—102no—
170C2×D5—102no—
171C2×D5—102no—
172C2×D5—102no—
173C2×D5—102no—
174C2×D5—204no—
175C2×D5—208no—
176C4×C5—22no—
177C4×C5—21no—
178Dic5—54no—
179Dic5—102no—
180C24—251no—
181C24—252no—
182C24C2×D2511yescharacteristic, complemented
183C2×D4—252no—
184C2×D4—252no—
185C2×D4—252no—
186C2×D4—252no—
187C2×D4—252no—
188C2×D4—252no—
189C2×D4—251no—
190C2×D4—508no—
191C2×D4—508no—
192C2×D4C2×D2512yescomplemented
193C2×D4C2×D2511yescharacteristic, complemented
194C22×C4—252no—
195C22×C4—252no—
196C4⋊C4—252no—
197C22⋊C4—251no—
198C22⋊C4—252no—
199C22⋊C4—252no—
200C22⋊C4C2×D2512yescomplemented
201C22⋊C4C2×D2511yescharacteristic, complemented
202C42—251no—
203C2×C5—24no—
204C2×C5—41no—
205C2×C5—41no—
206C2×C5C2×D4×D512yes—
207C2×C5#414411yescharacteristic
208D5—104no—
209D5—202no—
210C23—24no—
211C23—41no—
212C23—252no—
213C23—252no—
214C23—504no—
215C23—504no—
216C23—504no—
217C23—1002no—
218C23—1001no—
219C23C22×D2511yescharacteristic
220C23C22×D2511yescharacteristic
221C23C22×D2512yes—
222D4—24no—
223D4—41no—
224D4—258no—
225D4—504no—
226D4—504no—
227D4—504no—
228D4—504no—
229D4—504no—
230D4—1001no—
231C2×C4—252no—
232C2×C4—252no—
233C2×C4—504no—
234C2×C4—504no—
235C2×C4C22×D2511yescharacteristic
236C2×C4C22×D2512yes—
237C5#6592411yescharacteristic
238C22—22no—
239C22—22no—
240C22—22no—
241C22—22no—
242C22—21no—
243C22—21no—
244C22—44no—
245C22—254no—
246C22—502no—
247C22—502no—
248C22—502no—
249C22—502no—
250C22—502no—
251C22—1008no—
252C22—1004no—
253C22D4×D2514yescomplemented
254C22C23×D2511yescharacteristic
255C4—22no—
256C4—21no—
257C4—254no—
258C4—502no—
259C2—24no—
260C2—41no—
261C2—41no—
262C2—504no—
263C2—1002no—
264C2C2×D4×D2512yes—
265C2#1171656311yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#120C2
hypercenter#120D25
hypocenterC25D42
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D25C2semidirect
2. C2×D4×D25C2semidirect
3. C25×#120C2semidirect
4. #11716502C2semidirect
5. #11716501C2semidirect
6. #11716499C2semidirect
7. #11716446C2semidirect
8. #11716444C2semidirect
9. #11716443C2semidirect
10. C24×C25C22semidirect
11. C23×D25C22semidirect
12. C23×D25C22semidirect
13. C2×D4×C25C22semidirect
14. C2×D4×C25C22semidirect
17. C2×C22⋊D25C22semidirect
18. C2×C22⋊D25C22semidirect
19. C2×C22⋊D25C22semidirect
20. C2×C22⋊D25C22semidirect
21. C22×Dic25C22semidirect
23. C2×D100C22semidirect
24. C2×D100C22semidirect
25. C2×C4×D25C22semidirect
26. C22⋊C4×C25C22semidirect
27. C22⋊C4×C25C22semidirect
28. C22⋊Dic25C22semidirect
29. #87720C22semidirect
30. #87720C22semidirect
31. #87718C22semidirect
32. C4×Dic25C22semidirect
54. C22⋊D25D4semidirect
77. C22×C25C2×D4semidirect
86. C2×D25C2×D4semidirect
90. Dic25C2×D4semidirect
156. #120D25semidirect
158. C25D42semidirect
182. C24C2×D25semidirect
192. C2×D4C2×D25semidirect
193. C2×D4C2×D25semidirect
200. C22⋊C4C2×D25semidirect
201. C22⋊C4C2×D25semidirect
253. C22D4×D25semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D252
C2×D4×D252
C25×#1202
#117165022
#117165012
#117164992
#117164462
#117164442
#117164432
#659245