Finite Group Databasebeta

← #12008943

Subgroups — #12008943

Order 1280.

394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C5×#2546C211yesmaximal, characteristic
2#10602418C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10598134C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C5×C4⋊Q8C412yes—
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#398—21no—
9C5×#398—21no—
10C5×#391C2212yes—
11C5×#389—21no—
12C5×#389—21no—
13C4×C5×C4⋊C4C411yescharacteristic
14#65215—21no—
15#65214—21no—
16#64748—21no—
17#64748—21no—
18#64748C2212yes—
19#64748C2212yes—
20#11568—51nomaximal, Sylow
21C22×C5×Q8C2×C412yes—
22C22×C5×Q8C2×C411yescharacteristic
23C5×C4⋊Q8—41no—
24C5×C4⋊Q8—41no—
25C5×C4⋊Q8—44no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C4⋊C4C2311yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C412yes—
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C5×#95—21no—
41C5×#95—22no—
42C5×#95—22no—
43C22⋊#168—22no—
44C22⋊#168—22no—
45C4⋊#168—41no—
46C4⋊#168—41no—
47#3935—41no—
48C4×#168—41no—
49#2546D511yescharacteristic
50#1467—51no—
51#1461—51no—
52#1319—54no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—24no—
56C2×C5×Q8—41no—
57C2×C5×Q8—42no—
58C2×C5×Q8—42no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C5×C4⋊C4—24no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—44no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—44no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—42no—
84C2×#168—42no—
85C2×#168—42no—
86C2×C4⋊Q8Dic511yescharacteristic
87C2×C4⋊Q8Dic512yes—
88C2×C4×Q8C2×D511yescharacteristic
89#432—101no—
90#431—101no—
91#398—21no—
92#398—21no—
93#391C2×D512yes—
94#389—21no—
95#389—21no—
96C4×C4⋊C4Dic511yescharacteristic
97#324—52no—
98#324—52no—
99#324—101no—
100#324—101no—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×Q8—44no—
103C5×Q8—84no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—22no—
109C2×C4×C5—24no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5#9911yescharacteristic
125C2×C4×C5#9911yescharacteristic
126C2×C4×C5#10012yes—
127C2×C4×C5#13112yes—
128#168—82no—
129#168—82no—
130C22×Q8C2×Dic512yes—
131C22×Q8C2×Dic511yescharacteristic
132C4⋊Q8—41no—
133C4⋊Q8—41no—
134C4⋊Q8—44no—
135C4×Q8—41no—
136C4×Q8—41no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4C22⋊D511yescharacteristic
143C2×C4⋊C4C22⋊D511yescharacteristic
144C2×C4⋊C4C22×D511yescharacteristic
145C2×C42C2×Dic511yescharacteristic
146C2×C42C2×Dic512yes—
147C2×C42C22⋊D511yescharacteristic
148C2×C42C22⋊D511yescharacteristic
149C4⋊C8—201no—
150C4⋊C8—201no—
151C22⋊C8—102no—
152C22⋊C8—102no—
153#97—201no—
154C4×C8—201no—
155#95—21no—
156#95—22no—
157#95—22no—
158C22×C5—21no—
159C22×C5—21no—
160C22×C5#40811yescharacteristic
161C22×C5C2×#9911yescharacteristic
162C22×C5C2×#10011yescharacteristic
163C4×C5—21no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—44no—
167C4×C5—41no—
168C4×C5—41no—
169C4×C5—41no—
170C4×C5—41no—
171C4×C5—82no—
172C4×C5#35612yes—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—24no—
176C2×Q8—41no—
177C2×Q8—42no—
178C2×Q8—42no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic511yescharacteristic
182C22×C4C22⋊Dic511yescharacteristic
183C22×C4C22⋊Dic511yescharacteristic
184C22×C4C22⋊Dic511yescharacteristic
185C22×C4C22×Dic511yescharacteristic
186C22×C4C2×C22⋊D511yescharacteristic
187C22×C4C2×C22⋊D511yescharacteristic
188C2×C8—202no—
189C2×C8—202no—
190C4⋊C4—24no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—44no—
195C4⋊C4—42no—
196C4⋊C4—44no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—42no—
206C2×C5—21no—
207C2×C5—21no—
208C2×C5#147111yescharacteristic
209C2×C5#212911yescharacteristic
210C2×C5C2×#35611yescharacteristic
211C23C2×C22⋊Dic511yescharacteristic
212Q8—44no—
213Q8—84no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4#396512yes—
235C2×C4#396611yescharacteristic
236C2×C4#396611yescharacteristic
237C2×C4#409412yes—
238C8—402no—
239C8—402no—
240C5#1156811yescharacteristic, complemented, Sylow
241C22—21no—
242C22—21no—
243C22C2×#396511yescharacteristic
244C22C2×#396611yescharacteristic
245C22#6552311yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—44no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—82no—
255C4#6476812yes—
256C2—21no—
257C2—21no—
258C2#1060246911yescharacteristic
259C2C2×#6476811yescharacteristic
260C2#1060266411yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2546C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2546D5
hypocenterC5#11568
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
240. C5#11568semidirect

Maximal subgroups

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

subgroupindex
C5×#25462
#106024182
#106024172
#105981342
#115685