Finite Group Databasebeta

← #11987612

Subgroups — #11987612

Order 1280.

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

normal subgroups only

This group has 468 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
1#10608023C211yesmaximal, characteristic
2#10599400C212yesmaximal, complemented
3C5×#1270C211yesmaximal, characteristic
4#10598130C211yesmaximal, characteristic
5#10597971C212yesmaximal, complemented
6C2×#4082C411yescharacteristic
7C2×D4×Dic5C411yescharacteristic
8C2×#4033C411yescharacteristic
9C5×#390C2211yescharacteristic
10#65266C411yescharacteristic
11#65233—22no—
12C22⋊C4×Dic5—22no—
13C42×Dic5C2211yescharacteristic
14#65218C2211yescharacteristic
15C5×#336C2212yes—
16#64770—22no—
17#64770—22no—
18#64744C2212yes—
19#7649—51nomaximal, Sylow
20C22×C5×D4C2×C411yescharacteristic
21C23×Dic5—21no—
22C22×Dic10C2×C411yescharacteristic
23C22×C5×C8—22no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C5×C22⋊C4—22no—
26C2×C42×C5C2311yescharacteristic
27C2×C22⋊Dic5—22no—
28C2×C22⋊Dic5—21no—
29#4082—22no—
30#4082—22no—
31D4×Dic5—42no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—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—
41#3963—22no—
42#3963—22no—
43C4×#124—51no—
44#1839—52no—
45#1272—52no—
46#1270—51no—
47#1270D511yescharacteristic
48C24×C5—21no—
49C2×C5×D4—21no—
50C2×C5×D4—41no—
51C2×C5×D4—41no—
52C2×C5×D4M1612yes—
53C22×C4×C5—21no—
54C22×C4×C5C22×C411yescharacteristic
55C22×C4×C5C2×D412yes—
56C22×Dic5—21no—
57C22×Dic5—21no—
58C22×Dic5—44no—
59C22×Dic5—42no—
60C22×Dic5C22⋊C412yes—
61C22×Dic5C22⋊C411yescharacteristic
62C22×Dic5C22⋊C411yescharacteristic
63C2×Dic10—21no—
64C2×Dic10—41no—
65C2×Dic10—41no—
66C2×Dic10M1612yes—
67C2×C5×C8—42no—
68C2×C5×C8—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—41no—
71C5×C22⋊C4—42no—
72C5×C22⋊C4—42no—
73C42×C5—41no—
74C22⋊Dic5—28no—
75C22⋊Dic5—42no—
76C4⋊Dic5—41no—
77#683—42no—
78C4×Dic5—21no—
79C4×Dic5—21no—
80C4×Dic5—22no—
81C4×Dic5—22no—
82C4×Dic5—22no—
83C4×Dic5—42no—
84C4×Dic5—42no—
85C2×#168—42no—
86C2×#168—42no—
87C2×#168—42no—
88C2×#124—51no—
89C2×C4×Q8—51no—
90C2×C4×D4—51no—
91#391—51no—
92#390C2×D511yescharacteristic
93#388—102no—
94#382—51no—
95C4×C22⋊C4—102no—
96C43—51no—
97#336—52no—
98#336—102no—
99#336—102no—
100#336C2×D512yes—
101C23×C5—22no—
102C23×C5—41no—
103C23×C5—41no—
104C23×C5—42no—
105C23×C5—42no—
106C23×C5C2×C22⋊C411yescharacteristic
107C5×D4—42no—
108C5×D4—42no—
109C2×C4×C5—22no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—22no—
113C2×C4×C5—41no—
114C2×C4×C5—42no—
115C2×C4×C5C2×M1611yescharacteristic
116C2×C4×C5C2×M1611yescharacteristic
117C2×C4×C5#13512yes—
118C2×C4×C5#13512yes—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—22no—
122C2×Dic5—21no—
123C2×Dic5—22no—
124C2×Dic5—22no—
125C2×Dic5—22no—
126C2×Dic5—41no—
127C2×Dic5—41no—
128C2×Dic5—41no—
129C2×Dic5—42no—
130C2×Dic5—84no—
131C2×Dic5#10012yes—
132Dic10—42no—
133Dic10—42no—
134C5×C8—82no—
135#168—82no—
136C22×Q8—51no—
137C22×D4C4×D511yescharacteristic
138C23×C4—101no—
139C22×C8—22no—
140C22×C8—102no—
141#124—102no—
142#124—102no—
143C4×Q8—202no—
144C4×D4—202no—
145C2×C4⋊C4—51no—
146C2×C4⋊C4—101no—
147C2×C4⋊C4C4×D511yescharacteristic
148C2×C22⋊C4—22no—
149C2×C22⋊C4—102no—
150C2×C22⋊C4—101no—
151C2×C42—51no—
152C2×C42—51no—
153C2×C42—52no—
154C2×C42—52no—
155C2×C42—101no—
156C2×C42C22×D511yescharacteristic
157#95—102no—
158#95—102no—
159C22×C5—42no—
160C22×C5—44no—
161C22×C5—81no—
162C22×C5—82no—
163C22×C5—81no—
164C22×C5#40711yescharacteristic
165C22×C5#41011yescharacteristic
166C22×C5C2×#10011yescharacteristic
167C22×C5#41612yes—
168C22×C5#42112yes—
169C4×C5—21no—
170C4×C5—21no—
171C4×C5—22no—
172C4×C5—22no—
173C4×C5—81no—
174Dic5—22no—
175Dic5—41no—
176Dic5—42no—
177Dic5—42no—
178Dic5—81no—
179C24—21no—
180C2×Q8—52no—
181C2×Q8—101no—
182C2×Q8—201no—
183C2×Q8—201no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4#67612yes—
188C22×C4—21no—
189C22×C4—51no—
190C22×C4—52no—
191C22×C4—51no—
192C22×C4—101no—
193C22×C4—101no—
194C22×C4—202no—
195C22×C4—204no—
196C22×C4C2×C4×D511yescharacteristic
197C22×C4D4×D512yes—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—202no—
202C2×C8—202no—
203C2×C8—202no—
204C4⋊C4—41no—
205C4⋊C4—201no—
206C4⋊C4—202no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—108no—
210C22⋊C4—202no—
211C42—41no—
212C42—102no—
213C42—101no—
214C42—101no—
215C42—102no—
216C42—102no—
217C42—202no—
218C42—202no—
219C2×C5—82no—
220C2×C5#146611yescharacteristic
221C2×C5#148812yes—
222C2×C5#152112yes—
223C2×C5#153311yescharacteristic
224C2×C5#154311yescharacteristic
225C23—22no—
226C23—41no—
227C23—41no—
228C23—42no—
229C23—42no—
230C23D5×C22⋊C411yescharacteristic
231Q8—202no—
232Q8—202no—
233D4—42no—
234D4—42no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—52no—
242C2×C4—102no—
243C2×C4—101no—
244C2×C4—102no—
245C2×C4—102no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—201no—
250C2×C4—201no—
251C2×C4—201no—
252C2×C4—202no—
253C2×C4—404no—
254C2×C4C2×#67611yescharacteristic
255C2×C4D5×M1611yescharacteristic
256C2×C4#405812yes—
257C2×C4#406212yes—
258C8—82no—
259C8—402no—
260C5#764911yescharacteristic, complemented, Sylow
261C22—44no—
262C22—42no—
263C22—81no—
264C22—82no—
265C22—81no—
266C22#6501511yescharacteristic
267C22#6502911yescharacteristic
268C22D5×#10011yescharacteristic
269C22#6506112yes—
270C22#6511012yes—
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—81no—
276C4—102no—
277C4—201no—
278C4—202no—
279C4—202no—
280C4—401no—
281C2—82no—
282C2#1059889611yescharacteristic
283C2#1059896612yes—
284C2#1059907612yes—
285C2#1059914011yescharacteristic
286C2#1059917511yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1270C2
socleC23×C5C2×C22⋊C4
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenter#1270D5
hypocenterC5#7649
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #10599400C2semidirect
5. #10597971C2semidirect
260. C5#7649semidirect

Maximal subgroups

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

subgroupindex
#106080232
#105994002
C5×#12702
#105981302
#105979712
#76495