Finite Group Databasebeta

← #13023114

Subgroups — #13023114

Order 1280.

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

normal subgroups only

This group has 526 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
1#10615793C211yesmaximal, characteristic
2#10604877C212yesmaximal
3#10598819C214yesmaximal
4C23×C5×Q8C411yescharacteristic
5C2×#4072C411yescharacteristic
6C2×#4072C2211yescharacteristic
7#65748—22no—
8#65519—22no—
9#65519—22no—
10#65500C412yes—
11#65500C2212yes—
12#64933C2214yes—
13#64913—22no—
14#11428—51nomaximal, Sylow
15C22×C5×Q8—21no—
16C22×C5×Q8—21no—
17C22×C5×Q8—22no—
18C22×C5×Q8—42no—
19C22×C5×Q8—42no—
20C22×C5×Q8C814yescomplemented
21C23×C4×C5C2×C412yes—
22C23×C4×C5C2×C411yescharacteristic
23C2×C22⋊Dic5C2×C412yes—
24C2×C22⋊Dic5C2×C411yescharacteristic
25C2×C22⋊Dic5C2311yescharacteristic
26#4072—42no—
27#4072—42no—
28C2×C4⋊Dic5—21no—
29C2×C4⋊Dic5D412yes—
30C2×C4×Dic5—21no—
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
41C2×C5×Q8—24no—
42C2×C5×Q8—24no—
43C2×C5×Q8—48no—
44C2×C5×Q8—42no—
45C2×C5×Q8—42no—
46C2×C5×Q8—48no—
47C2×C5×Q8—42no—
48C2×C5×Q8—42no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5—22no—
53C22×C4×C5—42no—
54C22×C4×C5—42no—
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C2×C812yes—
58C22×C4×C5C2×C814yes—
59C22×C4×C5M1612yes—
60C22×Dic5—22no—
61C22×Dic5C22⋊C412yes—
62C22×Dic5C2×D412yes—
63C2×#170—44no—
64C22⋊Dic5—41no—
65C22⋊Dic5—41no—
66C22⋊Dic5—42no—
67C4⋊Dic5—42no—
68C4⋊Dic5—42no—
69C4×Dic5—22no—
70C4×Dic5—22no—
71C4×Dic5—42no—
72C23×Q8AGL(1,𝔽5)11yescharacteristic
73C2×#117—51no—
74C2×#117—51no—
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
88C5×Q8—48no—
89C5×Q8—48no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5—24no—
93C2×C4×C5—24no—
94C2×C4×C5—24no—
95C2×C4×C5—44no—
96C2×C4×C5—42no—
97C2×C4×C5—42no—
98C2×C4×C5—44no—
99C2×C4×C5C22⋊C812yes—
100C2×C4×C5C22⋊C812yes—
101C2×C4×C5#9912yes—
102C2×C4×C5#10012yes—
103C2×Dic5—22no—
104C2×Dic5—22no—
105C2×Dic5—42no—
106C2×Dic5—42no—
107C2×Dic5—44no—
108C2×Dic5—42no—
109#170—84no—
110C22×Q8—22no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8—42no—
114C22×Q8—42no—
115C22×Q8#17014yescomplemented
116C23×C4C2×AGL(1,𝔽5)12yes—
117C23×C4C2×AGL(1,𝔽5)11yescharacteristic
118#117—202no—
119#117—202no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—101no—
122C2×C22⋊C4—51no—
123C2×C22⋊C4—51no—
124C2×C22⋊C4—52no—
125C2×C42—52no—
126C2×C42—101no—
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—44no—
144C4×C5#32314yes—
145Dic5—42no—
146Dic5—42no—
147Dic5—82no—
148C24C22×AGL(1,𝔽5)11yescharacteristic
149C2×Q8—24no—
150C2×Q8—24no—
151C2×Q8—48no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—48no—
155C2×Q8—42no—
156C2×Q8—42no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—52no—
164C22×C4—52no—
165C22×C4—102no—
166C22×C4C2×#17012yes—
167C22×C4C2×#17014yes—
168C22×C4#70412yes—
169C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
170C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
171C2×C8—204no—
172C4⋊C4—202no—
173C4⋊C4—202no—
174C22⋊C4—201no—
175C22⋊C4—201no—
176C22⋊C4—202no—
177C42—102no—
178C42—102no—
179C42—202no—
180C2×C5—21no—
181C2×C5—21no—
182C2×C5—41no—
183C2×C5—41no—
184C2×C5C2×#32311yescharacteristic
185C2×C5#212312yes—
186C23—21no—
187C23—21no—
188C23—42no—
189C23C22×#17011yescharacteristic
190C23C2×#70411yescharacteristic
191C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
192Q8—48no—
193Q8—48no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—24no—
199C2×C4—44no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—44no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—202no—
206C2×C4—202no—
207C2×C4—204no—
208C2×C4—202no—
209C2×C4#401112yes—
210C2×C4C22⋊#17012yes—
211C2×C4C22⋊#17012yes—
212C2×C4#401312yes—
213C8—404no—
214C5#1142811yescharacteristic, complemented, Sylow
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—42no—
221C22—42no—
222C22C2×#401111yescharacteristic
223C22C2×C22⋊#17011yescharacteristic
224C22C2×#401311yescharacteristic
225C4—22no—
226C4—44no—
227C4—202no—
228C4—202no—
229C4—402no—
230C4#6493314yes—
231C2—21no—
232C2—21no—
233C2—41no—
234C2—41no—
235C2#1060498012yes—
236C2C2×#6493311yescharacteristic
subgroupG/H
centerC22C2×#4011
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC23×C5×Q8C4
socleC22×C5C2×#99
prime radicalC24×C5C22×C4
cosocleC2×C22⋊Dic5C23
hypercenterC23×Q8AGL(1,𝔽5)
hypocenterC5#11428
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
20. C22×C5×Q8C8semidirect
115. C22×Q8#170semidirect
214. C5#11428semidirect

Maximal subgroups

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

subgroupindex
#106157932
#106048772
#105988192
#114285