Finite Group Databasebeta

← #11987493

Subgroups — #11987493

Order 1280.

410 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#125C211yesmaximal, characteristic
2#10600185C211yesmaximal, characteristic
3#10600182C211yesmaximal, characteristic
4#10598129C212yesmaximal
5#10598129C212yesmaximal
6C2×C5×#125C411yescharacteristic
7C5×#389C2211yescharacteristic
8C5×#389C2211yescharacteristic
9C5×#387—21no—
10C5×#387—21no—
11C5×#382C411yescharacteristic
12C4×C5×C4⋊C4—21no—
13C4×C5×C4⋊C4—21no—
14C4×C5×C4⋊C4C411yescharacteristic
15C4×C5×C4⋊C4C411yescharacteristic
16C43×C5C2211yescharacteristic
17C2×C4⋊#168—21no—
18C2×#3935—21no—
19#64744—21no—
20#64744—21no—
21#64744C2212yes—
22#64744C2212yes—
23#7619—51nomaximal, Sylow
24C5×#125—22no—
25C5×#125—22no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C42×C5—21no—
35C2×C42×C5—21no—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×C42×C5D411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C42×C5C2311yescharacteristic
43C22×#168—22no—
44C22×#168—22no—
45C5×#95—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C4⋊#168—42no—
52#3935—24no—
53C4×#125D511yescharacteristic
54#1831—51no—
55#1745—51no—
56#1271—52no—
57#1271—52no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C5×C4⋊C4—24no—
70C5×C4⋊C4—24no—
71C5×C4⋊C4—21no—
72C5×C4⋊C4—21no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4M1612yes—
79C5×C4⋊C4M1612yes—
80C42×C5—22no—
81C42×C5—22no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—22no—
85C42×C5—21no—
86C42×C5—21no—
87C42×C5—41no—
88C42×C5—41no—
89C42×C5—42no—
90C42×C5—42no—
91C2×#168—24no—
92C2×#168—42no—
93C2×#168—42no—
94C2×#168—42no—
95C2×#168—42no—
96C2×#168—42no—
97C2×#125Dic511yescharacteristic
98C2×C4⋊C8—101no—
99C2×#97—101no—
100#389C2×D511yescharacteristic
101#389C2×D511yescharacteristic
102#387—21no—
103#387—21no—
104#382Dic511yescharacteristic
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C4×C4⋊C4Dic511yescharacteristic
108C4×C4⋊C4Dic511yescharacteristic
109C43C2×D511yescharacteristic
110#336—52no—
111#336—52no—
112#336—101no—
113#336—101no—
114C23×C5C2×C22⋊C411yescharacteristic
115C2×C4×C5—21no—
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—21no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5#10112yes—
144C2×C4×C5#10412yes—
145C2×C4×C5C2×M1611yescharacteristic
146C2×C4×C5C2×M1611yescharacteristic
147C2×C4×C5#13512yes—
148C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C5#13711yescharacteristic
150#168—44no—
151#168—82no—
152C22×C8—102no—
153C22×C8—102no—
154#125—22no—
155#125—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4C2×Dic511yescharacteristic
161C2×C4⋊C4C2×Dic511yescharacteristic
162C2×C4⋊C4C2×Dic511yescharacteristic
163C2×C4⋊C4C2×Dic511yescharacteristic
164C2×C42—21no—
165C2×C42—21no—
166C2×C42C2×Dic511yescharacteristic
167C2×C42C2×Dic511yescharacteristic
168C2×C42C22⋊D511yescharacteristic
169C2×C42C22⋊D511yescharacteristic
170C2×C42C22⋊D511yescharacteristic
171C2×C42C22⋊D511yescharacteristic
172C2×C42C22×D511yescharacteristic
173C4⋊C8—202no—
174#97—104no—
175#95—21no—
176#95—21no—
177#95—21no—
178#95—21no—
179#95—21no—
180#95—21no—
181C22×C5#40711yescharacteristic
182C22×C5#41011yescharacteristic
183C22×C5C2×#10111yescharacteristic
184C22×C5#41611yescharacteristic
185C22×C5#41711yescharacteristic
186C22×C5C2×#10411yescharacteristic
187C22×C5#42111yescharacteristic
188C4×C5—22no—
189C4×C5—21no—
190C4×C5—21no—
191C4×C5—22no—
192C4×C5—21no—
193C4×C5—21no—
194C4×C5—22no—
195C4×C5—41no—
196C4×C5—42no—
197C4×C5—41no—
198C4×C5—42no—
199C4×C5—81no—
200C4×C5—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4C22⋊Dic511yescharacteristic
206C22×C4C22⋊Dic511yescharacteristic
207C22×C4C22⋊Dic511yescharacteristic
208C22×C4C22⋊Dic511yescharacteristic
209C22×C4C22×Dic511yescharacteristic
210C22×C4C2×C22⋊D511yescharacteristic
211C22×C4C2×C22⋊D511yescharacteristic
212C2×C8—104no—
213C2×C8—202no—
214C2×C8—202no—
215C2×C8—202no—
216C2×C8—202no—
217C2×C8—202no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4#68112yes—
228C4⋊C4#68112yes—
229C42—22no—
230C42—21no—
231C42—22no—
232C42—22no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—41no—
237C42—41no—
238C42—42no—
239C42—42no—
240C2×C5#146711yescharacteristic
241C2×C5#148811yescharacteristic
242C2×C5#148911yescharacteristic
243C2×C5#150011yescharacteristic
244C2×C5#151211yescharacteristic
245C2×C5#152811yescharacteristic
246C2×C5#155211yescharacteristic
247C23C2×C22⋊Dic511yescharacteristic
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—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#396812yes—
277C2×C4#396912yes—
278C2×C4C2×#68111yescharacteristic
279C2×C4C2×#68111yescharacteristic
280C2×C4#409511yescharacteristic
281C2×C4#409612yes—
282C2×C4#409711yescharacteristic
283C8—204no—
284C8—402no—
285C5#761911yescharacteristic, complemented, Sylow
286C22#6549611yescharacteristic
287C22C2×#396811yescharacteristic
288C22#6552111yescharacteristic
289C22#6552211yescharacteristic
290C22C2×#396911yescharacteristic
291C22#6552511yescharacteristic
292C22#6552911yescharacteristic
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—22no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—42no—
302C4—41no—
303C4—42no—
304C4—81no—
305C4—81no—
306C2#1060241811yescharacteristic
307C2#1060243311yescharacteristic
308C2#1060243411yescharacteristic
309C2#1060252811yescharacteristic
310C2#1060254711yescharacteristic
311C2#1060254911yescharacteristic
312C2#1060262411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC4×C5×#125C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenterC4×#125D5
hypocenterC5#7619
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
285. C5#7619semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1252
#106001852
#106001822
#105981292
#76195