Finite Group Databasebeta

← #11992749

Subgroups — #11992749

Order 1280.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#10613960C211yesmaximal, characteristic
2C5×#1458C211yesmaximal, characteristic
3#10602364C211yesmaximal, characteristic
4#10598228C212yesmaximal, complemented
5#10598227C212yesmaximal, complemented
6C2×C5×#117C2211yescharacteristic
7C5×#431C2212yes—
8C4×C22⋊Dic5C411yescharacteristic
9C4×C22⋊Dic5C411yescharacteristic
10#65270—21no—
11#65270—21no—
12#65240—21no—
13#65240—21no—
14C4×C4⋊Dic5C411yescharacteristic
15C4×C4⋊Dic5C411yescharacteristic
16#65221C2211yescharacteristic
17C42×Dic5C2211yescharacteristic
18#65214C2212yes—
19C5×#324—21no—
20C5×#323—21no—
21#64748—21no—
22#64745—21no—
23#8732—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C5×#117—22no—
26C5×#117—22no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5C2311yescharacteristic
33C2×C22⋊Dic5—21no—
34C2×C22⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4×Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5C2×C411yescharacteristic
43C5×C4⋊C8—22no—
44C5×C22⋊C8—22no—
45C4×C5×C8—22no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52C22⋊#168—22no—
53C4⋊#168—22no—
54C4×#168—22no—
55#2298—51no—
56#1458—51no—
57#1458D511yescharacteristic
58#1276—52no—
59#1274—52no—
60C24×C5C22⋊C411yescharacteristic
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×Dic5—21no—
72C22×Dic5—21no—
73C22×Dic5—21no—
74C22×Dic5—21no—
75C2×C5×C8—42no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C5×C22⋊C4—22no—
79C5×C22⋊C4—22no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5#4112yes—
83C42×C5#4112yes—
84C22⋊Dic5—42no—
85C22⋊Dic5—42no—
86C4⋊Dic5—42no—
87C4⋊Dic5—42no—
88C4×Dic5—22no—
89C4×Dic5—22no—
90C4×Dic5—22no—
91C4×Dic5—22no—
92C4×Dic5—42no—
93C4×Dic5—42no—
94C2×#168—42no—
95C2×#117C2×D511yescharacteristic
96#431—52no—
97#431C2×D512yes—
98#388—101no—
99#388—101no—
100#387—101no—
101#387—101no—
102C4×C4⋊C4—51no—
103C4×C4⋊C4—51no—
104C4×C22⋊C4—51no—
105C4×C22⋊C4—51no—
106#376—51no—
107C43—51no—
108#324—21no—
109#324—101no—
110#323—21no—
111#323—101no—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5C2×C22⋊C411yescharacteristic
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5#11711yescharacteristic
130C2×C4×C5#11711yescharacteristic
131C2×C4×C5#12312yes—
132C2×C4×C5#12312yes—
133C2×C4×C5#13112yes—
134C2×C4×C5#13112yes—
135C2×Dic5—22no—
136C2×Dic5—22no—
137C2×Dic5—41no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C5×C8—82no—
148#168—82no—
149C23×C4C4×D511yescharacteristic
150#117—22no—
151#117—22no—
152C2×C4⋊C4—101no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4D2011yescharacteristic
155C2×C4⋊C4C22⋊D511yescharacteristic
156C2×C22⋊C4—101no—
157C2×C22⋊C4—101no—
158C2×C22⋊C4D2011yescharacteristic
159C2×C22⋊C4C22⋊D511yescharacteristic
160C2×C42—51no—
161C2×C42—51no—
162C2×C42—51no—
163C2×C42—51no—
164C2×C42—101no—
165C2×C42—101no—
166C2×C42C4×D511yescharacteristic
167C2×C42C22×D511yescharacteristic
168C4⋊C8—22no—
169C4⋊C8—102no—
170C22⋊C8—22no—
171C22⋊C8—102no—
172C4×C8—22no—
173C4×C8—102no—
174#95—101no—
175#95—101no—
176#95—101no—
177#95—101no—
178#95—101no—
179#95—101no—
180C22×C5—21no—
181C22×C5—21no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—41no—
185C22×C5—81no—
186C22×C5—81no—
187C22×C5#38111yescharacteristic
188C22×C5#40811yescharacteristic
189C22×C5#40811yescharacteristic
190C4×C5—22no—
191C4×C5—22no—
192C4×C5—41no—
193C4×C5—41no—
194C4×C5—41no—
195C4×C5#43312yes—
196C4×C5#43312yes—
197Dic5—42no—
198Dic5—42no—
199Dic5—81no—
200Dic5—81no—
201C24#68511yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—101no—
207C22×C4—101no—
208C22×C4—101no—
209C22×C4—101no—
210C22×C4#68511yescharacteristic
211C22×C4#68511yescharacteristic
212C22×C4#68511yescharacteristic
213C22×C4C2×C4×D511yescharacteristic
214C22×C4C2×D2011yescharacteristic
215C22×C4C2×C22⋊D511yescharacteristic
216C2×C8—42no—
217C2×C8—202no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—202no—
221C4⋊C4—202no—
222C22⋊C4—22no—
223C22⋊C4—22no—
224C22⋊C4—202no—
225C22⋊C4—202no—
226C42—21no—
227C42—21no—
228C42—102no—
229C42—102no—
230C42—102no—
231C42—102no—
232C42—202no—
233C42—202no—
234C42#71112yes—
235C42#71112yes—
236C2×C5—21no—
237C2×C5—21no—
238C2×C5—81no—
239C2×C5#181811yescharacteristic
240C2×C5#182711yescharacteristic
241C2×C5#182711yescharacteristic
242C23—21no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23C2×#68511yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—102no—
260C2×C4—102no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4—201no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—201no—
270C2×C4—201no—
271C2×C4#402311yescharacteristic
272C2×C4#402311yescharacteristic
273C2×C4#403212yes—
274C2×C4#404712yes—
275C2×C4#405312yes—
276C2×C4#408112yes—
277C8—82no—
278C8—402no—
279C5#873211yescharacteristic, complemented, Sylow
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#6523211yescharacteristic
288C22#6539911yescharacteristic
289C22#6541811yescharacteristic
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—202no—
296C4—202no—
297C4—401no—
298C4—401no—
299C4#6500912yes—
300C4#6500912yes—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#1060070411yescharacteristic
305C2#1060083211yescharacteristic
306C2#1060092411yescharacteristic
subgroupG/H
centerC2×C4#4023
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1458C2
socleC22×C5#381
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1458D5
hypocenterC5#8732
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
4. #10598228C2semidirect
5. #10598227C2semidirect
279. C5#8732semidirect

Maximal subgroups

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

subgroupindex
#106139602
C5×#14582
#106023642
#105982282
#105982272
#87325