Finite Group Databasebeta

← #12008992

Subgroups — #12008992

Order 1280.

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

normal subgroups only

This group has 424 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#10614105C211yesmaximal, characteristic
2C5×#1465C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10597938C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic
7C5×#407—21no—
8#65509C412yes—
9#65501—21no—
10#65501C411yescharacteristic
11#65275—21no—
12#65238—21no—
13#65235C2212yes—
14#65217—21no—
15#65214—21no—
16C5×#324—21no—
17C5×#323C2212yes—
18#64745—21no—
19#64745C2212yes—
20#11579—51nomaximal, Sylow
21C22×C5×D4C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5C2×C412yes—
25C2×C5×M16—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5C2×C412yes—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—41no—
38C2×C4⋊Dic5—41no—
39C2×#683—22no—
40C5×C22⋊C8—22no—
41C5×C22⋊C8—41no—
42#3963—22no—
43#3963—21no—
44#3963—22no—
45C22⋊#168—22no—
46C4⋊#168—41no—
47C4×#168—41no—
48#2487—51no—
49#1465D511yescharacteristic
50#1460—51no—
51#1326—54no—
52C24×C5C22⋊C411yescharacteristic
53C24×C5C22×C411yescharacteristic
54C2×C5×D4—22no—
55C2×C5×D4—22no—
56C2×C5×D4—41no—
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—42no—
62C22×C4×C5—42no—
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×Dic5—22no—
69C22×Dic5—22no—
70C22×Dic5—42no—
71C22×Dic5—82no—
72C5×M16—82no—
73C2×C5×C8—42no—
74C5×C4⋊C4—41no—
75C5×C22⋊C4—41no—
76C5×C22⋊C4—41no—
77C42×C5—21no—
78C42×C5—21no—
79C22⋊Dic5—24no—
80C22⋊Dic5—82no—
81C4⋊Dic5—42no—
82C4⋊Dic5—42no—
83C4⋊Dic5—41no—
84C4⋊Dic5—41no—
85#683—82no—
86C2×#168—42no—
87C2×C4×D4C2×D511yescharacteristic
88C22×C4⋊C4—51no—
89#431—101no—
90#407—21no—
91#400—101no—
92#399—101no—
93#389—101no—
94#386—52no—
95#385—52no—
96#380—51no—
97#380—101no—
98#324—21no—
99#323—52no—
100#323—101no—
101#323C2×D512yes—
102C23×C5—21no—
103C23×C5—21no—
104C23×C5—21no—
105C23×C5—21no—
106C23×C5—21no—
107C23×C5—41no—
108C23×C5—41no—
109C23×C5—41no—
110C23×C5—41no—
111C23×C5C2×C22⋊C411yescharacteristic
112C23×C5#13112yes—
113C5×D4—44no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—22no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—42no—
121C2×C4×C5—42no—
122C2×C4×C5—42no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5—41no—
126C2×C4×C5—81no—
127C2×C4×C5#9911yescharacteristic
128C2×C4×C5#9911yescharacteristic
129C2×C4×C5#10112yes—
130C2×Dic5—42no—
131C2×Dic5—42no—
132C2×Dic5—42no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—84no—
137C5×C8—82no—
138#168—82no—
139C22×D4C4×D511yescharacteristic
140C23×C4—52no—
141C23×C4C4×D511yescharacteristic
142C23×C4C22⋊D511yescharacteristic
143C2×M16—41no—
144C4×D4—41no—
145C4×D4—41no—
146C2×C4⋊C4—101no—
147C2×C4⋊C4—101no—
148C2×C4⋊C4—101no—
149C2×C4⋊C4—102no—
150C2×C4⋊C4—201no—
151C2×C4⋊C4—201no—
152C2×C4⋊C4C22⋊D511yescharacteristic
153C2×C22⋊C4—52no—
154C2×C22⋊C4—102no—
155C2×C22⋊C4D2011yescharacteristic
156C2×C22⋊C4C22×D511yescharacteristic
157C2×C42D2011yescharacteristic
158C4⋊C8—201no—
159C22⋊C8—22no—
160C22⋊C8—41no—
161C22⋊C8—102no—
162C4×C8—201no—
163#95—101no—
164#95—102no—
165#95—102no—
166C22×C5—21no—
167C22×C5—21no—
168C22×C5—22no—
169C22×C5—42no—
170C22×C5—42no—
171C22×C5—42no—
172C22×C5—41no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5—81no—
178C22×C5#40811yescharacteristic
179C22×C5C2×#9911yescharacteristic
180C22×C5C2×#10111yescharacteristic
181C4×C5—21no—
182C4×C5—22no—
183C4×C5—41no—
184C4×C5—41no—
185C4×C5—41no—
186C4×C5#35212yes—
187Dic5—82no—
188Dic5—82no—
189C24#68511yescharacteristic
190C24C2×C4×D511yescharacteristic
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—102no—
201C22×C4—102no—
202C22×C4—202no—
203C22×C4—402no—
204C22×C4#68511yescharacteristic
205C22×C4#68511yescharacteristic
206C22×C4#68511yescharacteristic
207C22×C4C2×D2011yescharacteristic
208C22×C4C2×C22⋊D511yescharacteristic
209M16—82no—
210C2×C8—42no—
211C2×C8—202no—
212C4⋊C4—41no—
213C4⋊C4—202no—
214C4⋊C4—202no—
215C4⋊C4—201no—
216C4⋊C4—201no—
217C4⋊C4—402no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—104no—
221C22⋊C4—402no—
222C42—21no—
223C42—21no—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5—42no—
227C2×C5—81no—
228C2×C5#147211yescharacteristic
229C2×C5C2×#35211yescharacteristic
230C2×C5#212211yescharacteristic
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23#405312yes—
241C23C2×#68511yescharacteristic
242D4—44no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—81no—
256C2×C4—202no—
257C2×C4—202no—
258C2×C4—202no—
259C2×C4—202no—
260C2×C4—202no—
261C2×C4—202no—
262C2×C4—404no—
263C2×C4#393811yescharacteristic
264C2×C4#393811yescharacteristic
265C2×C4#395612yes—
266C8—82no—
267C8—402no—
268C5#1157911yescharacteristic, complemented, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C2×#393811yescharacteristic
282C22#6541811yescharacteristic
283C22C2×#395611yescharacteristic
284C4—22no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—402no—
290C4—402no—
291C4#6469212yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—81no—
296C2#1060076511yescharacteristic
297C2C2×#6469211yescharacteristic
298C2#1060093911yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1465C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C22⋊C4C23
hypercenter#1465D5
hypocenterC5#11579
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
4. #10597938C2semidirect
268. C5#11579semidirect

Maximal subgroups

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

subgroupindex
#106141052
C5×#14652
#106023942
#105979382
#115795