Finite Group Databasebeta

← #10608925

Subgroups — #10608925

Order 640.

412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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×#395C211yesmaximal, characteristic
2#65519C212yesmaximal
3#65274C212yesmaximal
4#65272C211yesmaximal, characteristic
5#65267C212yesmaximal
6#65263C211yesmaximal, characteristic
7#64945C212yesmaximal
8#64944C212yesmaximal
9#64938C212yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C2×C5×C4⋊C4C2212yes—
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic5C2212yes—
15C2×C4⋊Dic5C2212yes—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×C4×Dic5C2212yes—
20C2×C4×Dic5C2211yescharacteristic
21C2×C4×Dic5C2212yes—
22C5×#95C2212yes—
23C5×#95C2211yescharacteristic
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2211yescharacteristic
31#2586—51nomaximal, Sylow
32C2×C5×Q8—24no—
33C2×C5×Q8—41no—
34C22×C4×C5C2311yescharacteristic
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C2×Dic10—22no—
44C2×Dic10—41no—
45C2×Dic10—41no—
46C5×C4⋊C4—24no—
47C5×C4⋊C4—41no—
48C4⋊Dic5—42no—
49C4⋊Dic5—41no—
50C4⋊Dic5—42no—
51#683—24no—
52#683Q818yescomplemented
53C4×Dic5—24no—
54C4×Dic5—41no—
55C4×Dic5—42no—
56#398—51no—
57#395—52no—
58#395D511yescharacteristic
59#391—52no—
60#391—51no—
61#389—52no—
62#387—52no—
63#387—52no—
64C4×C4⋊C4—52no—
65C23×C5C2411yescharacteristic
66C5×Q8—44no—
67C2×C4×C5—22no—
68C2×C4×C5—22no—
69C2×C4×C5—22no—
70C2×C4×C5—21no—
71C2×C4×C5—22no—
72C2×C4×C5—21no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—21no—
76C2×C4×C5—21no—
77C2×C4×C5C2×Q814yes—
78C2×C4×C5#4114yes—
79C2×C4×C5#4112yes—
80C2×Dic5—22no—
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×Dic5C2×Q814yes—
91C2×Dic5C2×Q814yes—
92Dic10—44no—
93C22×Q8—51no—
94C22×Q8C2×D511yescharacteristic
95C2×C4⋊C4—52no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4—51no—
99C2×C4⋊C4—52no—
100C2×C4⋊C4C2×D512yes—
101C2×C4⋊C4C2×D511yescharacteristic
102C2×C42—52no—
103C2×C42—51no—
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#95C2×D512yes—
113#95C2×D511yescharacteristic
114C22×C5C22×Q812yes—
115C22×C5C2×#4112yes—
116C22×C5C2×#4111yescharacteristic
117C22×C5H(5,𝔽2)11yescharacteristic
118C22×C5H(5,𝔽2)11yescharacteristic
119C4×C5—22no—
120C4×C5—24no—
121C4×C5—24no—
122C4×C5—41no—
123C4×C5—41no—
124Dic5—24no—
125Dic5—24no—
126Dic5—42no—
127Dic5—42no—
128C2×Q8—24no—
129C2×Q8—41no—
130C2×Q8—102no—
131C2×Q8—201no—
132C2×Q8—201no—
133C22×C4—52no—
134C22×C4—52no—
135C22×C4—52no—
136C22×C4—52no—
137C22×C4C22×D511yescharacteristic
138C22×C4C22×D511yescharacteristic
139C22×C4C22×D512yes—
140C22×C4C22×D512yes—
141C22×C4C22×D511yescharacteristic
142C4⋊C4—24no—
143C4⋊C4—41no—
144C4⋊C4—58no—
145C4⋊C4—104no—
146C4⋊C4—202no—
147C4⋊C4—202no—
148C4⋊C4—201no—
149C42—104no—
150C42—202no—
151C42—201no—
152C2×C5#53312yes—
153C2×C5#53811yescharacteristic
154C2×C5#55111yescharacteristic
155C2×C5#55412yes—
156C2×C5Q8211yescharacteristic
157C23C23×D511yescharacteristic
158Q8—44no—
159Q8—204no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—54no—
171C2×C4—54no—
172C2×C4—102no—
173C2×C4—102no—
174C2×C4—102no—
175C2×C4—102no—
176C2×C4—102no—
177C2×C4—102no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4#71114yes—
183C2×C4Q8×D514yes—
184C2×C4#71312yes—
185C5#258611yescharacteristic, complemented, Sylow
186C22C2×#71112yes—
187C22#414411yescharacteristic
188C22C2×Q8×D512yes—
189C22C2×#71311yescharacteristic
190C22#414911yescharacteristic
191C4—24no—
192C4—24no—
193C4—22no—
194C4—41no—
195C4—41no—
196C4—104no—
197C4—104no—
198C4—202no—
199C4—202no—
200C2#6592111yescharacteristic
201C2#6596912yes—
202C2#6597811yescharacteristic
203C2#6605611yescharacteristic
204C2#6606212yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#395C2
hypercenter#395D5
hypocenterC5#2586
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
52. #683Q8semidirect
185. C5#2586semidirect

Maximal subgroups

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

subgroupindex
C5×#3952
#655192
#652742
#652722
#652672
#652632
#649452
#649442
#649382
#25865