Finite Group Databasebeta

← #12009892

Subgroups — #12009892

Order 1280.

482 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 87 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#10614207C211yesmaximal, characteristic
2C5×#1467C211yesmaximal, characteristic, complemented
3C4×#3968C211yesmaximal, characteristic, complemented
4#10597947C214yesmaximal, complemented
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4093—21no—
7C2×#4020C411yescharacteristic
8C5×#432—21no—
9C2×#3968—21no—
10#65280C412yes—
11#65280C2212yes—
12#65277—21no—
13#65228—21no—
14#65228—21no—
15C4×C4⋊Dic5C411yescharacteristic
16C4×#681—21no—
17C5×#324—21no—
18C5×#324C2212yes—
19#64750C2212yes—
20#11781—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×D20—21no—
23C22×D20—21no—
24C22×D20C2×C412yes—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4C2311yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33#4093—44no—
34C2×#685—22no—
35C2×#685—22no—
36C2×#685—22no—
37C2×#685—22no—
38C2×C4⋊Dic5—21no—
39C2×C4×Dic5—21no—
40C2×#681—22no—
41#4020—41no—
42#4020—41no—
43C5×C4⋊C8—41no—
44C5×C22⋊C8—22no—
45C5×#97—41no—
46#3968—24no—
47#3963C2×C412yes—
48#3935—41no—
49C4×#168—41no—
50#2548—51no—
51C4×#101—51no—
52#1467D511yescharacteristic, complemented
53#1345—54no—
54C23×D5—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—22no—
57C2×C5×Q8—41no—
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22×C411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×Dic5—22no—
66C2×D20—42no—
67C2×D20—42no—
68C2×D20—42no—
69C2×D20—42no—
70C2×D20—42no—
71C2×D20—41no—
72C2×D20—41no—
73C2×D20—42no—
74C2×D20—82no—
75C2×C5×C8—42no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—21no—
85#685—44no—
86#685—44no—
87#685—82no—
88#685—82no—
89C4⋊Dic5—42no—
90C4×Dic5—42no—
91#681—24no—
92#681—42no—
93C2×#168—42no—
94C2×#127—51no—
95C2×#124—101no—
96C2×C4×Q8C2×D511yescharacteristic
97#432—21no—
98C2×#101—101no—
99C4×M16—101no—
100#394—52no—
101#394—52no—
102#390—101no—
103#390—101no—
104#390—101no—
105C4×C4⋊C4—51no—
106#343—52no—
107#324—21no—
108#324C2×D512yes—
109C23×C5C2×C22⋊C411yescharacteristic
110C22×D5—42no—
111C22×D5—42no—
112C22×D5—42no—
113C22×D5—42no—
114C22×D5—42no—
115C22×D5—42no—
116C22×D5—42no—
117C5×Q8—44no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—22no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5#9911yescharacteristic
133C2×C4×C5#9911yescharacteristic
134C2×C4×C5#10412yes—
135C2×C4×C5AGL(1,ℤ/8)12yes—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139D20—82no—
140D20—84no—
141D20—84no—
142D20—82no—
143C5×C8—82no—
144#168—44no—
145C22×Q8D2011yescharacteristic
146C22×D4—52no—
147C22×D4—101no—
148C22×D4—101no—
149C2×M16—102no—
150#127—201no—
151#127—201no—
152#124—204no—
153C4×Q8—41no—
154C4×Q8—41no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4C4×D511yescharacteristic
157C2×C4⋊C4C22⋊D511yescharacteristic
158C2×C4⋊C4C22×D511yescharacteristic
159C2×C22⋊C4—102no—
160C2×C22⋊C4—102no—
161C2×C22⋊C4—102no—
162C2×C22⋊C4—102no—
163C2×C42—101no—
164C2×C42C4×D511yescharacteristic
165C2×C42D2011yescharacteristic
166C2×C42C22⋊D511yescharacteristic
167C4⋊C8—41no—
168#101—104no—
169C22⋊C8—22no—
170#97—41no—
171#97—201no—
172C4×C8—201no—
173#95—52no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5C2×#9911yescharacteristic
177C22×C5#41811yescharacteristic
178C22×C5C2×#10411yescharacteristic
179C2×D5—82no—
180C2×D5—82no—
181C2×D5—82no—
182C2×D5—82no—
183C2×D5—82no—
184C2×D5—82no—
185C2×D5—82no—
186C4×C5—21no—
187C4×C5—22no—
188C4×C5—22no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5#35512yes—
194Dic5—82no—
195C24—102no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8—41no—
199C2×D4—202no—
200C2×D4—202no—
201C2×D4—202no—
202C2×D4—202no—
203C2×D4—202no—
204C2×D4—201no—
205C2×D4—201no—
206C2×D4—202no—
207C2×D4—402no—
208C22×C4—102no—
209C22×C4#68511yescharacteristic
210C22×C4#68511yescharacteristic
211C22×C4#68511yescharacteristic
212C22×C4#68511yescharacteristic
213C22×C4C2×C4×D511yescharacteristic
214C22×C4C2×D2011yescharacteristic
215C22×C4C2×C22⋊D511yescharacteristic
216M16—104no—
217M16—202no—
218C2×C8—42no—
219C2×C8—202no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—202no—
224C22⋊C4—204no—
225C22⋊C4—204no—
226C22⋊C4—402no—
227C22⋊C4—402no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—202no—
235C2×C5—21no—
236C2×C5—21no—
237C2×C5#150711yescharacteristic
238C2×C5#212211yescharacteristic
239C2×C5C2×#35511yescharacteristic
240D5—162no—
241C23—202no—
242C23—202no—
243C23—202no—
244C23—202no—
245C23—202no—
246C23—202no—
247C23—202no—
248C23C2×#68511yescharacteristic
249Q8—44no—
250D4—404no—
251D4—402no—
252D4—404no—
253D4—402no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4#393811yescharacteristic
272C2×C4#393811yescharacteristic
273C2×C4#395712yes—
274C2×C4#405412yes—
275C8—82no—
276C8—204no—
277C5#1178111yescharacteristic, complemented, Sylow
278C22—21no—
279C22—21no—
280C22—402no—
281C22—402no—
282C22—402no—
283C22—402no—
284C22—402no—
285C22—402no—
286C22—402no—
287C22C2×#393811yescharacteristic
288C22#6542011yescharacteristic
289C22C2×#395711yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—402no—
298C4#6469712yes—
299C2—21no—
300C2—21no—
301C2—802no—
302C2#1060077011yescharacteristic
303C2#1060085011yescharacteristic
304C2C2×#6469711yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1467C2
socleC22×C5C2×#99
prime radicalC2×#4020C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1467D5
hypocenterC5#11781
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C5×#1467C2semidirect
3. C4×#3968C2semidirect
4. #10597947C2semidirect
52. #1467D5semidirect
277. C5#11781semidirect

Maximal subgroups

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

subgroupindex
#106142072
C5×#14672
C4×#39682
#105979472
#117815