Finite Group Databasebeta

← #13106597

Subgroups — #13106597

Order 1600.

626 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 136 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
1#11717273C211yesmaximal, characteristic
2C2×C5×C22⋊Dic5C212yesmaximal, complemented
3#11717093C211yesmaximal, characteristic, complemented
4#11717084C212yesmaximal, complemented
5#11717082C212yesmaximal, complemented
6#11717074C212yesmaximal, complemented
7#11717073C212yesmaximal, complemented
8#11717071C211yesmaximal, characteristic, complemented
9#11717070C212yesmaximal, complemented
10C24×C52C2211yescharacteristic
11C2×C22⋊(C5⋊D5)C2212yes—
12C2×C22⋊(C5⋊D5)C2211yescharacteristic
13C22×C5×Dic5C2212yes—
14C22×C5×Dic5C2212yes—
15C2×#6039C2211yescharacteristic, complemented
16C2×#6036C2211yescharacteristic, complemented
17C22⋊#1039C2212yes—
18C22⋊#1039C2211yescharacteristic
19C5×C22⋊Dic5C2212yes—
20C5×C22⋊Dic5C2212yes—
21C5×C22⋊Dic5C2212yes—
22C5×C22⋊Dic5C2212yes—
23#87781C2212yescomplemented
24#87780C2212yescomplemented
25#87780C2212yescomplemented
26#87780C2212yescomplemented
27#87779C2212yescomplemented
28#87779C2211yescharacteristic, complemented
29Dic52C2212yescomplemented
30Dic52C2211yescharacteristic, complemented
31#65829—52nomaximal
32C23×C52—24no—
33C23×C52—41no—
34C23×C52C2311yescharacteristic
35C23×C52C2312yes—
36C22×C5⋊D5C2311yescharacteristic
37C22⋊(C5⋊D5)—24no—
38C22⋊(C5⋊D5)—41no—
39C2×#1039C2311yescharacteristic
40C2×#1039C2312yes—
41C2×C5×Dic5—24no—
42C2×C5×Dic5—42no—
43C2×C5×Dic5C2312yes—
44C2×C5×Dic5C2312yes—
45C2×C5×Dic5C2312yes—
46C2×C5×Dic5C2312yes—
47#6039—41no—
48#6036—41no—
49C2×C5×C22⋊C4—52no—
50#4099—52no—
51#4099—102no—
52C2×C22⋊Dic5D512yescomplemented
53#4075—52no—
54C4×C22⋊D5—52no—
55#4072—52no—
56#4070—52no—
57#4032—52no—
58#4031—52no—
59#4029—52no—
60#4027—52no—
61#4025—52no—
62#4025—52no—
63#4024—52no—
64#4023—52no—
65C22×C52—22no—
66C22×C52—22no—
67C22×C52—22no—
68C22×C52—21no—
69C22×C52—44no—
70C22×C52#4114yes—
71C22×C52C2411yescharacteristic
72C2×C5⋊D5—22no—
73C2×C5⋊D5—21no—
74#1039—22no—
75#1039—21no—
76C5×Dic5—22no—
77C5×Dic5—22no—
78C5×Dic5—22no—
79C5×Dic5—22no—
80C24×C5—22no—
81C24×C5C2×D512yes—
82C22×C4×C5—52no—
83C22×C4×C5—52no—
84C2×C22⋊D5—52no—
85C2×C22⋊D5—52no—
86C2×C22⋊D5—52no—
87C2×C22⋊D5—104no—
88C2×C22⋊D5—102no—
89C22×Dic5C2×D512yes—
90C22×Dic5C2×D512yes—
91C2×C4×D5—52no—
92C2×Dic10—52no—
93C5×C22⋊C4—52no—
94C5×C22⋊C4—52no—
95C5×C22⋊C4—52no—
96C5×C22⋊C4—52no—
97C22⋊Dic5—52no—
98C22⋊Dic5—52no—
99C22⋊Dic5—52no—
100C22⋊Dic5—104no—
101C22⋊Dic5—102no—
102C22⋊Dic5C2×D512yes—
103C22⋊Dic5C2×D512yes—
104C22⋊Dic5C2×D512yes—
105C22⋊Dic5C2×D512yes—
106#685—52no—
107#685—52no—
108#685—52no—
109C4⋊Dic5—52no—
110C4⋊Dic5—52no—
111C4⋊Dic5—52no—
112#683—52no—
113#683—52no—
114#683—52no—
115#683—52no—
116#683—52no—
117C4×Dic5—52no—
118C4×Dic5—52no—
119C4×Dic5—52no—
120#551—251noSylow
121C2×C52—24no—
122C2×C52—41no—
123C2×C52C2×#4112yes—
124C2×C52H(5,𝔽2)11yescharacteristic
125C5⋊D5—41no—
126C23×C5—24no—
127C23×C5—24no—
128C23×C5—22no—
129C23×C5—24no—
130C23×C5—48no—
131C23×C5—42no—
132C23×C5—44no—
133C23×C5C22×D512yes—
134C23×C5C22×D512yes—
135C23×C5C22×D512yes—
136C22×D5—52no—
137C22×D5—102no—
138C2×C4×C5—52no—
139C2×C4×C5—52no—
140C2×C4×C5—52no—
141C2×C4×C5—52no—
142C2×C4×C5—104no—
143C2×C4×C5—202no—
144C22⋊D5—104no—
145C22⋊D5—104no—
146C22⋊D5—208no—
147C22⋊D5—202no—
148C22⋊D5—204no—
149C2×Dic5—24no—
150C2×Dic5—42no—
151C2×Dic5—52no—
152C2×Dic5—52no—
153C2×Dic5—52no—
154C2×Dic5—104no—
155C2×Dic5—102no—
156C2×Dic5C22×D512yes—
157C2×Dic5C22×D512yes—
158C2×Dic5C22×D512yes—
159C2×Dic5C22×D512yes—
160C4×D5—202no—
161Dic10—202no—
162#126—252no—
163#124—251no—
164#123—251no—
165#123—252no—
166C22⋊Q8—252no—
167#120—251no—
168C4×D4—252no—
169#117—252no—
170C2×C22⋊C4—52no—
171C52#55111yescharacteristic, complemented, Sylow
172C22×C5—22no—
173C22×C5—22no—
174C22×C5—22no—
175C22×C5—22no—
176C22×C5—24no—
177C22×C5—22no—
178C22×C5—22no—
179C22×C5—22no—
180C22×C5—28no—
181C22×C5—22no—
182C22×C5—44no—
183C22×C5—44no—
184C22×C5—44no—
185C22×C5—48no—
186C22×C5—416no—
187C22×C5#70914yes—
188C22×C5#71114yes—
189C22×C5C23×D512yes—
190C2×D5—102no—
191C2×D5—102no—
192C2×D5—102no—
193C2×D5—204no—
194C2×D5—202no—
195C4×C5—102no—
196C4×C5—102no—
197C4×C5—102no—
198C4×C5—102no—
199Dic5—22no—
200Dic5—22no—
201Dic5—22no—
202Dic5—22no—
203Dic5—102no—
204Dic5—102no—
205Dic5—102no—
206Dic5—204no—
207Dic5—202no—
208C24D5211yescharacteristic
209C2×Q8—251no—
210C2×D4—252no—
211C2×D4—251no—
212C22×C4—52no—
213C22×C4—52no—
214C22×C4—251no—
215C4⋊C4—252no—
216C4⋊C4—252no—
217C4⋊C4—252no—
218C4⋊C4—252no—
219C22⋊C4—52no—
220C22⋊C4—52no—
221C22⋊C4—52no—
222C22⋊C4—52no—
223C22⋊C4—252no—
224C22⋊C4—251no—
225C22⋊C4—252no—
226C22⋊C4—251no—
227C42—251no—
228C42—252no—
229C2×C5—24no—
230C2×C5—24no—
231C2×C5—24no—
232C2×C5—22no—
233C2×C5—48no—
234C2×C5—44no—
235C2×C5—42no—
236C2×C5C2×#70912yes—
237C2×C5C2×#71112yes—
238C2×C5#414412yes—
239D5—202no—
240D5—402no—
241C23—24no—
242C23—41no—
243C23—251no—
244C23C2×D5211yescharacteristic
245C23C2×D5212yes—
246Q8—1001no—
247D4—504no—
248D4—1001no—
249C2×C4—52no—
250C2×C4—52no—
251C2×C4—52no—
252C2×C4—52no—
253C2×C4—104no—
254C2×C4—202no—
255C2×C4—252no—
256C2×C4—251no—
257C2×C4—1001no—
258C5—22no—
259C5#6582912yescomplemented
260C22—22no—
261C22—22no—
262C22—22no—
263C22—21no—
264C22—44no—
265C22—502no—
266C22—501no—
267C22#8787914yes—
268C22C22×D5211yescharacteristic
269C4—102no—
270C4—102no—
271C4—102no—
272C4—102no—
273C4—502no—
274C4—501no—
275C2—24no—
276C2—41no—
277C2—1001no—
278C2C2×#8787912yes—
279C2#1171749511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC24×C52C22
prime radical#11717273C2
hypercenterC24D52
hypocenterC52#551
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×C5×C22⋊Dic5C2semidirect
3. #11717093C2semidirect
4. #11717084C2semidirect
5. #11717082C2semidirect
6. #11717074C2semidirect
7. #11717073C2semidirect
8. #11717071C2semidirect
9. #11717070C2semidirect
15. C2×#6039C22semidirect
16. C2×#6036C22semidirect
23. #87781C22semidirect
24. #87780C22semidirect
25. #87780C22semidirect
26. #87780C22semidirect
27. #87779C22semidirect
28. #87779C22semidirect
29. Dic52C22semidirect
30. Dic52C22semidirect
52. C2×C22⋊Dic5D5semidirect
171. C52#551semidirect
259. C5#65829semidirect

Maximal subgroups

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

subgroupindex
#117172732
C2×C5×C22⋊Dic52
#117170932
#117170842
#117170822
#117170742
#117170732
#117170712
#117170702
#658295