Finite Group Databasebeta

← #13017530

Subgroups — #13017530

Order 1280.

814 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 120 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×#65851C211yesmaximal, characteristic
2#10604897C212yesmaximal
3C2×#64870C214yesmaximal, complemented
4C2×C5×#117C411yescharacteristic
5C2×#4072C411yescharacteristic
6C22×C4×Dic5C2211yescharacteristic
7#65851—28no—
8C2×#4036C2212yes—
9C2×#4034C412yes—
10C2×#4024—22no—
11C2×C4×Dic10—22no—
12C2×C22⋊#170—22no—
13C2×#4002C2214yes—
14#64918—22no—
15#64870—28no—
16#8338—51nomaximal, Sylow
17C23×C4×C5C2×C411yescharacteristic
18C23×Dic5D412yes—
19C22×Dic10—22no—
20C22×#170—24no—
21C5×#117—24no—
22C2×C5×C4⋊C4C2×C412yes—
23C2×C5×C22⋊C4—21no—
24C2×C42×C5—21no—
25C2×C22⋊Dic5—21no—
26#4072—24no—
27C2×C4⋊Dic5—22no—
28C2×C4⋊Dic5C2×C412yes—
29C2×#683—22no—
30C2×#683—22no—
31C2×C4×Dic5—21no—
32C2×C4×Dic5—24no—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35C2×C4×Dic5C2311yescharacteristic
36#4036—24no—
37#4036D418yes—
38#4034—24no—
39#4034—24no—
40#4024—216no—
41C4×Dic10—216no—
42C22⋊#170—28no—
43#4002—28no—
44C2×#533—51no—
45#1749—52no—
46C2×#330—54no—
47C24×C5C22⋊C411yescharacteristic
48C22×C4×C5—22no—
49C22×C4×C5—22no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—22no—
55C22×Dic5—24no—
56C22×Dic5—24no—
57C22×Dic5—42no—
58C22×Dic5C22⋊C412yes—
59C22×Dic5C2×D412yes—
60C2×Dic10—28no—
61C2×Dic10—44no—
62C2×Dic10—44no—
63C2×#170—28no—
64C2×#170—44no—
65C2×#170—44no—
66C5×C4⋊C4—22no—
67C5×C4⋊C4C22⋊C414yes—
68C5×C22⋊C4—24no—
69C42×C5—24no—
70C22⋊Dic5—24no—
71C4⋊Dic5—22no—
72C4⋊Dic5—28no—
73C4⋊Dic5C22⋊C414yes—
74#683—28no—
75#683—28no—
76C4×Dic5—24no—
77C4×Dic5—22no—
78C4×Dic5—24no—
79C4×Dic5C2×D414yes—
80#533—108no—
81C2×C4⋊Q8—52no—
82C2×#125—52no—
83C2×C22⋊Q8—102no—
84C2×C4×Q8—102no—
85C2×#117—51no—
86C2×#117AGL(1,𝔽5)11yescharacteristic
87C22×C42—51no—
88C2×C22⋊C8—102no—
89C2×#97—54no—
90#336—102no—
91#330—108no—
92C23×C5—21no—
93C23×C5—21no—
94C23×C5—22no—
95C23×C5—22no—
96C23×C5#10112yes—
97C23×C5C2×C22⋊C411yescharacteristic
98C2×C4×C5—28no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—24no—
104C2×C4×C5—42no—
105C2×C4×C5—42no—
106C2×C4×C5#10112yes—
107C2×C4×C5C2×C22⋊C412yes—
108C2×Dic5—22no—
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—22no—
112C2×Dic5—24no—
113C2×Dic5—48no—
114C2×Dic5—42no—
115C2×Dic5—42no—
116C2×Dic5#10414yes—
117C2×Dic5#12014yes—
118Dic10—416no—
119#170—48no—
120C22×Q8—102no—
121C23×C4—52no—
122C23×C4C2×AGL(1,𝔽5)11yescharacteristic
123C22×C8—104no—
124C4⋊Q8—104no—
125C4⋊Q8—104no—
126#125—58no—
127#125—104no—
128C22⋊Q8—1016no—
129C4×Q8—1016no—
130#117—24no—
131#117—104no—
132C2×C4⋊C4—52no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—102no—
135C2×C4⋊C4—102no—
136C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—101no—
139C2×C42—21no—
140C2×C42—51no—
141C2×C42—52no—
142C2×C42—51no—
143C2×C42—104no—
144C2×C42—101no—
145C22⋊C8—108no—
146#97—108no—
147C22×C5—22no—
148C22×C5—24no—
149C22×C5—41no—
150C22×C5—41no—
151C22×C5—42no—
152C22×C5#37911yescharacteristic
153C22×C5C2×#10111yescharacteristic
154C22×C5C2×#10111yescharacteristic
155C22×C5C2×#10412yes—
156C22×C5#42112yes—
157C4×C5—22no—
158C4×C5—22no—
159C4×C5—44no—
160Dic5—24no—
161Dic5—24no—
162Dic5—44no—
163C24C22⋊AGL(1,𝔽5)11yescharacteristic
164C2×Q8—108no—
165C2×Q8—204no—
166C2×Q8—204no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—52no—
172C22×C4—52no—
173C22×C4—104no—
174C22×C4—104no—
175C22×C4—102no—
176C22×C4—202no—
177C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
178C22×C4C22×AGL(1,𝔽5)11yescharacteristic
179C2×C8—108no—
180C2×C8—204no—
181C2×C8—204no—
182C4⋊C4—22no—
183C4⋊C4—54no—
184C4⋊C4—108no—
185C4⋊C4—108no—
186C4⋊C4—108no—
187C4⋊C4—102no—
188C4⋊C4C22⋊AGL(1,𝔽5)14yes—
189C22⋊C4—24no—
190C22⋊C4—104no—
191C42—24no—
192C42—54no—
193C42—104no—
194C42—104no—
195C42—102no—
196C2×C5—42no—
197C2×C5#152611yescharacteristic
198C2×C5#153112yes—
199C2×C5#153711yescharacteristic
200C2×C5#178411yescharacteristic
201C2×C5#178912yes—
202C23—22no—
203C23—22no—
204C23—21no—
205C23—21no—
206C23#400512yes—
207C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
208Q8—2016no—
209C2×C4—28no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—54no—
218C2×C4—54no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—104no—
224C2×C4—208no—
225C2×C4—202no—
226C2×C4—202no—
227C2×C4#400512yes—
228C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
229C8—208no—
230C5#833811yescharacteristic, complemented, Sylow
231C22—24no—
232C22—22no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×#400511yescharacteristic
237C22C2×#400511yescharacteristic
238C22D5⋊#10412yes—
239C22#6579512yes—
240C22#6580011yescharacteristic
241C4—22no—
242C4—22no—
243C4—44no—
244C4—104no—
245C4—104no—
246C4—204no—
247C2—42no—
248C2#1060435011yescharacteristic
249C2#1060435112yes—
250C2#1060435211yescharacteristic
251C2#1060490511yescharacteristic
252C2#1060501412yes—
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5#8338
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. C2×#64870C2semidirect
230. C5#8338semidirect

Maximal subgroups

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

subgroupindex
C2×#658512
#106048972
C2×#648702
#83385