Finite Group Databasebeta

← #10609554

Subgroups — #10609554

Order 640.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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
2C2×#4033C211yesmaximal, characteristic
3C5×#398C211yesmaximal, characteristic
4#65275C211yesmaximal, characteristic
5#65270C212yesmaximal
6#65269C211yesmaximal, characteristic
7#65268C212yesmaximal
8#64948C211yesmaximal, characteristic
9#64947C212yesmaximal
10#64944C212yesmaximal
11#64940C211yesmaximal, characteristic
12C22×Dic10C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2212yes—
16C2×C4⋊Dic5C2212yes—
17C2×C4⋊Dic5C2211yescharacteristic
18C2×#683C2211yescharacteristic
19C2×#683C2211yescharacteristic
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×C4×Dic5C2211yescharacteristic
23C2×C4×Dic5C2211yescharacteristic
24C2×C4×Dic5C2211yescharacteristic
25#4036—24no—
26#4033—24no—
27C5×#95C2211yescharacteristic
28C5×#95C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#3963C2211yescharacteristic
32#3963C2212yes—
33#3963C2212yes—
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2634—51nomaximal, Sylow
38C22×C4×C5C2312yes—
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×Dic5C2312yes—
44C22×Dic5C2311yescharacteristic
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×Dic10—22no—
50C2×Dic10—22no—
51C2×Dic10—22no—
52C5×C4⋊C4—22no—
53C5×C4⋊C4—22no—
54C5×C4⋊C4—24no—
55C4⋊Dic5—22no—
56C4⋊Dic5—24no—
57#683—22no—
58#683—22no—
59#683—24no—
60#683—24no—
61C4×Dic5—22no—
62C4×Dic5—22no—
63C4×Dic5D414yes—
64C2×#125—51no—
65C2×C4×Q8—51no—
66#400—51no—
67#400—52no—
68#400—51no—
69#398—51no—
70#398D511yescharacteristic
71#395—52no—
72#387—52no—
73#387—52no—
74#383—51no—
75C23×C5C2411yescharacteristic
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—22no—
79C2×C4×C5—21no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5—22no—
86C2×C4×C5—22no—
87C2×C4×C5C2×D412yes—
88C2×C4×C5#4112yes—
89C2×Dic5—21no—
90C2×Dic5—21no—
91C2×Dic5—21no—
92C2×Dic5—21no—
93C2×Dic5—22no—
94C2×Dic5—21no—
95C2×Dic5—22no—
96C2×Dic5—22no—
97C2×Dic5—24no—
98C2×Dic5—22no—
99C2×Dic5—22no—
100C2×Dic5—22no—
101C2×Dic5C2×D412yes—
102C2×Dic5C2×D412yes—
103C2×Dic5#4112yes—
104Dic10—28no—
105C22×Q8—51no—
106#125—104no—
107C4×Q8—104no—
108C2×C4⋊C4—51no—
109C2×C4⋊C4—51no—
110C2×C4⋊C4—52no—
111C2×C4⋊C4—52no—
112C2×C4⋊C4—51no—
113C2×C4⋊C4—52no—
114C2×C4⋊C4C2×D511yescharacteristic
115C2×C4⋊C4C2×D511yescharacteristic
116C2×C4⋊C4C2×D512yes—
117C2×C42—51no—
118C2×C42—51no—
119C2×C42—51no—
120#95—52no—
121#95—52no—
122#95—51no—
123#95—52no—
124#95—52no—
125#95—52no—
126#95—52no—
127#95—52no—
128#95C2×D511yescharacteristic
129#95C2×D512yes—
130C22×C5C22×D411yescharacteristic
131C22×C5C2×#4111yescharacteristic
132C22×C5C2×#4111yescharacteristic
133C22×C52−1+412yes—
134C22×C52−1+412yes—
135C4×C5—22no—
136C4×C5—22no—
137C4×C5—42no—
138C4×C5—41no—
139C4×C5—42no—
140Dic5—22no—
141Dic5—22no—
142Dic5—22no—
143Dic5—42no—
144Dic5—41no—
145Dic5—42no—
146C2×Q8—102no—
147C2×Q8—102no—
148C2×Q8—102no—
149C22×C4—51no—
150C22×C4—51no—
151C22×C4—51no—
152C22×C4—52no—
153C22×C4—51no—
154C22×C4—52no—
155C22×C4C22×D512yes—
156C22×C4C22×D511yescharacteristic
157C22×C4C22×D512yes—
158C22×C4C22×D511yescharacteristic
159C22×C4C22×D511yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—24no—
163C4⋊C4—102no—
164C4⋊C4—104no—
165C4⋊C4—104no—
166C4⋊C4—104no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C42—54no—
170C42—102no—
171C42—102no—
172C2×C5#52511yescharacteristic
173C2×C5#53611yescharacteristic
174C2×C5#53611yescharacteristic
175C2×C5#54112yes—
176C2×C5#54112yes—
177C23C23×D511yescharacteristic
178Q8—108no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—52no—
191C2×C4—52no—
192C2×C4—52no—
193C2×C4—101no—
194C2×C4—101no—
195C2×C4—101no—
196C2×C4—102no—
197C2×C4—101no—
198C2×C4—101no—
199C2×C4—102no—
200C2×C4—104no—
201C2×C4—102no—
202C2×C4—102no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4D4×D512yes—
206C2×C4#71112yes—
207C5#263411yescharacteristic, complemented, Sylow
208C22C2×D4×D511yescharacteristic
209C22C2×#71111yescharacteristic
210C22#414712yes—
211C22D5×#4111yescharacteristic
212C22#415012yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—42no—
217C4—41no—
218C4—102no—
219C4—102no—
220C4—102no—
221C4—202no—
222C4—201no—
223C4—202no—
224C2#6594011yescharacteristic
225C2#6595912yes—
226C2#6598211yescharacteristic
227C2#6603012yes—
228C2#6605811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2634
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
207. C5#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#40362
C2×#40332
C5×#3982
#652752
#652702
#652692
#652682
#649482
#649472
#649442
#649402
#26345