Finite Group Databasebeta

← #13023116

Subgroups — #13023116

Order 1280.

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

normal subgroups only

This group has 526 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#10613961C211yesmaximal, characteristic
2#10604877C212yesmaximal
3#10598703C214yesmaximal
4C23×Dic10C411yescharacteristic
5C2×C5×#117C411yescharacteristic
6C2×#4072C2211yescharacteristic
7#65748—22no—
8#65263—22no—
9#65232C412yes—
10#65232C2212yes—
11#65218—22no—
12#64933C2214yes—
13#64913—22no—
14#11428—51nomaximal, Sylow
15C23×C4×C5C2×C411yescharacteristic
16C23×Dic5C2×C412yes—
17C22×Dic10—21no—
18C22×Dic10—21no—
19C22×Dic10—22no—
20C22×Dic10—42no—
21C22×Dic10—42no—
22C22×Dic10C814yescomplemented
23C5×#117—42no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C22⋊C4C2×C412yes—
26C2×C42×C5—21no—
27C2×C22⋊Dic5C2×C411yescharacteristic
28C2×C22⋊Dic5C2311yescharacteristic
29#4072—42no—
30C2×C4⋊Dic5D412yes—
31C2×C4×Dic5D412yes—
32C22⋊#170—24no—
33C4⋊#170—42no—
34C4×#170—42no—
35#3963—24no—
36#3963—24no—
37#2310—51no—
38#1458—52no—
39#1317—54no—
40C24×C5C22×C411yescharacteristic
41C22×C4×C5—22no—
42C22×C4×C5—22no—
43C22×C4×C5—22no—
44C22×C4×C5C22⋊C411yescharacteristic
45C22×C4×C5C22⋊C411yescharacteristic
46C22×C4×C5C2×C812yes—
47C22×C4×C5M1612yes—
48C22×Dic5—22no—
49C22×Dic5—22no—
50C22×Dic5—42no—
51C22×Dic5—42no—
52C22×Dic5C22⋊C412yes—
53C22×Dic5C2×C814yes—
54C22×Dic5C2×D412yes—
55C2×Dic10—24no—
56C2×Dic10—24no—
57C2×Dic10—42no—
58C2×Dic10—42no—
59C2×Dic10—48no—
60C2×Dic10—42no—
61C2×Dic10—42no—
62C2×Dic10—48no—
63C2×#170—44no—
64C5×C4⋊C4—42no—
65C5×C22⋊C4—42no—
66C42×C5—42no—
67C22⋊Dic5—41no—
68C22⋊Dic5—41no—
69C4⋊Dic5—42no—
70C4×Dic5—22no—
71C4×Dic5—22no—
72C23×Q8—51no—
73C2×#117—51no—
74C2×#117AGL(1,𝔽5)11yescharacteristic
75#431—102no—
76#391—102no—
77#391—102no—
78#381—52no—
79#381—52no—
80#324—102no—
81#323—54no—
82C23×C5—21no—
83C23×C5—21no—
84C23×C5—42no—
85C23×C5C2×C22⋊C411yescharacteristic
86C23×C5C22×C811yescharacteristic
87C23×C5C2×M1611yescharacteristic
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5—24no—
91C2×C4×C5—24no—
92C2×C4×C5—44no—
93C2×C4×C5—42no—
94C2×C4×C5C22⋊C812yes—
95C2×C4×C5C22⋊C812yes—
96C2×C4×C5#9912yes—
97C2×C4×C5#10012yes—
98C2×Dic5—24no—
99C2×Dic5—22no—
100C2×Dic5—22no—
101C2×Dic5—44no—
102C2×Dic5—42no—
103C2×Dic5—42no—
104C2×Dic5—44no—
105C2×Dic5—42no—
106C2×Dic5—42no—
107Dic10—48no—
108Dic10—48no—
109#170—84no—
110C22×Q8—54no—
111C22×Q8—102no—
112C22×Q8—101no—
113C22×Q8—101no—
114C22×Q8—202no—
115C22×Q8—202no—
116C23×C4—52no—
117C23×C4C2×AGL(1,𝔽5)11yescharacteristic
118#117—42no—
119#117—202no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—52no—
122C2×C22⋊C4—51no—
123C2×C22⋊C4—51no—
124C2×C22⋊C4C2×AGL(1,𝔽5)12yes—
125C2×C42—21no—
126C2×C42—52no—
127C4⋊C8—202no—
128C22⋊C8—104no—
129C4×C8—202no—
130#95—104no—
131#95—104no—
132C22×C5—22no—
133C22×C5—21no—
134C22×C5—21no—
135C22×C5—41no—
136C22×C5—41no—
137C22×C5—42no—
138C22×C5—42no—
139C22×C5C2×C22⋊C811yescharacteristic
140C22×C5C2×#9911yescharacteristic
141C22×C5C2×#10011yescharacteristic
142C4×C5—22no—
143C4×C5—82no—
144C4×C5#32314yes—
145Dic5—42no—
146Dic5—42no—
147Dic5—44no—
148C24C22×AGL(1,𝔽5)11yescharacteristic
149C2×Q8—104no—
150C2×Q8—104no—
151C2×Q8—208no—
152C2×Q8—202no—
153C2×Q8—202no—
154C2×Q8—208no—
155C2×Q8—202no—
156C2×Q8—202no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—54no—
161C22×C4—52no—
162C22×C4—52no—
163C22×C4—102no—
164C22×C4—102no—
165C22×C4—202no—
166C22×C4—202no—
167C22×C4D5⋊C812yes—
168C22×C4#70012yes—
169C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
170C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
171C2×C8—204no—
172C4⋊C4—42no—
173C4⋊C4—202no—
174C22⋊C4—42no—
175C22⋊C4—201no—
176C22⋊C4—201no—
177C42—42no—
178C42—102no—
179C42—102no—
180C2×C5—21no—
181C2×C5—21no—
182C2×C5—41no—
183C2×C5—41no—
184C2×C5C2×#32311yescharacteristic
185C2×C5#212312yes—
186C23—21no—
187C23—21no—
188C23—42no—
189C23C2×D5⋊C811yescharacteristic
190C23C2×#70011yescharacteristic
191C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
192Q8—208no—
193Q8—208no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—42no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4—104no—
203C2×C4—204no—
204C2×C4—202no—
205C2×C4—202no—
206C2×C4—204no—
207C2×C4—202no—
208C2×C4—202no—
209C2×C4#399912yes—
210C2×C4#400312yes—
211C2×C4#400312yes—
212C2×C4#401312yes—
213C8—404no—
214C5#1142811yescharacteristic, complemented, Sylow
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22—42no—
222C22C2×#399911yescharacteristic
223C22C2×#400311yescharacteristic
224C22C2×#401311yescharacteristic
225C4—22no—
226C4—82no—
227C4—204no—
228C4—202no—
229C4—202no—
230C4#6491514yes—
231C2—21no—
232C2—21no—
233C2—41no—
234C2—41no—
235C2#1060438312yes—
236C2C2×#6491511yescharacteristic
subgroupG/H
centerC22C2×#3999
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC22×C5C2×#99
prime radicalC24×C5C22×C4
cosocleC2×C22⋊Dic5C23
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5#11428
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
22. C22×Dic10C8semidirect
214. C5#11428semidirect

Maximal subgroups

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

subgroupindex
#106139612
#106048772
#105987032
#114285