Finite Group Databasebeta

← #11994332

Subgroups — #11994332

Order 1280.

572 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#65275C211yesmaximal, characteristic
2#10613886C211yesmaximal, characteristic
3C2×C5×#324C211yesmaximal, characteristic
4#10600718C212yesmaximal
5#10598166C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic5C2211yescharacteristic
8C2×C5×C22⋊C8C2212yes—
9#65501C2212yes—
10#65500—21no—
11C4×C22⋊Dic5—21no—
12C2×#3963—21no—
13C2×#3963—21no—
14C2×#3963C2211yescharacteristic
15#65275—22no—
16#65275C414yescomplemented
17#65270—24no—
18C5×#324—22no—
19#64771—24no—
20#9022—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C22×C5×C8—22no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4C2×C412yes—
30C2×C5×C4⋊C4D412yes—
31C2×C22⋊Dic5—22no—
32C2×C4⋊Dic5—22no—
33C2×C4⋊Dic5—22no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5C2×C412yes—
36C2×C4⋊Dic5D414yes—
37C2×C4×Dic5—22no—
38C5×C22⋊C8—22no—
39C5×C22⋊C8—22no—
40#3963—22no—
41#3963—24no—
42#3963—24no—
43#3963—24no—
44#3963—21no—
45#3963—22no—
46#3963C2×C412yes—
47C2×#400—51no—
48#2313—51no—
49#1824—52no—
50C2×#324D511yescharacteristic
51#1294—52no—
52C24×C5C2×D411yescharacteristic
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—21no—
59C22×C4×C5—42no—
60C22×C4×C5—42no—
61C22×C4×C5C22⋊C412yes—
62C22×C4×C5C22⋊C412yes—
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D412yes—
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5#4112yes—
67C22×Dic5—22no—
68C22×Dic5—22no—
69C22×Dic5—24no—
70C22×Dic5—42no—
71C22×Dic5—42no—
72C22×Dic5—44no—
73C22×Dic5—41no—
74C22×Dic5—41no—
75C22×Dic5—42no—
76C2×C5×C8—44no—
77C2×C5×C8—42no—
78C5×C4⋊C4—24no—
79C5×C4⋊C4—24no—
80C22⋊Dic5—42no—
81C22⋊Dic5—42no—
82C4⋊Dic5—24no—
83C4⋊Dic5—42no—
84C4⋊Dic5—44no—
85C4×Dic5—82no—
86C22×C4⋊C4—51no—
87C22×C4⋊C4C2×D511yescharacteristic
88C2×C22⋊C8C2×D512yes—
89#400—54no—
90#400—102no—
91#387—104no—
92#381—101no—
93#380—52no—
94C4×C22⋊C4—101no—
95C2×#95—51no—
96C2×#95—101no—
97C2×#95—101no—
98#340—104no—
99#324—22no—
100C23×C5—22no—
101C23×C5—22no—
102C23×C5C2×C22⋊C411yescharacteristic
103C23×C5#12011yescharacteristic
104C23×C5#12311yescharacteristic
105C23×C5#13512yes—
106C23×C5#13712yes—
107C2×C4×C5—24no—
108C2×C4×C5—22no—
109C2×C4×C5—22no—
110C2×C4×C5—22no—
111C2×C4×C5—22no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5—81no—
120C2×C4×C5C4×D412yes—
121C2×C4×C5#12112yes—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—44no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—44no—
128C2×Dic5—44no—
129C2×Dic5—44no—
130C2×Dic5—84no—
131C2×Dic5—82no—
132C2×Dic5—82no—
133C5×C8—82no—
134C23×C4—101no—
135C23×C4—101no—
136C23×C4D2011yescharacteristic
137C23×C4D2011yescharacteristic
138C23×C4C22×D511yescharacteristic
139C22×C8—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—52no—
143C2×C4⋊C4—54no—
144C2×C4⋊C4—102no—
145C2×C4⋊C4—102no—
146C2×C4⋊C4—101no—
147C2×C4⋊C4C4×D512yes—
148C2×C4⋊C4C22⋊D512yes—
149C2×C22⋊C4—102no—
150C2×C42—102no—
151C22⋊C8—22no—
152C22⋊C8—22no—
153#95—52no—
154#95—102no—
155#95—104no—
156#95—104no—
157#95—104no—
158#95—102no—
159#95—101no—
160C22×C5—24no—
161C22×C5—24no—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5—21no—
165C22×C5—21no—
166C22×C5#38611yescharacteristic
167C22×C5#41611yescharacteristic
168C22×C5#41911yescharacteristic
169C22×C5#45212yes—
170C22×C5#45412yes—
171C22×C5#45812yes—
172C22×C5#48512yes—
173C4×C5—22no—
174C4×C5—22no—
175C4×C5—42no—
176C4×C5—42no—
177Dic5—82no—
178Dic5—84no—
179Dic5—82no—
180C24C2×D2011yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—104no—
190C22×C4—102no—
191C22×C4—102no—
192C22×C4—202no—
193C22×C4—202no—
194C22×C4—204no—
195C22×C4—201no—
196C22×C4—201no—
197C22×C4—202no—
198C22×C4#68512yes—
199C22×C4#68512yes—
200C22×C4C2×C4×D511yescharacteristic
201C22×C4D4×D512yes—
202C22×C4#71112yes—
203C22×C4C2×C22⋊D511yescharacteristic
204C2×C8—44no—
205C2×C8—42no—
206C4⋊C4—24no—
207C4⋊C4—24no—
208C4⋊C4—104no—
209C4⋊C4—204no—
210C4⋊C4—202no—
211C22⋊C4—202no—
212C22⋊C4—202no—
213C42—402no—
214C2×C5—21no—
215C2×C5—21no—
216C2×C5—22no—
217C2×C5#161514yes—
218C2×C5#187311yescharacteristic
219C2×C5#188811yescharacteristic
220C2×C5#189011yescharacteristic
221C23—22no—
222C23—22no—
223C23#402811yescharacteristic
224C23#403211yescharacteristic
225C23#405012yes—
226C23#405512yes—
227C23C2×#68511yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—202no—
242C2×C4—202no—
243C2×C4—204no—
244C2×C4—204no—
245C2×C4—204no—
246C2×C4—202no—
247C2×C4—202no—
248C2×C4—204no—
249C2×C4—404no—
250C2×C4—402no—
251C2×C4—402no—
252C2×C4#402712yes—
253C2×C4#408512yes—
254C8—82no—
255C5#902211yescharacteristic, complemented, Sylow
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#6501212yes—
263C22#6502212yes—
264C22#6503112yes—
265C22#6504212yes—
266C22#6524711yescharacteristic
267C22#6540211yescharacteristic
268C22#6540911yescharacteristic
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—402no—
274C4—404no—
275C4—402no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#1059892914yes—
280C2#1060072411yescharacteristic
281C2#1060081611yescharacteristic
282C2#1060089711yescharacteristic
subgroupG/H
centerC23#4028
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#324C2
socleC23×C5#120
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#324D5
hypocenterC5#9022
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
16. #65275C4semidirect
255. C5#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#652752
#106138862
C2×C5×#3242
#106007182
#105981662
#90225