Finite Group Databasebeta

← #13025846

Subgroups — #13025846

Order 1280.

464 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 102 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
3C4×#4005C212yesmaximal
4#10598724C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C2×#4005C2214yes—
9C4×#704—22no—
10#65519C411yescharacteristic
11#65267—22no—
12#65266C411yescharacteristic
13#65263C2211yescharacteristic
14#65222—22no—
15#65221C411yescharacteristic
16#64929C418yescomplemented
17#64919—22no—
18#12631—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#4090C2×C414yes—
29C2×C4⋊Dic5C2×C411yescharacteristic
30C2×#683—22no—
31C2×#683D412yes—
32C2×C4×Dic5C2×C411yescharacteristic
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35C4×Dic10—42no—
36#4005—24no—
37#4005C2×C418yes—
38#4002—42no—
39C4×#170—42no—
40#3963—21no—
41#3963—21no—
42#3963—22no—
43#3963—22no—
44#3963—22no—
45#2327—51no—
46C2×#356—52no—
47C4×#101—52no—
48#1394—52no—
49C2×C5×Q8—21no—
50C2×C5×Q8—41no—
51C2×C5×Q8—41no—
52C2×C5×Q8C4212yes—
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22×C411yescharacteristic
58C22×Dic5—21no—
59C22×Dic5—21no—
60C22×Dic5C22⋊C412yes—
61C22×Dic5C2×D412yes—
62C2×Dic10—41no—
63C2×Dic10—41no—
64C2×Dic10C22×C412yes—
65C2×Dic10#4112yes—
66#704—28no—
67#704—44no—
68C2×#170—44no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—42no—
71C42×C5—22no—
72C42×C5—42no—
73C4⋊Dic5—41no—
74#683—28no—
75#683—42no—
76C4×Dic5—22no—
77C4×Dic5—22no—
78C4×Dic5—21no—
79C4×Dic5—41no—
80C4×Dic5C4212yes—
81C2×C4⋊Q8—51no—
82C2×C4×Q8—51no—
83C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
84C2×#101—54no—
85C4×M16—102no—
86#391—51no—
87#391—51no—
88#387—102no—
89#387—102no—
90#382—51no—
91#376—51no—
92#356—58no—
93#343—102no—
94C23×C5C2×C22⋊C411yescharacteristic
95C5×Q8—42no—
96C5×Q8—42no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—22no—
100C2×C4×C5—21no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—41no—
104C2×C4×C5—41no—
105C2×C4×C5—42no—
106C2×C4×C5—41no—
107C2×C4×C5#9912yes—
108C2×C4×C5C2×C4211yescharacteristic
109C2×C4×C5#11711yescharacteristic
110C2×Dic5—22no—
111C2×Dic5—22no—
112C2×Dic5—22no—
113C2×Dic5—22no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5—42no—
117C2×Dic5—41no—
118C2×Dic5—41no—
119C2×Dic5—41no—
120C2×Dic5C4×D414yes—
121Dic10—42no—
122Dic10—42no—
123#170—48no—
124C22×Q8—51no—
125C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
126C2×M16—104no—
127C4⋊Q8—54no—
128C4⋊Q8—102no—
129C4×Q8—42no—
130C4×Q8—202no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—52no—
133C2×C4⋊C4—51no—
134C2×C4⋊C4—102no—
135C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
136C2×C42—21no—
137C2×C42—51no—
138C2×C42—52no—
139C2×C42—51no—
140C2×C42C2×AGL(1,𝔽5)11yescharacteristic
141#101—58no—
142#101—104no—
143#97—202no—
144C4×C8—202no—
145#95—102no—
146#95—102no—
147#95—102no—
148#95—101no—
149#95—101no—
150C22×C5—21no—
151C22×C5—21no—
152C22×C5C4×C22⋊C411yescharacteristic
153C22×C5C2×#9911yescharacteristic
154C22×C5#41011yescharacteristic
155C4×C5—22no—
156C4×C5—21no—
157C4×C5—21no—
158C4×C5—41no—
159C4×C5—42no—
160C4×C5—81no—
161Dic5—24no—
162Dic5—42no—
163Dic5—42no—
164Dic5—81no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—52no—
169C2×Q8—52no—
170C2×Q8—201no—
171C2×Q8—201no—
172C2×Q8C4×AGL(1,𝔽5)12yes—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—52no—
176C22×C4—52no—
177C22×C4—101no—
178C22×C4—101no—
179C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
180C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
181C22×C4C22×AGL(1,𝔽5)11yescharacteristic
182M16—108no—
183M16—204no—
184C2×C8—204no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—108no—
188C4⋊C4—202no—
189C4⋊C4—201no—
190C42—22no—
191C42—42no—
192C42—52no—
193C42—101no—
194C42—102no—
195C42—102no—
196C42—201no—
197C2×C5—21no—
198C2×C5—21no—
199C2×C5C4×#9911yescharacteristic
200C2×C5#213311yescharacteristic
201C2×C5#213511yescharacteristic
202C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—202no—
206Q8—202no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—54no—
218C2×C4—102no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—201no—
223C2×C4—201no—
224C2×C4—202no—
225C2×C4—201no—
226C2×C4—201no—
227C2×C4—201no—
228C2×C4#401112yes—
229C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
230C2×C4#413011yescharacteristic
231C8—208no—
232C5#1263111yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22#6574511yescharacteristic
236C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
237C22C2×#401111yescharacteristic
238C4—21no—
239C4—21no—
240C4—22no—
241C4—42no—
242C4—41no—
243C4—81no—
244C4—104no—
245C4—202no—
246C4—202no—
247C4—401no—
248C2—21no—
249C2—21no—
250C2C4×#401111yescharacteristic
251C2#1060496511yescharacteristic
252C2#1060499911yescharacteristic
subgroupG/H
centerC22C2×#4011
commutatorC2×C4×C5C2×C42
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#12631
LCSG ▷ C2×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
16. #64929C4semidirect
232. C5#12631semidirect

Maximal subgroups

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

subgroupindex
#106141872
C2×#649292
C4×#40052
#105987242
#126315