Finite Group Databasebeta

← #13098937

Subgroups — #13098937

Order 1600.

501 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 127 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, complemented
2C2×#87744C211yesmaximal, characteristic, complemented
3C25×#121C211yesmaximal, characteristic, complemented
4#11716500C212yesmaximal, complemented
5#11716499C212yesmaximal, complemented
6#11716498C211yesmaximal, characteristic, complemented
7C4×C22⋊D25C211yesmaximal, characteristic, complemented
8#11716459C211yesmaximal, characteristic, complemented
9#11716455C211yesmaximal, characteristic, complemented
10#11716445C212yesmaximal, complemented
11C22⋊C4×D25C212yesmaximal, complemented
12C23×D25C2212yes—
13C2×D4×C25C2211yescharacteristic
14C2×D4×C25C2212yescomplemented
15C22×C4×C25C2211yescharacteristic, complemented
16C2×C22⋊D25C2212yes—
17C2×C22⋊D25C2211yescharacteristic
18C2×C22⋊D25C2212yescomplemented
19D4×D25—24no—
20#87744—24no—
21C2×D100C2211yescharacteristic
22C2×C4×D25C2211yescharacteristic
23C2×C4×D25C2212yescomplemented
24C2×C4×D25C2212yescomplemented
25C2×Dic50C2211yescharacteristic, complemented
26C4⋊C4×C25C2211yescharacteristic, complemented
27C22⋊C4×C25C2212yescomplemented
28C22⋊Dic25C2212yescomplemented
29C22⋊Dic25C2212yescomplemented
30C22⋊Dic25C2211yescharacteristic, complemented
31#87720C2211yescharacteristic
32#87720C2212yes—
33#87720C2212yescomplemented
34C4⋊Dic25C2212yescomplemented
35#87718C2211yescharacteristic, complemented
36C4×Dic25C2211yescharacteristic, complemented
37#65946—51nomaximal
38C23×C25C2312yes—
39C23×C25C2311yescharacteristic
40C22×D25—24no—
41C22×D25—24no—
42C22×D25—42no—
43C22×D25C2312yes—
44C22×D25C2311yescharacteristic
45D4×C25—22no—
46D4×C25—42no—
47C2×C4×C25—22no—
48C2×C4×C25C2311yescharacteristic
49C2×C4×C25C2312yes—
50C2×C4×C25C2311yescharacteristic
51C22⋊D25—24no—
52C22⋊D25—24no—
53C22⋊D25—22no—
54C2×Dic25C2311yescharacteristic
55C2×Dic25C2311yescharacteristic
56C2×Dic25C2311yescharacteristic
57C2×Dic25C2312yes—
58D100D414yescomplemented
59C4×D25—24no—
60C4×D25—22no—
61C4×D25—42no—
62Dic50—22no—
63C2×D4×D5—51no—
64C2×#709—51no—
65C5×#121D511yescharacteristic
66#4084—52no—
67#4083—52no—
68#4082—51no—
69C4×C22⋊D5—51no—
70#4043—51no—
71#4039—51no—
72#4029—52no—
73D5×C22⋊C4—52no—
74C22×C25—21no—
75C22×C25—22no—
76C22×C25—21no—
77C22×C25—22no—
78C22×C25—21no—
79C22×C25—22no—
80C22×C25C2411yescharacteristic
81C2×D25—21no—
82C2×D25—22no—
83C2×D25—22no—
84C2×D25—21no—
85C2×D25—48no—
86C2×D25C2×D414yes—
87C2×D25#4112yescomplemented
88C4×C25—21no—
89C4×C25—22no—
90C4×C25C2×D412yes—
91Dic25—22no—
92Dic25—21no—
93Dic25—21no—
94Dic25—21no—
95C23×D5—52no—
96C2×C5×D4C2×D511yescharacteristic
97C2×C5×D4C2×D512yes—
98C22×C4×C5C2×D511yescharacteristic
99C2×C22⋊D5—52no—
100C2×C22⋊D5—52no—
101C2×C22⋊D5—51no—
102D4×D5—104no—
103#709—104no—
104C2×D20—51no—
105C2×C4×D5—52no—
106C2×C4×D5—51no—
107C2×C4×D5—52no—
108C2×Dic10—51no—
109C5×C4⋊C4C2×D511yescharacteristic
110C5×C22⋊C4C2×D512yes—
111C22⋊Dic5—52no—
112C22⋊Dic5—52no—
113C22⋊Dic5—51no—
114#685—51no—
115#685—52no—
116#685—52no—
117C4⋊Dic5—52no—
118#683—51no—
119C4×Dic5—51no—
120#546—251noSylow
121C2×C25—42no—
122C2×C25—41no—
123C2×C25C22×D411yescharacteristic
124C2×C25C2×#4111yescharacteristic
125C2×C25H(5,𝔽2)11yescharacteristic
126D25—22no—
127D25—24no—
128C23×C5C22×D512yes—
129C23×C5C22×D511yescharacteristic
130C22×D5—51no—
131C22×D5—52no—
132C22×D5—104no—
133C22×D5—104no—
134C22×D5—202no—
135C5×D4—22no—
136C5×D4—42no—
137C2×C4×C5—22no—
138C2×C4×C5C22×D511yescharacteristic
139C2×C4×C5C22×D512yes—
140C2×C4×C5C22×D511yescharacteristic
141C22⋊D5—104no—
142C22⋊D5—104no—
143C22⋊D5—102no—
144C2×Dic5—51no—
145C2×Dic5—51no—
146C2×Dic5—51no—
147C2×Dic5—52no—
148D20—54no—
149C4×D5—104no—
150C4×D5—102no—
151C4×D5—202no—
152Dic10—102no—
153C2×#41—251no—
154C22×D4—251no—
155#124—251no—
156#123—252no—
157C22⋊Q8—251no—
158#121—252no—
159#121D2511yescharacteristic, complemented
160#120—252no—
161C4×D4—251no—
162C4×D4—251no—
163C2×C22⋊C4—252no—
164C25#54611yescharacteristic, complemented, Sylow
165C22×C5—21no—
166C22×C5—22no—
167C22×C5—21no—
168C22×C5—22no—
169C22×C5—21no—
170C22×C5—22no—
171C22×C5C23×D511yescharacteristic
172C2×D5—54no—
173C2×D5—52no—
174C2×D5—101no—
175C2×D5—102no—
176C2×D5—101no—
177C2×D5—102no—
178C2×D5—208no—
179C4×C5—21no—
180C4×C5—22no—
181C4×C5D4×D512yes—
182Dic5—102no—
183Dic5—101no—
184Dic5—101no—
185Dic5—101no—
186C24—252no—
187#41—504no—
188C2×Q8—251no—
189C2×D4—251no—
190C2×D4—252no—
191C2×D4—252no—
192C2×D4—251no—
193C2×D4—504no—
194C2×D4C2×D2511yescharacteristic
195C2×D4C2×D2512yescomplemented
196C22×C4—252no—
197C22×C4—251no—
198C22×C4—252no—
199C22×C4C2×D2511yescharacteristic, complemented
200C4⋊C4—251no—
201C4⋊C4—252no—
202C4⋊C4C2×D2511yescharacteristic, complemented
203C22⋊C4—252no—
204C22⋊C4—251no—
205C22⋊C4—252no—
206C22⋊C4—251no—
207C22⋊C4—252no—
208C22⋊C4—252no—
209C22⋊C4C2×D2512yescomplemented
210C42—251no—
211C2×C5—42no—
212C2×C5—41no—
213C2×C5C2×D4×D511yescharacteristic
214C2×C5#414411yescharacteristic
215C2×C5D5×#4111yescharacteristic
216D5—102no—
217D5—104no—
218C23—251no—
219C23—252no—
220C23—504no—
221C23—504no—
222C23—1002no—
223C23C22×D2512yes—
224C23C22×D2511yescharacteristic
225Q8—502no—
226D4—22no—
227D4—42no—
228D4—254no—
229D4—504no—
230D4—504no—
231D4—502no—
232C2×C4—22no—
233C2×C4—251no—
234C2×C4—251no—
235C2×C4—252no—
236C2×C4—251no—
237C2×C4—504no—
238C2×C4—502no—
239C2×C4—1002no—
240C2×C4C22×D2512yes—
241C2×C4C22×D2511yescharacteristic
242C2×C4C22×D2511yescharacteristic
243C5#6594611yescharacteristic
244C22—21no—
245C22—22no—
246C22—21no—
247C22—22no—
248C22—21no—
249C22—22no—
250C22—254no—
251C22—252no—
252C22—501no—
253C22—502no—
254C22—501no—
255C22—502no—
256C22—1008no—
257C22C23×D2511yescharacteristic
258C4—21no—
259C4—22no—
260C4—501no—
261C4—502no—
262C4—501no—
263C4—501no—
264C4D4×D2512yes—
265C2—42no—
266C2—41no—
267C2—502no—
268C2—504no—
269C2C2×D4×D2511yescharacteristic
270C2#1171656311yescharacteristic
271C2#41×D2511yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#546
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D25C2semidirect
2. C2×#87744C2semidirect
3. C25×#121C2semidirect
4. #11716500C2semidirect
5. #11716499C2semidirect
6. #11716498C2semidirect
7. C4×C22⋊D25C2semidirect
8. #11716459C2semidirect
9. #11716455C2semidirect
10. #11716445C2semidirect
11. C22⋊C4×D25C2semidirect
14. C2×D4×C25C22semidirect
15. C22×C4×C25C22semidirect
18. C2×C22⋊D25C22semidirect
23. C2×C4×D25C22semidirect
24. C2×C4×D25C22semidirect
25. C2×Dic50C22semidirect
26. C4⋊C4×C25C22semidirect
27. C22⋊C4×C25C22semidirect
28. C22⋊Dic25C22semidirect
29. C22⋊Dic25C22semidirect
30. C22⋊Dic25C22semidirect
33. #87720C22semidirect
34. C4⋊Dic25C22semidirect
35. #87718C22semidirect
36. C4×Dic25C22semidirect
58. D100D4semidirect
87. C2×D25#41semidirect
159. #121D25semidirect
164. C25#546semidirect
195. C2×D4C2×D25semidirect
199. C22×C4C2×D25semidirect
202. C4⋊C4C2×D25semidirect
209. 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
C2×#877442
C25×#1212
#117165002
#117164992
#117164982
C4×C22⋊D252
#117164592
#117164552
#117164452
C22⋊C4×D252
#659465