Finite Group Databasebeta

← #10607912

Subgroups — #10607912

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×#389C211yesmaximal, characteristic
2#65271C212yesmaximal
3#65270C212yesmaximal
4#65268C212yesmaximal
5#65261C212yesmaximal
6#65218C211yesmaximal, characteristic
7#65217C211yesmaximal, characteristic
8#64949C212yesmaximal
9#64942C212yesmaximal
10C22×Dic10C2211yescharacteristic
11C2×C5×C4⋊C4C2212yes—
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C42×C5C2211yescharacteristic
15C2×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2211yescharacteristic
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2212yes—
22C5×#95C2212yes—
23#3963C2212yes—
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#2805—51nomaximal, Sylow
32C22×C4×C5C2312yes—
33C22×C4×C5C2312yes—
34C22×C4×C5C2311yescharacteristic
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C2×Dic10—22no—
42C2×Dic10—41no—
43C2×Dic10—41no—
44C5×C4⋊C4—22no—
45C5×C4⋊C4—24no—
46C5×C4⋊C4—41no—
47C42×C5—41no—
48C4⋊Dic5—41no—
49C4⋊Dic5—41no—
50C4⋊Dic5Q814yescomplemented
51#683—24no—
52#683—42no—
53#683—42no—
54C4×Dic5—42no—
55#400—52no—
56#400—52no—
57#395—52no—
58#391—51no—
59#389—52no—
60#389—51no—
61#389D511yescharacteristic
62#387—52no—
63#387—52no—
64C23×C5C2411yescharacteristic
65C2×C4×C5—21no—
66C2×C4×C5—21no—
67C2×C4×C5—21no—
68C2×C4×C5—21no—
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×C5—22no—
77C2×C4×C5C2×Q812yes—
78C2×C4×C5#4112yes—
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×Dic5—22no—
91C2×Dic5C2×Q814yes—
92Dic10—44no—
93C22×Q8—51no—
94C2×C4⋊C4—51no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—51no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—51no—
100C2×C4⋊C4C2×D512yes—
101C2×C4⋊C4C2×D511yescharacteristic
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#95—52no—
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—102no—
131C2×Q8—201no—
132C2×Q8—201no—
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—22no—
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—54no—
146C4⋊C4—104no—
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—204no—
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×C4#71112yes—
188C2×C4Q8×D512yes—
189C5#280511yescharacteristic, complemented, Sylow
190C22C2×#70911yescharacteristic
191C22C2×#71111yescharacteristic
192C22#414411yescharacteristic
193C22C2×Q8×D511yescharacteristic
194C22#414711yescharacteristic
195C22#414911yescharacteristic
196C22#415011yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—104no—
203C4—202no—
204C4—202no—
205C4—202no—
206C2#6584911yescharacteristic
207C2#6587611yescharacteristic
208C2#6591311yescharacteristic
209C2#6595111yescharacteristic
210C2#6595711yescharacteristic
211C2#6603311yescharacteristic
212C2#6605511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#389C2
hypercenter#389D5
hypocenterC5#2805
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
50. 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×#3892
#652712
#652702
#652682
#652612
#652182
#652172
#649492
#649422
#28055