Finite Group Databasebeta

← #13023192

Subgroups — #13023192

Order 1280.

462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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#10613800C211yesmaximal, characteristic
2#10604877C212yesmaximal
3#10598820C214yesmaximal
4C22×C42×C5C411yescharacteristic
5C2×#4072C411yescharacteristic
6C2×#4072C2211yescharacteristic
7#65748—22no—
8#65499C412yes—
9#65499C2212yes—
10C4×#683—22no—
11#65217—22no—
12#64933C2214yes—
13#64913—22no—
14#11452—51nomaximal, Sylow
15C23×C4×C5C2×C412yes—
16C23×C4×C5C2×C411yescharacteristic
17C2×C42×C5—21no—
18C2×C42×C5—21no—
19C2×C42×C5—41no—
20C2×C42×C5—41no—
21C2×C22⋊Dic5C2×C412yes—
22C2×C22⋊Dic5C2×C411yescharacteristic
23C2×C22⋊Dic5C2311yescharacteristic
24#4072—22no—
25#4072—41no—
26#4072—41no—
27#4072C814yescomplemented
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5D412yes—
30C2×#683—22no—
31C2×#683—22no—
32C2×C4×Dic5—21no—
33C2×C4×Dic5D412yes—
34C22⋊#170—24no—
35C4⋊#170—42no—
36C4×#170—42no—
37#3963—22no—
38#3963—22no—
39#2296—51no—
40#1458—52no—
41#1326—54no—
42C24×C5C22×C411yescharacteristic
43C22×C4×C5—21no—
44C22×C4×C5—21no—
45C22×C4×C5—22no—
46C22×C4×C5—22no—
47C22×C4×C5—44no—
48C22×C4×C5—42no—
49C22×C4×C5C22⋊C411yescharacteristic
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C2×C812yes—
52C22×C4×C5M1612yes—
53C22×Dic5—22no—
54C22×Dic5C22⋊C412yes—
55C22×Dic5C2×D412yes—
56C2×#170—44no—
57C42×C5—42no—
58C42×C5—41no—
59C42×C5—41no—
60C22⋊Dic5—22no—
61C22⋊Dic5—41no—
62C22⋊Dic5—41no—
63C22⋊Dic5C2×C814yes—
64C4⋊Dic5—24no—
65C4⋊Dic5—42no—
66#683—44no—
67#683—44no—
68C4×Dic5—24no—
69C4×Dic5—22no—
70C4×Dic5—22no—
71C2×#117—51no—
72C2×#117—51no—
73C22×C42AGL(1,𝔽5)11yescharacteristic
74#431—102no—
75#389—102no—
76#385—52no—
77#385—52no—
78C4×C4⋊C4—102no—
79#324—102no—
80#323—54no—
81C23×C5—21no—
82C23×C5—21no—
83C23×C5—42no—
84C23×C5C2×C22⋊C411yescharacteristic
85C23×C5C22×C811yescharacteristic
86C23×C5C2×M1611yescharacteristic
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5—22no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5—24no—
94C2×C4×C5—42no—
95C2×C4×C5—44no—
96C2×C4×C5—42no—
97C2×C4×C5—44no—
98C2×C4×C5C22⋊C812yes—
99C2×C4×C5C22⋊C812yes—
100C2×C4×C5#9911yescharacteristic
101C2×C4×C5#9911yescharacteristic
102C2×C4×C5#10112yes—
103C2×Dic5—24no—
104C2×Dic5—22no—
105C2×Dic5—22no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5—42no—
109C2×Dic5—42no—
110#170—84no—
111C23×C4C2×AGL(1,𝔽5)12yes—
112C23×C4C2×AGL(1,𝔽5)11yescharacteristic
113#117—54no—
114#117—102no—
115#117—201no—
116#117—201no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4—101no—
119C2×C4⋊C4—102no—
120C2×C4⋊C4—102no—
121C2×C22⋊C4—52no—
122C2×C22⋊C4—51no—
123C2×C22⋊C4—51no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42—41no—
127C2×C42—41no—
128C2×C42—52no—
129C2×C42—101no—
130C4⋊C8—202no—
131C22⋊C8—104no—
132C4×C8—202no—
133#95—102no—
134#95—102no—
135C22×C5—22no—
136C22×C5—21no—
137C22×C5—21no—
138C22×C5—41no—
139C22×C5—41no—
140C22×C5—42no—
141C22×C5—42no—
142C22×C5C2×C22⋊C811yescharacteristic
143C22×C5C2×#9911yescharacteristic
144C22×C5C2×#10111yescharacteristic
145C4×C5—22no—
146C4×C5—44no—
147C4×C5#32412yes—
148C4×C5#32412yes—
149Dic5—44no—
150Dic5—42no—
151Dic5—42no—
152C24C22×AGL(1,𝔽5)11yescharacteristic
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—22no—
157C22×C4—44no—
158C22×C4—42no—
159C22×C4—52no—
160C22×C4—52no—
161C22×C4—102no—
162C22×C4D5⋊C812yes—
163C22×C4#70012yes—
164C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
165C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
166C2×C8—204no—
167C4⋊C4—104no—
168C4⋊C4—202no—
169C4⋊C4—204no—
170C4⋊C4—204no—
171C22⋊C4—54no—
172C22⋊C4—102no—
173C22⋊C4—201no—
174C22⋊C4—201no—
175C42—42no—
176C42—41no—
177C42—41no—
178C42—104no—
179C42—102no—
180C42—102no—
181C2×C5—21no—
182C2×C5—21no—
183C2×C5—41no—
184C2×C5—41no—
185C2×C5C2×#32411yescharacteristic
186C2×C5#212012yes—
187C23—21no—
188C23—21no—
189C23—42no—
190C23C2×D5⋊C811yescharacteristic
191C23C2×#70011yescharacteristic
192C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—24no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—44no—
204C2×C4—102no—
205C2×C4—102no—
206C2×C4—104no—
207C2×C4—202no—
208C2×C4—202no—
209C2×C4—202no—
210C2×C4—202no—
211C2×C4#400312yes—
212C2×C4#400312yes—
213C2×C4#400512yes—
214C2×C4#401111yescharacteristic
215C2×C4#401111yescharacteristic
216C8—404no—
217C5#1145211yescharacteristic, complemented, Sylow
218C22—22no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22C2×#400311yescharacteristic
226C22C2×#400511yescharacteristic
227C22C2×#401111yescharacteristic
228C4—22no—
229C4—44no—
230C4—204no—
231C4—202no—
232C4—202no—
233C4#6491412yes—
234C4#6491412yes—
235C2—21no—
236C2—21no—
237C2—41no—
238C2—41no—
239C2C2×#6491411yescharacteristic
240C2#1060488712yes—
subgroupG/H
centerC2×C4#4011
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C42×C5C4
socleC22×C5C2×#99
prime radicalC24×C5C22×C4
cosocleC2×C22⋊Dic5C23
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5#11452
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
27. #4072C8semidirect
217. C5#11452semidirect

Maximal subgroups

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

subgroupindex
#106138002
#106048772
#105988202
#114525