Finite Group Databasebeta

← #12108775

Subgroups — #12108775

Order 1280.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C2×#65834C211yesmaximal, characteristic
2#10610351C212yesmaximal
3C5×#1821C211yesmaximal, characteristic
4#10602355C211yesmaximal, characteristic
5#10600767C212yesmaximal
6#10599768C214yesmaximal, complemented
7#10599767C214yesmaximal, complemented
8C22×C5×C4⋊C4C2211yescharacteristic
9C2×#4072C2211yescharacteristic
10C2×#4072C2211yescharacteristic
11C2×#4070C414yes—
12#65834—28no—
13C2×#4036C412yes—
14C2×#4036C2212yes—
15C2×#4034C412yes—
16C2×#4034C2212yes—
17C5×#407C2212yes—
18#65496C2212yes—
19#65407C2214yes—
20M16×Dic5C2214yes—
21#65009—28no—
22C5×#343C2214yes—
23#64774C2214yes—
24#64774C2214yes—
25#64750C2214yes—
26#21832—51nomaximal, Sylow
27C23×C4×C5C2×C412yes—
28C23×C4×C5C2311yescharacteristic
29C22×Dic10C2×C414yes—
30C2×C5×M16C2314yes—
31C2×C5×C4⋊C4—24no—
32C2×C5×C4⋊C4C2×C412yes—
33C2×C5×C4⋊C4C2312yes—
34C2×C22⋊Dic5C2×C412yes—
35C2×C22⋊Dic5C2×C412yes—
36#4072—24no—
37#4072D418yes—
38C2×C4⋊Dic5C2×C414yes—
39C2×C4⋊Dic5C2×C411yescharacteristic
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×C4⋊Dic5C2311yescharacteristic
42C2×C4⋊Dic5C2311yescharacteristic
43#4070—216no—
44C2×#683C2×C414yes—
45C2×#683C2×C414yes—
46C2×C4×Dic5C2×C412yes—
47C2×C4×Dic5C2312yes—
48C2×#681C2314yes—
49#4036—28no—
50#4036—24no—
51#4036—24no—
52#4034—28no—
53#4034—24no—
54#4034—24no—
55C5×C22⋊C8—24no—
56C22⋊#168—24no—
57#3947—24no—
58#3946—28no—
59C8×Dic5—24no—
60C2×#544—51no—
61#2921—52no—
62#1998—54no—
63#1997—54no—
64#1822—52no—
65#1821—51no—
66#1821D511yescharacteristic
67C24×C5C22×C411yescharacteristic
68C22×C4×C5—24no—
69C22×C4×C5—24no—
70C22×C4×C5—82no—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C22×C414yes—
73C22×C4×C5C2×D414yes—
74C22×C4×C5C2411yescharacteristic
75C22×Dic5C22×C412yes—
76C22×Dic5C22×C412yes—
77C22×Dic5C22×C412yes—
78C22×Dic5C22×C412yes—
79C2×Dic10—28no—
80C2×Dic10—84no—
81C5×M16—28no—
82C2×C5×C8—24no—
83C5×C4⋊C4—24no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C22⋊Dic5—24no—
87C22⋊Dic5C22⋊C418yes—
88C4⋊Dic5—22no—
89C4⋊Dic5—22no—
90C4⋊Dic5—28no—
91C4⋊Dic5C22⋊C414yes—
92C4⋊Dic5C22⋊C414yes—
93#683—28no—
94#683—28no—
95C4×Dic5—24no—
96C4×Dic5C2×D414yes—
97C4×Dic5C2×D414yes—
98#681—28no—
99C2×#168—24no—
100#544—108no—
101C2×C4⋊Q8—52no—
102C2×C4⋊Q8—52no—
103C2×#125—52no—
104C2×#125—52no—
105C2×C22⋊Q8—54no—
106C2×#117—51no—
107C2×#117—51no—
108C22×C4⋊C4C2×D511yescharacteristic
109#433—108no—
110#423—54no—
111#407—52no—
112#407C2×D512yes—
113C4×M16—54no—
114#343—54no—
115#343—54no—
116#343—54no—
117#343C2×D514yes—
118C23×C5—22no—
119C23×C5—41no—
120C23×C5—41no—
121C23×C5C2×C22⋊C412yes—
122C23×C5C23×C411yescharacteristic
123C2×C4×C5—22no—
124C2×C4×C5—28no—
125C2×C4×C5—24no—
126C2×C4×C5—44no—
127C2×C4×C5—84no—
128C2×C4×C5C2×C22⋊C412yes—
129C2×C4×C5C22×D412yes—
130C2×C4×C52−1+414yes—
131C2×Dic5—22no—
132C2×Dic5—22no—
133C2×Dic5—42no—
134C2×Dic5—42no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5C2×C22⋊C414yes—
138C2×Dic5C2×C22⋊C414yes—
139Dic10—88no—
140C5×C8—44no—
141#168—44no—
142C22×Q8—54no—
143C23×C4C4×D512yes—
144C23×C4C22×D511yescharacteristic
145C2×M16—54no—
146C2×M16C22×D514yes—
147C4⋊Q8—104no—
148C4⋊Q8—104no—
149C4⋊Q8—108no—
150#125—104no—
151#125—104no—
152#125—108no—
153C22⋊Q8—1016no—
154#117—58no—
155#117—104no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—54no—
160C2×C4⋊C4—54no—
161C2×C4⋊C4—54no—
162C2×C4⋊C4—51no—
163C2×C4⋊C4—51no—
164C2×C4⋊C4C4×D512yes—
165C2×C4⋊C4C22×D512yes—
166C2×C22⋊C4—52no—
167C2×C22⋊C4—52no—
168C2×C42—52no—
169C2×C42—52no—
170C4⋊C8—108no—
171C22⋊C8—24no—
172C22⋊C8—104no—
173#97—104no—
174C4×C8—104no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—22no—
178C22×C5—22no—
179C22×C5—22no—
180C22×C5—44no—
181C22×C5C22×C22⋊C411yescharacteristic
182C22×C5#51912yes—
183C4×C5—22no—
184C4×C5—44no—
185C4×C5#53614yes—
186Dic5—24no—
187Dic5—24no—
188Dic5—42no—
189Dic5—42no—
190C24C2×C4×D511yescharacteristic
191C2×Q8—108no—
192C2×Q8—404no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—52no—
196C22×C4—52no—
197C22×C4—52no—
198C22×C4—52no—
199C22×C4—82no—
200C22×C4C2×C4×D511yescharacteristic
201C22×C4C2×C4×D514yes—
202C22×C4D4×D514yes—
203C22×C4C23×D511yescharacteristic
204M16—28no—
205M16—108no—
206C2×C8—24no—
207C2×C8—104no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—54no—
212C4⋊C4—54no—
213C4⋊C4—108no—
214C4⋊C4—108no—
215C4⋊C4—108no—
216C4⋊C4—102no—
217C4⋊C4—102no—
218C22⋊C4—58no—
219C22⋊C4—104no—
220C42—54no—
221C42—54no—
222C42—104no—
223C2×C5—22no—
224C2×C5—42no—
225C2×C5#231011yescharacteristic
226C2×C5#288811yescharacteristic
227C2×C5#288911yescharacteristic
228C23—22no—
229C23—41no—
230C23—41no—
231C23D5×C22⋊C412yes—
232C23C22×C4×D511yescharacteristic
233Q8—408no—
234C2×C4—22no—
235C2×C4—28no—
236C2×C4—24no—
237C2×C4—44no—
238C2×C4—54no—
239C2×C4—54no—
240C2×C4—84no—
241C2×C4—102no—
242C2×C4—102no—
243C2×C4—202no—
244C2×C4—202no—
245C2×C4—202no—
246C2×C4—202no—
247C2×C4D5×C22⋊C412yes—
248C2×C4C2×D4×D512yes—
249C2×C4#415014yes—
250C8—44no—
251C8—204no—
252C5#2183211yescharacteristic, complemented, Sylow
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×D5×C22⋊C411yescharacteristic
260C22#6585012yes—
261C4—22no—
262C4—44no—
263C4—104no—
264C4—104no—
265C4—202no—
266C4—202no—
267C4#6598214yes—
268C2—22no—
269C2—42no—
270C2#1060578411yescharacteristic
271C2#1061042811yescharacteristic
272C2#1061043711yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1821C2
socleC22×C5C22×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC22×C4×C5C24
hypercenter#1821D5
hypocenterC5#21832
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
6. #10599768C2semidirect
7. #10599767C2semidirect
252. C5#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#658342
#106103512
C5×#18212
#106023552
#106007672
#105997682
#105997672
#218325