Finite Group Databasebeta

← #10608576

Subgroups — #10608576

Order 640.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C5×#393C211yesmaximal, characteristic
2#65519C212yesmaximal, complemented
3#65242C211yesmaximal, characteristic
4#65239C212yesmaximal
5#65233C212yesmaximal
6#65232C211yesmaximal, characteristic
7#64950C212yesmaximal, complemented
8#64949C212yesmaximal, complemented
9#64940C212yesmaximal, complemented
10C22×C5×Q8C2211yescharacteristic
11C23×Dic5C2211yescharacteristic
12C2×C5×C22⋊C4C2212yes—
13C2×C5×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic5C2212yes—
15C2×C22⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2212yes—
17C2×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊Dic5C2212yes—
19C2×#683C2212yes—
20C2×C4×Dic5C2212yes—
21C5×#95C2212yes—
22C5×#95C2211yescharacteristic
23#3963C2211yescharacteristic
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#2764—51nomaximal, Sylow
32C24×C5C2311yescharacteristic
33C2×C5×Q8—24no—
34C2×C5×Q8—41no—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2312yes—
38C22×C4×C5C2312yes—
39C22×Dic5—22no—
40C22×Dic5—41no—
41C22×Dic5—41no—
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C22×Dic5C2312yes—
45C22×Dic5C2312yes—
46C5×C22⋊C4—24no—
47C5×C22⋊C4—41no—
48C22⋊Dic5—24no—
49C22⋊Dic5—41no—
50C4⋊Dic5—42no—
51C4⋊Dic5—41no—
52C4⋊Dic5—42no—
53#683—42no—
54C4×Dic5—24no—
55#400—52no—
56#398—52no—
57#397—51no—
58#393D511yescharacteristic
59#391—52no—
60#388—52no—
61#385—52no—
62#383—52no—
63#381—51no—
64C23×C5—22no—
65C23×C5—21no—
66C23×C5—21no—
67C23×C5—22no—
68C23×C5#4112yes—
69C23×C5C2411yescharacteristic
70C5×Q8—44no—
71C2×C4×C5—22no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—22no—
79C2×C4×C5—22no—
80C2×C4×C5#4114yes—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—44no—
94C22×Q8C2×D511yescharacteristic
95C23×C4—51no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—51no—
100C2×C22⋊C4—52no—
101C2×C22⋊C4—51no—
102C2×C22⋊C4C2×D512yes—
103C2×C22⋊C4C2×D511yescharacteristic
104C2×C42—52no—
105#95—52no—
106#95—52no—
107#95—51no—
108#95—52no—
109#95—52no—
110#95—52no—
111#95—52no—
112#95—52no—
113#95C2×D512yes—
114#95C2×D511yescharacteristic
115C22×C5—22no—
116C22×C5—24no—
117C22×C5—42no—
118C22×C5—41no—
119C22×C5—41no—
120C22×C5C2×#4112yes—
121C22×C5C2×#4111yescharacteristic
122C22×C5H(5,𝔽2)11yescharacteristic
123C22×C5H(5,𝔽2)11yescharacteristic
124C22×C52−1+412yes—
125C4×C5—24no—
126C4×C5—42no—
127C4×C5—41no—
128C4×C5—41no—
129Dic5—42no—
130Dic5—42no—
131Dic5—42no—
132Dic5—42no—
133C24C22×D511yescharacteristic
134C2×Q8—24no—
135C2×Q8—41no—
136C22×C4—52no—
137C22×C4—52no—
138C22×C4—52no—
139C22×C4—52no—
140C22×C4—102no—
141C22×C4—201no—
142C22×C4—201no—
143C22×C4C22×D511yescharacteristic
144C22×C4C22×D511yescharacteristic
145C22×C4C22×D512yes—
146C22×C4C22×D512yes—
147C4⋊C4—202no—
148C4⋊C4—202no—
149C4⋊C4—201no—
150C4⋊C4—202no—
151C22⋊C4—24no—
152C22⋊C4—41no—
153C22⋊C4—104no—
154C22⋊C4—201no—
155C42—104no—
156C2×C5—42no—
157C2×C5#53811yescharacteristic
158C2×C5#54212yes—
159C2×C5#55111yescharacteristic
160C2×C5#55212yes—
161C2×C5#56311yescharacteristic
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#71312yes—
167C23C23×D511yescharacteristic
168Q8—44no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4—102no—
188C2×C4—102no—
189C2×C4—102no—
190C2×C4—204no—
191C2×C4#71114yes—
192C5#276411yescharacteristic, complemented, Sylow
193C22—24no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—42no—
198C22C2×#71112yes—
199C22#414411yescharacteristic
200C22C2×#71311yescharacteristic
201C22#414911yescharacteristic
202C22#415012yes—
203C4—24no—
204C4—41no—
205C4—41no—
206C4—42no—
207C4—202no—
208C4—202no—
209C4—202no—
210C4—202no—
211C2—42no—
212C2#6592111yescharacteristic
213C2#6597612yes—
214C2#6597811yescharacteristic
215C2#6600611yescharacteristic
216C2#6601612yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#393C2
prime radicalC24×C5C23
hypercenter#393D5
hypocenterC5#2764
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #65519C2semidirect
7. #64950C2semidirect
8. #64949C2semidirect
9. #64940C2semidirect
192. C5#2764semidirect

Maximal subgroups

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

subgroupindex
C5×#3932
#655192
#652422
#652392
#652332
#652322
#649502
#649492
#649402
#27645