Finite Group Databasebeta

← #10609268

Subgroups — #10609268

Order 640.

476 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 135 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×#4036C211yesmaximal, characteristic, complemented
2C2×#4023C211yesmaximal, characteristic
3C5×#397C211yesmaximal, characteristic
4#65269C211yesmaximal, characteristic, complemented
5#65240C212yesmaximal
6#65238C211yesmaximal, characteristic
7#65235C212yesmaximal
8#64948C211yesmaximal, characteristic, complemented
9#64941C212yesmaximal, complemented
10#64937C211yesmaximal, characteristic, complemented
11#64936C212yesmaximal, complemented
12C23×Dic5C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C22⋊C4C2211yescharacteristic
15C2×C5×C22⋊C4C2212yes—
16C2×C22⋊Dic5C2211yescharacteristic
17C2×C22⋊Dic5C2212yes—
18C2×C4⋊Dic5C2212yes—
19C2×C4⋊Dic5C2211yescharacteristic
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×#683C2212yes—
23C2×#683C2212yes—
24C2×#683C2212yes—
25C2×C4×Dic5C2211yescharacteristic
26C2×C4×Dic5C2212yes—
27C2×C4×Dic5C2211yescharacteristic
28#4036—24no—
29#4023—24no—
30C5×#95C2212yes—
31C5×#95C2211yescharacteristic
32#3963C2212yes—
33#3963C2212yes—
34#3963C2211yescharacteristic
35#3963C2212yes—
36#3963C2212yes—
37#2611—51nomaximal, Sylow
38C24×C5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C22×C4×C5C2312yes—
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×Dic5—22no—
44C22×Dic5—22no—
45C22×Dic5—22no—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2312yes—
48C22×Dic5C2311yescharacteristic
49C22×Dic5C2311yescharacteristic
50C22×Dic5C2312yes—
51C22×Dic5C2311yescharacteristic
52C5×C4⋊C4—22no—
53C5×C22⋊C4—24no—
54C5×C22⋊C4—22no—
55C22⋊Dic5—22no—
56C22⋊Dic5—24no—
57C4⋊Dic5—22no—
58C4⋊Dic5—24no—
59#683—22no—
60#683—22no—
61#683—24no—
62#683—24no—
63#683—24no—
64C4×Dic5—22no—
65C4×Dic5—24no—
66C4×Dic5D414yes—
67C2×#125—51no—
68C2×#117—51no—
69#400—51no—
70#399—51no—
71#398—51no—
72#397D511yescharacteristic
73#389—52no—
74#388—52no—
75#387—52no—
76#385—52no—
77#376—51no—
78C23×C5—21no—
79C23×C5—22no—
80C23×C5—21no—
81C23×C5—22no—
82C23×C5#4112yes—
83C23×C5C2411yescharacteristic
84C2×C4×C5—22no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—22no—
89C2×C4×C5—22no—
90C2×C4×C5—22no—
91C2×C4×C5—22no—
92C2×C4×C5—22no—
93C2×C4×C5C2×D412yes—
94C2×Dic5—28no—
95C2×Dic5—21no—
96C2×Dic5—22no—
97C2×Dic5—22no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—21no—
101C2×Dic5—22no—
102C2×Dic5—21no—
103C2×Dic5—22no—
104C2×Dic5—22no—
105C2×Dic5—22no—
106C2×Dic5—22no—
107C2×Dic5C2×D412yes—
108C2×Dic5C2×D412yes—
109C2×Dic5#4114yes—
110C2×Dic5#4112yes—
111C23×C4—51no—
112#125—104no—
113#117—104no—
114C2×C4⋊C4—51no—
115C2×C4⋊C4—51no—
116C2×C4⋊C4—52no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4—51no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4C2×D511yescharacteristic
122C2×C22⋊C4—51no—
123C2×C22⋊C4—52no—
124C2×C22⋊C4C2×D511yescharacteristic
125C2×C22⋊C4C2×D512yes—
126C2×C42—51no—
127C2×C42—51no—
128C2×C42—52no—
129#95—52no—
130#95—51no—
131#95—52no—
132#95—52no—
133#95—52no—
134#95C2×D511yescharacteristic
135#95C2×D512yes—
136C22×C5—22no—
137C22×C5—24no—
138C22×C5—41no—
139C22×C5—41no—
140C22×C5—42no—
141C22×C5C22×D411yescharacteristic
142C22×C5C2×#4111yescharacteristic
143C22×C5C2×#4111yescharacteristic
144C22×C5C2×#4112yes—
145C22×C52−1+412yes—
146C4×C5—22no—
147C4×C5—42no—
148C4×C5—41no—
149C4×C5—42no—
150Dic5—22no—
151Dic5—22no—
152Dic5—22no—
153Dic5—24no—
154Dic5—42no—
155Dic5—41no—
156C24C22×D511yescharacteristic
157C22×C4—52no—
158C22×C4—51no—
159C22×C4—51no—
160C22×C4—51no—
161C22×C4—51no—
162C22×C4—52no—
163C22×C4—102no—
164C22×C4—102no—
165C22×C4—102no—
166C22×C4C22×D512yes—
167C22×C4C22×D512yes—
168C22×C4C22×D511yescharacteristic
169C22×C4C22×D511yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—102no—
172C4⋊C4—104no—
173C4⋊C4—104no—
174C4⋊C4—104no—
175C4⋊C4—104no—
176C4⋊C4—102no—
177C4⋊C4—102no—
178C22⋊C4—24no—
179C22⋊C4—22no—
180C22⋊C4—102no—
181C22⋊C4—104no—
182C42—54no—
183C42—102no—
184C42—104no—
185C2×C5—42no—
186C2×C5#52511yescharacteristic
187C2×C5#53211yescharacteristic
188C2×C5#53611yescharacteristic
189C2×C5#55212yes—
190C2×C5#55212yes—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23#71112yes—
196C23C23×D511yescharacteristic
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—52no—
207C2×C4—52no—
208C2×C4—54no—
209C2×C4—52no—
210C2×C4—108no—
211C2×C4—101no—
212C2×C4—101no—
213C2×C4—101no—
214C2×C4—102no—
215C2×C4—102no—
216C2×C4—101no—
217C2×C4—102no—
218C2×C4—101no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4D4×D512yes—
224C5#261111yescharacteristic, complemented, Sylow
225C22—22no—
226C22—24no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22C2×D4×D511yescharacteristic
231C22C2×#71111yescharacteristic
232C22D5×#4111yescharacteristic
233C22D5×#4112yes—
234C22#415012yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—102no—
240C4—102no—
241C4—102no—
242C4—104no—
243C4—201no—
244C4—202no—
245C2—42no—
246C2#6594011yescharacteristic
247C2#6598211yescharacteristic
248C2#6598412yes—
249C2#6600211yescharacteristic
250C2#6604212yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#397C2
prime radicalC24×C5C23
hypercenter#397D5
hypocenterC5#2611
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#4036C2semidirect
4. #65269C2semidirect
8. #64948C2semidirect
9. #64941C2semidirect
10. #64937C2semidirect
11. #64936C2semidirect
224. C5#2611semidirect

Maximal subgroups

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

subgroupindex
C2×#40362
C2×#40232
C5×#3972
#652692
#652402
#652382
#652352
#649482
#649412
#649372
#649362
#26115