Finite Group Databasebeta

← #10609658

Subgroups — #10609658

Order 640.

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

normal subgroups only

This group has 380 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
1C2×#4035C212yesmaximal
2C5×#398C211yesmaximal, characteristic
3#65273C212yesmaximal
4#65273C212yesmaximal
5#65272C211yesmaximal, characteristic
6#65266C211yesmaximal, characteristic
7#64949C212yesmaximal
8#64947C212yesmaximal
9#64946C212yesmaximal
10C2×C5×C4⋊C4C2212yes—
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic5C2212yes—
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2211yescharacteristic
22#4035—28no—
23C5×#95C2212yes—
24C5×#95C2211yescharacteristic
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2211yescharacteristic
31#3963C2212yes—
32#2822—51nomaximal, Sylow
33C22×C4×C5C2311yescharacteristic
34C22×C4×C5C2312yes—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C5×C4⋊C4—24no—
43C5×C4⋊C4—41no—
44C5×C4⋊C4—41no—
45C4⋊Dic5—24no—
46C4⋊Dic5—41no—
47C4⋊Dic5—41no—
48#683—24no—
49#683—24no—
50#683—24no—
51#683—24no—
52#683—42no—
53C4×Dic5D414yes—
54C2×#125—52no—
55#400—52no—
56#400—52no—
57#398—51no—
58#398—52no—
59#398—52no—
60#398—52no—
61#398D511yescharacteristic
62#382—51no—
63C23×C5C2411yescharacteristic
64C2×C4×C5—21no—
65C2×C4×C5—21no—
66C2×C4×C5—22no—
67C2×C4×C5—22no—
68C2×C4×C5—22no—
69C2×C4×C5—21no—
70C2×C4×C5—21no—
71C2×C4×C5—22no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5C2×D412yes—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—24no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5C2×D414yes—
88#125—108no—
89C2×C4⋊C4—52no—
90C2×C4⋊C4—52no—
91C2×C4⋊C4—52no—
92C2×C4⋊C4—52no—
93C2×C4⋊C4—52no—
94C2×C4⋊C4—51no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—51no—
97C2×C4⋊C4C2×D512yes—
98C2×C4⋊C4C2×D511yescharacteristic
99C2×C4⋊C4C2×D511yescharacteristic
100C2×C42—51no—
101#95—52no—
102#95—52no—
103#95—52no—
104#95—52no—
105#95—52no—
106#95—52no—
107#95—51no—
108#95C2×D512yes—
109#95C2×D511yescharacteristic
110C22×C5C22×D411yescharacteristic
111C22×C5H(5,𝔽2)11yescharacteristic
112C22×C52−1+412yes—
113C22×C52−1+412yes—
114C22×C52−1+411yescharacteristic
115C4×C5—22no—
116C4×C5—42no—
117C4×C5—42no—
118C4×C5—41no—
119C4×C5—41no—
120Dic5—24no—
121Dic5—42no—
122Dic5—42no—
123Dic5—42no—
124C22×C4—52no—
125C22×C4—52no—
126C22×C4—52no—
127C22×C4—52no—
128C22×C4C22×D511yescharacteristic
129C22×C4C22×D511yescharacteristic
130C22×C4C22×D512yes—
131C22×C4C22×D512yes—
132C22×C4C22×D511yescharacteristic
133C4⋊C4—24no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—104no—
137C4⋊C4—104no—
138C4⋊C4—104no—
139C4⋊C4—104no—
140C4⋊C4—104no—
141C4⋊C4—202no—
142C4⋊C4—201no—
143C4⋊C4—201no—
144C42—54no—
145C2×C5#53612yes—
146C2×C5#53711yescharacteristic
147C2×C5#56311yescharacteristic
148C2×C5#56311yescharacteristic
149C2×C5#56412yes—
150C23C23×D511yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—54no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—102no—
168C2×C4—102no—
169C2×C4—102no—
170C2×C4—104no—
171C2×C4—102no—
172C2×C4—102no—
173C2×C4—102no—
174C2×C4D4×D512yes—
175C5#282211yescharacteristic, complemented, Sylow
176C22C2×D4×D511yescharacteristic
177C22#414411yescharacteristic
178C22#414712yes—
179C22#415011yescharacteristic
180C22#415012yes—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—104no—
187C4—202no—
188C4—202no—
189C4—202no—
190C2#6593111yescharacteristic
191C2#6596212yes—
192C2#6598511yescharacteristic
193C2C5⋊#56412yes—
194C2#6606911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2822
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
175. C5#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#40352
C5×#3982
#652732
#652722
#652662
#649492
#649472
#649462
#28225