Finite Group Databasebeta

← #13023175

Subgroups — #13023175

Order 1280.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#10613955C211yesmaximal, characteristic
2#10604877C212yesmaximal
3#10598711C212yesmaximal, complemented
4#10598710C212yesmaximal, complemented
5C2×C5×#117C411yescharacteristic
6C2×#4072C2211yescharacteristic
7C22×C4×Dic5C411yescharacteristic
8#65748—22no—
9#65266C411yescharacteristic
10#65266C2211yescharacteristic
11#65265C411yescharacteristic
12#65265C2211yescharacteristic
13#65231—22no—
14C4×#683—22no—
15#64933—22no—
16#64913C2214yes—
17#11447—51nomaximal, Sylow
18C23×C4×C5C2×C411yescharacteristic
19C23×Dic5—21no—
20C5×#117—41no—
21C5×#117—41no—
22C2×C5×C4⋊C4C2×C411yescharacteristic
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C5×C22⋊C4—21no—
25C2×C42×C5—21no—
26C2×C22⋊Dic5D412yes—
27#4072—41no—
28#4072—41no—
29C2×C4⋊Dic5C2×C411yescharacteristic
30C2×C4⋊Dic5C2311yescharacteristic
31C2×#683—22no—
32C2×#683—22no—
33C2×C4×Dic5—21no—
34C2×C4×Dic5—22no—
35C2×C4×Dic5C814yescomplemented
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5D412yes—
39C22⋊#170—24no—
40C4⋊#170—42no—
41C4×#170—42no—
42#3963—22no—
43#3963—22no—
44#2285—51no—
45#1458—52no—
46#1325—52no—
47#1324—52no—
48C24×C5C22⋊C411yescharacteristic
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5—22no—
52C22×C4×C5—21no—
53C22×C4×C5—21no—
54C22×C4×C5C22⋊C411yescharacteristic
55C22×C4×C5C2×C812yes—
56C22×C4×C5M1612yes—
57C22×C4×C5C22×C411yescharacteristic
58C22×Dic5—21no—
59C22×Dic5—24no—
60C22×Dic5—21no—
61C22×Dic5—42no—
62C22×Dic5—42no—
63C22×Dic5C22⋊C412yes—
64C22×Dic5C2×D412yes—
65C2×#170—44no—
66C5×C4⋊C4—41no—
67C5×C4⋊C4—41no—
68C5×C22⋊C4—42no—
69C42×C5—41no—
70C42×C5—41no—
71C22⋊Dic5—42no—
72C4⋊Dic5—41no—
73C4⋊Dic5—41no—
74#683—44no—
75#683—44no—
76C4×Dic5—24no—
77C4×Dic5—22no—
78C4×Dic5—22no—
79C4×Dic5—21no—
80C4×Dic5—21no—
81C4×Dic5C2×C812yes—
82C4×Dic5C2×C812yes—
83C2×#117—51no—
84C2×#117AGL(1,𝔽5)11yescharacteristic
85C22×C42—51no—
86#431—102no—
87#384—51no—
88#384—51no—
89#382—51no—
90#382—51no—
91#380—102no—
92C4×C4⋊C4—102no—
93#324—54no—
94#323—102no—
95C23×C5—21no—
96C23×C5—21no—
97C23×C5—41no—
98C23×C5—41no—
99C23×C5C22⋊C812yes—
100C23×C5C2×C22⋊C411yescharacteristic
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—41no—
110C2×C4×C5—41no—
111C2×C4×C5C22⋊C812yes—
112C2×C4×C5#9911yescharacteristic
113C2×C4×C5#9911yescharacteristic
114C2×C4×C5#10112yes—
115C2×C4×C5C22×C811yescharacteristic
116C2×C4×C5C2×M1611yescharacteristic
117C2×Dic5—22no—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—48no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128#170—84no—
129C23×C4—101no—
130C23×C4C2×AGL(1,𝔽5)11yescharacteristic
131#117—41no—
132#117—41no—
133#117—201no—
134#117—201no—
135C2×C4⋊C4—51no—
136C2×C4⋊C4—51no—
137C2×C4⋊C4—102no—
138C2×C4⋊C4—102no—
139C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
140C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
141C2×C22⋊C4—21no—
142C2×C22⋊C4—52no—
143C2×C42—21no—
144C2×C42—54no—
145C2×C42—51no—
146C2×C42—51no—
147C2×C42—52no—
148C2×C42—102no—
149C2×C42—101no—
150C4⋊C8—202no—
151C22⋊C8—104no—
152C4×C8—202no—
153#95—102no—
154#95—102no—
155C22×C5—21no—
156C22×C5—21no—
157C22×C5—22no—
158C22×C5—42no—
159C22×C5—42no—
160C22×C5—41no—
161C22×C5—41no—
162C22×C5C2×C22⋊C811yescharacteristic
163C22×C5C2×#9911yescharacteristic
164C22×C5C2×#10111yescharacteristic
165C4×C5—21no—
166C4×C5—21no—
167C4×C5—81no—
168C4×C5—81no—
169C4×C5#32412yes—
170C4×C5#32412yes—
171Dic5—24no—
172Dic5—42no—
173Dic5—42no—
174Dic5—42no—
175C24C22⋊AGL(1,𝔽5)11yescharacteristic
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—52no—
182C22×C4—52no—
183C22×C4—101no—
184C22×C4—101no—
185C22×C4—104no—
186C22×C4—202no—
187C22×C4—202no—
188C22×C4D5⋊C812yes—
189C22×C4#70012yes—
190C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
191C22×C4C22×AGL(1,𝔽5)11yescharacteristic
192C2×C8—204no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—201no—
196C4⋊C4—201no—
197C4⋊C4—204no—
198C4⋊C4—204no—
199C22⋊C4—42no—
200C22⋊C4—202no—
201C42—41no—
202C42—41no—
203C42—52no—
204C42—52no—
205C42—101no—
206C42—101no—
207C42—104no—
208C42—102no—
209C42—102no—
210C2×C5—21no—
211C2×C5—21no—
212C2×C5—42no—
213C2×C5C2×#32411yescharacteristic
214C2×C5#212611yescharacteristic
215C2×C5#213211yescharacteristic
216C23—21no—
217C23—21no—
218C23—41no—
219C23—41no—
220C23#400312yes—
221C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—102no—
233C2×C4—102no—
234C2×C4—102no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—102no—
238C2×C4—208no—
239C2×C4—201no—
240C2×C4—201no—
241C2×C4—202no—
242C2×C4—202no—
243C2×C4#400312yes—
244C2×C4#400512yes—
245C2×C4#401111yescharacteristic
246C2×C4#401111yescharacteristic
247C2×C4C2×D5⋊C811yescharacteristic
248C2×C4C2×#70011yescharacteristic
249C8—404no—
250C5#1144711yescharacteristic, complemented, Sylow
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×#400311yescharacteristic
259C22C2×#400511yescharacteristic
260C22C2×#401111yescharacteristic
261C4—21no—
262C4—21no—
263C4—81no—
264C4—81no—
265C4—104no—
266C4—202no—
267C4—202no—
268C4—202no—
269C4#6491412yes—
270C4#6491412yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#6491411yescharacteristic
275C2#1060499611yescharacteristic
276C2#1060499811yescharacteristic
subgroupG/H
centerC2×C4#4011
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C4⋊Dic5C23
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5#11447
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #10598711C2semidirect
4. #10598710C2semidirect
35. C2×C4×Dic5C8semidirect
250. C5#11447semidirect

Maximal subgroups

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

subgroupindex
#106139552
#106048772
#105987112
#105987102
#114475