Finite Group Databasebeta

← #10609646

Subgroups — #10609646

Order 640.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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×#398C211yesmaximal, characteristic
2#65275C211yesmaximal, characteristic
3#65270C212yesmaximal
4#65267C212yesmaximal
5#65267C212yesmaximal
6#65265C211yesmaximal, characteristic
7#64947C212yesmaximal
8#64947C212yesmaximal
9#64944C212yesmaximal
10C2×C5×C4⋊C4C2212yes—
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic5C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×#683C2212yes—
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×C4×Dic5C2211yescharacteristic
19C2×C4×Dic5C2212yes—
20C5×#95C2212yes—
21C5×#95C2211yescharacteristic
22#3963C2212yes—
23#3963C2212yes—
24#3963C2212yes—
25#3963C2212yes—
26#3963C2211yescharacteristic
27#3963C2212yes—
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#2794—51nomaximal, Sylow
32C22×C4×C5C2312yes—
33C22×C4×C5C2311yescharacteristic
34C22×C4×C5C2312yes—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C5×C4⋊C4—24no—
42C5×C4⋊C4—41no—
43C5×C4⋊C4—41no—
44C4⋊Dic5—41no—
45C4⋊Dic5—41no—
46#683—24no—
47#683—24no—
48#683—24no—
49C4×Dic5—22no—
50C4×Dic5—42no—
51#400—51no—
52#400—52no—
53#400—52no—
54#398D511yescharacteristic
55#387—52no—
56#387—52no—
57#387—52no—
58#387—52no—
59#384—51no—
60C23×C5C2411yescharacteristic
61C2×C4×C5—21no—
62C2×C4×C5—21no—
63C2×C4×C5—22no—
64C2×C4×C5—22no—
65C2×C4×C5—22no—
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#4112yes—
74C2×Dic5—22no—
75C2×Dic5—22no—
76C2×Dic5—22no—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—24no—
83C2×Dic5—22no—
84C2×Dic5#4114yes—
85C2×C4⋊C4—52no—
86C2×C4⋊C4—52no—
87C2×C4⋊C4—52no—
88C2×C4⋊C4—51no—
89C2×C4⋊C4—51no—
90C2×C4⋊C4C2×D512yes—
91C2×C4⋊C4C2×D511yescharacteristic
92C2×C4⋊C4C2×D511yescharacteristic
93C2×C42—51no—
94C2×C42—52no—
95#95—52no—
96#95—52no—
97#95—52no—
98#95—52no—
99#95—52no—
100#95—52no—
101#95—52no—
102#95—52no—
103#95—51no—
104#95C2×D512yes—
105#95C2×D511yescharacteristic
106C22×C5C2×#4111yescharacteristic
107C22×C5C2×#4112yes—
108C22×C5H(5,𝔽2)11yescharacteristic
109C22×C52−1+412yes—
110C22×C52−1+411yescharacteristic
111C4×C5—22no—
112C4×C5—42no—
113C4×C5—42no—
114C4×C5—41no—
115C4×C5—41no—
116Dic5—24no—
117Dic5—42no—
118Dic5—42no—
119Dic5—42no—
120C22×C4—52no—
121C22×C4—52no—
122C22×C4—52no—
123C22×C4—52no—
124C22×C4C22×D512yes—
125C22×C4C22×D512yes—
126C22×C4C22×D511yescharacteristic
127C22×C4C22×D511yescharacteristic
128C22×C4C22×D511yescharacteristic
129C4⋊C4—24no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—104no—
133C4⋊C4—104no—
134C4⋊C4—104no—
135C4⋊C4—201no—
136C4⋊C4—201no—
137C42—102no—
138C42—202no—
139C2×C5#53911yescharacteristic
140C2×C5#54112yes—
141C2×C5#55212yes—
142C2×C5#55911yescharacteristic
143C2×C5#56311yescharacteristic
144C23C23×D511yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—54no—
158C2×C4—102no—
159C2×C4—102no—
160C2×C4—102no—
161C2×C4—102no—
162C2×C4—104no—
163C2×C4—102no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—102no—
168C2×C4#71112yes—
169C5#279411yescharacteristic, complemented, Sylow
170C22C2×#71111yescharacteristic
171C22#414411yescharacteristic
172C22#414712yes—
173C22D5×#4112yes—
174C22#415011yescharacteristic
175C4—22no—
176C4—42no—
177C4—42no—
178C4—41no—
179C4—41no—
180C4—104no—
181C4—202no—
182C4—202no—
183C4—202no—
184C2#6593611yescharacteristic
185C2#6597312yes—
186C2#6599811yescharacteristic
187C2#6603012yes—
188C2#6606911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2794
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
169. C5#2794semidirect

Maximal subgroups

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

subgroupindex
C5×#3982
#652752
#652702
#652672
#652652
#649472
#649442
#27945