Finite Group Databasebeta

← #13018191

Subgroups — #13018191

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×#4093C211yesmaximal, characteristic
2C2×#64927C212yesmaximal
3#10604181C212yesmaximal, complemented
4#10598722C212yesmaximal, complemented
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4093C2211yescharacteristic
7C2×C4×D20C411yescharacteristic
8C2×#4002C2214yes—
9C2×C4⋊#170—22no—
10#65519C411yescharacteristic
11#65279—22no—
12#65277C411yescharacteristic
13#65266C2211yescharacteristic
14C4×#685—22no—
15C42×Dic5C2211yescharacteristic
16#64927—24no—
17#64918—22no—
18#8579—51nomaximal, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×D20C2×C411yescharacteristic
21C22×C4×D5—21no—
22C22×#170—24no—
23C4×C5×Q8—42no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C42×C5—21no—
27C2×C42×C5C2×C411yescharacteristic
28#4093—22no—
29#4093D412yes—
30#4093Q812yes—
31C2×#685—22no—
32C2×#685—21no—
33C2×#685—22no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D412yes—
37C2×C4×Dic5D412yes—
38C2×C4×Dic5C2311yescharacteristic
39C4×D20—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—
49C23×D5—21no—
50C2×C5×Q8—21no—
51C2×C5×Q8—41no—
52C2×C5×Q8—41no—
53C2×C5×Q8C4⋊C412yes—
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22×C411yescharacteristic
59C22×Dic5—21no—
60C22×Dic5C22⋊C412yes—
61C22×Dic5C2×D412yes—
62C2×D20—21no—
63C2×D20—41no—
64C2×D20—41no—
65C2×D20C4⋊C412yes—
66C2×C4×D5—42no—
67C2×C4×D5—44no—
68C2×#170—28no—
69C2×#170—44no—
70C2×#170—44no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—42no—
73C42×C5—22no—
74C42×C5—42no—
75#685—24no—
76#685—24no—
77#685—44no—
78#685—42no—
79C4⋊Dic5—41no—
80C4×Dic5—24no—
81C4×Dic5—41no—
82C4×Dic5—42no—
83C4×Dic5C2×D411yescharacteristic
84C4×Dic5C2×Q811yescharacteristic
85C4×Dic5#4112yes—
86C2×#124—51no—
87C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
88C2×C4×D4—51no—
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×C5C2×C22⋊C411yescharacteristic
100C22×D5—22no—
101C22×D5—41no—
102C22×D5—41no—
103C22×D5—42no—
104C22×D5—42no—
105C5×Q8—42no—
106C5×Q8—42no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—21no—
111C2×C4×C5—22no—
112C2×C4×C5—41no—
113C2×C4×C5—41no—
114C2×C4×C5—41no—
115C2×C4×C5—42no—
116C2×C4×C5#10012yes—
117C2×C4×C5#10414yes—
118C2×C4×C5C2×C4⋊C411yescharacteristic
119C2×C4×C5#11711yescharacteristic
120C2×Dic5—22no—
121C2×Dic5—22no—
122C2×Dic5—22no—
123C2×Dic5—22no—
124C2×Dic5—22no—
125C2×Dic5—41no—
126C2×Dic5—42no—
127C2×Dic5#12112yes—
128C2×Dic5C22⋊Q812yes—
129D20—42no—
130D20—42no—
131C4×D5—84no—
132#170—48no—
133C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
134C22×D4—51no—
135C23×C4—101no—
136C22×C8—104no—
137#124—52no—
138#124—52no—
139#124—102no—
140C4×Q8—42no—
141C4×D4—202no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—51no—
144C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
145C2×C22⋊C4—102no—
146C2×C22⋊C4—102no—
147C2×C22⋊C4—101no—
148C2×C42—21no—
149C2×C42—51no—
150C2×C42—52no—
151C2×C42—52no—
152C2×C42—51no—
153C2×C42C2×AGL(1,𝔽5)11yescharacteristic
154C4⋊C8—108no—
155#97—104no—
156#97—104no—
157#95—102no—
158#95—102no—
159C22×C5#38011yescharacteristic
160C22×C5C2×#10011yescharacteristic
161C22×C5#41311yescharacteristic
162C22×C5C2×#10412yes—
163C22×C5#42112yes—
164C2×D5—42no—
165C2×D5—44no—
166C2×D5—81no—
167C2×D5—81no—
168C2×D5—82no—
169C4×C5—21no—
170C4×C5—21no—
171C4×C5—41no—
172C4×C5—42no—
173C4×C5—81no—
174C4×C5#32914yescomplemented
175Dic5—22no—
176Dic5—22no—
177Dic5—42no—
178Dic5—81no—
179C24—101no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8C4⋊AGL(1,𝔽5)12yes—
184C2×D4—52no—
185C2×D4—101no—
186C2×D4—201no—
187C2×D4—201no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—52no—
191C22×C4—52no—
192C22×C4—101no—
193C22×C4—204no—
194C22×C4—202no—
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—42no—
203C4⋊C4—201no—
204C22⋊C4—104no—
205C22⋊C4—104no—
206C22⋊C4—202no—
207C22⋊C4—204no—
208C42—22no—
209C42—42no—
210C42—51no—
211C42—51no—
212C42—52no—
213C42—104no—
214C42—201no—
215C42—202no—
216C2×C5C2×#32911yescharacteristic
217C2×C5#152912yes—
218C2×C5#153611yescharacteristic
219C2×C5#180011yescharacteristic
220C2×C5#180612yes—
221D5—82no—
222C23—102no—
223C23—202no—
224C23—201no—
225C23—201no—
226C23—202no—
227C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
228Q8—42no—
229Q8—42no—
230D4—202no—
231D4—202no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—52no—
242C2×C4—52no—
243C2×C4—102no—
244C2×C4—102no—
245C2×C4—102no—
246C2×C4—102no—
247C2×C4—102no—
248C2×C4—201no—
249C2×C4—202no—
250C2×C4—404no—
251C2×C4#401014yes—
252C2×C4#401312yes—
253C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
254C2×C4#413011yescharacteristic
255C8—208no—
256C5#857911yescharacteristic, complemented, Sylow
257C22—202no—
258C22—204no—
259C22—402no—
260C22—401no—
261C22—401no—
262C22#6576111yescharacteristic
263C22#6576511yescharacteristic
264C22C2×#401012yes—
265C22#6579512yes—
266C22C2×#401311yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—41no—
271C4—81no—
272C4—102no—
273C4—102no—
274C4—202no—
275C4—401no—
276C4#6492714yescomplemented
277C2—402no—
278C2#1060443212yes—
279C2#1060445512yes—
280C2#1060490711yescharacteristic
281C2C2×#6492711yescharacteristic
282C2#1060499511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socleC23×C5C2×C22⋊C4
prime radicalC22×D20C2×C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#8579
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10604181C2semidirect
4. #10598722C2semidirect
174. C4×C5#329semidirect
256. C5#8579semidirect
276. C4#64927semidirect

Maximal subgroups

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

subgroupindex
C4×#40932
C2×#649272
#106041812
#105987222
#85795