Finite Group Databasebeta

← #11999400

Subgroups — #11999400

Order 1280.

432 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10605041C211yesmaximal, characteristic
2C4×C5×#97C211yesmaximal, characteristic
3#10600184C211yesmaximal, characteristic
4#10598150C212yesmaximal
5#10598150C212yesmaximal
6C2×C5×#97—21no—
7C2×C5×#97C2212yes—
8C2×C4×C5×C8—21no—
9C43×C5C2211yescharacteristic
10#65225C2211yescharacteristic
11#65225C2211yescharacteristic
12#65222—21no—
13#65222—21no—
14#65222—21no—
15#65222—21no—
16#65217C411yescharacteristic
17#65217C411yescharacteristic
18#65217C411yescharacteristic
19#65217C411yescharacteristic
20C2×C4⋊#168—21no—
21C2×#3935C2212yes—
22#64744—21no—
23#9892—51nomaximal, Sylow
24C22×C5×C8—22no—
25C2×C42×C5C2×C411yescharacteristic
26C2×C42×C5C2×C411yescharacteristic
27C2×C42×C5D411yescharacteristic
28C2×C42×C5D411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×#683—21no—
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40C22×#168—22no—
41C5×#97—24no—
42C5×#97—22no—
43C5×#97Q814yes—
44C4×C5×C8—24no—
45#3963—21no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53C4⋊#168—24no—
54#3935—24no—
55#2864—51no—
56#1767—51no—
57C4×#97D511yescharacteristic
58#1295—52no—
59#1295—52no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22×C411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×Dic5—21no—
68C22×Dic5—21no—
69C22×Dic5—21no—
70C22×Dic5—21no—
71C2×C5×C8—24no—
72C2×C5×C8—24no—
73C2×C5×C8—24no—
74C42×C5—22no—
75C42×C5—22no—
76C42×C5—22no—
77C42×C5—41no—
78C42×C5—41no—
79C42×C5—41no—
80C42×C5C2×Q812yes—
81C42×C5#4112yes—
82C4⋊Dic5—41no—
83C4⋊Dic5—41no—
84C4⋊Dic5—41no—
85C4⋊Dic5—41no—
86#683—42no—
87#683—42no—
88#683—42no—
89#683—42no—
90C2×#168—24no—
91C2×#168—42no—
92C2×#168—42no—
93C2×C4⋊C8—101no—
94C2×#97—21no—
95C2×#97—52no—
96C2×#97C2×D512yes—
97C2×C4×C8—21no—
98#389—51no—
99#389—51no—
100#389—51no—
101#389—51no—
102#387—101no—
103#387—101no—
104#387—101no—
105#387—101no—
106#382—51no—
107#382—51no—
108C43C2×D511yescharacteristic
109#336—101no—
110C23×C5C2×C22⋊C411yescharacteristic
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
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#10412yes—
127C2×C4×C5#10412yes—
128C2×C4×C5#10412yes—
129C2×C4×C5C4×Q812yes—
130C2×C4×C5C22⋊Q812yes—
131C2×C4×C5#12411yescharacteristic
132C2×C4×C5C4⋊Q811yescharacteristic
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5—41no—
136C2×Dic5—41no—
137C2×Dic5—41no—
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C5×C8—28no—
146#168—44no—
147C22×C8—22no—
148C22×C8—102no—
149C2×C4⋊C4—51no—
150C2×C4⋊C4—51no—
151C2×C4⋊C4—51no—
152C2×C4⋊C4—51no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C42C4×D511yescharacteristic
158C2×C42C4×D511yescharacteristic
159C2×C42D2011yescharacteristic
160C2×C42D2011yescharacteristic
161C2×C42C22⋊D511yescharacteristic
162C2×C42C22⋊D511yescharacteristic
163C2×C42C22×D511yescharacteristic
164C4⋊C8—104no—
165#97—24no—
166#97—22no—
167#97—104no—
168#97Dic1014yes—
169C4×C8—24no—
170#95—101no—
171#95—101no—
172#95—101no—
173#95—101no—
174#95—101no—
175#95—101no—
176#95—101no—
177#95—101no—
178C22×C5#39111yescharacteristic
179C22×C5#41311yescharacteristic
180C22×C5#41311yescharacteristic
181C22×C5C2×#10411yescharacteristic
182C22×C5C2×#10411yescharacteristic
183C22×C5C2×#10411yescharacteristic
184C22×C5#42111yescharacteristic
185C4×C5—21no—
186C4×C5—21no—
187C4×C5—22no—
188C4×C5—22no—
189C4×C5—22no—
190C4×C5—22no—
191C4×C5—22no—
192C4×C5—41no—
193Dic5—81no—
194Dic5—81no—
195Dic5—81no—
196Dic5—81no—
197C22×C4—101no—
198C22×C4—101no—
199C22×C4—101no—
200C22×C4—101no—
201C22×C4#68511yescharacteristic
202C22×C4#68511yescharacteristic
203C22×C4#68511yescharacteristic
204C22×C4#68511yescharacteristic
205C22×C4C2×C4×D511yescharacteristic
206C22×C4C2×D2011yescharacteristic
207C22×C4C2×C22⋊D511yescharacteristic
208C2×C8—24no—
209C2×C8—24no—
210C2×C8—24no—
211C2×C8—104no—
212C2×C8—202no—
213C2×C8—202no—
214C4⋊C4—201no—
215C4⋊C4—201no—
216C4⋊C4—201no—
217C4⋊C4—201no—
218C4⋊C4—202no—
219C4⋊C4—202no—
220C4⋊C4—202no—
221C4⋊C4—202no—
222C42—22no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42C2×Dic1012yes—
229C42#70912yes—
230C2×C5#152411yescharacteristic
231C2×C5#152411yescharacteristic
232C2×C5#152911yescharacteristic
233C2×C5#153211yescharacteristic
234C2×C5#198611yescharacteristic
235C2×C5#199411yescharacteristic
236C2×C5#199811yescharacteristic
237C23C2×#68511yescharacteristic
238C2×C4—21no—
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—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—201no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—201no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4#393712yes—
266C2×C4#393712yes—
267C2×C4#395712yes—
268C2×C4C4×Dic1012yes—
269C2×C4#401511yescharacteristic
270C2×C4#402111yescharacteristic
271C2×C4#407012yes—
272C8—28no—
273C8—204no—
274C5#989211yescharacteristic, complemented, Sylow
275C22C2×#393711yescharacteristic
276C22C2×#393711yescharacteristic
277C22#6521811yescharacteristic
278C22#6542111yescharacteristic
279C22#6542111yescharacteristic
280C22C2×#395711yescharacteristic
281C22#6542811yescharacteristic
282C4—22no—
283C4—22no—
284C4—22no—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—41no—
290C4—401no—
291C4—401no—
292C4—401no—
293C4—401no—
294C2#1060018911yescharacteristic
295C2#1060059011yescharacteristic
296C2#1060059211yescharacteristic
297C2#1060065111yescharacteristic
298C2#1060065411yescharacteristic
299C2#1060066111yescharacteristic
300C2#1060067311yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC4×C5×#97C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenterC4×#97D5
hypocenterC5#9892
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
274. C5#9892semidirect

Maximal subgroups

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

subgroupindex
#106050412
C4×C5×#972
#106001842
#105981502
#98925