Finite Group Databasebeta

← #12008942

Subgroups — #12008942

Order 1280.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#10614206C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10597946C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4090C412yes—
7C2×#4015C411yescharacteristic
8C5×#431—21no—
9#65272—21no—
10#65272—21no—
11#65263C2212yes—
12C4×C4⋊Dic5C411yescharacteristic
13#65217—21no—
14#65217—21no—
15#65215—21no—
16C5×#324—21no—
17C5×#324C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11568—51nomaximal, Sylow
21C22×C5×Q8C2×C411yescharacteristic
22C22×Dic10C2×C412yes—
23C4×C5×Q8—41no—
24C4×C5×Q8—41no—
25C2×C5×C4⋊C4D411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C4⋊C4C2311yescharacteristic
28C2×C42×C5C2×C411yescharacteristic
29C2×C42×C5D411yescharacteristic
30C2×C42×C5D411yescharacteristic
31#4090—44no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×#683—22no—
36C2×#683—22no—
37C2×C4×Dic5C2×C412yes—
38#4015—41no—
39#4015—41no—
40C5×C4⋊C8—41no—
41C5×C22⋊C8—22no—
42C4×C5×C8—41no—
43#3963—21no—
44#3963—22no—
45#3963—22no—
46C22⋊#168—22no—
47C4⋊#168—41no—
48#3935—41no—
49#2546—51no—
50#1467—51no—
51#1461D511yescharacteristic
52#1319—54no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—41no—
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—22no—
64C22×Dic5—22no—
65C2×Dic10—24no—
66C2×Dic10—42no—
67C2×Dic10—42no—
68C2×C5×C8—42no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C42×C5—21no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—21no—
78C4⋊Dic5—24no—
79C4⋊Dic5—42no—
80C4⋊Dic5—41no—
81C4⋊Dic5—41no—
82#683—44no—
83#683—44no—
84C4×Dic5—42no—
85C2×#168—42no—
86C2×C4⋊Q8—52no—
87C2×C4⋊Q8—51no—
88C2×C4×Q8C2×D511yescharacteristic
89#432—101no—
90#431—21no—
91#398—101no—
92#398—101no—
93#391—52no—
94#389—101no—
95#389—101no—
96C4×C4⋊C4—51no—
97#324—21no—
98#324—52no—
99#324—101no—
100#324C2×D512yes—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×Q8—44no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—22no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—41no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5#9911yescharacteristic
118C2×C4×C5#9911yescharacteristic
119C2×C4×C5#10012yes—
120C2×C4×C5#13112yes—
121C2×Dic5—24no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127Dic10—84no—
128C5×C8—82no—
129#168—82no—
130C22×Q8—52no—
131C22×Q8C4×D511yescharacteristic
132C4⋊Q8—201no—
133C4⋊Q8—201no—
134C4⋊Q8—204no—
135C4×Q8—41no—
136C4×Q8—41no—
137C2×C4⋊C4—101no—
138C2×C4⋊C4—102no—
139C2×C4⋊C4—102no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—101no—
142C2×C4⋊C4D2011yescharacteristic
143C2×C4⋊C4C22⋊D511yescharacteristic
144C2×C4⋊C4C22×D511yescharacteristic
145C2×C42—52no—
146C2×C42C4×D511yescharacteristic
147C2×C42D2011yescharacteristic
148C2×C42C22⋊D511yescharacteristic
149C4⋊C8—41no—
150C4⋊C8—201no—
151C22⋊C8—22no—
152C22⋊C8—102no—
153#97—201no—
154C4×C8—41no—
155#95—101no—
156#95—102no—
157#95—102no—
158C22×C5—21no—
159C22×C5—21no—
160C22×C5#40811yescharacteristic
161C22×C5C2×#9911yescharacteristic
162C22×C5C2×#10011yescharacteristic
163C4×C5—21no—
164C4×C5—22no—
165C4×C5—22no—
166C4×C5—41no—
167C4×C5—41no—
168C4×C5—41no—
169C4×C5—41no—
170C4×C5#35612yes—
171Dic5—44no—
172Dic5—82no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—104no—
177C2×Q8—202no—
178C2×Q8—202no—
179C22×C4—102no—
180C22×C4—102no—
181C22×C4#68511yescharacteristic
182C22×C4#68511yescharacteristic
183C22×C4#68511yescharacteristic
184C22×C4#68511yescharacteristic
185C22×C4C2×C4×D511yescharacteristic
186C22×C4C2×D2011yescharacteristic
187C22×C4C2×C22⋊D511yescharacteristic
188C2×C8—42no—
189C2×C8—202no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—104no—
194C4⋊C4—204no—
195C4⋊C4—202no—
196C4⋊C4—201no—
197C4⋊C4—201no—
198C4⋊C4—204no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—202no—
206C2×C5—21no—
207C2×C5—21no—
208C2×C5#147111yescharacteristic
209C2×C5#212911yescharacteristic
210C2×C5C2×#35611yescharacteristic
211C23C2×#68511yescharacteristic
212Q8—44no—
213Q8—404no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—104no—
229C2×C4—202no—
230C2×C4—202no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4#393811yescharacteristic
235C2×C4#393811yescharacteristic
236C2×C4#395512yes—
237C2×C4#404712yes—
238C8—82no—
239C8—402no—
240C5#1156811yescharacteristic, complemented, Sylow
241C22—21no—
242C22—21no—
243C22C2×#393811yescharacteristic
244C22#6539911yescharacteristic
245C22C2×#395511yescharacteristic
246C4—22no—
247C4—22no—
248C4—21no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—204no—
254C4—402no—
255C4#6469812yes—
256C2—21no—
257C2—21no—
258C2#1060071411yescharacteristic
259C2#1060085211yescharacteristic
260C2C2×#6469811yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1461C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1461D5
hypocenterC5#11568
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
240. C5#11568semidirect

Maximal subgroups

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

subgroupindex
#106142062
C5×#14612
#106024182
#105979462
#115685