Finite Group Databasebeta

← #12008463

Subgroups — #12008463

Order 1280.

434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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#10605956C211yesmaximal, characteristic
2#10598917C212yesmaximal
3C5×#1324C211yesmaximal, characteristic, complemented
4#10598123C211yesmaximal, characteristic, complemented
5#10597943C212yesmaximal, complemented
6C2×#4038C2211yescharacteristic
7C2×D5×C4⋊C4C411yescharacteristic
8C2×#4018C411yescharacteristic
9C5×#382C2211yescharacteristic
10#65266C2211yescharacteristic
11#65265C411yescharacteristic
12#65224C411yescharacteristic
13#65007—22no—
14#64957—22no—
15#64936—22no—
16C5×#324C2212yes—
17#64748C2212yes—
18#64688—22no—
19#11449—51nomaximal, Sylow
20C22×C4×D5—21no—
21C22×C4×D5C2×C411yescharacteristic
22C2×C5×C4⋊C4C2×C411yescharacteristic
23C2×C5×C4⋊C4C2311yescharacteristic
24C2×C42×C5C2×C411yescharacteristic
25C2×#685—21no—
26C2×#685D412yes—
27C2×C4⋊Dic5—22no—
28C2×C4⋊Dic5C2×C411yescharacteristic
29C2×C4⋊Dic5C2×C411yescharacteristic
30C2×#683—21no—
31C2×#683—21no—
32C2×#683—22no—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35#4038—42no—
36D5×C4⋊C4—42no—
37#4018—22no—
38#4018C814yescomplemented
39C5×C22⋊C8—22no—
40C5×#95—22no—
41#3963—22no—
42C22⋊#168—22no—
43#3946—42no—
44C8×Dic5—42no—
45#2317—51no—
46#1458—52no—
47#1324—51no—
48#1324—52no—
49#1324D511yescharacteristic, complemented
50C23×D5C22⋊C411yescharacteristic
51C22×C4×C5—21no—
52C22×C4×C5—21no—
53C22×C4×C5C22×C411yescharacteristic
54C22×C4×C5C2×D412yes—
55C22×Dic5—21no—
56C22×Dic5—21no—
57C22×Dic5C22⋊C412yes—
58C22×Dic5C22⋊C411yescharacteristic
59C2×C4×D5—22no—
60C2×C4×D5—22no—
61C2×C4×D5—42no—
62C2×C4×D5—82no—
63C2×C4×D5C2×C812yes—
64C2×C4×D5M1612yes—
65C2×C5×C8—42no—
66C5×C4⋊C4—41no—
67C5×C4⋊C4—41no—
68C42×C5—21no—
69C42×C5C2×C812yes—
70#685—24no—
71#685—42no—
72C4⋊Dic5—41no—
73C4⋊Dic5—41no—
74C4⋊Dic5—82no—
75#683—24no—
76#683—42no—
77#683—82no—
78C4×Dic5—21no—
79C4×Dic5—22no—
80C4×Dic5—22no—
81C4×Dic5C2×C812yes—
82C2×#168—42no—
83C2×#117—51no—
84C2×#117—51no—
85C22×C4⋊C4—51no—
86#431—102no—
87#389—102no—
88#385—102no—
89#384—51no—
90#384—51no—
91#382—51no—
92#382C2×D511yescharacteristic
93#324—52no—
94#324C2×D512yes—
95#323—102no—
96C23×C5C2×C22⋊C411yescharacteristic
97C22×D5—21no—
98C22×D5—21no—
99C22×D5—41no—
100C22×D5—41no—
101C22×D5C22⋊C812yes—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—22no—
105C2×C4×C5—22no—
106C2×C4×C5—41no—
107C2×C4×C5—41no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—41no—
111C2×C4×C5C22×C811yescharacteristic
112C2×C4×C5C2×M1611yescharacteristic
113C2×Dic5—22no—
114C2×Dic5—22no—
115C2×Dic5—41no—
116C2×Dic5—41no—
117C2×Dic5—42no—
118C2×Dic5—42no—
119C2×Dic5—41no—
120C2×Dic5C22⋊C812yes—
121C2×Dic5#9912yes—
122C2×Dic5#10112yes—
123C4×D5—24no—
124C4×D5—24no—
125C4×D5—84no—
126C5×C8—82no—
127#168—82no—
128C23×C4—51no—
129C23×C4—101no—
130#117—54no—
131#117—102no—
132#117—202no—
133C2×C4⋊C4—51no—
134C2×C4⋊C4—51no—
135C2×C4⋊C4—101no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4—102no—
138C2×C4⋊C4—102no—
139C2×C4⋊C4—202no—
140C2×C4⋊C4C4×D511yescharacteristic
141C2×C4⋊C4C22×D511yescharacteristic
142C2×C22⋊C4—52no—
143C2×C22⋊C4—101no—
144C2×C42—51no—
145C2×C42—52no—
146C2×C42C4×D511yescharacteristic
147C4⋊C8—202no—
148C22⋊C8—22no—
149C22⋊C8—102no—
150C4×C8—202no—
151#95—22no—
152#95—102no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5C2×C22⋊C811yescharacteristic
156C22×C5C2×#9911yescharacteristic
157C22×C5C2×#10111yescharacteristic
158C2×D5—22no—
159C2×D5—42no—
160C2×D5—41no—
161C2×D5—41no—
162C2×D5—42no—
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—42no—
166C4×C5—42no—
167C4×C5—81no—
168Dic5—42no—
169Dic5—42no—
170Dic5—81no—
171Dic5#32414yes—
172C24—51no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—51no—
176C22×C4—52no—
177C22×C4—52no—
178C22×C4—52no—
179C22×C4—102no—
180C22×C4—102no—
181C22×C4—101no—
182C22×C4—101no—
183C22×C4—202no—
184C22×C4—402no—
185C22×C4C2×C4×D511yescharacteristic
186C22×C4D4×D512yes—
187C2×C8—42no—
188C2×C8—202no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—104no—
192C4⋊C4—201no—
193C4⋊C4—201no—
194C4⋊C4—202no—
195C4⋊C4—402no—
196C4⋊C4—402no—
197C22⋊C4—104no—
198C22⋊C4—202no—
199C42—21no—
200C42—52no—
201C42—102no—
202C42—102no—
203C42—101no—
204C42C8×D512yes—
205C2×C5—21no—
206C2×C5—21no—
207C2×C5C2×#32411yescharacteristic
208C2×C5#212911yescharacteristic
209C2×C5#213411yescharacteristic
210D5—42no—
211C23—52no—
212C23—101no—
213C23—101no—
214C23—201no—
215C23—201no—
216C23D5×C22⋊C411yescharacteristic
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—52no—
227C2×C4—52no—
228C2×C4—52no—
229C2×C4—104no—
230C2×C4—104no—
231C2×C4—102no—
232C2×C4—102no—
233C2×C4—201no—
234C2×C4—201no—
235C2×C4—202no—
236C2×C4—202no—
237C2×C4—201no—
238C2×C4—404no—
239C2×C4C2×C8×D511yescharacteristic
240C2×C4D5×M1611yescharacteristic
241C8—82no—
242C8—402no—
243C5#1144911yescharacteristic, complemented, Sylow
244C22—21no—
245C22—21no—
246C22—102no—
247C22—202no—
248C22—202no—
249C22—201no—
250C22—201no—
251C22D5×C22⋊C811yescharacteristic
252C22D5×#9911yescharacteristic
253C22D5×#10111yescharacteristic
254C4—21no—
255C4—21no—
256C4—42no—
257C4—42no—
258C4—54no—
259C4—81no—
260C4—202no—
261C4—202no—
262C4—401no—
263C2—21no—
264C2—21no—
265C2—202no—
266C2D5×#32411yescharacteristic
267C2#1059995211yescharacteristic
268C2#1059995911yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC2×C4×C5C22×C8
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1324C2
socleC22×C5C2×#99
prime radicalC23×D5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1324D5
hypocenterC5#11449
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. C5×#1324C2semidirect
4. #10598123C2semidirect
5. #10597943C2semidirect
38. #4018C8semidirect
49. #1324D5semidirect
243. C5#11449semidirect

Maximal subgroups

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

subgroupindex
#106059562
#105989172
C5×#13242
#105981232
#105979432
#114495