Finite Group Databasebeta

← #13017067

Subgroups — #13017067

Order 1280.

528 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 116 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#10608211C211yesmaximal, characteristic
2C2×#64927C212yesmaximal
3#10604175C212yesmaximal, complemented
4#10598722C212yesmaximal, complemented
5C2×#4093C2211yescharacteristic
6C2×Q8×Dic5C411yescharacteristic
7C2×#4039C411yescharacteristic
8C2×#4002C2214yes—
9C5×#391C411yescharacteristic
10#65266C2211yescharacteristic
11#65228C411yescharacteristic
12C42×Dic5C2211yescharacteristic
13#64959—22no—
14#64955—22no—
15#64927C418yescomplemented
16#64918—22no—
17#64918—22no—
18#8224—51nomaximal, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×D20C2×C411yescharacteristic
21C22×C4×D5—21no—
22C22×#170—24no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C42×C5C2×C411yescharacteristic
25#4093—22no—
26#4093C2×C414yes—
27Q8×Dic5—42no—
28C2×#685—22no—
29C2×#685—22no—
30C2×#685—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×C4×Dic5—21no—
34C2×C4×Dic5C2×C411yescharacteristic
35C2×C4×Dic5D412yes—
36C2×C4×Dic5D412yes—
37C2×C4×Dic5C2311yescharacteristic
38#4039—42no—
39#4002—24no—
40#4002C2×C418yescomplemented
41C5×#95—22no—
42#3963—22no—
43C4×#124—51no—
44#1745—52no—
45C2×#329—52no—
46#1295—52no—
47C23×D5—21no—
48C2×C5×Q8—21no—
49C2×C5×Q8—41no—
50C2×C5×Q8—41no—
51C2×C5×Q8C4212yes—
52C22×C4×C5—21no—
53C22×C4×C5—21no—
54C22×C4×C5C22⋊C412yes—
55C22×C4×C5C22×C411yescharacteristic
56C22×Dic5—21no—
57C22×Dic5C22⋊C411yescharacteristic
58C22×Dic5C22⋊C411yescharacteristic
59C22×Dic5C2×D412yes—
60C2×D20—21no—
61C2×D20—41no—
62C2×D20—41no—
63C2×D20C4212yes—
64C2×C4×D5—44no—
65C2×C4×D5—42no—
66C2×#170—28no—
67C2×#170—44no—
68C2×#170—44no—
69C5×C4⋊C4—41no—
70C42×C5—41no—
71#685—28no—
72#685—42no—
73#685—44no—
74C4⋊Dic5—42no—
75C4⋊Dic5—41no—
76C4×Dic5—22no—
77C4×Dic5—42no—
78C4×Dic5—42no—
79C4×Dic5—42no—
80C4×Dic5C22×C412yes—
81C4×Dic5#4112yes—
82C2×#124—51no—
83C2×C4×Q8—51no—
84C2×C4×D4—51no—
85C2×#97—54no—
86#391AGL(1,𝔽5)11yescharacteristic
87#390—51no—
88#388—102no—
89#382—51no—
90C4×C22⋊C4—102no—
91C43—51no—
92#336—102no—
93#336—102no—
94#329—58no—
95C23×C5C2×C22⋊C411yescharacteristic
96C22×D5—22no—
97C22×D5—41no—
98C22×D5—41no—
99C22×D5—42no—
100C22×D5—42no—
101C5×Q8—42no—
102C5×Q8—42no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—22no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5—41no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5C2×C4211yescharacteristic
114C2×C4×C5#11711yescharacteristic
115C2×Dic5—22no—
116C2×Dic5—22no—
117C2×Dic5—22no—
118C2×Dic5—21no—
119C2×Dic5—22no—
120C2×Dic5—41no—
121C2×Dic5—42no—
122C2×Dic5#10012yes—
123C2×Dic5C4×D414yes—
124D20—42no—
125D20—42no—
126C4×D5—84no—
127#170—48no—
128C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
129C22×D4—51no—
130C23×C4—101no—
131C22×C8—104no—
132#124—54no—
133#124—102no—
134C4×Q8—202no—
135C4×D4—202no—
136C2×C4⋊C4—51no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
139C2×C22⋊C4—102no—
140C2×C22⋊C4—101no—
141C2×C22⋊C4—102no—
142C2×C42—51no—
143C2×C42—51no—
144C2×C42—52no—
145C2×C42—52no—
146C2×C42—101no—
147C2×C42C2×AGL(1,𝔽5)11yescharacteristic
148#97—58no—
149#97—104no—
150#95—22no—
151#95—102no—
152C22×C5C4×C22⋊C411yescharacteristic
153C22×C5C2×#10011yescharacteristic
154C22×C5#41311yescharacteristic
155C22×C5#42112yes—
156C22×C5#42112yes—
157C2×D5—42no—
158C2×D5—44no—
159C2×D5—81no—
160C2×D5—81no—
161C2×D5—82no—
162C4×C5—21no—
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—42no—
166C4×C5—81no—
167Dic5—24no—
168Dic5—22no—
169Dic5—41no—
170Dic5—81no—
171C24—101no—
172C2×Q8—21no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8C4×AGL(1,𝔽5)12yes—
176C2×D4—52no—
177C2×D4—101no—
178C2×D4—201no—
179C2×D4—201no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—52no—
183C22×C4—51no—
184C22×C4—51no—
185C22×C4—101no—
186C22×C4—202no—
187C22×C4—204no—
188C22×C4C22⋊AGL(1,𝔽5)12yes—
189C22×C4C22×AGL(1,𝔽5)11yescharacteristic
190C2×C8—108no—
191C2×C8—204no—
192C2×C8—204no—
193C4⋊C4—41no—
194C4⋊C4—201no—
195C4⋊C4—202no—
196C22⋊C4—108no—
197C22⋊C4—204no—
198C22⋊C4—202no—
199C42—41no—
200C42—52no—
201C42—52no—
202C42—102no—
203C42—202no—
204C42—202no—
205C42—202no—
206C2×C5#153311yescharacteristic
207C2×C5#153512yes—
208C2×C5#153611yescharacteristic
209C2×C5C4×#10011yescharacteristic
210C2×C5#175912yes—
211D5—82no—
212C23—102no—
213C23—202no—
214C23—201no—
215C23—201no—
216C23—202no—
217C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
218Q8—42no—
219Q8—42no—
220D4—202no—
221D4—202no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—54no—
233C2×C4—52no—
234C2×C4—102no—
235C2×C4—102no—
236C2×C4—102no—
237C2×C4—101no—
238C2×C4—102no—
239C2×C4—201no—
240C2×C4—202no—
241C2×C4—404no—
242C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
243C2×C4#413011yescharacteristic
244C8—208no—
245C5#822411yescharacteristic, complemented, Sylow
246C22—204no—
247C22—202no—
248C22—401no—
249C22—402no—
250C22—401no—
251C22C4×C22⋊AGL(1,𝔽5)11yescharacteristic
252C22#6577711yescharacteristic
253C22D5⋊#10011yescharacteristic
254C22#6578412yes—
255C22#6579512yes—
256C4—21no—
257C4—21no—
258C4—42no—
259C4—42no—
260C4—81no—
261C4—104no—
262C4—102no—
263C4—201no—
264C4—401no—
265C2—402no—
266C2#1060424511yescharacteristic
267C2#1060445012yes—
268C2#1060450812yes—
269C2#1060454311yescharacteristic
270C2#1060463811yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC5×#391C4
socleC23×C5C2×C22⋊C4
prime radicalC22×D20C2×C4
cosocleC2×C4×Dic5C23
hypercenter#391AGL(1,𝔽5)
hypocenterC5#8224
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #10604175C2semidirect
4. #10598722C2semidirect
15. #64927C4semidirect
40. #4002C2×C4semidirect
245. C5#8224semidirect

Maximal subgroups

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

subgroupindex
#106082112
C2×#649272
#106041752
#105987222
#82245