Finite Group Databasebeta

← #12008954

Subgroups — #12008954

Order 1280.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#10614208C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10597944C212yesmaximal
5#10597943C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4016C411yescharacteristic
8C5×#431—21no—
9#65519C411yescharacteristic
10#65519C411yescharacteristic
11#65273—21no—
12#65273—21no—
13#65266C2211yescharacteristic
14#65265C2211yescharacteristic
15C4×C4⋊Dic5C411yescharacteristic
16#65222—21no—
17#65222—21no—
18#65215—21no—
19C5×#324—21no—
20C5×#324C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11571—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4C2311yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×#683—21no—
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42#4016—41no—
43#4016—41no—
44C5×C4⋊C8—41no—
45C5×C22⋊C8—22no—
46C4×C5×C8—41no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54C22⋊#168—22no—
55C4⋊#168—41no—
56#3935—41no—
57#2565—51no—
58#1467—51no—
59#1461D511yescharacteristic
60#1325—52no—
61#1324—52no—
62C2×C5×Q8—22no—
63C2×C5×Q8—22no—
64C2×C5×Q8—41no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×Dic5—21no—
73C22×Dic5—21no—
74C22×Dic5—21no—
75C22×Dic5—21no—
76C2×C5×C8—42no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—21no—
86C4⋊Dic5—42no—
87C4⋊Dic5—41no—
88C4⋊Dic5—41no—
89#683—42no—
90#683—42no—
91#683—42no—
92#683—41no—
93#683—41no—
94C4×Dic5—22no—
95C4×Dic5—22no—
96C2×#168—42no—
97C2×#125—51no—
98C2×C4×Q8C2×D511yescharacteristic
99#432—101no—
100#431—21no—
101#398—101no—
102#398—101no—
103#391—51no—
104#391—51no—
105#387—101no—
106#387—101no—
107#384—51no—
108#382—51no—
109C4×C4⋊C4—51no—
110#324—21no—
111#324—52no—
112#324—101no—
113#324C2×D512yes—
114C23×C5C2×C22⋊C411yescharacteristic
115C5×Q8—44no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#9911yescharacteristic
132C2×C4×C5#10112yes—
133C2×C4×C5#13112yes—
134C2×Dic5—22no—
135C2×Dic5—41no—
136C2×Dic5—41no—
137C2×Dic5—41no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—42no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C5×C8—82no—
146#168—82no—
147C22×Q8C4×D511yescharacteristic
148#125—201no—
149#125—201no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—51no—
153C2×C4⋊C4—51no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4—101no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4D2011yescharacteristic
160C2×C4⋊C4C22⋊D511yescharacteristic
161C2×C4⋊C4C22×D511yescharacteristic
162C2×C42—51no—
163C2×C42—51no—
164C2×C42C4×D511yescharacteristic
165C2×C42D2011yescharacteristic
166C2×C42C22⋊D511yescharacteristic
167C4⋊C8—41no—
168C4⋊C8—201no—
169C22⋊C8—22no—
170C22⋊C8—102no—
171#97—201no—
172C4×C8—41no—
173#95—101no—
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#40811yescharacteristic
183C22×C5C2×#9911yescharacteristic
184C22×C5C2×#10111yescharacteristic
185C4×C5—21no—
186C4×C5—21no—
187C4×C5—22no—
188C4×C5—22no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193Dic5—42no—
194Dic5—81no—
195Dic5—81no—
196Dic5—81no—
197C2×Q8—22no—
198C2×Q8—22no—
199C2×Q8—41no—
200C22×C4—101no—
201C22×C4—101no—
202C22×C4—101no—
203C22×C4—101no—
204C22×C4#68511yescharacteristic
205C22×C4#68511yescharacteristic
206C22×C4#68511yescharacteristic
207C22×C4#68511yescharacteristic
208C22×C4C2×C4×D511yescharacteristic
209C22×C4C2×D2011yescharacteristic
210C22×C4C2×C22⋊D511yescharacteristic
211C2×C8—42no—
212C2×C8—202no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—201no—
217C4⋊C4—201no—
218C4⋊C4—202no—
219C4⋊C4—202no—
220C4⋊C4—202no—
221C4⋊C4—202no—
222C4⋊C4—201no—
223C4⋊C4—201no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—102no—
231C42—102no—
232C2×C5—21no—
233C2×C5—21no—
234C2×C5#147211yescharacteristic
235C2×C5#212611yescharacteristic
236C2×C5#213311yescharacteristic
237C23C2×#68511yescharacteristic
238Q8—44no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—102no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—202no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4#393811yescharacteristic
265C2×C4#393811yescharacteristic
266C2×C4#395612yes—
267C2×C4#404712yes—
268C8—82no—
269C8—402no—
270C5#1157111yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22C2×#393811yescharacteristic
274C22#6539911yescharacteristic
275C22C2×#395611yescharacteristic
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—202no—
285C4—401no—
286C4—401no—
287C4—401no—
288C2—21no—
289C2—21no—
290C2#1060071611yescharacteristic
291C2#1060085311yescharacteristic
292C2#1060092111yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1461C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1461D5
hypocenterC5#11571
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
270. C5#11571semidirect

Maximal subgroups

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

subgroupindex
#106142082
C5×#14612
#106024182
#105979442
#105979432
#115715