Finite Group Databasebeta

← #13021069

Subgroups — #13021069

Order 1280.

456 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 102 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#10606086C211yesmaximal, characteristic
2C2×#64870C214yesmaximal
3#10604180C211yesmaximal, characteristic
4#10604175C211yesmaximal, characteristic
5C2×#4036C2212yes—
6C2×#4004—21no—
7C2×#4002C2212yes—
8C2×#4002C2212yes—
9C5×#384C411yescharacteristic
10#65274—21no—
11#65274—21no—
12#65266C412yes—
13#65262—21no—
14#65262—21no—
15#65224C411yescharacteristic
16C42×Dic5C2211yescharacteristic
17#64918—21no—
18#64918—21no—
19#64918—21no—
20#64870—28no—
21#9690—51nomaximal, Sylow
22C22×#170—22no—
23C22×#170—22no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4C2×C412yes—
27C2×C42×C5C2×C411yescharacteristic
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—22no—
31C2×C4⋊Dic5C2×C412yes—
32C2×#683—22no—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D411yescharacteristic
35C2×C4×Dic5D411yescharacteristic
36C2×C4×Dic5D411yescharacteristic
37C2×C4×Dic5D411yescharacteristic
38C2×C4×Dic5C2311yescharacteristic
39#4036—24no—
40#4036—24no—
41#4004—24no—
42#4002—24no—
43#4002—22no—
44#4002D414yes—
45#3963—22no—
46#3963—22no—
47#2859—51no—
48#1767—51no—
49#1745—51no—
50C2×#330—54no—
51C22×C4×C5—22no—
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22⋊C411yescharacteristic
54C22×C4×C5C22×C411yescharacteristic
55C22×Dic5—22no—
56C22×Dic5C22⋊C411yescharacteristic
57C22×Dic5C22⋊C411yescharacteristic
58C22×Dic5C2×D411yescharacteristic
59C22×Dic5C2×D411yescharacteristic
60C2×#170—24no—
61C2×#170—24no—
62C2×#170—42no—
63C2×#170—42no—
64C2×#170—42no—
65C2×#170—42no—
66C5×C4⋊C4—24no—
67C5×C4⋊C4—42no—
68C5×C4⋊C4—42no—
69C42×C5—22no—
70C4⋊Dic5—24no—
71C4⋊Dic5—42no—
72C4⋊Dic5—42no—
73C4⋊Dic5—42no—
74C4⋊Dic5—42no—
75#683—44no—
76C4×Dic5—22no—
77C4×Dic5—22no—
78C4×Dic5—41no—
79C4×Dic5—41no—
80C4×Dic5—41no—
81C4×Dic5C2×D412yes—
82C4×Dic5#4112yes—
83C2×#125—52no—
84C2×C4⋊C8—101no—
85C2×#97—52no—
86C2×#97—52no—
87#389—101no—
88#389—101no—
89#389—101no—
90#389—101no—
91#384—51no—
92#384AGL(1,𝔽5)11yescharacteristic
93#382—52no—
94C43—51no—
95#336—101no—
96#336—101no—
97#336—101no—
98#330—108no—
99C23×C5C2×C22⋊C411yescharacteristic
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5#10112yes—
110C2×C4×C5#10412yes—
111C2×C4×C5C4×D412yes—
112C2×Dic5—21no—
113C2×Dic5—21no—
114C2×Dic5—21no—
115C2×Dic5—21no—
116C2×Dic5—21no—
117C2×Dic5—21no—
118C2×Dic5—21no—
119C2×Dic5—21no—
120C2×Dic5—21no—
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5#10112yes—
125C2×Dic5#12112yes—
126C2×Dic5#12411yescharacteristic
127C2×Dic5#12711yescharacteristic
128#170—44no—
129#170—44no—
130C22×C8—102no—
131C22×C8—102no—
132#125—104no—
133#125—104no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—52no—
137C2×C4⋊C4—102no—
138C2×C4⋊C4—102no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
142C2×C42—51no—
143C2×C42—51no—
144C2×C42—51no—
145C2×C42—51no—
146C2×C42—51no—
147C2×C42—51no—
148C2×C42C2×AGL(1,𝔽5)11yescharacteristic
149C4⋊C8—104no—
150#97—54no—
151#97—102no—
152#97—104no—
153#95—102no—
154#95—102no—
155C22×C5#39011yescharacteristic
156C22×C5C2×#10111yescharacteristic
157C22×C5C2×#10111yescharacteristic
158C22×C5C2×#10411yescharacteristic
159C22×C5#42111yescharacteristic
160C22×C5#42111yescharacteristic
161C22×C5#42111yescharacteristic
162C4×C5—22no—
163C4×C5—22no—
164C4×C5—22no—
165C4×C5—82no—
166Dic5—22no—
167Dic5—21no—
168Dic5—21no—
169Dic5—22no—
170Dic5—41no—
171Dic5—82no—
172C22×C4—22no—
173C22×C4—51no—
174C22×C4—51no—
175C22×C4—51no—
176C22×C4—51no—
177C22×C4—102no—
178C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
179C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
180C22×C4C22×AGL(1,𝔽5)11yescharacteristic
181C2×C8—104no—
182C2×C8—104no—
183C2×C8—202no—
184C2×C8—202no—
185C2×C8—202no—
186C2×C8—202no—
187C4⋊C4—24no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—104no—
191C4⋊C4—202no—
192C4⋊C4—204no—
193C4⋊C4—202no—
194C4⋊C4—202no—
195C4⋊C4—202no—
196C42—22no—
197C42—52no—
198C42—52no—
199C42—102no—
200C42—102no—
201C42—201no—
202C42—201no—
203C42—201no—
204C2×C5#152811yescharacteristic
205C2×C5#153111yescharacteristic
206C2×C5#153411yescharacteristic
207C2×C5#153711yescharacteristic
208C2×C5#196311yescharacteristic
209C2×C5#196611yescharacteristic
210C2×C5#198011yescharacteristic
211C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—52no—
222C2×C4—51no—
223C2×C4—51no—
224C2×C4—52no—
225C2×C4—101no—
226C2×C4—101no—
227C2×C4—101no—
228C2×C4—101no—
229C2×C4—101no—
230C2×C4—101no—
231C2×C4—101no—
232C2×C4—101no—
233C2×C4—101no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4—202no—
237C2×C4#400512yes—
238C2×C4#401012yes—
239C2×C4D4×AGL(1,𝔽5)12yes—
240C8—204no—
241C8—204no—
242C5#969011yescharacteristic, complemented, Sylow
243C22C2×#400511yescharacteristic
244C22#6576911yescharacteristic
245C22#6576911yescharacteristic
246C22#6578011yescharacteristic
247C22C2×#401011yescharacteristic
248C22#6578411yescharacteristic
249C22D5⋊#10111yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—102no—
255C4—102no—
256C4—101no—
257C4—101no—
258C4—201no—
259C4—402no—
260C2#1060426611yescharacteristic
261C2#1060426711yescharacteristic
262C2#1060433911yescharacteristic
263C2#1060461211yescharacteristic
264C2#1060463711yescharacteristic
265C2#1060463911yescharacteristic
266C2#1060467811yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#384C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenter#384AGL(1,𝔽5)
hypocenterC5#9690
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
242. C5#9690semidirect

Maximal subgroups

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

subgroupindex
#106060862
C2×#648702
#106041802
#106041752
#96905