Finite Group Databasebeta

← #12009895

Subgroups — #12009895

Order 1280.

414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C5×#2546C211yesmaximal, characteristic
2C4×#3968C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10598141C214yesmaximal
5C2×C5×C4⋊Q8—21no—
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#398C412yes—
9C5×#398C2212yes—
10C5×#391—21no—
11C5×#389—21no—
12C5×#389—21no—
13C4×C5×C4⋊C4C411yescharacteristic
14C2×#3968—21no—
15#65215—21no—
16C4×#681—21no—
17#64750C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11782—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C22×C5×Q8D411yescharacteristic
23C5×C4⋊Q8—41no—
24C5×C4⋊Q8—41no—
25C5×C4⋊Q8—44no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4C2×C412yes—
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C5×C4⋊C4D411yescharacteristic
35C2×C5×C4⋊C4C2311yescharacteristic
36C2×C42×C5—21no—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×#681—22no—
41C5×#95—22no—
42C5×#95—22no—
43C5×#95C2×C412yes—
44#3968—24no—
45C22⋊#168—22no—
46C4⋊#168—41no—
47#3935—41no—
48#3935—41no—
49C4×#168—41no—
50#2546D511yescharacteristic
51C4×#101—51no—
52#1467—51no—
53#1346—54no—
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—41no—
57C2×C5×Q8—42no—
58C2×C5×Q8—42no—
59C2×C5×Q8—42no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C5×C4⋊C4—24no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—44no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—44no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—42no—
85#681—24no—
86#681—42no—
87C2×#168—42no—
88C2×#168—42no—
89C2×C4⋊Q8—21no—
90C2×C4⋊Q8Dic511yescharacteristic
91C2×C4×Q8C2×D511yescharacteristic
92#432—101no—
93C2×#101—101no—
94C4×M16—101no—
95#398Dic512yes—
96#398C2×D512yes—
97#391—21no—
98#389—21no—
99#389—21no—
100C4×C4⋊C4Dic511yescharacteristic
101#343—52no—
102#324—52no—
103#324—101no—
104C23×C5C2×C22⋊C411yescharacteristic
105C5×Q8—44no—
106C5×Q8—84no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—22no—
112C2×C4×C5—24no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—42no—
120C2×C4×C5—42no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—42no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5#9911yescharacteristic
128C2×C4×C5#9911yescharacteristic
129C2×C4×C5#10412yes—
130C2×C4×C5AGL(1,ℤ/8)12yes—
131#168—44no—
132#168—82no—
133C22×Q8—21no—
134C22×Q8C22⋊D511yescharacteristic
135C2×M16—102no—
136C4⋊Q8—41no—
137C4⋊Q8—41no—
138C4⋊Q8—44no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4C2×Dic512yes—
146C2×C4⋊C4C2×Dic511yescharacteristic
147C2×C4⋊C4C22⋊D511yescharacteristic
148C2×C4⋊C4C22×D511yescharacteristic
149C2×C42—21no—
150C2×C42C2×Dic511yescharacteristic
151C2×C42C22⋊D511yescharacteristic
152C2×C42C22⋊D511yescharacteristic
153C4⋊C8—201no—
154#101—104no—
155C22⋊C8—102no—
156#97—201no—
157#97—201no—
158C4×C8—201no—
159#95—22no—
160#95—22no—
161#95C2×Dic512yes—
162C22×C5—21no—
163C22×C5—21no—
164C22×C5C2×#9911yescharacteristic
165C22×C5#41811yescharacteristic
166C22×C5C2×#10411yescharacteristic
167C4×C5—21no—
168C4×C5—22no—
169C4×C5—22no—
170C4×C5—44no—
171C4×C5—41no—
172C4×C5—41no—
173C4×C5—41no—
174C4×C5—41no—
175C4×C5—82no—
176C4×C5#35612yes—
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—42no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C22⋊Dic511yescharacteristic
186C22×C4C22⋊Dic511yescharacteristic
187C22×C4C22⋊Dic511yescharacteristic
188C22×C4C22⋊Dic511yescharacteristic
189C22×C4C22×Dic511yescharacteristic
190C22×C4C2×C22⋊D511yescharacteristic
191C22×C4C2×C22⋊D511yescharacteristic
192M16—104no—
193M16—202no—
194C2×C8—202no—
195C2×C8—202no—
196C4⋊C4—24no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—44no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—42no—
212C2×C5—21no—
213C2×C5—21no—
214C2×C5#150711yescharacteristic
215C2×C5#212311yescharacteristic
216C2×C5C2×#35611yescharacteristic
217C23C2×C22⋊Dic511yescharacteristic
218Q8—44no—
219Q8—84no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4#396611yescharacteristic
241C2×C4#396611yescharacteristic
242C2×C4#396912yes—
243C2×C4#407812yes—
244C8—204no—
245C8—402no—
246C5#1178211yescharacteristic, complemented, Sylow
247C22—21no—
248C22—21no—
249C22#6550411yescharacteristic
250C22C2×#396611yescharacteristic
251C22C2×#396911yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#6476812yes—
262C2—21no—
263C2—21no—
264C2#1060246611yescharacteristic
265C2C2×#6476811yescharacteristic
266C2#1060266311yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2546C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2546D5
hypocenterC5#11782
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
246. C5#11782semidirect

Maximal subgroups

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

subgroupindex
C5×#25462
C4×#39682
#106024182
#105981412
#117825