Finite Group Databasebeta

← #11990227

Subgroups — #11990227

Order 1280.

444 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4016C211yesmaximal, characteristic
2C5×#1745C211yesmaximal, characteristic
3C2×#64685C212yesmaximal
4#10600182C211yesmaximal, characteristic
5#10598150C212yesmaximal
6C2×#4016C2211yescharacteristic
7C2×C5×#97C2212yes—
8C43×C5C2211yescharacteristic
9#65225C2211yescharacteristic
10C4×C4⋊Dic5C411yescharacteristic
11C4×C4⋊Dic5C411yescharacteristic
12#65222—21no—
13#65222—21no—
14C4×#683—21no—
15C4×#683—21no—
16#65217C411yescharacteristic
17#65217C411yescharacteristic
18C2×#3935C2212yes—
19C5×#336—21no—
20C5×#336—21no—
21#64744—21no—
22#64744—21no—
23#64685C418yescomplemented
24#8225—51nomaximal, Sylow
25C22×C5×C8—22no—
26C2×C42×C5C2×C411yescharacteristic
27C2×C42×C5C2×C411yescharacteristic
28C2×C42×C5D411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5C2311yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40C2×#683—21no—
41C2×C4×Dic5—21no—
42C2×C4×Dic5—21no—
43C22×#168—22no—
44#4016—22no—
45#4016C2×C414yes—
46C5×#97—22no—
47C5×#97C2×C414yes—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3935—22no—
55#3935C2×C414yes—
56C4×#125—51no—
57#1745—51no—
58#1745D511yescharacteristic
59C2×#330—52no—
60#1295—52no—
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22×C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×Dic5—21no—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—21no—
72C2×C5×C8—24no—
73C2×C5×C8—42no—
74C2×C5×C8—42no—
75C42×C5—22no—
76C42×C5—41no—
77C42×C5—41no—
78C42×C5—41no—
79C42×C5—41no—
80C42×C5—41no—
81C42×C5C22×C412yes—
82C42×C5#4112yes—
83C4⋊Dic5—21no—
84C4⋊Dic5—21no—
85C4⋊Dic5—41no—
86C4⋊Dic5—41no—
87C4⋊Dic5C4212yes—
88C4⋊Dic5C4212yes—
89#683—24no—
90#683—24no—
91#683—42no—
92#683—42no—
93C4×Dic5—42no—
94C4×Dic5—42no—
95C2×#168—24no—
96C2×#168—42no—
97C2×#168—42no—
98C2×#125—51no—
99C2×#97—52no—
100C2×#97C2×D512yes—
101#389—51no—
102#389—51no—
103#387—101no—
104#387—101no—
105#382—51no—
106C4×C4⋊C4—51no—
107C4×C4⋊C4—51no—
108C4×C4⋊C4—101no—
109C4×C4⋊C4—101no—
110C43C2×D511yescharacteristic
111#336—21no—
112#336—21no—
113#336—101no—
114#336—101no—
115#330—58no—
116C23×C5C2×C22⋊C411yescharacteristic
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—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5#10112yes—
135C2×C4×C5C2×C4211yescharacteristic
136C2×C4×C5#11711yescharacteristic
137C2×C4×C5C4×D412yes—
138C2×C4×C5C4×D412yes—
139C2×Dic5—22no—
140C2×Dic5—22no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C5×C8—44no—
152#168—44no—
153C22×C8—22no—
154C22×C8—102no—
155#125—54no—
156#125—102no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—51no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—101no—
162C2×C4⋊C4—101no—
163C2×C4⋊C4—101no—
164C2×C4⋊C4—101no—
165C2×C42—101no—
166C2×C42—101no—
167C2×C42C4×D511yescharacteristic
168C2×C42C4×D511yescharacteristic
169C2×C42D2011yescharacteristic
170C2×C42D2011yescharacteristic
171C2×C42C22⋊D511yescharacteristic
172C2×C42C22⋊D511yescharacteristic
173C2×C42C22×D511yescharacteristic
174#97—22no—
175#97—54no—
176#97—102no—
177#97C4×D514yes—
178#95—101no—
179#95—101no—
180#95—101no—
181#95—101no—
182#95—101no—
183#95—101no—
184C22×C5C4×C22⋊C411yescharacteristic
185C22×C5C2×#10111yescharacteristic
186C22×C5#41311yescharacteristic
187C22×C5#42111yescharacteristic
188C22×C5#42111yescharacteristic
189C22×C5#42111yescharacteristic
190C22×C5#42111yescharacteristic
191C4×C5—21no—
192C4×C5—21no—
193C4×C5—22no—
194C4×C5—22no—
195C4×C5—22no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5—41no—
199Dic5—42no—
200Dic5—42no—
201Dic5—81no—
202Dic5—81no—
203C22×C4—101no—
204C22×C4—101no—
205C22×C4—101no—
206C22×C4—101no—
207C22×C4#68511yescharacteristic
208C22×C4#68511yescharacteristic
209C22×C4#68511yescharacteristic
210C22×C4#68511yescharacteristic
211C22×C4C2×C4×D511yescharacteristic
212C22×C4C2×D2011yescharacteristic
213C22×C4C2×C22⋊D511yescharacteristic
214C2×C8—24no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—104no—
218C2×C8—202no—
219C2×C8—202no—
220C4⋊C4—52no—
221C4⋊C4—52no—
222C4⋊C4—101no—
223C4⋊C4—101no—
224C4⋊C4—104no—
225C4⋊C4—104no—
226C4⋊C4—201no—
227C4⋊C4—201no—
228C4⋊C4—202no—
229C4⋊C4—202no—
230C42—22no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—202no—
237C42—202no—
238C42C2×C4×D512yes—
239C42#70912yes—
240C2×C5#153411yescharacteristic
241C2×C5#153511yescharacteristic
242C2×C5#153511yescharacteristic
243C2×C5#153711yescharacteristic
244C2×C5C4×#10111yescharacteristic
245C2×C5#175911yescharacteristic
246C2×C5#175911yescharacteristic
247C23C2×#68511yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—102no—
266C2×C4—102no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—201no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—201no—
273C2×C4—201no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—201no—
277C2×C4#395612yes—
278C2×C4C42×D511yescharacteristic
279C2×C4#401811yescharacteristic
280C2×C4C4×D2012yes—
281C2×C4C4×C22⋊D512yes—
282C8—44no—
283C8—204no—
284C5#822511yescharacteristic, complemented, Sylow
285C22C4×#68511yescharacteristic
286C22#6529411yescharacteristic
287C22#6529411yescharacteristic
288C22#6542111yescharacteristic
289C22C2×#395611yescharacteristic
290C22#6542811yescharacteristic
291C22#6542811yescharacteristic
292C4—22no—
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—202no—
301C4—202no—
302C4—401no—
303C4—401no—
304C2#1060022311yescharacteristic
305C2#1060065911yescharacteristic
306C2C4×#395611yescharacteristic
307C2#1060160211yescharacteristic
308C2#1060160311yescharacteristic
309C2#1060160711yescharacteristic
310C2#1060160811yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1745C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1745D5
hypocenterC5#8225
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
23. #64685C4semidirect
284. C5#8225semidirect

Maximal subgroups

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

subgroupindex
C4×#40162
C5×#17452
C2×#646852
#106001822
#105981502
#82255