Finite Group Databasebeta

← #12008780

Subgroups — #12008780

Order 1280.

412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C4×C5×C4⋊Q8C211yesmaximal, characteristic
2#10602418C212yesmaximal
3#10598134C212yesmaximal
4#10598126C212yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#391C411yescharacteristic
9C5×#391C2211yescharacteristic
10C5×#389—22no—
11C5×#384C2211yescharacteristic
12C4×C5×C4⋊C4—22no—
13C43×C5C411yescharacteristic
14#65215—22no—
15#64748—22no—
16#64748C2214yes—
17#11532—51nomaximal, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×C5×Q8C2×C411yescharacteristic
20C5×C4⋊Q8—22no—
21C5×C4⋊Q8—22no—
22C4×C5×Q8—41no—
23C4×C5×Q8—41no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4C2311yescharacteristic
32C2×C42×C5—21no—
33C2×C42×C5—21no—
34C2×C42×C5—21no—
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D412yes—
39C5×#95—22no—
40C5×#95—22no—
41C22⋊#168—24no—
42C4⋊#168—42no—
43#3935—42no—
44C4×C4⋊Q8D511yescharacteristic
45#1467—52no—
46#1325—52no—
47#1319—52no—
48C2×C5×Q8—21no—
49C2×C5×Q8—21no—
50C2×C5×Q8—21no—
51C2×C5×Q8—41no—
52C2×C5×Q8—41no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8M1612yes—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5C22⋊C412yes—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D412yes—
65C5×C4⋊C4—28no—
66C5×C4⋊C4—42no—
67C5×C4⋊C4—41no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—44no—
70C5×C4⋊C4—42no—
71C42×C5—24no—
72C42×C5—21no—
73C42×C5—21no—
74C42×C5—22no—
75C42×C5—22no—
76C42×C5—21no—
77C42×C5—41no—
78C42×C5—42no—
79C42×C5—41no—
80C42×C5—41no—
81C42×C5M1612yes—
82C2×#168—44no—
83C2×C4⋊Q8Dic511yescharacteristic
84C2×C4×Q8Dic511yescharacteristic
85C2×C4×Q8C2×D511yescharacteristic
86#432—102no—
87#391Dic511yescharacteristic
88#391C2×D511yescharacteristic
89#389—22no—
90#384C2×D511yescharacteristic
91C4×C4⋊C4—22no—
92C43Dic511yescharacteristic
93#324—54no—
94#324—102no—
95C23×C5C2×C22⋊C411yescharacteristic
96C5×Q8—42no—
97C5×Q8—42no—
98C5×Q8—42no—
99C5×Q8—42no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5—22no—
110C2×C4×C5—21no—
111C2×C4×C5—22no—
112C2×C4×C5—22no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—41no—
121C2×C4×C5#9911yescharacteristic
122C2×C4×C5#9911yescharacteristic
123C2×C4×C5C2×M1611yescharacteristic
124C2×C4×C5C2×M1611yescharacteristic
125#168—84no—
126C22×Q8C2×Dic511yescharacteristic
127C22×Q8C2×Dic511yescharacteristic
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C2×Dic511yescharacteristic
138C2×C4⋊C4C22⋊D512yes—
139C2×C4⋊C4C22×D511yescharacteristic
140C2×C42—21no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42C2×Dic511yescharacteristic
144C2×C42C2×Dic511yescharacteristic
145C2×C42C2×Dic511yescharacteristic
146C2×C42C22⋊D512yes—
147C4⋊C8—202no—
148C22⋊C8—104no—
149#97—202no—
150#95—22no—
151#95—22no—
152C22×C5—21no—
153C22×C5—21no—
154C22×C5#40711yescharacteristic
155C22×C5C2×#9911yescharacteristic
156C22×C5#41311yescharacteristic
157C4×C5—24no—
158C4×C5—21no—
159C4×C5—21no—
160C4×C5—21no—
161C4×C5—42no—
162C4×C5—42no—
163C4×C5—41no—
164C4×C5—42no—
165C4×C5—42no—
166C4×C5—81no—
167C4×C5#35612yes—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8#68112yes—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4C22⋊Dic512yes—
181C22×C4C22⋊Dic511yescharacteristic
182C22×C4C22⋊Dic511yescharacteristic
183C22×C4C22×Dic511yescharacteristic
184C22×C4C2×C22⋊D512yes—
185C2×C8—204no—
186C4⋊C4—28no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C42—24no—
193C42—22no—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—41no—
199C42—42no—
200C42—41no—
201C42—41no—
202C42#68112yes—
203C2×C5—21no—
204C2×C5—21no—
205C2×C5#146511yescharacteristic
206C2×C5#212611yescharacteristic
207C2×C5C2×#35611yescharacteristic
208C23C2×C22⋊Dic511yescharacteristic
209Q8—42no—
210Q8—42no—
211Q8—42no—
212Q8—42no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4#396611yescharacteristic
235C2×C4#396611yescharacteristic
236C2×C4C2×#68111yescharacteristic
237C2×C4C2×#68111yescharacteristic
238C8—404no—
239C5#1153211yescharacteristic, complemented, Sylow
240C22—21no—
241C22—21no—
242C22#6549611yescharacteristic
243C22C2×#396611yescharacteristic
244C22#6552611yescharacteristic
245C4—24no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—42no—
254C4—81no—
255C4#6476812yes—
256C2—21no—
257C2—21no—
258C2#1060239511yescharacteristic
259C2C2×#6476811yescharacteristic
260C2#1060261211yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC4×C5×C4⋊Q8C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenterC4×C4⋊Q8D5
hypocenterC5#11532
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
239. C5#11532semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C4⋊Q82
#106024182
#105981342
#105981262
#115325