Finite Group Databasebeta

← #13098876

Subgroups — #13098876

Order 1600.

501 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 501 conjugacy classes of subgroups — too many to draw. Only its 131 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×#87744C211yesmaximal, characteristic, complemented
2C22×D100C211yesmaximal, characteristic, complemented
3C4×D4×C25C211yesmaximal, characteristic, complemented
4#11716499C212yesmaximal, complemented
5#11716492C211yesmaximal, characteristic, complemented
6#11716486C211yesmaximal, characteristic, complemented
7#11716456C212yesmaximal, complemented
8#11716446C212yesmaximal, complemented
9C22⋊C4×D25C212yesmaximal, complemented
10#11716437C211yesmaximal, characteristic, complemented
11C4×D100C211yesmaximal, characteristic, complemented
12C23×D25C2212yes—
13C2×D4×C25C2211yescharacteristic
14C22×C4×C25C2211yescharacteristic
15C22×C4×C25C2211yescharacteristic, complemented
16C2×C22⋊D25C2212yescomplemented
17C2×C22⋊D25C2212yescomplemented
18#87744—24no—
19C2×D100—24no—
20C2×D100C2211yescharacteristic
21C2×D100C2212yes—
22C2×D100C2211yescharacteristic
23C2×C4×D25C2212yescomplemented
24C2×C4×D25C2212yescomplemented
25C2×Dic50C2211yescharacteristic, complemented
26C4⋊C4×C25C2211yescharacteristic, complemented
27C22⋊C4×C25C2211yescharacteristic
28C22⋊C4×C25C2211yescharacteristic, complemented
29C42×C25C2211yescharacteristic, complemented
30C22⋊Dic25C2212yes—
31#87720C2212yescomplemented
32#87720C2212yescomplemented
33#87720C2212yescomplemented
34#87720C2212yescomplemented
35C4⋊Dic25C2211yescharacteristic, complemented
36#87718C2212yescomplemented
37#65884—51nomaximal
38C23×C25C2311yescharacteristic
39C23×C25C2311yescharacteristic
40C22×D25—24no—
41C22×D25—24no—
42C22×D25—42no—
43C22×D25C2312yes—
44C22×D25C2312yes—
45D4×C25—22no—
46C2×C4×C25—22no—
47C2×C4×C25—22no—
48C2×C4×C25C2311yescharacteristic
49C2×C4×C25C2311yescharacteristic
50C2×C4×C25C2311yescharacteristic
51C2×C4×C25C2311yescharacteristic
52C2×C4×C25C2311yescharacteristic
53C22⋊D25—24no—
54C22⋊D25—42no—
55C2×Dic25C2312yes—
56C2×Dic25C2312yes—
57D100—24no—
58D100—22no—
59D100D414yescomplemented
60C4×D25—24no—
61C4×D25—42no—
62Dic50—22no—
63C2×#709—51no—
64C22×D20—51no—
65C4×C5×D4D511yescharacteristic
66#4083—52no—
67#4076—51no—
68#4070—51no—
69#4040—52no—
70#4030—52no—
71D5×C22⋊C4—52no—
72#4021—51no—
73C4×D20—51no—
74C22×C25—21no—
75C22×C25—21no—
76C22×C25—21no—
77C22×C25—21no—
78C22×C25—21no—
79C22×C25#4112yescomplemented
80C22×C25C2411yescharacteristic
81C2×D25—22no—
82C2×D25—22no—
83C2×D25—22no—
84C2×D25—22no—
85C2×D25—22no—
86C2×D25—48no—
87C2×D25C2×D414yes—
88C4×C25—21no—
89C4×C25—21no—
90C4×C25—21no—
91C4×C25—21no—
92C4×C25C2×D412yes—
93Dic25—22no—
94Dic25—22no—
95C23×D5—52no—
96C2×C5×D4C2×D511yescharacteristic
97C22×C4×C5C2×D511yescharacteristic
98C22×C4×C5C2×D511yescharacteristic
99C2×C22⋊D5—52no—
100C2×C22⋊D5—52no—
101#709—104no—
102C2×D20—51no—
103C2×D20—51no—
104C2×D20—52no—
105C2×D20—104no—
106C2×C4×D5—52no—
107C2×C4×D5—52no—
108C2×Dic10—51no—
109C5×C4⋊C4C2×D511yescharacteristic
110C5×C22⋊C4C2×D511yescharacteristic
111C5×C22⋊C4C2×D511yescharacteristic
112C42×C5C2×D511yescharacteristic
113C22⋊Dic5—52no—
114#685—52no—
115#685—52no—
116#685—52no—
117#685—52no—
118C4⋊Dic5—51no—
119#683—52no—
120#546—251noSylow
121C2×C25—22no—
122C2×C25—41no—
123C2×C25C22×D411yescharacteristic
124C2×C25C2×#4111yescharacteristic
125C2×C25H(5,𝔽2)11yescharacteristic
126D25—24no—
127D25—42no—
128C23×C5C22×D511yescharacteristic
129C23×C5C22×D511yescharacteristic
130C22×D5—52no—
131C22×D5—52no—
132C22×D5—104no—
133C22×D5—104no—
134C22×D5—202no—
135C5×D4—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5C22×D511yescharacteristic
139C2×C4×C5C22×D511yescharacteristic
140C2×C4×C5C22×D511yescharacteristic
141C2×C4×C5C22×D511yescharacteristic
142C2×C4×C5C22×D511yescharacteristic
143C22⋊D5—104no—
144C22⋊D5—202no—
145C2×Dic5—52no—
146C2×Dic5—52no—
147D20—54no—
148D20—104no—
149D20—102no—
150C4×D5—104no—
151C4×D5—202no—
152Dic10—102no—
153C2×#41—251no—
154C22×D4—251no—
155#124—251no—
156#123—252no—
157C22⋊Q8—251no—
158#121—251no—
159#121—252no—
160#120—252no—
161C4×D4—251no—
162C4×D4D2511yescharacteristic, complemented
163C2×C22⋊C4—252no—
164C25#54611yescharacteristic, complemented, Sylow
165C22×C5—21no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—21no—
169C22×C5—21no—
170C22×C5#70912yes—
171C22×C5C23×D511yescharacteristic
172C2×D5—54no—
173C2×D5—102no—
174C2×D5—102no—
175C2×D5—102no—
176C2×D5—102no—
177C2×D5—102no—
178C2×D5—208no—
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—21no—
182C4×C5—21no—
183C4×C5D4×D512yes—
184Dic5—102no—
185Dic5—102no—
186C24—252no—
187#41—504no—
188C2×Q8—251no—
189C2×D4—252no—
190C2×D4—252no—
191C2×D4—251no—
192C2×D4—252no—
193C2×D4—251no—
194C2×D4—504no—
195C2×D4C2×D2511yescharacteristic
196C22×C4—252no—
197C22×C4—252no—
198C22×C4C2×D2511yescharacteristic
199C22×C4C2×D2511yescharacteristic, complemented
200C4⋊C4—251no—
201C4⋊C4—252no—
202C4⋊C4C2×D2511yescharacteristic, complemented
203C22⋊C4—252no—
204C22⋊C4—252no—
205C22⋊C4—252no—
206C22⋊C4—252no—
207C22⋊C4—252no—
208C22⋊C4C2×D2511yescharacteristic
209C22⋊C4C2×D2511yescharacteristic, complemented
210C42C2×D2511yescharacteristic, complemented
211C2×C5—22no—
212C2×C5—41no—
213C2×C5C2×#70911yescharacteristic
214C2×C5C2×D4×D511yescharacteristic
215C2×C5#414911yescharacteristic
216D5—104no—
217D5—202no—
218C23—252no—
219C23—252no—
220C23—504no—
221C23—504no—
222C23—1002no—
223C23C22×D2511yescharacteristic
224C23C22×D2511yescharacteristic
225Q8—502no—
226D4—22no—
227D4—254no—
228D4—504no—
229D4—504no—
230D4—502no—
231D4—1002no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—252no—
235C2×C4—252no—
236C2×C4—504no—
237C2×C4—1002no—
238C2×C4C22×D2511yescharacteristic
239C2×C4C22×D2511yescharacteristic
240C2×C4C22×D2511yescharacteristic
241C2×C4C22×D2511yescharacteristic
242C2×C4C22×D2511yescharacteristic
243C5#6588411yescharacteristic
244C22—21no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—254no—
250C22—502no—
251C22—502no—
252C22—502no—
253C22—502no—
254C22—502no—
255C22—1008no—
256C22#8774412yescomplemented
257C22C23×D2511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—502no—
263C4—502no—
264C4D4×D2512yes—
265C2—22no—
266C2—41no—
267C2—504no—
268C2—1002no—
269C2C2×#8774411yescharacteristic
270C2C2×D4×D2511yescharacteristic
271C2#1171656811yescharacteristic
subgroupG/H
centerC22C23×D25
commutator, cosocleC22×C25C24
Frattini, socleC22×C5C23×D5
FittingC4×D4×C25C2
hypercenterC4×D4D25
hypocenterC25#546
LCSG ▷ C22×C25 ▷ C25
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#87744C2semidirect
2. C22×D100C2semidirect
3. C4×D4×C25C2semidirect
4. #11716499C2semidirect
5. #11716492C2semidirect
6. #11716486C2semidirect
7. #11716456C2semidirect
8. #11716446C2semidirect
9. C22⋊C4×D25C2semidirect
10. #11716437C2semidirect
11. C4×D100C2semidirect
15. C22×C4×C25C22semidirect
16. C2×C22⋊D25C22semidirect
17. C2×C22⋊D25C22semidirect
23. C2×C4×D25C22semidirect
24. C2×C4×D25C22semidirect
25. C2×Dic50C22semidirect
26. C4⋊C4×C25C22semidirect
28. C22⋊C4×C25C22semidirect
29. C42×C25C22semidirect
31. #87720C22semidirect
32. #87720C22semidirect
33. #87720C22semidirect
34. #87720C22semidirect
35. C4⋊Dic25C22semidirect
36. #87718C22semidirect
59. D100D4semidirect
79. C22×C25#41semidirect
162. C4×D4D25semidirect
164. C25#546semidirect
199. C22×C4C2×D25semidirect
202. C4⋊C4C2×D25semidirect
209. C22⋊C4C2×D25semidirect
210. C42C2×D25semidirect
256. C22#87744semidirect

Maximal subgroups

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

subgroupindex
C2×#877442
C22×D1002
C4×D4×C252
#117164992
#117164922
#117164862
#117164562
#117164462
C22⋊C4×D252
#117164372
C4×D1002
#658845