Finite Group Databasebeta

← #13026414

Subgroups — #13026414

Order 1280.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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#10614187C211yesmaximal, characteristic
2C2×#64929C212yesmaximal
3#10604194C212yesmaximal
4#10598724C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C2×#4005C2214yes—
9#65758—22no—
10#65519C411yescharacteristic
11#65267—22no—
12#65266C411yescharacteristic
13#65263C2211yescharacteristic
14#65222—22no—
15#65221C411yescharacteristic
16#64929—24no—
17#64919—22no—
18#12804—51nomaximal, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×Dic10C2311yescharacteristic
21C2×#704—24no—
22C4×C5×Q8—42no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C42×C5—21no—
26C2×C42×C5C2×C411yescharacteristic
27#4090—22no—
28#4090D412yes—
29#4090Q812yes—
30C2×C4⋊Dic5C2×C411yescharacteristic
31C2×#683—22no—
32C2×#683D412yes—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5C2×C411yescharacteristic
35C2×C4×Dic5D412yes—
36C4×Dic10—42no—
37#4005—24no—
38#4005—24no—
39#4004—42no—
40C4⋊#170—42no—
41#3963—21no—
42#3963—21no—
43#3963—22no—
44#3963—22no—
45#3963—22no—
46#2327—51no—
47C2×#356—52no—
48#1801—52no—
49#1394—52no—
50C2×C5×Q8—21no—
51C2×C5×Q8—41no—
52C2×C5×Q8—41no—
53C2×C5×Q8C4⋊C412yes—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22×C411yescharacteristic
59C22×Dic5—21no—
60C22×Dic5—21no—
61C22×Dic5C22⋊C412yes—
62C22×Dic5C2×D412yes—
63C2×Dic10—41no—
64C2×Dic10—41no—
65C2×Dic10C2×D411yescharacteristic
66C2×Dic10C2×Q811yescharacteristic
67C2×Dic10#4112yes—
68#704—44no—
69#704—44no—
70C2×#170—44no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C42×C5—22no—
74C42×C5—42no—
75C4⋊Dic5—41no—
76#683—24no—
77#683—24no—
78#683—42no—
79C4×Dic5—22no—
80C4×Dic5—22no—
81C4×Dic5—21no—
82C4×Dic5—41no—
83C4×Dic5C4⋊C412yes—
84C2×C4⋊Q8—51no—
85C2×C4×Q8—51no—
86C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
87#423—102no—
88C2×#101—54no—
89#391—51no—
90#391—51no—
91#387—102no—
92#387—102no—
93#382—51no—
94#376—51no—
95#356—104no—
96#343—102no—
97C23×C5C2×C22⋊C411yescharacteristic
98C5×Q8—42no—
99C5×Q8—42no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—41no—
105C2×C4×C5—41no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5—41no—
110C2×C4×C5#9912yes—
111C2×C4×C5C2×C4⋊C411yescharacteristic
112C2×C4×C5#11711yescharacteristic
113C2×Dic5—22no—
114C2×Dic5—22no—
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5—41no—
118C2×Dic5—41no—
119C2×Dic5—42no—
120C2×Dic5—41no—
121C2×Dic5—41no—
122C2×Dic5—41no—
123C2×Dic5#12112yes—
124C2×Dic5C22⋊Q812yes—
125Dic10—41no—
126Dic10—41no—
127Dic10—42no—
128#170—84no—
129C22×Q8—51no—
130C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
131C2×M16—104no—
132C4⋊Q8—52no—
133C4⋊Q8—52no—
134C4⋊Q8—102no—
135C4×Q8—42no—
136C4×Q8—202no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—52no—
139C2×C4⋊C4—51no—
140C2×C4⋊C4—102no—
141C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
142C2×C42—21no—
143C2×C42—51no—
144C2×C42—52no—
145C2×C42—51no—
146C2×C42C2×AGL(1,𝔽5)11yescharacteristic
147C4⋊C8—202no—
148C4⋊C8—202no—
149#101—104no—
150#101—104no—
151#95—102no—
152#95—102no—
153#95—102no—
154#95—101no—
155#95—101no—
156C22×C5—21no—
157C22×C5—21no—
158C22×C5#38011yescharacteristic
159C22×C5C2×#9911yescharacteristic
160C22×C5#41011yescharacteristic
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—22no—
164C4×C5—42no—
165C4×C5—41no—
166C4×C5—81no—
167Dic5—22no—
168Dic5—22no—
169Dic5—42no—
170Dic5—42no—
171Dic5—81no—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—51no—
176C2×Q8—51no—
177C2×Q8—52no—
178C2×Q8—201no—
179C2×Q8—201no—
180C2×Q8C4⋊AGL(1,𝔽5)12yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—52no—
184C22×C4—52no—
185C22×C4—101no—
186C22×C4—101no—
187C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
188C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
189C22×C4C22×AGL(1,𝔽5)11yescharacteristic
190M16—204no—
191M16—204no—
192C2×C8—204no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—104no—
196C4⋊C4—104no—
197C4⋊C4—202no—
198C4⋊C4—201no—
199C42—22no—
200C42—42no—
201C42—52no—
202C42—101no—
203C42—102no—
204C42—102no—
205C42—201no—
206C2×C5—21no—
207C2×C5—21no—
208C2×C5#179911yescharacteristic
209C2×C5#213311yescharacteristic
210C2×C5#213511yescharacteristic
211C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
212Q8—42no—
213Q8—42no—
214Q8—201no—
215Q8—201no—
216Q8—202no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—52no—
228C2×C4—52no—
229C2×C4—102no—
230C2×C4—102no—
231C2×C4—102no—
232C2×C4—102no—
233C2×C4—201no—
234C2×C4—201no—
235C2×C4—202no—
236C2×C4—201no—
237C2×C4—201no—
238C2×C4—201no—
239C2×C4#401112yes—
240C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
241C2×C4#413011yescharacteristic
242C8—404no—
243C5#1280411yescharacteristic, complemented, Sylow
244C22—21no—
245C22—21no—
246C22#6574511yescharacteristic
247C22#6576511yescharacteristic
248C22C2×#401111yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—81no—
255C4—102no—
256C4—102no—
257C4—202no—
258C4—202no—
259C4—401no—
260C2—21no—
261C2—21no—
262C2#1060489211yescharacteristic
263C2#1060496511yescharacteristic
264C2#1060499911yescharacteristic
subgroupG/H
centerC22C2×#4011
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×Dic10C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#12804
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
243. C5#12804semidirect

Maximal subgroups

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

subgroupindex
#106141872
C2×#649292
#106041942
#105987242
#128045