Finite Group Databasebeta

← #11998721

Subgroups — #11998721

Order 1280.

374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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#10610206C211yesmaximal, characteristic
2C5×#1568C211yesmaximal, characteristic
3#10601629C212yesmaximal
4#10601606C212yesmaximal
5#10600544C211yesmaximal, characteristic
6#65804C2212yes—
7C5×#432C2212yes—
8C2×C4×C5×C8C2211yescharacteristic
9#65405—21no—
10#65405—21no—
11#65221C2211yescharacteristic
12C2×#3935C2211yescharacteristic
13#64988C411yescharacteristic, complemented
14C4×Dic20—21no—
15C4×Dic20—21no—
16#64971C411yescharacteristic, complemented
17#64970C412yescomplemented
18C5×#335—21no—
19C5×#334—21no—
20#64770—21no—
21#64770—21no—
22#64687—24no—
23#64685—24no—
24#9765—51nomaximal, Sylow
25C22×C5×C8D411yescharacteristic
26C22×C5×C8D411yescharacteristic
27C2×C42×C5C2311yescharacteristic
28#4072—22no—
29#4070—22no—
30#4070—22no—
31C2×C4×Dic5—21no—
32C22×#168—21no—
33C2×Dic20—21no—
34C2×Dic20—21no—
35#4016—22no—
36#4015C2×C412yes—
37#4015C2×C412yes—
38C4×Dic10—22no—
39C4×Dic10—22no—
40C5×C4⋊C8—22no—
41C5×C22⋊C8—22no—
42C5×#97—22no—
43C4×C5×C8C2×C411yescharacteristic
44C4×C5×C8C2×C411yescharacteristic
45C4×C5×C8D411yescharacteristic
46C4×C5×C8D411yescharacteristic
47#3963—21no—
48#3963D412yes—
49#3950—21no—
50#3950—21no—
51#3948—22no—
52#3948—22no—
53#3935—21no—
54#3935D412yes—
55#3170—51no—
56#1746—51no—
57#1568D511yescharacteristic
58#1531—52no—
59#1506—52no—
60C22×C4×C5C2×D411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5#4111yescharacteristic
63C22×Dic5—22no—
64C2×Dic10—22no—
65C2×Dic10—22no—
66C2×C5×C8—41no—
67C2×C5×C8—41no—
68C2×C5×C8—42no—
69C2×C5×C8C22⋊C411yescharacteristic
70C2×C5×C8C22⋊C411yescharacteristic
71C2×C5×C8C22⋊C411yescharacteristic
72C2×C5×C8C22⋊C411yescharacteristic
73C42×C5C22×C411yescharacteristic
74C42×C5C2×D411yescharacteristic
75C42×C5C2×D411yescharacteristic
76C42×C5#4111yescharacteristic
77C22⋊Dic5—42no—
78C4⋊Dic5—22no—
79C4⋊Dic5—22no—
80C4⋊Dic5—22no—
81C4⋊Dic5—22no—
82#683—42no—
83#683—42no—
84C4×Dic5—41no—
85C4×Dic5—41no—
86C4×Dic5—42no—
87C2×#168—22no—
88C2×#168—41no—
89C2×#168—41no—
90Dic20—42no—
91Dic20—42no—
92#533—52no—
93#500—51no—
94#494—51no—
95#487—52no—
96#467—101no—
97#467—101no—
98C4×Q16—101no—
99C4×Q16—101no—
100#432C2×D512yes—
101C2×#97—51no—
102C2×C4×C8C2×D511yescharacteristic
103#376—51no—
104#336—101no—
105#336—101no—
106#335—21no—
107#334—21no—
108#330—104no—
109#328—104no—
110C23×C5#12111yescharacteristic
111C2×C4×C5—22no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—41no—
115C2×C4×C5C2×C22⋊C411yescharacteristic
116C2×C4×C5C4×D411yescharacteristic
117C2×C4×C5C4×D411yescharacteristic
118C2×C4×C5#12111yescharacteristic
119C2×C4×C5#12411yescharacteristic
120C2×C4×C5#12711yescharacteristic
121C2×Dic5—42no—
122C2×Dic5—42no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126Dic10—42no—
127Dic10—42no—
128Dic10—82no—
129C5×C8—21no—
130C5×C8—21no—
131C5×C8—21no—
132C5×C8—21no—
133C5×C8—82no—
134#168—42no—
135C2×Q16—101no—
136C2×Q16—101no—
137C22×C8—101no—
138C22×C8D2011yescharacteristic
139C22×C8D2011yescharacteristic
140C4⋊Q8—52no—
141C4⋊Q8—52no—
142#125—102no—
143C22⋊Q8—102no—
144C22⋊Q8—102no—
145C4×Q8—102no—
146C4×Q8—102no—
147#117—102no—
148C2×C42—101no—
149C2×C42C22×D511yescharacteristic
150#107—101no—
151#107—101no—
152C4⋊C8—22no—
153#103—102no—
154#103—102no—
155C22⋊C8—22no—
156#97—22no—
157#97—52no—
158#97—101no—
159C4×C8C4×D511yescharacteristic
160C4×C8C4×D511yescharacteristic
161C4×C8C22⋊D511yescharacteristic
162C4×C8C22⋊D511yescharacteristic
163#95—52no—
164#95—101no—
165C22×C5—21no—
166C22×C5—21no—
167C22×C5#39011yescharacteristic
168C22×C5#47312yes—
169C4×C5—21no—
170C4×C5—21no—
171C4×C5—21no—
172C4×C5—21no—
173C4×C5—21no—
174C4×C5#42111yescharacteristic
175C4×C5#42111yescharacteristic
176Dic5—82no—
177Dic5—82no—
178Dic5—82no—
179C2×Q8—102no—
180C2×Q8—102no—
181C22×C4—102no—
182C22×C4C2×D2011yescharacteristic
183C22×C4D4×D511yescharacteristic
184C22×C4#71311yescharacteristic
185Q16—202no—
186Q16—202no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—102no—
191C2×C8—201no—
192C2×C8—201no—
193C2×C8#68511yescharacteristic
194C2×C8#68511yescharacteristic
195C2×C8#68511yescharacteristic
196C2×C8#68511yescharacteristic
197C4⋊C4—102no—
198C4⋊C4—102no—
199C4⋊C4—102no—
200C4⋊C4—102no—
201C4⋊C4—202no—
202C4⋊C4—202no—
203C22⋊C4—202no—
204C42—201no—
205C42—201no—
206C42—202no—
207C42C2×C4×D511yescharacteristic
208C42D4×D511yescharacteristic
209C42#71311yescharacteristic
210C42C2×C22⋊D511yescharacteristic
211C2×C5—22no—
212C2×C5#196311yescharacteristic
213C2×C5#197611yescharacteristic
214C2×C5#197911yescharacteristic
215C23#404111yescharacteristic
216Q8—202no—
217Q8—202no—
218Q8—402no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—202no—
224C2×C4—202no—
225C2×C4—202no—
226C2×C4—202no—
227C2×C4—202no—
228C2×C4#403911yescharacteristic
229C2×C4#403911yescharacteristic
230C2×C4#404111yescharacteristic
231C2×C4C2×#68511yescharacteristic
232C2×C4#408611yescharacteristic
233C2×C4#409311yescharacteristic
234C8—21no—
235C8—21no—
236C8—21no—
237C8—21no—
238C8—82no—
239C8—202no—
240C5#976511yescharacteristic, complemented, Sylow
241C22—21no—
242C22—21no—
243C22#6518512yes—
244C22#6527711yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—402no—
251C4—402no—
252C4—402no—
253C4#6542811yescharacteristic
254C4#6542811yescharacteristic
255C2—22no—
256C2#1060130611yescharacteristic
257C2#1060145111yescharacteristic
258C2#1060150311yescharacteristic
subgroupG/H
centerC22#65277
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1568C2
socleC22×C5#390
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1568D5
hypocenterC5#9765
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
13. #64988C4semidirect
16. #64971C4semidirect
17. #64970C4semidirect
240. C5#9765semidirect

Maximal subgroups

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

subgroupindex
#106102062
C5×#15682
#106016292
#106016062
#106005442
#97655