Finite Group Databasebeta

← #13105518

Subgroups — #13105518

Order 1600.

494 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 124 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#11717207C211yesmaximal, characteristic, complemented
2C5×#4044C212yesmaximal, complemented
3#11717037C211yesmaximal, characteristic, complemented
4C4×#6039C211yesmaximal, characteristic, complemented
5#11717033C211yesmaximal, characteristic
6#11717033C211yesmaximal, characteristic
7#11717020C211yesmaximal, characteristic
8#11717015C212yesmaximal, complemented
9#11716995C212yesmaximal, complemented
10#11716976C212yesmaximal, complemented
11#11716956C211yesmaximal, characteristic, complemented
12C2×#6045C2211yescharacteristic
13C2×#6039C2211yescharacteristic
14C2×#6039C2211yescharacteristic
15C2×#6037C2211yescharacteristic
16C2×D5×Dic5C2212yes—
17C52×C4⋊C4C2211yescharacteristic
18#87806C2211yescharacteristic
19#87806C2211yescharacteristic
20C4×#1039C2211yescharacteristic
21C4×#1039C2211yescharacteristic
22C4×#1039C2211yescharacteristic
23C5×#685C2212yes—
24C5×#685C2212yes—
25C5×#685C2212yes—
26C5×C4⋊Dic5C2212yes—
27C5×#683C2212yes—
28C4×C5×Dic5C2212yes—
29#87781C2211yescharacteristic
30#87781C2212yes—
31#87780C2212yes—
32#87778C2212yes—
33#87778C2212yes—
34Dic52C2212yes—
35#66036—52nomaximal
36C22×C5×D5C2312yes—
37C2×C4×C52C2311yescharacteristic
38C2×C4×C52C2311yescharacteristic
39C2×C4×C52C2311yescharacteristic
40C2×#1039C2311yescharacteristic
41C2×#1039C2311yescharacteristic
42C2×#1039C2311yescharacteristic
43C2×#1039C2311yescharacteristic
44#6045—22no—
45C2×C5×Dic5C2312yes—
46C2×C5×Dic5C2312yes—
47C2×C5×Dic5C2312yes—
48#6039—22no—
49#6039—22no—
50#6037—22no—
51D5×Dic5—24no—
52C5×#126—52no—
53#4044—52no—
54#4044D512yescomplemented
55#4042—52no—
56#4034—52no—
57#4033—52no—
58#4033—52no—
59#4033—102no—
60#4031—52no—
61#4031—52no—
62#4027—52no—
63#4025—52no—
64#4024—52no—
65#4023—52no—
66#4018—52no—
67C4×Dic10—52no—
68C22×C52C2411yescharacteristic
69C2×C5×D5—22no—
70C2×C5×D5—22no—
71C2×C5×D5—22no—
72C4×C52—21no—
73C4×C52—21no—
74C4×C52—21no—
75#1039—21no—
76#1039—21no—
77#1039#4112yes—
78#1039#4112yes—
79C5×Dic5—22no—
80C5×Dic5—22no—
81C5×Dic5—22no—
82C2×C22⋊D5—52no—
83C22×Dic5—52no—
84C2×C4×D5—52no—
85C2×Dic10—52no—
86C2×Dic10—52no—
87C2×Dic10—52no—
88C2×Dic10—102no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—52no—
91C5×C4⋊C4—52no—
92C5×C4⋊C4C2×D512yes—
93C5×C22⋊C4—52no—
94C5×C22⋊C4—52no—
95C5×C22⋊C4—52no—
96C42×C5—52no—
97C22⋊Dic5—52no—
98C22⋊Dic5—52no—
99#685—52no—
100#685—52no—
101#685C2×D512yes—
102#685C2×D512yes—
103#685C2×D512yes—
104C4⋊Dic5—52no—
105C4⋊Dic5C2×D512yes—
106#683—52no—
107#683—52no—
108#683—52no—
109#683—52no—
110#683—52no—
111#683—52no—
112#683—102no—
113#683—102no—
114#683C2×D512yes—
115C4×Dic5—52no—
116C4×Dic5—52no—
117C4×Dic5—52no—
118C4×Dic5—52no—
119C4×Dic5—52no—
120C4×Dic5—102no—
121C4×Dic5—102no—
122C4×Dic5—102no—
123C4×Dic5C2×D512yes—
124#556—251noSylow
125C2×C52C2×#4111yescharacteristic
126C2×C52C2×#4111yescharacteristic
127C2×C522−1+411yescharacteristic
128C5×D5—42no—
129C23×C5—52no—
130C22×D5C22×D512yes—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—52no—
135C2×C4×C5—52no—
136C2×C4×C5—52no—
137C2×C4×C5C22×D512yes—
138C2×C4×C5C22×D512yes—
139C2×C4×C5C22×D512yes—
140C22⋊D5—104no—
141C2×Dic5—52no—
142C2×Dic5—52no—
143C2×Dic5—52no—
144C2×Dic5—52no—
145C2×Dic5—102no—
146C2×Dic5—102no—
147C2×Dic5—102no—
148C2×Dic5—102no—
149C2×Dic5—104no—
150C2×Dic5C22×D512yes—
151C2×Dic5C22×D512yes—
152C2×Dic5C22×D512yes—
153C4×D5—104no—
154Dic10—104no—
155Dic10—104no—
156Dic10—104no—
157Dic10—108no—
158C4⋊Q8—251no—
159#126—52no—
160#126—252no—
161#124—251no—
162#124—251no—
163C22⋊Q8—252no—
164C4×Q8—251no—
165C4×Q8—251no—
166C4×Q8—251no—
167C4×D4—251no—
168#117—252no—
169C52#55611yescharacteristic, complemented, Sylow
170C22×C5—22no—
171C22×C5—102no—
172C22×C5—102no—
173C22×C5—102no—
174C22×C5C23×D512yes—
175C2×D5—22no—
176C2×D5—22no—
177C2×D5—22no—
178C4×C5—24no—
179C4×C5—22no—
180C4×C5—22no—
181C4×C5—22no—
182C4×C5—42no—
183C4×C5—42no—
184C4×C5—102no—
185C4×C5—102no—
186C4×C5—102no—
187Dic5—22no—
188Dic5—22no—
189Dic5—22no—
190Dic5—54no—
191Dic5—54no—
192Dic5—104no—
193Dic5—104no—
194Dic5—104no—
195Dic5—102no—
196Dic5—102no—
197Dic5—202no—
198C2×Q8—251no—
199C2×Q8—251no—
200C2×Q8—251no—
201C2×D4—251no—
202C22×C4—252no—
203C4⋊C4—52no—
204C4⋊C4—52no—
205C4⋊C4—252no—
206C4⋊C4—251no—
207C4⋊C4—252no—
208C4⋊C4—251no—
209C4⋊C4—251no—
210C4⋊C4D5211yescharacteristic
211C22⋊C4—52no—
212C22⋊C4—52no—
213C22⋊C4—52no—
214C22⋊C4—252no—
215C22⋊C4—252no—
216C42—52no—
217C42—252no—
218C42—251no—
219C42—251no—
220C42—251no—
221C2×C5—22no—
222C2×C5—22no—
223C2×C5—22no—
224C2×C5—202no—
225C2×C5D5×#4112yes—
226C2×C5D5×#4112yes—
227C2×C5#415012yes—
228D5—42no—
229C23—52no—
230Q8—502no—
231Q8—502no—
232Q8—502no—
233D4—502no—
234C2×C4—52no—
235C2×C4—52no—
236C2×C4—52no—
237C2×C4—251no—
238C2×C4—251no—
239C2×C4—251no—
240C2×C4—251no—
241C2×C4—504no—
242C2×C4C2×D5211yescharacteristic
243C2×C4C2×D5211yescharacteristic
244C2×C4C2×D5211yescharacteristic
245C5—22no—
246C5#6603612yescomplemented
247C22—102no—
248C22—102no—
249C22—102no—
250C22C22×D5211yescharacteristic
251C4—21no—
252C4—21no—
253C4—21no—
254C4—102no—
255C4—102no—
256C4—102no—
257C4—252no—
258C4—252no—
259C4—501no—
260C4—501no—
261C2—202no—
262C2#1171747111yescharacteristic
263C2#1171747411yescharacteristic
264C2#1171748411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C4⋊C4C22
prime radicalC2×#6037C22
hypercenterC4⋊C4D52
hypocenterC52#556
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11717207C2semidirect
2. C5×#4044C2semidirect
3. #11717037C2semidirect
4. C4×#6039C2semidirect
8. #11717015C2semidirect
9. #11716995C2semidirect
10. #11716976C2semidirect
11. #11716956C2semidirect
54. #4044D5semidirect
169. C52#556semidirect
246. C5#66036semidirect

Maximal subgroups

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

subgroupindex
#117172072
C5×#40442
#117170372
C4×#60392
#117170332
#117170202
#117170152
#117169952
#117169762
#117169562
#660365