Finite Group Databasebeta

← #10609945

Subgroups — #10609945

Order 640.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#4035C211yesmaximal, characteristic
2C2×#4034C211yesmaximal, characteristic
3C5×#400C211yesmaximal, characteristic
4#65275C211yesmaximal, characteristic
5#65271C211yesmaximal, characteristic
6#64949C212yesmaximal
7#64948C211yesmaximal, characteristic
8#64947C212yesmaximal
9#64937C211yesmaximal, characteristic
10#64935C212yesmaximal
11#64935C212yesmaximal
12C22×Dic10C2212yes—
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2212yes—
18C2×#683C2211yescharacteristic
19C2×#683C2211yescharacteristic
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×C4×Dic5C2212yes—
23C2×C4×Dic5C2211yescharacteristic
24#4035—24no—
25#4034—24no—
26C5×#95C2212yes—
27C5×#95C2212yes—
28C5×#95C2211yescharacteristic
29#3963C2212yes—
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2212yes—
34#3963C2212yes—
35#3963C2212yes—
36#3963C2211yescharacteristic
37#2642—51nomaximal, Sylow
38C22×C4×C5C2312yes—
39C22×C4×C5C2311yescharacteristic
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×Dic5C2312yes—
44C22×Dic5C2312yes—
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×Dic10—24no—
50C2×Dic10—28no—
51C5×C4⋊C4—22no—
52C5×C4⋊C4—22no—
53C4⋊Dic5—22no—
54C4⋊Dic5—22no—
55#683—22no—
56#683—24no—
57#683—22no—
58#683—22no—
59#683—22no—
60C4×Dic5—24no—
61C4×Dic5D414yes—
62C2×C4⋊Q8—51no—
63C2×#125—51no—
64#400—51no—
65#400—51no—
66#400—52no—
67#400—51no—
68#400—52no—
69#400D511yescharacteristic
70#391—52no—
71#391—52no—
72#376—51no—
73C23×C5C2411yescharacteristic
74C2×C4×C5—22no—
75C2×C4×C5—21no—
76C2×C4×C5—21no—
77C2×C4×C5—22no—
78C2×C4×C5—22no—
79C2×C4×C5—24no—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5C2×D412yes—
86C2×Dic5—21no—
87C2×Dic5—21no—
88C2×Dic5—21no—
89C2×Dic5—21no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—24no—
93C2×Dic5—21no—
94C2×Dic5—22no—
95C2×Dic5—22no—
96C2×Dic5—21no—
97C2×Dic5—22no—
98C2×Dic5C2×D412yes—
99C2×Dic5C2×D412yes—
100C2×Dic5#4114yes—
101Dic10—48no—
102C22×Q8—52no—
103C4⋊Q8—104no—
104#125—104no—
105C2×C4⋊C4—51no—
106C2×C4⋊C4—51no—
107C2×C4⋊C4—51no—
108C2×C4⋊C4—51no—
109C2×C4⋊C4—51no—
110C2×C4⋊C4—52no—
111C2×C4⋊C4—51no—
112C2×C4⋊C4C2×D511yescharacteristic
113C2×C4⋊C4C2×D511yescharacteristic
114C2×C42—51no—
115C2×C42—52no—
116#95—52no—
117#95—51no—
118#95—52no—
119#95—52no—
120#95—52no—
121#95—52no—
122#95—52no—
123#95—52no—
124#95C2×D511yescharacteristic
125#95C2×D512yes—
126#95C2×D512yes—
127C22×C5C22×D411yescharacteristic
128C22×C5C2×#4112yes—
129C22×C52−1+411yescharacteristic
130C22×C52−1+411yescharacteristic
131C22×C52−1+412yes—
132C4×C5—22no—
133C4×C5—42no—
134C4×C5—41no—
135C4×C5—41no—
136C4×C5—42no—
137Dic5—22no—
138Dic5—42no—
139Dic5—41no—
140Dic5—41no—
141Dic5—42no—
142Dic5#12414yes—
143C2×Q8—104no—
144C2×Q8—108no—
145C22×C4—51no—
146C22×C4—51no—
147C22×C4—52no—
148C22×C4—51no—
149C22×C4—51no—
150C22×C4—52no—
151C22×C4C22×D512yes—
152C22×C4C22×D511yescharacteristic
153C22×C4C22×D511yescharacteristic
154C22×C4C22×D512yes—
155C22×C4C22×D511yescharacteristic
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—102no—
159C4⋊C4—102no—
160C4⋊C4—102no—
161C4⋊C4—102no—
162C4⋊C4—104no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C42—54no—
166C42—104no—
167C2×C5C2×#12411yescharacteristic
168C2×C5#53611yescharacteristic
169C2×C5#53611yescharacteristic
170C2×C5#54112yes—
171C2×C5#54112yes—
172C23C23×D511yescharacteristic
173Q8—208no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—52no—
186C2×C4—54no—
187C2×C4—52no—
188C2×C4—101no—
189C2×C4—101no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4—102no—
193C2×C4—101no—
194C2×C4—102no—
195C2×C4—102no—
196C2×C4—104no—
197C2×C4—101no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4D4×D512yes—
201C5#264211yescharacteristic, complemented, Sylow
202C22C2×D4×D511yescharacteristic
203C22#414711yescharacteristic
204C22D5×#4112yes—
205C22#415011yescharacteristic
206C22#415012yes—
207C4—22no—
208C4—41no—
209C4—41no—
210C4—42no—
211C4—42no—
212C4—54no—
213C4—102no—
214C4—201no—
215C4—201no—
216C4—202no—
217C4—202no—
218C2#6596211yescharacteristic
219C2#6598211yescharacteristic
220C2D5×#12411yescharacteristic
221C2#6603012yes—
222C2#6603512yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#400C2
hypercenter#400D5
hypocenterC5#2642
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
201. C5#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#40352
C2×#40342
C5×#4002
#652752
#652712
#649492
#649482
#649472
#649372
#649352
#26425