Finite Group Databasebeta

← #11996695

Subgroups — #11996695

Order 1280.

514 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C5×#2975C211yesmaximal, characteristic
2#10614115C211yesmaximal, characteristic
3#10602410C211yesmaximal, characteristic
4#10601572C212yesmaximal, complemented
5#10598237C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4015C2211yescharacteristic
8C5×#436—24no—
9C5×#431C2212yes—
10C5×#407—22no—
11#65510—21no—
12C2×#3965—21no—
13#65501—22no—
14#65266—21no—
15#65236C414yes—
16C4×C4⋊Dic5C2211yescharacteristic
17#65213C2212yes—
18#64750—21no—
19#64701—24no—
20#9399—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5D412yes—
23C22×Dic10C2×C412yes—
24C2×C5×M16—24no—
25C4×C5×D4—22no—
26C4×C5×D4—22no—
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C22⋊C4C2×C412yes—
29C2×C42×C5C2311yescharacteristic
30C2×C22⋊Dic5—24no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4×Dic5—21no—
35C2×#681—22no—
36#4015—22no—
37#4015—22no—
38C5×C4⋊C8D414yes—
39C5×C22⋊C8—24no—
40C5×C22⋊C8—22no—
41C4×C5×C8—22no—
42#3965—42no—
43#3963—24no—
44#3963C2×C412yes—
45C4⋊#168—22no—
46C4⋊#168—22no—
47#2975D511yescharacteristic
48#2563—51no—
49#1800—51no—
50#1548—52no—
51#1303—52no—
52C24×C5C22⋊C412yes—
53C2×C5×D4—22no—
54C2×C5×D4—21no—
55C2×C5×D4—22no—
56C2×C5×D4—21no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—44no—
60C22×C4×C5C22⋊C412yes—
61C22×C4×C5C22×C411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×C4×C5C2×D411yescharacteristic
64C22×Dic5—22no—
65C22×Dic5—22no—
66C2×Dic10—24no—
67C2×Dic10—82no—
68C5×M16—84no—
69C2×C5×C8—24no—
70C5×C4⋊C4—22no—
71C5×C22⋊C4—24no—
72C42×C5C2×D412yes—
73C42×C5#4112yes—
74C22⋊Dic5—84no—
75C4⋊Dic5—42no—
76C4⋊Dic5—41no—
77C4⋊Dic5—42no—
78C4⋊Dic5—41no—
79C4×Dic5—41no—
80C4×Dic5—41no—
81#681—42no—
82#681—42no—
83C2×#168—42no—
84C2×C4⋊Q8—51no—
85C2×C4×D4C2×D511yescharacteristic
86#436—24no—
87#431C2×D512yes—
88#423—52no—
89C2×#100—101no—
90#407—22no—
91#393—54no—
92#390—101no—
93#382—101no—
94#380—102no—
95C4×C4⋊C4—51no—
96#343—101no—
97#333—104no—
98C23×C5—22no—
99C23×C5—22no—
100C23×C5—22no—
101C23×C5—42no—
102C23×C5—42no—
103C23×C5C2×C22⋊C411yescharacteristic
104C5×D4—42no—
105C5×D4—42no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—41no—
109C2×C4×C5—44no—
110C2×C4×C5—42no—
111C2×C4×C5—82no—
112C2×C4×C5C4×D412yes—
113C2×C4×C5#12011yescharacteristic
114C2×C4×C5#12112yes—
115C2×C4×C5#12311yescharacteristic
116C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C5#13712yes—
118C2×C4×C5#13711yescharacteristic
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—44no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124Dic10—84no—
125C5×C8—44no—
126#168—82no—
127C22×Q8—52no—
128C22×D4D2011yescharacteristic
129C23×C4C22⋊D512yes—
130C2×M16—24no—
131C2×M16—102no—
132C4⋊Q8—102no—
133C4⋊Q8—102no—
134C4×D4—22no—
135C4×D4—22no—
136C2×C4⋊C4—101no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4—101no—
139C2×C4⋊C4D2011yescharacteristic
140C2×C22⋊C4—104no—
141C2×C22⋊C4C4×D512yes—
142C2×C42—101no—
143C2×C42C22×D511yescharacteristic
144C4⋊C8—102no—
145C4⋊C8—102no—
146C4⋊C8C22⋊D514yes—
147#100—202no—
148C22⋊C8—24no—
149C22⋊C8—22no—
150C4×C8—22no—
151#95—52no—
152#95—104no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5—44no—
156C22×C5—42no—
157C22×C5—42no—
158C22×C5—42no—
159C22×C5—82no—
160C22×C5#38611yescharacteristic
161C22×C5#41711yescharacteristic
162C22×C5#41911yescharacteristic
163C4×C5—21no—
164C4×C5—22no—
165C4×C5—42no—
166C4×C5#45512yes—
167C4×C5#46812yes—
168C4×C5#47012yes—
169Dic5—82no—
170Dic5—82no—
171C24#68512yes—
172C2×Q8—104no—
173C2×Q8—402no—
174C2×D4—21no—
175C2×D4—22no—
176C2×D4—21no—
177C2×D4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—44no—
181C22×C4—102no—
182C22×C4—102no—
183C22×C4#68512yes—
184C22×C4C2×C4×D511yescharacteristic
185C22×C4C2×D2011yescharacteristic
186C22×C4C2×C22⋊D511yescharacteristic
187M16—84no—
188M16—202no—
189M16—202no—
190C2×C8—24no—
191C2×C8—202no—
192C4⋊C4—22no—
193C4⋊C4—202no—
194C4⋊C4—201no—
195C4⋊C4—201no—
196C4⋊C4—202no—
197C22⋊C4—24no—
198C22⋊C4—404no—
199C42—201no—
200C42—201no—
201C42#70912yes—
202C42C2×C22⋊D512yes—
203C2×C5—21no—
204C2×C5—21no—
205C2×C5—82no—
206C2×C5#188511yescharacteristic
207C2×C5#189411yescharacteristic
208C2×C5#191411yescharacteristic
209C23—22no—
210C23—22no—
211C23—22no—
212C23—42no—
213C23—42no—
214C23C2×#68511yescharacteristic
215Q8—404no—
216D4—42no—
217D4—42no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—44no—
222C2×C4—42no—
223C2×C4—82no—
224C2×C4—202no—
225C2×C4—204no—
226C2×C4—202no—
227C2×C4—202no—
228C2×C4—202no—
229C2×C4#405411yescharacteristic
230C2×C4#405512yes—
231C2×C4#405511yescharacteristic
232C2×C4C4×C22⋊D512yes—
233C2×C4#407511yescharacteristic
234C2×C4#407612yes—
235C2×C4#409911yescharacteristic
236C8—44no—
237C8—402no—
238C5#939911yescharacteristic, complemented, Sylow
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#6540911yescharacteristic
247C22#6542211yescharacteristic
248C22#6550211yescharacteristic
249C4—22no—
250C4—21no—
251C4—42no—
252C4—402no—
253C4—402no—
254C4#6542312yes—
255C4#6542612yes—
256C4#6553112yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1060244211yescharacteristic
261C2#1060278211yescharacteristic
262C2#1060282311yescharacteristic
subgroupG/H
centerC22#65502
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2975C2
socleC22×C5#386
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#2975D5
hypocenterC5#9399
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
4. #10601572C2semidirect
5. #10598237C2semidirect
238. C5#9399semidirect

Maximal subgroups

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

subgroupindex
C5×#29752
#106141152
#106024102
#106015722
#105982372
#93995