Finite Group Databasebeta

← #13098932

Subgroups — #13098932

Order 1600.

501 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 125 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#11716502C212yesmaximal, complemented
5#11716500C211yesmaximal, characteristic, complemented
6#11716499C212yesmaximal, complemented
7#11716492C211yesmaximal, characteristic, complemented
8#11716457C211yesmaximal, characteristic, complemented
9#11716454C211yesmaximal, characteristic, complemented
10#11716447C212yesmaximal, complemented
11#11716444C212yesmaximal, complemented
12C23×D25C2212yes—
13C2×D4×C25C2211yescharacteristic
14C2×D4×C25C2212yescomplemented
15C22×C4×C25C2211yescharacteristic, complemented
16C2×C22⋊D25C2212yes—
17C2×C22⋊D25C2211yescharacteristic
18C2×C22⋊D25C2211yescharacteristic, complemented
19C2×C22⋊D25C2212yescomplemented
20C2×C22⋊D25C2212yescomplemented
21D4×D25—24no—
22#87744—24no—
23C2×D100C2211yescharacteristic
24C2×D100C2211yescharacteristic
25C2×D100C2212yescomplemented
26C2×C4×D25C2211yescharacteristic
27C2×C4×D25C2211yescharacteristic, complemented
28C2×Dic50C2211yescharacteristic, complemented
29C4⋊C4×C25C2211yescharacteristic, complemented
30C22⋊C4×C25C2212yescomplemented
31C22⋊Dic25C2212yescomplemented
32#87720C2212yes—
33#87720C2212yescomplemented
34#87720C2212yescomplemented
35C4⋊Dic25C2211yescharacteristic, complemented
36C4×Dic25C2212yescomplemented
37#65941—51nomaximal
38C23×C25C2312yes—
39C23×C25C2311yescharacteristic
40C22×D25—24no—
41C22×D25—42no—
42C22×D25—42no—
43C22×D25C2312yes—
44C22×D25C2311yescharacteristic
45C22×D25C2311yescharacteristic
46D4×C25—22no—
47D4×C25—42no—
48C2×C4×C25—22no—
49C2×C4×C25C2312yes—
50C2×C4×C25C2311yescharacteristic
51C2×C4×C25C2311yescharacteristic
52C22⋊D25—22no—
53C22⋊D25—22no—
54C22⋊D25—24no—
55C22⋊D25—42no—
56C22⋊D25—42no—
57C2×Dic25C2312yes—
58C2×Dic25C2311yescharacteristic
59C2×Dic25C2311yescharacteristic
60D100—22no—
61D100—22no—
62D100—42no—
63C4×D25—22no—
64C4×D25D414yescomplemented
65Dic50—22no—
66C2×D4×D5—51no—
67C2×#709—51no—
68C5×#121D511yescharacteristic
69#4086—52no—
70#4084—51no—
71#4083—52no—
72#4076—51no—
73#4041—51no—
74#4038—51no—
75#4031—52no—
76#4028—52no—
77C22×C25—21no—
78C22×C25—22no—
79C22×C25—21no—
80C22×C25—22no—
81C22×C25—21no—
82C22×C25—22no—
83C22×C25C2411yescharacteristic
84C2×D25—21no—
85C2×D25—21no—
86C2×D25—21no—
87C2×D25—22no—
88C2×D25—21no—
89C2×D25—22no—
90C2×D25—21no—
91C2×D25—22no—
92C2×D25—48no—
93C2×D25C2×D412yes—
94C4×C25—21no—
95C4×C25—22no—
96C4×C25C2×D412yes—
97Dic25—21no—
98Dic25—22no—
99Dic25C2×D412yes—
100C23×D5—52no—
101C2×C5×D4C2×D511yescharacteristic
102C2×C5×D4C2×D512yes—
103C22×C4×C5C2×D511yescharacteristic
104C2×C22⋊D5—51no—
105C2×C22⋊D5—51no—
106C2×C22⋊D5—52no—
107C2×C22⋊D5—52no—
108C2×C22⋊D5—52no—
109D4×D5—104no—
110#709—104no—
111C2×D20—51no—
112C2×D20—51no—
113C2×D20—52no—
114C2×C4×D5—51no—
115C2×C4×D5—51no—
116C2×Dic10—51no—
117C5×C4⋊C4C2×D511yescharacteristic
118C5×C22⋊C4C2×D512yes—
119C22⋊Dic5—52no—
120#685—52no—
121#685—52no—
122#685—52no—
123C4⋊Dic5—51no—
124C4×Dic5—52no—
125#535—251noSylow
126C2×C25—42no—
127C2×C25—41no—
128C2×C25C22×D411yescharacteristic
129C2×C25H(5,𝔽2)11yescharacteristic
130C2×C25H(5,𝔽2)11yescharacteristic
131D25—22no—
132D25—41no—
133D25—42no—
134C23×C5C22×D512yes—
135C23×C5C22×D511yescharacteristic
136C22×D5—51no—
137C22×D5—52no—
138C22×D5—51no—
139C22×D5—104no—
140C22×D5—202no—
141C22×D5—202no—
142C5×D4—22no—
143C5×D4—42no—
144C2×C4×C5—22no—
145C2×C4×C5C22×D512yes—
146C2×C4×C5C22×D511yescharacteristic
147C2×C4×C5C22×D511yescharacteristic
148C22⋊D5—102no—
149C22⋊D5—104no—
150C22⋊D5—102no—
151C22⋊D5—202no—
152C22⋊D5—202no—
153C2×Dic5—51no—
154C2×Dic5—52no—
155C2×Dic5—51no—
156D20—102no—
157D20—102no—
158D20—202no—
159C4×D5—54no—
160C4×D5—102no—
161Dic10—102no—
162C2×#41—251no—
163C22×D4—251no—
164#127—252no—
165#124—252no—
166#121—251no—
167#121—251no—
168#121—251no—
169#121D2511yescharacteristic, complemented
170#120—252no—
171#120—252no—
172#117—251no—
173C25#53511yescharacteristic, complemented, Sylow
174C22×C5—21no—
175C22×C5—22no—
176C22×C5—21no—
177C22×C5—22no—
178C22×C5—21no—
179C22×C5—22no—
180C22×C5C23×D511yescharacteristic
181C2×D5—52no—
182C2×D5—101no—
183C2×D5—101no—
184C2×D5—101no—
185C2×D5—102no—
186C2×D5—101no—
187C2×D5—102no—
188C2×D5—101no—
189C2×D5—102no—
190C2×D5—208no—
191C4×C5—21no—
192C4×C5—22no—
193C4×C5D4×D512yes—
194Dic5—52no—
195Dic5—101no—
196Dic5—102no—
197C24—252no—
198#41—504no—
199C2×Q8—251no—
200C2×D4—251no—
201C2×D4—252no—
202C2×D4—251no—
203C2×D4—252no—
204C2×D4—252no—
205C2×D4—251no—
206C2×D4—251no—
207C2×D4—252no—
208C2×D4—504no—
209C2×D4C2×D2511yescharacteristic
210C2×D4C2×D2512yescomplemented
211C22×C4—251no—
212C22×C4—251no—
213C22×C4C2×D2511yescharacteristic, complemented
214C4⋊C4—251no—
215C4⋊C4C2×D2511yescharacteristic, complemented
216C22⋊C4—252no—
217C22⋊C4—252no—
218C22⋊C4—252no—
219C22⋊C4—252no—
220C22⋊C4C2×D2512yescomplemented
221C42—252no—
222C2×C5—42no—
223C2×C5—41no—
224C2×C5C2×D4×D511yescharacteristic
225C2×C5#414411yescharacteristic
226C2×C5#414911yescharacteristic
227D5—102no—
228D5—202no—
229D5—201no—
230C23—251no—
231C23—252no—
232C23—251no—
233C23—504no—
234C23—1002no—
235C23—1002no—
236C23C22×D2512yes—
237C23C22×D2511yescharacteristic
238Q8—502no—
239D4—22no—
240D4—42no—
241D4—502no—
242D4—504no—
243D4—502no—
244D4—502no—
245D4—502no—
246D4—1002no—
247D4—1002no—
248D4—1002no—
249C2×C4—22no—
250C2×C4—251no—
251C2×C4—254no—
252C2×C4—252no—
253C2×C4—251no—
254C2×C4—502no—
255C2×C4C22×D2512yes—
256C2×C4C22×D2511yescharacteristic
257C2×C4C22×D2511yescharacteristic
258C5#6594111yescharacteristic
259C22—21no—
260C22—22no—
261C22—21no—
262C22—22no—
263C22—21no—
264C22—22no—
265C22—252no—
266C22—501no—
267C22—501no—
268C22—501no—
269C22—502no—
270C22—501no—
271C22—502no—
272C22—501no—
273C22—502no—
274C22—1008no—
275C22C23×D2511yescharacteristic
276C4—21no—
277C4—22no—
278C4—252no—
279C4—501no—
280C4—502no—
281C4D4×D2512yes—
282C2—42no—
283C2—41no—
284C2—502no—
285C2—1002no—
286C2—1001no—
287C2C2×D4×D2511yescharacteristic
288C2#1171656311yescharacteristic
289C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC25×#121C2
hypercenter#121D25
hypocenterC25#535
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. #11716502C2semidirect
5. #11716500C2semidirect
6. #11716499C2semidirect
7. #11716492C2semidirect
8. #11716457C2semidirect
9. #11716454C2semidirect
10. #11716447C2semidirect
11. #11716444C2semidirect
14. C2×D4×C25C22semidirect
15. C22×C4×C25C22semidirect
18. C2×C22⋊D25C22semidirect
19. C2×C22⋊D25C22semidirect
20. C2×C22⋊D25C22semidirect
25. C2×D100C22semidirect
27. C2×C4×D25C22semidirect
28. C2×Dic50C22semidirect
29. C4⋊C4×C25C22semidirect
30. C22⋊C4×C25C22semidirect
31. C22⋊Dic25C22semidirect
33. #87720C22semidirect
34. #87720C22semidirect
35. C4⋊Dic25C22semidirect
36. C4×Dic25C22semidirect
64. C4×D25D4semidirect
169. #121D25semidirect
173. C25#535semidirect
210. C2×D4C2×D25semidirect
213. C22×C4C2×D25semidirect
215. C4⋊C4C2×D25semidirect
220. 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
#117165022
#117165002
#117164992
#117164922
#117164572
#117164542
#117164472
#117164442
#659415