Finite Group Databasebeta

← #12009952

Subgroups — #12009952

Order 1280.

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

normal subgroups only

This group has 394 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×#2567C211yesmaximal, characteristic
2C4×#3968C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10598139C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×Q8C2211yescharacteristic
7C5×#395C412yes—
8C5×#395C2212yes—
9C5×#391—21no—
10C5×#389—21no—
11C5×#389—21no—
12C5×#384—21no—
13C4×C5×C4⋊C4C411yescharacteristic
14C2×#3968—21no—
15#65215—21no—
16C4×#681—21no—
17#64750C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11795—51nomaximal, Sylow
21C22×C5×Q8C2×C412yes—
22C22×C5×Q8D411yescharacteristic
23C5×C4⋊Q8—41no—
24C5×C4⋊Q8—41no—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4D411yescharacteristic
34C2×C5×C4⋊C4C2311yescharacteristic
35C2×C42×C5—21no—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5D411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×#681—22no—
40C5×#95—22no—
41C5×#95—22no—
42C5×#95C2×C412yes—
43#3968—24no—
44C22⋊#168—22no—
45C4⋊#168—41no—
46#3935—41no—
47#3935—41no—
48C4×#168—41no—
49#2567D511yescharacteristic
50C4×#101—51no—
51#1467—51no—
52#1354—54no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—41no—
56C2×C5×Q8—42no—
57C2×C5×Q8—82no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22×C411yescharacteristic
65C22×C4×C5C2×D411yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C5×C4⋊C4—24no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—42no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—82no—
75C5×C4⋊C4—82no—
76C42×C5—21no—
77C42×C5—21no—
78C42×C5—21no—
79C42×C5—21no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—42no—
83#681—24no—
84#681—42no—
85C2×#168—42no—
86C2×#168—42no—
87C2×C4⋊Q8Dic511yescharacteristic
88C2×C4×Q8C2×D511yescharacteristic
89#432—101no—
90C2×#101—101no—
91C4×M16—101no—
92#395Dic512yes—
93#395C2×D512yes—
94#391—21no—
95#389—21no—
96#389—21no—
97#384—21no—
98C4×C4⋊C4Dic511yescharacteristic
99#343—52no—
100#324—52no—
101#324—101no—
102C23×C5C2×C22⋊C411yescharacteristic
103C5×Q8—44no—
104C5×Q8—84no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—22no—
110C2×C4×C5—24no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—42no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5#9911yescharacteristic
126C2×C4×C5#9911yescharacteristic
127C2×C4×C5#10412yes—
128C2×C4×C5#13712yes—
129#168—44no—
130#168—82no—
131C22×Q8C2×Dic512yes—
132C22×Q8C22⋊D511yescharacteristic
133C2×M16—102no—
134C4⋊Q8—41no—
135C4⋊Q8—41no—
136C4×Q8—41no—
137C4×Q8—41no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4C2×Dic511yescharacteristic
144C2×C4⋊C4C22⋊D511yescharacteristic
145C2×C4⋊C4C22×D511yescharacteristic
146C2×C42—21no—
147C2×C42C2×Dic511yescharacteristic
148C2×C42C22⋊D511yescharacteristic
149C2×C42C22⋊D511yescharacteristic
150C4⋊C8—201no—
151#101—104no—
152C22⋊C8—102no—
153#97—201no—
154#97—201no—
155C4×C8—201no—
156#95—22no—
157#95—22no—
158#95C2×Dic512yes—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5C2×#9911yescharacteristic
162C22×C5#41911yescharacteristic
163C22×C5C2×#10411yescharacteristic
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—44no—
168C4×C5—41no—
169C4×C5—41no—
170C4×C5—41no—
171C4×C5—41no—
172C4×C5—82no—
173C4×C5#35612yes—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—42no—
178C2×Q8—82no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4C22⋊Dic511yescharacteristic
182C22×C4C22⋊Dic511yescharacteristic
183C22×C4C22⋊Dic511yescharacteristic
184C22×C4C22⋊Dic511yescharacteristic
185C22×C4C22×Dic511yescharacteristic
186C22×C4C2×C22⋊D511yescharacteristic
187C22×C4C2×C22⋊D511yescharacteristic
188M16—104no—
189M16—202no—
190C2×C8—202no—
191C2×C8—202no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—42no—
208C2×C5—21no—
209C2×C5—21no—
210C2×C5#150811yescharacteristic
211C2×C5#212211yescharacteristic
212C2×C5C2×#35611yescharacteristic
213C23C2×C22⋊Dic511yescharacteristic
214Q8—44no—
215Q8—84no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—24no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4#396611yescharacteristic
237C2×C4#396611yescharacteristic
238C2×C4#396912yes—
239C2×C4#408812yes—
240C8—204no—
241C8—402no—
242C5#1179511yescharacteristic, complemented, Sylow
243C22—21no—
244C22—21no—
245C22C2×#396611yescharacteristic
246C22#6551411yescharacteristic
247C22C2×#396911yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—44no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—41no—
256C4—82no—
257C4#6476812yes—
258C2—21no—
259C2—21no—
260C2#1060248111yescharacteristic
261C2C2×#6476811yescharacteristic
262C2#1060265211yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2567C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2567D5
hypocenterC5#11795
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
242. C5#11795semidirect

Maximal subgroups

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

subgroupindex
C5×#25672
C4×#39682
#106024182
#105981392
#117955