Finite Group Databasebeta

← #13025851

Subgroups — #13025851

Order 1280.

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

normal subgroups only

This group has 512 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#10614059C211yesmaximal, characteristic
2C2×#64923C212yesmaximal
3C4×#4005C212yesmaximal, complemented
4#10598724C212yesmaximal, complemented
5C2×C4×C5×D4C411yescharacteristic
6C2×#4082C2211yescharacteristic
7C2×C4×Dic10C2211yescharacteristic
8C2×#4005C2214yes—
9C4×#704—22no—
10#65510C411yescharacteristic
11#65499—22no—
12#65265C411yescharacteristic
13#65263C2211yescharacteristic
14#65233—22no—
15#65221C411yescharacteristic
16#64923C418yescomplemented
17#64919—22no—
18#12632—51nomaximal, Sylow
19C22×C5×D4C2×C411yescharacteristic
20C23×C4×C5—21no—
21C22×Dic10C2311yescharacteristic
22C2×#704—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#4082C2×C414yes—
31C2×C4⋊Dic5C2×C411yescharacteristic
32C2×#683—22no—
33C2×#683D412yes—
34C2×C4×Dic5C2×C411yescharacteristic
35C2×C4×Dic5C2×C411yescharacteristic
36C2×C4×Dic5D412yes—
37C4×Dic10—42no—
38#4005—24no—
39#4005C2×C418yescomplemented
40#4002—42no—
41C4×#170—42no—
42#3963—21no—
43#3963—21no—
44#3963—22no—
45#2326—51no—
46C2×#355—52no—
47C4×#101—52no—
48#1394—52no—
49C24×C5—21no—
50C2×C5×D4—21no—
51C2×C5×D4—41no—
52C2×C5×D4—41no—
53C2×C5×D4C4212yes—
54C22×C4×C5—21no—
55C22×C4×C5—42no—
56C22×C4×C5—82no—
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—41no—
65C2×Dic10—41no—
66C2×Dic10C22×C412yes—
67C2×Dic10#4112yes—
68#704—28no—
69#704—44no—
70C2×#170—44no—
71C5×C4⋊C4—41no—
72C5×C22⋊C4—42no—
73C42×C5—22no—
74C22⋊Dic5—28no—
75C22⋊Dic5—82no—
76C4⋊Dic5—41no—
77#683—42no—
78#683—82no—
79C4×Dic5—22no—
80C4×Dic5—22no—
81C4×Dic5—21no—
82C4×Dic5—41no—
83C4×Dic5C4212yes—
84C2×#124—51no—
85C2×C4×Q8—51no—
86C2×C4×D4AGL(1,𝔽5)11yescharacteristic
87C2×#101—54no—
88C4×M16—102no—
89#391—51no—
90#390—51no—
91#388—102no—
92#385—102no—
93#384—51no—
94#376—51no—
95#355—58no—
96#343—102no—
97C23×C5—22no—
98C23×C5—42no—
99C23×C5—42no—
100C23×C5—41no—
101C23×C5—41no—
102C23×C5C2×C22⋊C411yescharacteristic
103C5×D4—42no—
104C5×D4—42no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—41no—
109C2×C4×C5—41no—
110C2×C4×C5—42no—
111C2×C4×C5—41no—
112C2×C4×C5—84no—
113C2×C4×C5#9912yes—
114C2×C4×C5C2×C4211yescharacteristic
115C2×C4×C5#11711yescharacteristic
116C2×Dic5—22no—
117C2×Dic5—22no—
118C2×Dic5—22no—
119C2×Dic5—22no—
120C2×Dic5—41no—
121C2×Dic5—41no—
122C2×Dic5—42no—
123C2×Dic5—41no—
124C2×Dic5—41no—
125C2×Dic5—41no—
126C2×Dic5C4×D414yes—
127Dic10—42no—
128Dic10—42no—
129#170—48no—
130C22×Q8—51no—
131C22×D4C2×AGL(1,𝔽5)11yescharacteristic
132C23×C4—21no—
133C2×M16—104no—
134#124—54no—
135#124—102no—
136C4×Q8—202no—
137C4×D4—42no—
138C2×C4⋊C4—52no—
139C2×C4⋊C4—51no—
140C2×C4⋊C4—102no—
141C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
142C2×C22⋊C4—21no—
143C2×C22⋊C4—102no—
144C2×C22⋊C4—102no—
145C2×C42—51no—
146C2×C42—52no—
147C2×C42—51no—
148C2×C42C2×AGL(1,𝔽5)11yescharacteristic
149#101—58no—
150#101—104no—
151#97—202no—
152C4×C8—202no—
153#95—102no—
154#95—101no—
155#95—101no—
156C22×C5—21no—
157C22×C5—21no—
158C22×C5—44no—
159C22×C5—42no—
160C22×C5—82no—
161C22×C5—81no—
162C22×C5—81no—
163C22×C5C4×C22⋊C411yescharacteristic
164C22×C5C2×#9911yescharacteristic
165C22×C5#41011yescharacteristic
166C4×C5—22no—
167C4×C5—21no—
168C4×C5—21no—
169C4×C5—41no—
170C4×C5—81no—
171Dic5—24no—
172Dic5—42no—
173Dic5—42no—
174Dic5—81no—
175C24—21no—
176C2×Q8—52no—
177C2×Q8—52no—
178C2×Q8—201no—
179C2×Q8—201no—
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4C4×AGL(1,𝔽5)12yes—
184C22×C4—21no—
185C22×C4—42no—
186C22×C4—52no—
187C22×C4—52no—
188C22×C4—82no—
189C22×C4—101no—
190C22×C4—101no—
191C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
192C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
193C22×C4C22×AGL(1,𝔽5)11yescharacteristic
194M16—108no—
195M16—204no—
196C2×C8—204no—
197C4⋊C4—41no—
198C4⋊C4—202no—
199C4⋊C4—201no—
200C4⋊C4—402no—
201C22⋊C4—42no—
202C22⋊C4—108no—
203C22⋊C4—402no—
204C42—22no—
205C42—52no—
206C42—101no—
207C42—102no—
208C42—102no—
209C42—201no—
210C2×C5—21no—
211C2×C5—21no—
212C2×C5—82no—
213C2×C5C4×#9911yescharacteristic
214C2×C5#213311yescharacteristic
215C2×C5#213411yescharacteristic
216C23—22no—
217C23—42no—
218C23—42no—
219C23—41no—
220C23—41no—
221C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
222Q8—202no—
223Q8—202no—
224D4—42no—
225D4—42no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—54no—
234C2×C4—84no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—102no—
238C2×C4—102no—
239C2×C4—201no—
240C2×C4—201no—
241C2×C4—202no—
242C2×C4—201no—
243C2×C4—201no—
244C2×C4—201no—
245C2×C4#401112yes—
246C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
247C2×C4#413011yescharacteristic
248C8—208no—
249C5#1263211yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22—44no—
253C22—42no—
254C22—82no—
255C22—81no—
256C22—81no—
257C22#6574511yescharacteristic
258C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
259C22C2×#401111yescharacteristic
260C4—21no—
261C4—21no—
262C4—22no—
263C4—41no—
264C4—81no—
265C4—104no—
266C4—202no—
267C4—202no—
268C4—401no—
269C2—21no—
270C2—21no—
271C2—82no—
272C2C4×#401111yescharacteristic
273C2#1060492011yescharacteristic
274C2#1060499911yescharacteristic
subgroupG/H
centerC22C2×#4011
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC22×Dic10C23
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5#12632
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C4×#4005C2semidirect
4. #10598724C2semidirect
16. #64923C4semidirect
39. #4005C2×C4semidirect
249. C5#12632semidirect

Maximal subgroups

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

subgroupindex
#106140592
C2×#649232
C4×#40052
#105987242
#126325