Finite Group Databasebeta

← #13018190

Subgroups — #13018190

Order 1280.

540 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C4×#4082C211yesmaximal, characteristic
2C2×#64921C212yesmaximal
3#10604181C212yesmaximal, complemented
4#10598722C212yesmaximal, complemented
5C2×C4×C5×D4C411yescharacteristic
6C2×#4082C2211yescharacteristic
7C2×C4×Dic10C411yescharacteristic
8C2×#4002C2214yes—
9C2×C4⋊#170—22no—
10#65510C411yescharacteristic
11C4×C22⋊Dic5—22no—
12#65266C2211yescharacteristic
13#65263C411yescharacteristic
14#65234—22no—
15C42×Dic5C2211yescharacteristic
16#64921—24no—
17#64918—22no—
18#8579—51nomaximal, Sylow
19C22×C5×D4C2×C411yescharacteristic
20C23×C4×C5—21no—
21C22×Dic10C2×C411yescharacteristic
22C22×#170—24no—
23C4×C5×D4—42no—
24C2×C5×C4⋊C4C2×C411yescharacteristic
25C2×C5×C22⋊C4—21no—
26C2×C42×C5C2×C411yescharacteristic
27C2×C22⋊Dic5—22no—
28C2×C22⋊Dic5—22no—
29#4082—22no—
30#4082D412yes—
31#4082Q812yes—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×#683—21no—
34C2×C4×Dic5—21no—
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D412yes—
37C2×C4×Dic5D412yes—
38C2×C4×Dic5C2311yescharacteristic
39C4×Dic10—42no—
40#4002—24no—
41#4002—24no—
42C4⋊#170—28no—
43#3963—22no—
44#3963—22no—
45C4×#124—51no—
46#1767—52no—
47C2×#329—52no—
48#1295—52no—
49C24×C5—21no—
50C2×C5×D4—21no—
51C2×C5×D4—41no—
52C2×C5×D4—41no—
53C2×C5×D4C4⋊C412yes—
54C22×C4×C5—21no—
55C22×C4×C5—42no—
56C22×C4×C5—44no—
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C22×Dic5—21no—
61C22×Dic5—21no—
62C22×Dic5C22⋊C412yes—
63C22×Dic5C2×D412yes—
64C2×Dic10—21no—
65C2×Dic10—41no—
66C2×Dic10—41no—
67C2×Dic10C4⋊C412yes—
68C2×#170—28no—
69C2×#170—44no—
70C2×#170—44no—
71C5×C4⋊C4—41no—
72C5×C22⋊C4—42no—
73C42×C5—22no—
74C22⋊Dic5—24no—
75C22⋊Dic5—24no—
76C22⋊Dic5—44no—
77C4⋊Dic5—41no—
78#683—42no—
79C4×Dic5—24no—
80C4×Dic5—41no—
81C4×Dic5—42no—
82C4×Dic5—42no—
83C4×Dic5C2×D411yescharacteristic
84C4×Dic5C2×Q811yescharacteristic
85C4×Dic5#4112yes—
86C2×#124—51no—
87C2×C4×Q8—51no—
88C2×C4×D4AGL(1,𝔽5)11yescharacteristic
89C2×C4⋊C8—102no—
90C2×#97—54no—
91#391—51no—
92#390—51no—
93#388—102no—
94#382—51no—
95C4×C22⋊C4—102no—
96C43—51no—
97#336—102no—
98#329—104no—
99C23×C5—22no—
100C23×C5—41no—
101C23×C5—41no—
102C23×C5—42no—
103C23×C5—42no—
104C23×C5C2×C22⋊C411yescharacteristic
105C5×D4—42no—
106C5×D4—42no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—22no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5—84no—
114C2×C4×C5#10012yes—
115C2×C4×C5#10414yes—
116C2×C4×C5C2×C4⋊C411yescharacteristic
117C2×C4×C5#11711yescharacteristic
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—22no—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—22no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5—41no—
127C2×Dic5—42no—
128C2×Dic5#12112yes—
129C2×Dic5C22⋊Q812yes—
130Dic10—42no—
131Dic10—42no—
132#170—48no—
133C22×Q8—51no—
134C22×D4C2×AGL(1,𝔽5)11yescharacteristic
135C23×C4—21no—
136C22×C8—104no—
137#124—52no—
138#124—52no—
139#124—102no—
140C4×Q8—202no—
141C4×D4—42no—
142C2×C4⋊C4—51no—
143C2×C4⋊C4—101no—
144C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
145C2×C22⋊C4—21no—
146C2×C22⋊C4—102no—
147C2×C22⋊C4—102no—
148C2×C42—51no—
149C2×C42—52no—
150C2×C42—52no—
151C2×C42—51no—
152C2×C42—101no—
153C2×C42C2×AGL(1,𝔽5)11yescharacteristic
154C4⋊C8—108no—
155#97—104no—
156#97—104no—
157#95—102no—
158#95—102no—
159C22×C5—42no—
160C22×C5—44no—
161C22×C5—81no—
162C22×C5—81no—
163C22×C5—82no—
164C22×C5#38011yescharacteristic
165C22×C5C2×#10011yescharacteristic
166C22×C5#41311yescharacteristic
167C22×C5C2×#10412yes—
168C22×C5#42112yes—
169C4×C5—21no—
170C4×C5—21no—
171C4×C5—41no—
172C4×C5—81no—
173C4×C5#32914yescomplemented
174Dic5—22no—
175Dic5—22no—
176Dic5—42no—
177Dic5—42no—
178Dic5—81no—
179C24—21no—
180C2×Q8—52no—
181C2×Q8—101no—
182C2×Q8—201no—
183C2×Q8—201no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4C4⋊AGL(1,𝔽5)12yes—
188C22×C4—21no—
189C22×C4—44no—
190C22×C4—42no—
191C22×C4—52no—
192C22×C4—52no—
193C22×C4—101no—
194C22×C4—101no—
195C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
196C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
197C22×C4C22×AGL(1,𝔽5)11yescharacteristic
198C2×C8—108no—
199C2×C8—204no—
200C2×C8—204no—
201C4⋊C4—41no—
202C4⋊C4—201no—
203C4⋊C4—202no—
204C22⋊C4—42no—
205C22⋊C4—104no—
206C22⋊C4—104no—
207C22⋊C4—204no—
208C42—22no—
209C42—51no—
210C42—51no—
211C42—52no—
212C42—104no—
213C42—201no—
214C42—202no—
215C42—202no—
216C2×C5—82no—
217C2×C5C2×#32911yescharacteristic
218C2×C5#152912yes—
219C2×C5#153611yescharacteristic
220C2×C5#180011yescharacteristic
221C2×C5#180612yes—
222C23—22no—
223C23—42no—
224C23—41no—
225C23—41no—
226C23—42no—
227C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
228Q8—202no—
229Q8—202no—
230D4—42no—
231D4—42no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—52no—
239C2×C4—52no—
240C2×C4—84no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—102no—
245C2×C4—102no—
246C2×C4—102no—
247C2×C4—201no—
248C2×C4—201no—
249C2×C4—202no—
250C2×C4—201no—
251C2×C4#400814yes—
252C2×C4#401312yes—
253C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
254C2×C4#413011yescharacteristic
255C8—208no—
256C5#857911yescharacteristic, complemented, Sylow
257C22—42no—
258C22—44no—
259C22—82no—
260C22—81no—
261C22—81no—
262C22#6576111yescharacteristic
263C22#6576511yescharacteristic
264C22C2×#400812yes—
265C22#6579512yes—
266C22C2×#401311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—81no—
271C4—102no—
272C4—102no—
273C4—202no—
274C4—202no—
275C4—401no—
276C4#6492114yescomplemented
277C2—82no—
278C2#1060439712yes—
279C2#1060442112yes—
280C2#1060490711yescharacteristic
281C2C2×#6492111yescharacteristic
282C2#1060499511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC23×C5C2×C22⋊C4
prime radicalC22×C5×D4C2×C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5#8579
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. #10604181C2semidirect
4. #10598722C2semidirect
173. C4×C5#329semidirect
256. C5#8579semidirect
276. C4#64921semidirect

Maximal subgroups

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

subgroupindex
C4×#40822
C2×#649212
#106041812
#105987222
#85795