Finite Group Databasebeta

← #13098971

Subgroups — #13098971

Order 1600.

495 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 495 conjugacy classes of subgroups — too many to draw. Only its 129 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×#87746C211yesmaximal, characteristic, complemented
2C22×C4×D25C211yesmaximal, characteristic, complemented
3C25×#123C211yesmaximal, characteristic, complemented
4#11716499C211yesmaximal, characteristic, complemented
5#11716491C211yesmaximal, characteristic, complemented
6#11716458C212yesmaximal, complemented
7#11716455C212yesmaximal, complemented
8#11716446C212yesmaximal, complemented
9#11716444C211yesmaximal, characteristic, complemented
10#11716443C212yesmaximal, complemented
11#11716439C211yesmaximal, characteristic, complemented
12C23×D25C2211yescharacteristic
13C2×D4×C25C2211yescharacteristic
14C22×C4×C25C2211yescharacteristic
15C2×C22⋊D25C2212yes—
16C2×C22⋊D25C2211yescharacteristic
17C2×C22⋊D25C2211yescharacteristic, complemented
18C22×Dic25C2211yescharacteristic
19C22×Dic25C2211yescharacteristic, complemented
20#87746—24no—
21C2×D100C2212yes—
22C2×C4×D25—24no—
23C2×C4×D25C2212yes—
24C2×C4×D25C2212yes—
25C2×C4×D25C2211yescharacteristic, complemented
26C2×Dic50C2211yescharacteristic, complemented
27C4⋊C4×C25C2212yescomplemented
28C22⋊C4×C25C2211yescharacteristic
29C22⋊C4×C25C2212yescomplemented
30C22⋊Dic25C2211yescharacteristic
31#87720C2212yes—
32#87720C2212yes—
33#87720C2212yescomplemented
34#87718C2212yescomplemented
35#87718C2212yescomplemented
36C4×Dic25C2212yescomplemented
37#65990—51nomaximal
38C23×C25C2311yescharacteristic
39C23×C25C2311yescharacteristic
40C22×D25—22no—
41C22×D25—24no—
42C22×D25C2311yescharacteristic
43C22×D25C2312yes—
44D4×C25—22no—
45C2×C4×C25—22no—
46C2×C4×C25C2312yes—
47C2×C4×C25C2312yes—
48C2×C4×C25C2311yescharacteristic
49C22⋊D25—22no—
50C22⋊D25—24no—
51C22⋊D25—22no—
52C2×Dic25—22no—
53C2×Dic25D414yescomplemented
54C2×Dic25C2312yes—
55C2×Dic25C2311yescharacteristic
56C2×Dic25C2311yescharacteristic
57C2×Dic25C2311yescharacteristic
58D100—24no—
59C4×D25—24no—
60C4×D25—24no—
61C4×D25—22no—
62Dic50—22no—
63C2×#711—51no—
64C22×C4×D5—51no—
65C5×#123D511yescharacteristic
66#4083—51no—
67#4075—51no—
68#4042—52no—
69#4039—52no—
70#4030—52no—
71#4028—51no—
72#4027—52no—
73#4023—51no—
74C22×C25—22no—
75C22×C25—21no—
76C22×C25—22no—
77C22×C25C2×D412yes—
78C22×C25C2411yescharacteristic
79C2×D25—28no—
80C2×D25—22no—
81C2×D25—22no—
82C2×D25—21no—
83C2×D25—22no—
84C2×D25#4114yescomplemented
85C4×C25—21no—
86C4×C25—22no—
87C4×C25—22no—
88Dic25—21no—
89Dic25—22no—
90Dic25C2×D412yes—
91Dic25C2×D412yes—
92C23×D5—51no—
93C2×C5×D4C2×D511yescharacteristic
94C22×C4×C5C2×D511yescharacteristic
95C2×C22⋊D5—51no—
96C2×C22⋊D5—51no—
97C2×C22⋊D5—52no—
98C22×Dic5—51no—
99C22×Dic5—51no—
100#711—104no—
101C2×D20—52no—
102C2×C4×D5—52no—
103C2×C4×D5—52no—
104C2×C4×D5—51no—
105C2×C4×D5—104no—
106C2×Dic10—51no—
107C5×C4⋊C4C2×D512yes—
108C5×C22⋊C4C2×D511yescharacteristic
109C5×C22⋊C4C2×D512yes—
110C22⋊Dic5—51no—
111#685—52no—
112#685—52no—
113#685—52no—
114#683—52no—
115#683—52no—
116C4×Dic5—52no—
117#525—251noSylow
118C2×C25—22no—
119C2×C25—41no—
120C2×C25C22×D411yescharacteristic
121C2×C25C2×#4112yes—
122D25—24no—
123D25—41no—
124C23×C5C22×D511yescharacteristic
125C23×C5C22×D511yescharacteristic
126C22×D5—52no—
127C22×D5—51no—
128C22×D5—104no—
129C22×D5—102no—
130C5×D4—22no—
131C2×C4×C5—22no—
132C2×C4×C5C22×D512yes—
133C2×C4×C5C22×D512yes—
134C2×C4×C5C22×D511yescharacteristic
135C22⋊D5—102no—
136C22⋊D5—104no—
137C22⋊D5—102no—
138C2×Dic5—54no—
139C2×Dic5—51no—
140C2×Dic5—51no—
141C2×Dic5—52no—
142C2×Dic5—51no—
143C2×Dic5—102no—
144D20—104no—
145C4×D5—104no—
146C4×D5—104no—
147C4×D5—102no—
148Dic10—102no—
149C2×#41—251no—
150C23×C4—251no—
151#123—251no—
152#123D2511yescharacteristic, complemented
153C22⋊Q8—252no—
154#121—252no—
155#120—251no—
156#120—251no—
157C4×D4—252no—
158C4×D4—252no—
159#117—251no—
160C25#52511yescharacteristic, complemented, Sylow
161C22×C5—22no—
162C22×C5—21no—
163C22×C5—22no—
164C22×C5D4×D512yes—
165C22×C5C23×D511yescharacteristic
166C2×D5—54no—
167C2×D5—108no—
168C2×D5—102no—
169C2×D5—102no—
170C2×D5—101no—
171C2×D5—102no—
172C4×C5—21no—
173C4×C5—22no—
174C4×C5—22no—
175Dic5—52no—
176Dic5—52no—
177Dic5—101no—
178Dic5—102no—
179C24—251no—
180#41—504no—
181C2×Q8—251no—
182C2×D4—252no—
183C2×D4—251no—
184C2×D4—251no—
185C2×D4—252no—
186C2×D4C2×D2511yescharacteristic
187C22×C4—251no—
188C22×C4—251no—
189C22×C4—252no—
190C22×C4—251no—
191C22×C4—252no—
192C22×C4—504no—
193C22×C4C2×D2511yescharacteristic
194C4⋊C4—252no—
195C4⋊C4—252no—
196C4⋊C4C2×D2512yescomplemented
197C22⋊C4—251no—
198C22⋊C4—252no—
199C22⋊C4—252no—
200C22⋊C4—252no—
201C22⋊C4C2×D2511yescharacteristic
202C22⋊C4C2×D2512yescomplemented
203C42—252no—
204C2×C5—22no—
205C2×C5—41no—
206C2×C5C2×D4×D511yescharacteristic
207C2×C5D5×#4112yes—
208D5—104no—
209D5—201no—
210C23—252no—
211C23—251no—
212C23—504no—
213C23—502no—
214C23C22×D2511yescharacteristic
215C23C22×D2511yescharacteristic
216Q8—502no—
217D4—22no—
218D4—504no—
219D4—502no—
220D4—504no—
221D4—502no—
222C2×C4—22no—
223C2×C4—254no—
224C2×C4—251no—
225C2×C4—251no—
226C2×C4—252no—
227C2×C4—251no—
228C2×C4—504no—
229C2×C4—504no—
230C2×C4—502no—
231C2×C4—502no—
232C2×C4C22×D2512yes—
233C2×C4C22×D2511yescharacteristic
234C2×C4C22×D2512yes—
235C5#6599011yescharacteristic
236C22—22no—
237C22—21no—
238C22—22no—
239C22—254no—
240C22—508no—
241C22—502no—
242C22—502no—
243C22—501no—
244C22—502no—
245C22D4×D2512yes—
246C22C23×D2511yescharacteristic
247C4—22no—
248C4—21no—
249C4—22no—
250C4—252no—
251C4—252no—
252C4—501no—
253C4—502no—
254C2—22no—
255C2—41no—
256C2—504no—
257C2—1001no—
258C2C2×D4×D2511yescharacteristic
259C2#41×D2512yes—
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#123C2
hypercenter#123D25
hypocenterC25#525
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#87746C2semidirect
2. C22×C4×D25C2semidirect
3. C25×#123C2semidirect
4. #11716499C2semidirect
5. #11716491C2semidirect
6. #11716458C2semidirect
7. #11716455C2semidirect
8. #11716446C2semidirect
9. #11716444C2semidirect
10. #11716443C2semidirect
11. #11716439C2semidirect
17. C2×C22⋊D25C22semidirect
19. C22×Dic25C22semidirect
25. C2×C4×D25C22semidirect
26. C2×Dic50C22semidirect
27. C4⋊C4×C25C22semidirect
29. C22⋊C4×C25C22semidirect
33. #87720C22semidirect
34. #87718C22semidirect
35. #87718C22semidirect
36. C4×Dic25C22semidirect
53. C2×Dic25D4semidirect
84. C2×D25#41semidirect
152. #123D25semidirect
160. C25#525semidirect
196. C4⋊C4C2×D25semidirect
202. C22⋊C4C2×D25semidirect

Maximal subgroups

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

subgroupindex
C2×#877462
C22×C4×D252
C25×#1232
#117164992
#117164912
#117164582
#117164552
#117164462
#117164442
#117164432
#117164392
#659905