Finite Group Databasebeta

← #11992641

Subgroups — #11992641

Order 1280.

830 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 147 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×C5×#380C211yesmaximal, characteristic
2#10602919C212yesmaximal
3#10598104C214yesmaximal, complemented
4C24×C4×C5C2211yescharacteristic
5C22×C5×C4⋊C4C412yes—
6C22×C5×C22⋊C4C412yes—
7C5×#380—22no—
8C5×#380—22no—
9C2×C5×#95C2212yes—
10C2×C22⋊#168—22no—
11C2×C22⋊#168—22no—
12C2×C22⋊#168C2214yes—
13#8704—51nomaximal, Sylow
14C25×C5C2×C411yescharacteristic
15C23×C4×C5—24no—
16C23×C4×C5—44no—
17C23×C4×C5C2×C411yescharacteristic
18C23×C4×C5C2×C414yes—
19C23×C4×C5D412yes—
20C23×C4×C5D412yes—
21C23×C4×C5C2311yescharacteristic
22C2×C5×C4⋊C4—22no—
23C2×C5×C4⋊C4—22no—
24C2×C5×C4⋊C4—44no—
25C2×C5×C22⋊C4—22no—
26C2×C5×C22⋊C4—22no—
27C2×C5×C22⋊C4—44no—
28C22×#168—24no—
29C5×#95—24no—
30C22⋊#168—28no—
31C22⋊#168—44no—
32C22⋊#168—44no—
33C2×#380D511yescharacteristic
34#1779—52no—
35#1280—54no—
36C24×C5—22no—
37C24×C5—22no—
38C24×C5—22no—
39C24×C5—24no—
40C24×C5—42no—
41C24×C5C22⋊C411yescharacteristic
42C24×C5C22⋊C411yescharacteristic
43C24×C5C22×C411yescharacteristic
44C22×C4×C5—22no—
45C22×C4×C5—24no—
46C22×C4×C5—24no—
47C22×C4×C5—24no—
48C22×C4×C5—24no—
49C22×C4×C5—24no—
50C22×C4×C5—24no—
51C22×C4×C5—28no—
52C22×C4×C5—42no—
53C22×C4×C5—42no—
54C22×C4×C5—42no—
55C22×C4×C5—416no—
56C22×C4×C5—44no—
57C22×C4×C5—44no—
58C22×C4×C5C22⋊C412yes—
59C22×C4×C5C2×D412yes—
60C22×C4×C5#4114yes—
61C5×C4⋊C4—44no—
62C5×C4⋊C4—44no—
63C5×C22⋊C4—44no—
64C5×C22⋊C4—44no—
65C2×#168—44no—
66C2×#168—44no—
67C2×#168—44no—
68C24×C4C2×D511yescharacteristic
69C22×C4⋊C4Dic512yes—
70C22×C22⋊C4Dic512yes—
71C2×C22⋊C8—54no—
72C2×C22⋊C8—102no—
73C2×C22⋊C8—102no—
74#380—22no—
75#380—22no—
76C2×#95C2×D512yes—
77C23×C5—22no—
78C23×C5—21no—
79C23×C5—21no—
80C23×C5—28no—
81C23×C5—21no—
82C23×C5—21no—
83C23×C5—22no—
84C23×C5—22no—
85C23×C5—22no—
86C23×C5—22no—
87C23×C5—21no—
88C23×C5—21no—
89C23×C5—48no—
90C23×C5—48no—
91C23×C5—44no—
92C23×C5—44no—
93C23×C5#10012yes—
94C23×C5#10112yes—
95C23×C5C2×C22⋊C411yescharacteristic
96C23×C5#11712yes—
97C23×C5#13114yes—
98C2×C4×C5—28no—
99C2×C4×C5—22no—
100C2×C4×C5—22no—
101C2×C4×C5—22no—
102C2×C4×C5—22no—
103C2×C4×C5—44no—
104C2×C4×C5—48no—
105C2×C4×C5—48no—
106C2×C4×C5—44no—
107C2×C4×C5—44no—
108C2×C4×C5—44no—
109C2×C4×C5—88no—
110C2×C4×C5#9914yes—
111C2×C4×C5#12314yes—
112#168—84no—
113C25C2×Dic511yescharacteristic
114C23×C4—24no—
115C23×C4—44no—
116C23×C4C2×Dic511yescharacteristic
117C23×C4C2×Dic514yes—
118C23×C4C22⋊D512yes—
119C23×C4C22⋊D512yes—
120C23×C4C22×D511yescharacteristic
121C22×C8—104no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—44no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4—44no—
128C22⋊C8—108no—
129C22⋊C8—204no—
130C22⋊C8—204no—
131#95—24no—
132C22×C5—22no—
133C22×C5—22no—
134C22×C5—24no—
135C22×C5—24no—
136C22×C5—22no—
137C22×C5—22no—
138C22×C5—24no—
139C22×C5—24no—
140C22×C5—416no—
141C22×C5—41no—
142C22×C5—41no—
143C22×C5—41no—
144C22×C5—41no—
145C22×C5—42no—
146C22×C5—42no—
147C22×C5#38111yescharacteristic
148C22×C5#40812yes—
149C22×C5C2×#9912yes—
150C22×C5C2×#10011yescharacteristic
151C22×C5C2×#10111yescharacteristic
152C22×C5#43314yes—
153C4×C5—24no—
154C4×C5—24no—
155C4×C5—84no—
156C24—22no—
157C24—22no—
158C24—22no—
159C24—24no—
160C24—42no—
161C24C22⋊Dic511yescharacteristic
162C24C22⋊Dic511yescharacteristic
163C24C22×Dic511yescharacteristic
164C22×C4—22no—
165C22×C4—24no—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—24no—
171C22×C4—28no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—416no—
176C22×C4—44no—
177C22×C4—44no—
178C22×C4C22⋊Dic512yes—
179C22×C4#70914yes—
180C22×C4C2×C22⋊D512yes—
181C2×C8—204no—
182C2×C8—204no—
183C2×C8—204no—
184C4⋊C4—44no—
185C4⋊C4—44no—
186C22⋊C4—44no—
187C22⋊C4—44no—
188C2×C5—24no—
189C2×C5—42no—
190C2×C5—42no—
191C2×C5#147112yes—
192C2×C5#147212yes—
193C2×C5#181811yescharacteristic
194C2×C5#181911yescharacteristic
195C2×C5#182111yescharacteristic
196C23—21no—
197C23—22no—
198C23—21no—
199C23—28no—
200C23—21no—
201C23—21no—
202C23—21no—
203C23—22no—
204C23—22no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—48no—
209C23—48no—
210C23—44no—
211C23—44no—
212C23#396512yes—
213C23#396812yes—
214C23#407212yes—
215C23#409414yes—
216C23C2×C22⋊Dic511yescharacteristic
217C2×C4—28no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—44no—
223C2×C4—48no—
224C2×C4—48no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—88no—
229C2×C4#396614yes—
230C2×C4#407514yes—
231C8—404no—
232C5#870411yescharacteristic, complemented, Sylow
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—22no—
239C22—24no—
240C22—24no—
241C22—416no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22#6528914yes—
249C22#6550011yescharacteristic
250C22C2×#396511yescharacteristic
251C22C2×#396612yes—
252C22C2×#396811yescharacteristic
253C22#6552312yes—
254C4—24no—
255C4—24no—
256C4—84no—
257C2—24no—
258C2—42no—
259C2—42no—
260C2#1060233511yescharacteristic
261C2#1060235511yescharacteristic
262C2#1060237711yescharacteristic
263C2#1060246912yes—
264C2#1060248412yes—
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#380C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenterC2×#380D5
hypocenterC5#8704
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #10598104C2semidirect
232. C5#8704semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3802
#106029192
#105981042
#87045