Finite Group Databasebeta

← #12008966

Subgroups — #12008966

Order 1280.

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

normal subgroups only

This group has 358 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#10614210C211yesmaximal, characteristic
2C5×#1467C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10597943C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4015C411yescharacteristic
7C5×#432—21no—
8#65519C412yes—
9#65275—21no—
10#65275—21no—
11#65266C2212yes—
12C4×C4⋊Dic5C411yescharacteristic
13#65218—21no—
14#65218—21no—
15#65214—21no—
16C5×#324—21no—
17C5×#324C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11573—51nomaximal, Sylow
21C22×C5×Q8C2×C411yescharacteristic
22C22×Dic10—21no—
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
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C412yes—
34C2×C4×Dic5C2×C412yes—
35#4015—41no—
36#4015—41no—
37C5×C4⋊C8—41no—
38C5×C22⋊C8—22no—
39C5×#97—41no—
40#3963—22no—
41#3963—22no—
42#3963—21no—
43#3963—22no—
44#3963—22no—
45C22⋊#168—22no—
46C4⋊#168—41no—
47C4×#168—41no—
48#2568—51no—
49#1467D511yescharacteristic
50#1461—51no—
51#1324—54no—
52C2×C5×Q8—22no—
53C2×C5×Q8—22no—
54C2×C5×Q8—41no—
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22×C411yescharacteristic
60C22×C4×C5C2×D411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×Dic5—22no—
63C22×Dic5—22no—
64C2×Dic10—44no—
65C2×Dic10—41no—
66C2×Dic10—41no—
67C2×C5×C8—42no—
68C5×C4⋊C4—41no—
69C5×C4⋊C4—41no—
70C5×C4⋊C4—41no—
71C42×C5—21no—
72C42×C5—21no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C4⋊Dic5—42no—
78C4⋊Dic5—42no—
79C4⋊Dic5—42no—
80C4×Dic5—24no—
81C2×#168—42no—
82C2×C4⋊Q8—51no—
83C2×C4×Q8C2×D511yescharacteristic
84#432—21no—
85#431—101no—
86#400—101no—
87#400—101no—
88#391—52no—
89#391—101no—
90#391—101no—
91#382—52no—
92C4×C4⋊C4—51no—
93#324—21no—
94#324—52no—
95#324—101no—
96#324C2×D512yes—
97C23×C5C2×C22⋊C411yescharacteristic
98C5×Q8—44no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—41no—
111C2×C4×C5—41no—
112C2×C4×C5—41no—
113C2×C4×C5#9911yescharacteristic
114C2×C4×C5#9911yescharacteristic
115C2×C4×C5#10112yes—
116C2×C4×C5#13112yes—
117C2×Dic5—42no—
118C2×Dic5—44no—
119C2×Dic5—42no—
120C2×Dic5—42no—
121C2×Dic5—42no—
122Dic10—82no—
123Dic10—82no—
124C5×C8—82no—
125#168—82no—
126C22×Q8—101no—
127C22×Q8C4×D511yescharacteristic
128C4⋊Q8—201no—
129C4⋊Q8—201no—
130C4×Q8—41no—
131C4×Q8—41no—
132C2×C4⋊C4—52no—
133C2×C4⋊C4—101no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4D2011yescharacteristic
136C2×C4⋊C4C22⋊D511yescharacteristic
137C2×C4⋊C4C22×D511yescharacteristic
138C2×C42—52no—
139C2×C42C4×D511yescharacteristic
140C2×C42D2011yescharacteristic
141C2×C42C22⋊D511yescharacteristic
142C4⋊C8—41no—
143C4⋊C8—201no—
144C22⋊C8—22no—
145C22⋊C8—102no—
146#97—41no—
147C4×C8—201no—
148#95—101no—
149#95—102no—
150#95—102no—
151#95—102no—
152#95—102no—
153C22×C5—21no—
154C22×C5—21no—
155C22×C5#40811yescharacteristic
156C22×C5C2×#9911yescharacteristic
157C22×C5C2×#10111yescharacteristic
158C4×C5—21no—
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—41no—
162C4×C5—41no—
163C4×C5—41no—
164C4×C5—41no—
165C4×C5#35512yes—
166Dic5—82no—
167Dic5—82no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—41no—
171C2×Q8—204no—
172C2×Q8—201no—
173C2×Q8—201no—
174C22×C4—102no—
175C22×C4—102no—
176C22×C4#68511yescharacteristic
177C22×C4#68511yescharacteristic
178C22×C4#68511yescharacteristic
179C22×C4#68511yescharacteristic
180C22×C4C2×C4×D511yescharacteristic
181C22×C4C2×D2011yescharacteristic
182C22×C4C2×C22⋊D511yescharacteristic
183C2×C8—42no—
184C2×C8—202no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—202no—
189C4⋊C4—202no—
190C4⋊C4—202no—
191C42—21no—
192C42—21no—
193C42—21no—
194C42—21no—
195C42—21no—
196C42—21no—
197C42—104no—
198C2×C5—21no—
199C2×C5—21no—
200C2×C5#147211yescharacteristic
201C2×C5#212911yescharacteristic
202C2×C5C2×#35511yescharacteristic
203C23C2×#68511yescharacteristic
204Q8—44no—
205Q8—402no—
206Q8—402no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—202no—
222C2×C4—204no—
223C2×C4—202no—
224C2×C4—202no—
225C2×C4—202no—
226C2×C4#393811yescharacteristic
227C2×C4#393811yescharacteristic
228C2×C4#395612yes—
229C2×C4#405312yes—
230C8—82no—
231C8—402no—
232C5#1157311yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22C2×#393811yescharacteristic
236C22#6541811yescharacteristic
237C22C2×#395611yescharacteristic
238C4—22no—
239C4—22no—
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—402no—
246C4—402no—
247C4#6469712yes—
248C2—21no—
249C2—21no—
250C2#1060076511yescharacteristic
251C2#1060085211yescharacteristic
252C2C2×#6469711yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1467C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1467D5
hypocenterC5#11573
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
232. C5#11573semidirect

Maximal subgroups

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

subgroupindex
#106142102
C5×#14672
#106024172
#105979432
#115735