Finite Group Databasebeta

← #10609527

Subgroups — #10609527

Order 640.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#4033C212yesmaximal
2C5×#398C211yesmaximal, characteristic
3#65273C212yesmaximal
4#65272C211yesmaximal, characteristic
5#65265C211yesmaximal, characteristic
6#65261C212yesmaximal
7#64936C212yesmaximal
8#64935C212yesmaximal
9#64935C212yesmaximal
10C22×Dic10C2212yes—
11C2×C5×C4⋊C4C2212yes—
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2212yes—
22C2×C4×Dic5C2212yes—
23C2×C4×Dic5C2211yescharacteristic
24#4033—28no—
25C5×#95C2211yescharacteristic
26C5×#95C2212yes—
27#3963C2211yescharacteristic
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#3963C2212yes—
32#2582—51nomaximal, Sylow
33C22×C4×C5C2311yescharacteristic
34C22×C4×C5C2312yes—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C2×Dic10—24no—
43C2×Dic10—24no—
44C2×Dic10Q818yescomplemented
45C5×C4⋊C4—24no—
46C5×C4⋊C4—41no—
47C5×C4⋊C4—41no—
48C4⋊Dic5—41no—
49C4⋊Dic5—41no—
50#683—24no—
51#683—24no—
52#683—24no—
53#683—24no—
54#683—42no—
55C4×Dic5—24no—
56C4×Dic5—24no—
57C4×Dic5D414yes—
58C2×C4×Q8—52no—
59#398—51no—
60#398—52no—
61#398D511yescharacteristic
62#391—52no—
63#391—52no—
64#389—52no—
65#389—52no—
66#384—51no—
67C23×C5C2411yescharacteristic
68C2×C4×C5—22no—
69C2×C4×C5—22no—
70C2×C4×C5—21no—
71C2×C4×C5—21no—
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×C5C2×D412yes—
80C2×C4×C5C2×Q814yes—
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×Dic5C2×D414yes—
90C2×Dic5C2×Q814yes—
91C2×Dic5C2×Q814yes—
92C2×Dic5#4114yes—
93Dic10—216no—
94C22×Q8—52no—
95C4×Q8—108no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—52no—
100C2×C4⋊C4—51no—
101C2×C4⋊C4—52no—
102C2×C4⋊C4—51no—
103C2×C4⋊C4C2×D512yes—
104C2×C4⋊C4C2×D511yescharacteristic
105C2×C4⋊C4C2×D511yescharacteristic
106C2×C42—51no—
107C2×C42—52no—
108C2×C42—52no—
109#95—52no—
110#95—52no—
111#95—52no—
112#95—51no—
113#95—52no—
114#95C2×D512yes—
115#95C2×D511yescharacteristic
116C22×C5C22×D411yescharacteristic
117C22×C5C22×Q812yes—
118C22×C5C2×#4112yes—
119C22×C5H(5,𝔽2)11yescharacteristic
120C22×C52−1+411yescharacteristic
121C4×C5—24no—
122C4×C5—22no—
123C4×C5—42no—
124C4×C5—41no—
125C4×C5—41no—
126Dic5—24no—
127Dic5—42no—
128Dic5—42no—
129Dic5C22⋊Q818yes—
130C2×Q8—58no—
131C2×Q8—104no—
132C2×Q8—104no—
133C22×C4—52no—
134C22×C4—52no—
135C22×C4—52no—
136C22×C4—52no—
137C22×C4C22×D511yescharacteristic
138C22×C4C22×D511yescharacteristic
139C22×C4C22×D512yes—
140C22×C4C22×D511yescharacteristic
141C22×C4C22×D512yes—
142C4⋊C4—24no—
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—104no—
146C4⋊C4—104no—
147C4⋊C4—104no—
148C4⋊C4—104no—
149C4⋊C4—202no—
150C4⋊C4—201no—
151C4⋊C4—201no—
152C42—54no—
153C42—104no—
154C42—104no—
155C2×C5C2×C22⋊Q812yes—
156C2×C5#53711yescharacteristic
157C2×C5#55712yes—
158C2×C5Q8211yescharacteristic
159C2×C5#55911yescharacteristic
160C23C23×D511yescharacteristic
161Q8—1016no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—54no—
174C2×C4—54no—
175C2×C4—54no—
176C2×C4—54no—
177C2×C4—102no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4D4×D512yes—
186C2×C4Q8×D514yes—
187C5#258211yescharacteristic, complemented, Sylow
188C22C2×D4×D511yescharacteristic
189C22#414411yescharacteristic
190C22C2×Q8×D512yes—
191C22D5×#4112yes—
192C22#415011yescharacteristic
193C4—22no—
194C4—24no—
195C4—42no—
196C4—41no—
197C4—41no—
198C4—58no—
199C4—104no—
200C4—202no—
201C4—202no—
202C2#6593111yescharacteristic
203C2D5×C22⋊Q812yes—
204C2#6599811yescharacteristic
205C2#6601912yes—
206C2#6605611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2582
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
44. C2×Dic10Q8semidirect
187. C5#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#40332
C5×#3982
#652732
#652722
#652652
#652612
#649362
#649352
#25825