Finite Group Databasebeta

← #11987626

Subgroups — #11987626

Order 1280.

456 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 119 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#10608212C211yesmaximal, characteristic
2#10599398C212yesmaximal
3C5×#1272C211yesmaximal, characteristic
4#10598133C211yesmaximal, characteristic
5#10597971C212yesmaximal
6C2×Q8×Dic5C411yescharacteristic
7C2×#4090C411yescharacteristic
8C2×#4033C411yescharacteristic
9C5×#391C2211yescharacteristic
10C2×#3946—22no—
11#65265C411yescharacteristic
12C42×Dic5C2211yescharacteristic
13#65218C2211yescharacteristic
14#64938—22no—
15#64936—22no—
16C5×#336C2212yes—
17#64770—22no—
18#64744C2212yes—
19#7653—51nomaximal, Sylow
20C22×C5×Q8C2×C411yescharacteristic
21C22×Dic10C2×C411yescharacteristic
22C22×C5×C8—22no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C42×C5C2311yescharacteristic
25Q8×Dic5—42no—
26#4090—22no—
27#4090—22no—
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5C2×C411yescharacteristic
30C2×#683—22no—
31C2×#683—21no—
32C2×#683—22no—
33C2×C4×Dic5—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5C2×C411yescharacteristic
37C2×C4×Dic5D412yes—
38C2×C4×Dic5D412yes—
39C22×#168—22no—
40#4033—42no—
41C5×#95—22no—
42#3963—22no—
43#3946—44no—
44C4×C4⋊Q8—51no—
45#1831—52no—
46#1272—51no—
47#1272—52no—
48#1272D511yescharacteristic
49C2×C5×Q8—21no—
50C2×C5×Q8—41no—
51C2×C5×Q8—41no—
52C2×C5×Q8M1612yes—
53C22×C4×C5—21no—
54C22×C4×C5—21no—
55C22×C4×C5C22×C411yescharacteristic
56C22×C4×C5C2×D412yes—
57C22×Dic5—21no—
58C22×Dic5—21no—
59C22×Dic5C22⋊C411yescharacteristic
60C22×Dic5C22⋊C412yes—
61C22×Dic5C22⋊C411yescharacteristic
62C2×Dic10—21no—
63C2×Dic10—41no—
64C2×Dic10—41no—
65C2×Dic10M1612yes—
66C2×C5×C8—42no—
67C2×C5×C8—42no—
68C2×C5×C8—42no—
69C5×C4⋊C4—41no—
70C42×C5—41no—
71C4⋊Dic5—42no—
72C4⋊Dic5—41no—
73#683—28no—
74#683—42no—
75#683—44no—
76C4×Dic5—21no—
77C4×Dic5—21no—
78C4×Dic5—22no—
79C4×Dic5—42no—
80C4×Dic5—42no—
81C4×Dic5—42no—
82C4×Dic5SD1614yes—
83C4×Dic5Q1614yes—
84C2×#168—42no—
85C2×#168—42no—
86C2×#168—42no—
87C2×C4⋊Q8—51no—
88C2×C4×Q8—51no—
89C2×C4×Q8—51no—
90C2×C4⋊C8—102no—
91#391—51no—
92#391C2×D511yescharacteristic
93#389—102no—
94#384—51no—
95C4×C4⋊C4—102no—
96C43—51no—
97#336—52no—
98#336—102no—
99#336C2×D512yes—
100C23×C5C2×C22⋊C411yescharacteristic
101C5×Q8—42no—
102C5×Q8—42no—
103C2×C4×C5—22no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×C4×C5—41no—
111C2×C4×C5—42no—
112C2×C4×C5C2×M1611yescharacteristic
113C2×C4×C5C2×M1611yescharacteristic
114C2×C4×C5C2×SD1612yes—
115C2×C4×C5C2×Q1612yes—
116C2×Dic5—22no—
117C2×Dic5—22no—
118C2×Dic5—22no—
119C2×Dic5—21no—
120C2×Dic5—22no—
121C2×Dic5—41no—
122C2×Dic5—41no—
123C2×Dic5—41no—
124C2×Dic5—42no—
125C2×Dic5#10012yes—
126C2×Dic5#10314yes—
127C2×Dic5#10314yes—
128Dic10—42no—
129Dic10—42no—
130C5×C8—82no—
131#168—82no—
132C22×Q8—51no—
133C22×Q8C4×D511yescharacteristic
134C22×C8—22no—
135C22×C8—102no—
136C4⋊Q8—102no—
137C4⋊Q8—102no—
138C4×Q8—202no—
139C4×Q8—202no—
140C2×C4⋊C4—51no—
141C2×C4⋊C4—102no—
142C2×C4⋊C4—101no—
143C2×C4⋊C4—101no—
144C2×C4⋊C4—102no—
145C2×C4⋊C4C4×D511yescharacteristic
146C2×C42—52no—
147C2×C42—51no—
148C2×C42—51no—
149C2×C42—52no—
150C2×C42—101no—
151C2×C42—101no—
152C2×C42C22×D511yescharacteristic
153C4⋊C8—204no—
154#95—22no—
155#95—102no—
156C22×C5#40711yescharacteristic
157C22×C5#41011yescharacteristic
158C22×C5C2×#10011yescharacteristic
159C22×C5C2×#10312yes—
160C22×C5#42112yes—
161C4×C5—21no—
162C4×C5—21no—
163C4×C5—22no—
164C4×C5—22no—
165C4×C5—42no—
166C4×C5—81no—
167Dic5—24no—
168Dic5—41no—
169Dic5—42no—
170Dic5—81no—
171Dic5#33314yes—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—52no—
176C2×Q8—101no—
177C2×Q8—201no—
178C2×Q8—201no—
179C2×Q8#67612yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—51no—
183C22×C4—52no—
184C22×C4—51no—
185C22×C4—101no—
186C22×C4—101no—
187C22×C4C2×C4×D511yescharacteristic
188C22×C4D4×D512yes—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—202no—
193C2×C8—202no—
194C2×C8—202no—
195C4⋊C4—41no—
196C4⋊C4—108no—
197C4⋊C4—201no—
198C4⋊C4—202no—
199C4⋊C4—202no—
200C4⋊C4—204no—
201C42—41no—
202C42—54no—
203C42—54no—
204C42—102no—
205C42—101no—
206C42—101no—
207C42—202no—
208C42—202no—
209C42—202no—
210C2×C5#146611yescharacteristic
211C2×C5#148712yes—
212C2×C5#151812yes—
213C2×C5#153611yescharacteristic
214C2×C5C2×#33311yescharacteristic
215C23D5×C22⋊C411yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—202no—
219Q8—202no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—52no—
230C2×C4—54no—
231C2×C4—54no—
232C2×C4—102no—
233C2×C4—102no—
234C2×C4—101no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—201no—
238C2×C4—201no—
239C2×C4—201no—
240C2×C4—202no—
241C2×C4C2×#67611yescharacteristic
242C2×C4D5×M1611yescharacteristic
243C2×C4D5×SD1612yes—
244C2×C4D5×Q1612yes—
245C8—82no—
246C8—402no—
247C5#765311yescharacteristic, complemented, Sylow
248C22#6501511yescharacteristic
249C22#6502911yescharacteristic
250C22D5×#10011yescharacteristic
251C22D5×#10312yes—
252C22#6511012yes—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—54no—
259C4—81no—
260C4—104no—
261C4—201no—
262C4—202no—
263C4—401no—
264C2#1059889611yescharacteristic
265C2#1059902912yes—
266C2#1059910712yes—
267C2#1059914211yescharacteristic
268C2D5×#33311yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1272C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1272D5
hypocenterC5#7653
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
247. C5#7653semidirect

Maximal subgroups

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

subgroupindex
#106082122
#105993982
C5×#12722
#105981332
#105979712
#76535