Finite Group Databasebeta

← #13105394

Subgroups — #13105394

Order 1600.

574 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 128 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#11717206C211yesmaximal, characteristic, complemented
2C5×#4029C212yesmaximal, complemented
3#11717101C211yesmaximal, characteristic
4#11717091C212yesmaximal, complemented
5#11717071C211yesmaximal, characteristic, complemented
6D5×#685C212yesmaximal, complemented
7#11717007C212yesmaximal, complemented
8#11716966C212yesmaximal, complemented
9#11716959C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C2×C22⋊(C5⋊D5)C2211yescharacteristic
12C22×#1039C2211yescharacteristic, complemented
13C2×C5×C22⋊D5C2212yes—
14C2×C4×C5×D5C2212yes—
15C2×#6039C2211yescharacteristic, complemented
16C2×D5×Dic5C2212yes—
17C52×C22⋊C4C2211yescharacteristic, complemented
18#87808C2212yes—
19C4⋊#1039C2212yescomplemented
20C5×C22⋊Dic5C2212yescomplemented
21C5×#685C2212yes—
22C5×C4⋊Dic5C2212yescomplemented
23C5×#683C2212yescomplemented
24#87780C2212yescomplemented
25#87779C2211yescharacteristic
26#87779C2212yes—
27#87778C2212yes—
28#87778C2212yes—
29Dic52C2211yescharacteristic, complemented
30Dic52C2212yescomplemented
31#65992—52nomaximal
32C23×C52C2311yescharacteristic
33C22×C5⋊D5C2311yescharacteristic
34C22×C5×D5C2312yes—
35C2×D52—24no—
36C2×D52—41no—
37C2×C4×C52C2312yes—
38C22⋊(C5⋊D5)—41no—
39C2×#1039—41no—
40C2×#1039C2312yes—
41C2×#1039C2311yescharacteristic
42C5×C22⋊D5—24no—
43C2×C5×Dic5C2312yes—
44C2×C5×Dic5C2312yes—
45C2×C5×Dic5C2312yes—
46C4×C5×D5—24no—
47#6039—41no—
48D5×Dic5—42no—
49C5×#123—52no—
50#4083—52no—
51D4×Dic5—52no—
52C2×#685—52no—
53#4072—52no—
54#4044—52no—
55#4044—52no—
56#4043—52no—
57#4038—52no—
58#4032—52no—
59#4032—102no—
60#4031—52no—
61#4029D512yescomplemented
62#4027—52no—
63D5×C22⋊C4—52no—
64#4024—52no—
65C22×C52—22no—
66C22×C52—21no—
67C22×C52C2411yescharacteristic
68C2×C5⋊D5—22no—
69C2×C5⋊D5—21no—
70C2×C5×D5—22no—
71C2×C5×D5—22no—
72C2×C5×D5#4114yes—
73D52—44no—
74C4×C52—22no—
75#1039—22no—
76#1039—21no—
77C5×Dic5—22no—
78C5×Dic5—22no—
79C5×Dic5—22no—
80C23×D5—52no—
81C2×C5×D4—52no—
82C22×C4×C5—52no—
83C2×C22⋊D5—52no—
84C2×C22⋊D5—102no—
85C2×C22⋊D5C2×D512yes—
86C22×Dic5—52no—
87C22×Dic5—52no—
88C22×Dic5—102no—
89C2×C4×D5—52no—
90C2×C4×D5C2×D512yes—
91C2×Dic10—52no—
92C5×C4⋊C4—52no—
93C5×C4⋊C4—52no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—52no—
96C5×C22⋊C4—52no—
97C5×C22⋊C4C2×D512yescomplemented
98C22⋊Dic5—52no—
99C22⋊Dic5—52no—
100C22⋊Dic5C2×D512yescomplemented
101#685—52no—
102#685—52no—
103#685—52no—
104#685—52no—
105#685—52no—
106#685—52no—
107#685—52no—
108#685—104no—
109#685C2×D512yes—
110C4⋊Dic5—52no—
111C4⋊Dic5—52no—
112C4⋊Dic5—52no—
113C4⋊Dic5—104no—
114C4⋊Dic5C2×D512yescomplemented
115#683—52no—
116#683C2×D512yescomplemented
117C4×Dic5—52no—
118C4×Dic5—52no—
119C4×Dic5—52no—
120#551—251noSylow
121C2×C52—41no—
122C2×C52C2×#4112yes—
123C2×C52H(5,𝔽2)11yescharacteristic
124C5⋊D5—41no—
125C5×D5—24no—
126C23×C5—22no—
127C23×C5—52no—
128C23×C5C22×D512yes—
129C22×D5—52no—
130C22×D5—102no—
131C22×D5—104no—
132C22×D5—104no—
133C22×D5—202no—
134C22×D5C22×D512yes—
135C5×D4—104no—
136C2×C4×C5—24no—
137C2×C4×C5—52no—
138C2×C4×C5—52no—
139C2×C4×C5—52no—
140C2×C4×C5—104no—
141C2×C4×C5C22×D512yes—
142C2×C4×C5C22×D512yes—
143C22⋊D5—24no—
144C22⋊D5—202no—
145C22⋊D5—204no—
146C2×Dic5—52no—
147C2×Dic5—52no—
148C2×Dic5—52no—
149C2×Dic5—102no—
150C2×Dic5—104no—
151C2×Dic5—202no—
152C2×Dic5—202no—
153C2×Dic5—204no—
154C2×Dic5C22×D512yes—
155C2×Dic5C22×D512yes—
156C2×Dic5C22×D512yes—
157C4×D5—24no—
158C4×D5—202no—
159Dic10—202no—
160#126—252no—
161#124—251no—
162#123—52no—
163#123—251no—
164C22⋊Q8—252no—
165#120—251no—
166C4×D4—252no—
167#117—252no—
168C2×C22⋊C4—252no—
169C52#55111yescharacteristic, complemented, Sylow
170C22×C5—24no—
171C22×C5—22no—
172C22×C5—22no—
173C22×C5—22no—
174C22×C5—22no—
175C22×C5—44no—
176C22×C5—54no—
177C22×C5—102no—
178C22×C5—102no—
179C22×C5C23×D512yes—
180C2×D5—22no—
181C2×D5—22no—
182C2×D5—102no—
183C2×D5—102no—
184C2×D5—102no—
185C2×D5—202no—
186C2×D5—204no—
187C2×D5—208no—
188C2×D5#71114yes—
189C4×C5—22no—
190C4×C5—22no—
191C4×C5—44no—
192C4×C5—102no—
193C4×C5—102no—
194C4×C5—102no—
195Dic5—22no—
196Dic5—22no—
197Dic5—22no—
198Dic5—102no—
199Dic5—102no—
200Dic5—102no—
201Dic5—204no—
202Dic5—202no—
203C24—251no—
204C2×Q8—251no—
205C2×D4—52no—
206C2×D4—251no—
207C22×C4—52no—
208C22×C4—252no—
209C22×C4—251no—
210C4⋊C4—52no—
211C4⋊C4—52no—
212C4⋊C4—252no—
213C4⋊C4—252no—
214C22⋊C4—52no—
215C22⋊C4—52no—
216C22⋊C4—252no—
217C22⋊C4—251no—
218C22⋊C4—252no—
219C22⋊C4—252no—
220C22⋊C4—252no—
221C22⋊C4D5211yescharacteristic, complemented
222C42—251no—
223C42—252no—
224C2×C5—22no—
225C2×C5—24no—
226C2×C5—44no—
227C2×C5—42no—
228C2×C5—104no—
229C2×C5C2×#71112yes—
230C2×C5D5×#4112yes—
231C2×C5#414912yes—
232D5—24no—
233D5—202no—
234D5—402no—
235C23—52no—
236C23—251no—
237C23—504no—
238C23—1001no—
239C23C2×D5211yescharacteristic
240Q8—1001no—
241D4—104no—
242D4—1001no—
243C2×C4—52no—
244C2×C4—52no—
245C2×C4—52no—
246C2×C4—104no—
247C2×C4—252no—
248C2×C4—251no—
249C2×C4—1002no—
250C2×C4—1001no—
251C2×C4C2×D5212yes—
252C5—22no—
253C5#6599212yescomplemented
254C22—21no—
255C22—22no—
256C22—54no—
257C22—102no—
258C22—102no—
259C22—501no—
260C22—502no—
261C22—1004no—
262C22C22×D5211yescharacteristic
263C4—22no—
264C4—102no—
265C4—102no—
266C4—102no—
267C4—502no—
268C4—501no—
269C2—41no—
270C2—104no—
271C2—1001no—
272C2#1171747311yescharacteristic
273C2D5×#71112yes—
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
prime radical#11717101C2
hypercenterC22⋊C4D52
hypocenterC52#551
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11717206C2semidirect
2. C5×#4029C2semidirect
4. #11717091C2semidirect
5. #11717071C2semidirect
6. D5×#685C2semidirect
7. #11717007C2semidirect
8. #11716966C2semidirect
9. #11716959C2semidirect
12. C22×#1039C22semidirect
15. C2×#6039C22semidirect
17. C52×C22⋊C4C22semidirect
19. C4⋊#1039C22semidirect
20. C5×C22⋊Dic5C22semidirect
22. C5×C4⋊Dic5C22semidirect
23. C5×#683C22semidirect
24. #87780C22semidirect
29. Dic52C22semidirect
30. Dic52C22semidirect
61. #4029D5semidirect
97. C5×C22⋊C4C2×D5semidirect
100. C22⋊Dic5C2×D5semidirect
114. C4⋊Dic5C2×D5semidirect
116. #683C2×D5semidirect
169. C52#551semidirect
221. C22⋊C4D52semidirect
253. C5#65992semidirect

Maximal subgroups

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

subgroupindex
#117172062
C5×#40292
#117171012
#117170912
#117170712
D5×#6852
#117170072
#117169662
#117169592
#659925