Finite Group Databasebeta

← #11989427

Subgroups — #11989427

Order 1280.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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#10610350C211yesmaximal, characteristic
2#10605168C212yesmaximal
3C5×#1297C211yesmaximal, characteristic
4#10598174C211yesmaximal, characteristic
5#10598109C212yesmaximal
6C22×C4×Dic5C2211yescharacteristic
7C5×#407C2211yescharacteristic
8C4×C5×C22⋊C4C2212yes—
9C4×C22⋊Dic5C2212yes—
10#65496C2211yescharacteristic
11#65407C412yescomplemented
12M16×Dic5C412yescomplemented
13#65232—22no—
14#65231—22no—
15#65221—22no—
16C4×#683—22no—
17#65008—22no—
18#65007—22no—
19#64940C414yescomplemented
20#64939C414yescomplemented
21#8050—51nomaximal, Sylow
22C23×C4×C5C2311yescharacteristic
23C23×Dic5D412yes—
24C2×C5×M16C2×C412yes—
25C2×C5×C22⋊C4—22no—
26C2×C42×C5—22no—
27C2×C22⋊Dic5—22no—
28C2×#683—24no—
29C2×C4×Dic5—22no—
30C2×C4×Dic5C2×C411yescharacteristic
31C2×C4×Dic5C2×C411yescharacteristic
32C2×C4×Dic5C2×C412yes—
33C2×C4×Dic5C2×C412yes—
34C2×C4×Dic5D412yes—
35C2×C4×Dic5D412yes—
36C2×C4×Dic5Q812yes—
37C2×#681C2×C412yes—
38C5×C22⋊C8—22no—
39C5×#95C2×C414yes—
40#3963—24no—
41#3963—24no—
42#3963—24no—
43#3963C2×C414yes—
44C22⋊#168—22no—
45#3947—22no—
46#3946—24no—
47C8×Dic5—22no—
48#2920—51no—
49#2283—52no—
50#1297—51no—
51#1297—52no—
52#1297D511yescharacteristic
53C24×C5C2×D411yescharacteristic
54C22×C4×C5—24no—
55C22×C4×C5—42no—
56C22×C4×C5C22×C411yescharacteristic
57C22×C4×C5C22×C412yes—
58C22×C4×C5C2×D412yes—
59C22×C4×C5C2×Q811yescharacteristic
60C22×Dic5—24no—
61C22×Dic5—44no—
62C22×Dic5C22⋊C412yes—
63C22×Dic5C22⋊C412yes—
64C22×Dic5C22⋊C412yes—
65C22×Dic5C22⋊C412yes—
66C22×Dic5C4⋊C412yes—
67C22×Dic5C4⋊C412yes—
68C5×M16—42no—
69C2×C5×C8—22no—
70C5×C22⋊C4—44no—
71C42×C5—44no—
72C22⋊Dic5—44no—
73#683—48no—
74C4×Dic5—44no—
75C4×Dic5C4212yes—
76C4×Dic5C4211yescharacteristic
77C4×Dic5C4211yescharacteristic
78C4×Dic5C22⋊C411yescharacteristic
79C4×Dic5C22⋊C412yes—
80C4×Dic5C22⋊C411yescharacteristic
81C4×Dic5C4⋊C412yes—
82C4×Dic5C4⋊C412yes—
83C4×Dic5C4⋊C412yes—
84C4×Dic5C4⋊C412yes—
85#681—42no—
86C2×#168—22no—
87C22×C42—51no—
88#432—102no—
89#431—102no—
90#423—52no—
91#407—51no—
92#407C2×D511yescharacteristic
93C4×M16—52no—
94#383—54no—
95#382—54no—
96#381—102no—
97#380—102no—
98C4×C4⋊C4—102no—
99C4×C22⋊C4—52no—
100C4×C22⋊C4C2×D512yes—
101#376—102no—
102C23×C5—24no—
103C23×C5—41no—
104C23×C5C2×C22⋊C412yes—
105C23×C5C2×C4⋊C411yescharacteristic
106C2×C4×C5—22no—
107C2×C4×C5—24no—
108C2×C4×C5—42no—
109C2×C4×C5—41no—
110C2×C4×C5—44no—
111C2×C4×C5—44no—
112C2×C4×C5—44no—
113C2×C4×C5C2×C4211yescharacteristic
114C2×C4×C5C2×C22⋊C411yescharacteristic
115C2×C4×C5C2×C4⋊C412yes—
116C2×Dic5—24no—
117C2×Dic5—24no—
118C2×Dic5—42no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122C2×Dic5—44no—
123C2×Dic5—44no—
124C2×Dic5—44no—
125C2×Dic5#9512yes—
126C2×Dic5#9512yes—
127C2×Dic5#9512yes—
128C2×Dic5#9512yes—
129C5×C8—42no—
130#168—42no—
131C23×C4—52no—
132C23×C4C22×D511yescharacteristic
133C2×M16—52no—
134C2×M16C4×D512yes—
135C2×C4⋊C4—104no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4—102no—
138C2×C42—22no—
139C2×C42—52no—
140C2×C42—52no—
141C2×C42—51no—
142C2×C42—51no—
143C2×C42—52no—
144C2×C42—52no—
145C2×C42—52no—
146C2×C42—102no—
147C4⋊C8—104no—
148C22⋊C8—22no—
149C22⋊C8—102no—
150#97—102no—
151C4×C8—102no—
152#95—54no—
153#95—104no—
154#95—104no—
155#95—104no—
156#95C4×D514yes—
157C22×C5—22no—
158C22×C5—22no—
159C22×C5—22no—
160C22×C5—21no—
161C22×C5—44no—
162C22×C5C2×#9511yescharacteristic
163C22×C5#42114yes—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—84no—
167C4×C5#41012yes—
168Dic5—22no—
169Dic5—22no—
170Dic5—22no—
171Dic5—22no—
172Dic5—84no—
173C24D4×D511yescharacteristic
174C22×C4—24no—
175C22×C4—42no—
176C22×C4—52no—
177C22×C4—52no—
178C22×C4—52no—
179C22×C4—52no—
180C22×C4—52no—
181C22×C4—52no—
182C22×C4—104no—
183C22×C4—204no—
184C22×C4C2×C4×D511yescharacteristic
185C22×C4C2×C4×D512yes—
186C22×C4D4×D512yes—
187C22×C4Q8×D511yescharacteristic
188M16—42no—
189M16—202no—
190C2×C8—22no—
191C2×C8—102no—
192C4⋊C4—208no—
193C22⋊C4—44no—
194C22⋊C4—204no—
195C42—44no—
196C42—51no—
197C42—52no—
198C42—51no—
199C42—51no—
200C42—51no—
201C42—52no—
202C42—52no—
203C42—52no—
204C42—52no—
205C42—52no—
206C42—204no—
207C2×C5—24no—
208C2×C5—41no—
209C2×C5#173312yes—
210C2×C5#174011yescharacteristic
211C23—24no—
212C23—41no—
213C23D5×C22⋊C412yes—
214C23D5×C4⋊C411yescharacteristic
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—52no—
223C2×C4—52no—
224C2×C4—52no—
225C2×C4—52no—
226C2×C4—104no—
227C2×C4—104no—
228C2×C4—202no—
229C2×C4—202no—
230C2×C4—202no—
231C2×C4—202no—
232C2×C4—204no—
233C2×C4—204no—
234C2×C4—204no—
235C2×C4C42×D511yescharacteristic
236C2×C4D5×C22⋊C411yescharacteristic
237C2×C4D5×C4⋊C412yes—
238C8—42no—
239C8—202no—
240C5#805011yescharacteristic, complemented, Sylow
241C22—22no—
242C22—22no—
243C22—21no—
244C22—22no—
245C22—44no—
246C22D5×#9511yescharacteristic
247C22#6511014yes—
248C4—21no—
249C4—22no—
250C4—84no—
251C4—102no—
252C4—102no—
253C4—102no—
254C4—102no—
255C4—404no—
256C4#6502912yes—
257C2—24no—
258C2—41no—
259C2#1059954612yes—
260C2#1059974411yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC5×#1297C2
socleC22×C5C2×#95
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenter#1297D5
hypocenterC5#8050
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
11. #65407C4semidirect
12. M16×Dic5C4semidirect
19. #64940C4semidirect
20. #64939C4semidirect
240. C5#8050semidirect

Maximal subgroups

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

subgroupindex
#106103502
#106051682
C5×#12972
#105981742
#105981092
#80505