Finite Group Databasebeta

← #10608328

Subgroups — #10608328

Order 640.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#391C211yesmaximal, characteristic
2#65518C212yesmaximal
3#65267C212yesmaximal
4#65217C211yesmaximal, characteristic
5#65217C211yesmaximal, characteristic
6#64949C212yesmaximal
7#64948C212yesmaximal
8#64943C212yesmaximal
9#64936C212yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C42×C5C2211yescharacteristic
13C2×C4⋊Dic5C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2212yes—
22C5×#95C2212yes—
23C5×#95C2212yes—
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#2805—51nomaximal, Sylow
32C2×C5×Q8—22no—
33C2×C5×Q8—41no—
34C2×C5×Q8—41no—
35C22×C4×C5C2312yes—
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2311yescharacteristic
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C5×C4⋊C4—41no—
45C42×C5—41no—
46C4⋊Dic5—22no—
47C4⋊Dic5—41no—
48C4⋊Dic5—41no—
49C4⋊Dic5Q814yescomplemented
50#683—24no—
51#683—24no—
52#683—42no—
53#683—42no—
54C4×Dic5—42no—
55#400—52no—
56#400—52no—
57#395—52no—
58#391D511yescharacteristic
59#389—51no—
60#389—51no—
61#389—52no—
62#387—52no—
63#387—52no—
64C23×C5C2411yescharacteristic
65C5×Q8—44no—
66C2×C4×C5—21no—
67C2×C4×C5—21no—
68C2×C4×C5—21no—
69C2×C4×C5—21no—
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—22no—
77C2×C4×C5—22no—
78C2×C4×C5C2×Q812yes—
79C2×C4×C5#4112yes—
80C2×C4×C5#4112yes—
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×Dic5C2×Q814yes—
93C22×Q8C2×D511yescharacteristic
94C2×C4⋊C4—51no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—51no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—51no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—51no—
102C2×C4⋊C4C2×D511yescharacteristic
103C2×C42—52no—
104C2×C42C2×D511yescharacteristic
105#95—52no—
106#95—52no—
107#95—52no—
108#95—52no—
109#95—52no—
110#95—52no—
111#95—52no—
112#95C2×D512yes—
113#95C2×D512yes—
114C22×C5C22×Q811yescharacteristic
115C22×C5C2×#4111yescharacteristic
116C22×C5C2×#4111yescharacteristic
117C22×C5H(5,𝔽2)11yescharacteristic
118C22×C5H(5,𝔽2)11yescharacteristic
119C22×C52−1+411yescharacteristic
120C22×C52−1+411yescharacteristic
121C4×C5—22no—
122C4×C5—22no—
123C4×C5—22no—
124C4×C5—42no—
125C4×C5—42no—
126Dic5—24no—
127Dic5—42no—
128Dic5—42no—
129Dic5—42no—
130C2×Q8—22no—
131C2×Q8—41no—
132C2×Q8—41no—
133C22×C4—52no—
134C22×C4—52no—
135C22×C4—52no—
136C22×C4—52no—
137C22×C4C22×D512yes—
138C22×C4C22×D512yes—
139C22×C4C22×D511yescharacteristic
140C22×C4C22×D511yescharacteristic
141C22×C4C22×D511yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—54no—
144C4⋊C4—104no—
145C4⋊C4—104no—
146C4⋊C4—102no—
147C4⋊C4—202no—
148C4⋊C4—202no—
149C4⋊C4—201no—
150C4⋊C4—201no—
151C42—41no—
152C42—202no—
153C2×C5#53811yescharacteristic
154C2×C5#53911yescharacteristic
155C2×C5#54411yescharacteristic
156C2×C5#55411yescharacteristic
157C2×C5#55611yescharacteristic
158C2×C5#55711yescharacteristic
159C2×C5#56311yescharacteristic
160C23C23×D511yescharacteristic
161Q8—44no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—54no—
175C2×C4—102no—
176C2×C4—102no—
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×C4—102no—
186C2×C4#70912yes—
187C2×C4Q8×D512yes—
188C2×C4#71312yes—
189C5#280511yescharacteristic, complemented, Sylow
190C22C2×#70911yescharacteristic
191C22#414411yescharacteristic
192C22#414411yescharacteristic
193C22C2×Q8×D511yescharacteristic
194C22C2×#71311yescharacteristic
195C22#415011yescharacteristic
196C22#415011yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—104no—
203C4—202no—
204C4—202no—
205C4—202no—
206C2#6582811yescharacteristic
207C2#6590111yescharacteristic
208C2#6591811yescharacteristic
209C2#6595711yescharacteristic
210C2#6597911yescharacteristic
211C2#6600611yescharacteristic
212C2#6606411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2805
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
49. C4⋊Dic5Q8semidirect
189. C5#2805semidirect

Maximal subgroups

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

subgroupindex
C5×#3912
#655182
#652672
#652172
#649492
#649482
#649432
#649362
#28055