Finite Group Databasebeta

← #13018509

Subgroups — #13018509

Order 1280.

530 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C2×#65266C211yesmaximal, characteristic
2#10604902C212yesmaximal
3#10598821C214yesmaximal
4C22×C5×C4⋊C4C411yescharacteristic
5C22×C4⋊Dic5C411yescharacteristic
6C22×C4×Dic5C2211yescharacteristic
7C2×C22⋊#170C2214yes—
8C2×#3963C412yes—
9C2×#3963C2212yes—
10#65266—22no—
11#65266—22no—
12#64918—22no—
13#64918—22no—
14#8703—51nomaximal, Sylow
15C23×C4×C5C2×C412yes—
16C23×C4×C5C2×C411yescharacteristic
17C23×Dic5C2×C411yescharacteristic
18C23×Dic5C2×C412yes—
19C23×Dic5C2311yescharacteristic
20C22×#170—24no—
21C2×C5×C4⋊C4—21no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—42no—
24C2×C4⋊Dic5—21no—
25C2×C4⋊Dic5—21no—
26C2×C4⋊Dic5—42no—
27C2×C4×Dic5—24no—
28C2×C4×Dic5D412yes—
29C2×C4×Dic5D412yes—
30C22⋊#170—28no—
31#3963—24no—
32#3963—24no—
33C2×#382—51no—
34#1817—52no—
35#1280—54no—
36C24×C5C22×C411yescharacteristic
37C22×C4×C5—22no—
38C22×C4×C5—22no—
39C22×C4×C5—22no—
40C22×C4×C5—22no—
41C22×C4×C5—24no—
42C22×C4×C5—42no—
43C22×C4×C5—42no—
44C22×C4×C5C22⋊C411yescharacteristic
45C22×C4×C5C22⋊C411yescharacteristic
46C22×Dic5—22no—
47C22×Dic5—22no—
48C22×Dic5—22no—
49C22×Dic5—22no—
50C22×Dic5—24no—
51C22×Dic5—41no—
52C22×Dic5—41no—
53C22×Dic5—42no—
54C22×Dic5—42no—
55C22×Dic5C22⋊C412yes—
56C22×Dic5C2×D412yes—
57C22×Dic5#4114yes—
58C2×#170—44no—
59C2×#170—44no—
60C2×#170—44no—
61C5×C4⋊C4—42no—
62C5×C4⋊C4—42no—
63C4⋊Dic5—42no—
64C4⋊Dic5—42no—
65C4×Dic5—24no—
66C4×Dic5—24no—
67C22×C4⋊C4—51no—
68C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
69C22×C42—51no—
70C2×C22⋊C8—54no—
71#382—102no—
72#382—102no—
73C2×#95—52no—
74C2×#95—52no—
75#336—102no—
76#336—102no—
77C23×C5—21no—
78C23×C5—21no—
79C23×C5—21no—
80C23×C5—21no—
81C23×C5C2×C22⋊C411yescharacteristic
82C23×C5#11712yes—
83C23×C5#13112yes—
84C23×C5#13112yes—
85C2×C4×C5—28no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—42no—
91C2×C4×C5—42no—
92C2×C4×C5—42no—
93C2×C4×C5—84no—
94C2×C4×C5#10012yes—
95C2×C4×C5#10112yes—
96C2×Dic5—22no—
97C2×Dic5—22no—
98C2×Dic5—22no—
99C2×Dic5—22no—
100C2×Dic5—22no—
101C2×Dic5—44no—
102C2×Dic5—44no—
103C2×Dic5—42no—
104C2×Dic5—42no—
105C2×Dic5—42no—
106C2×Dic5—84no—
107C2×Dic5#12314yes—
108#170—84no—
109C23×C4—51no—
110C23×C4—51no—
111C23×C4—52no—
112C23×C4C2×AGL(1,𝔽5)12yes—
113C23×C4C2×AGL(1,𝔽5)11yescharacteristic
114C22×C8—104no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—101no—
119C2×C4⋊C4—101no—
120C2×C4⋊C4—202no—
121C2×C42—52no—
122C2×C42—52no—
123C2×C42—104no—
124C22⋊C8—108no—
125#95—104no—
126#95—104no—
127C22×C5—22no—
128C22×C5—22no—
129C22×C5—22no—
130C22×C5—22no—
131C22×C5—22no—
132C22×C5—22no—
133C22×C5#38111yescharacteristic
134C22×C5#40811yescharacteristic
135C22×C5#40811yescharacteristic
136C22×C5#41011yescharacteristic
137C22×C5#41011yescharacteristic
138C22×C5C2×#10011yescharacteristic
139C22×C5C2×#10111yescharacteristic
140C22×C5#43314yes—
141C4×C5—22no—
142C4×C5—22no—
143C4×C5—82no—
144Dic5—24no—
145Dic5—42no—
146Dic5—82no—
147C24C22×AGL(1,𝔽5)11yescharacteristic
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—24no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—52no—
156C22×C4—54no—
157C22×C4—52no—
158C22×C4—102no—
159C22×C4—102no—
160C22×C4—102no—
161C22×C4—102no—
162C22×C4—104no—
163C22×C4—201no—
164C22×C4—201no—
165C22×C4—202no—
166C22×C4—202no—
167C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
168C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
169C2×C8—204no—
170C2×C8—204no—
171C2×C8—204no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—202no—
175C4⋊C4—202no—
176C42—104no—
177C42—104no—
178C2×C5—24no—
179C2×C5#146911yescharacteristic
180C2×C5#146911yescharacteristic
181C2×C5#147011yescharacteristic
182C2×C5#147011yescharacteristic
183C2×C5#181811yescharacteristic
184C2×C5#182011yescharacteristic
185C2×C5#182111yescharacteristic
186C23—21no—
187C23—21no—
188C23—21no—
189C23—21no—
190C23#413012yes—
191C23#413112yes—
192C23#413312yes—
193C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
194C2×C4—28no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—54no—
203C2×C4—84no—
204C2×C4—102no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—102no—
208C2×C4—102no—
209C2×C4—204no—
210C2×C4—204no—
211C2×C4—202no—
212C2×C4—202no—
213C2×C4—202no—
214C2×C4—404no—
215C2×C4#400512yes—
216C2×C4#401312yes—
217C8—404no—
218C5#870311yescharacteristic, complemented, Sylow
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#6570614yes—
226C22C2×#400511yescharacteristic
227C22#6576411yescharacteristic
228C22#6577111yescharacteristic
229C22#6577611yescharacteristic
230C22#6578511yescharacteristic
231C22#6578711yescharacteristic
232C22C2×#401311yescharacteristic
233C4—22no—
234C4—22no—
235C4—82no—
236C4—104no—
237C4—202no—
238C4—402no—
239C2—24no—
240C2#1060429811yescharacteristic
241C2#1060429911yescharacteristic
242C2#1060430711yescharacteristic
243C2#1060431811yescharacteristic
244C2#1060490811yescharacteristic
245C2#1060493611yescharacteristic
246C2#1060497811yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutator, prime radicalC24×C5C22×C4
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
cosocleC23×Dic5C23
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8703
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
218. C5#8703semidirect

Maximal subgroups

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

subgroupindex
C2×#652662
#106049022
#105988212
#87035