Finite Group Databasebeta

← #10608327

Subgroups — #10608327

Order 640.

376 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 137 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#65519C212yesmaximal
3#65275C211yesmaximal, characteristic
4#65268C211yesmaximal, characteristic
5#65222C212yesmaximal
6#64949C212yesmaximal
7#64946C212yesmaximal
8#64944C212yesmaximal
9#64935C212yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C42×C5C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2212yes—
16C2×#683C2212yes—
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×C4×Dic5C2212yes—
20C5×#95C2212yes—
21C5×#95C2212yes—
22#3963C2212yes—
23#3963C2212yes—
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2211yescharacteristic
28#3963C2211yescharacteristic
29#3963C2212yes—
30#3963C2212yes—
31#2799—51nomaximal, Sylow
32C2×C5×Q8—41no—
33C2×C5×Q8—41no—
34C2×C5×Q8Q814yescomplemented
35C22×C4×C5C2312yes—
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C22×Dic5C2312yes—
44C2×Dic10—24no—
45C2×Dic10—41no—
46C5×C4⋊C4—41no—
47C42×C5—41no—
48C4⋊Dic5—41no—
49C4⋊Dic5—42no—
50#683—24no—
51#683—24no—
52#683—42no—
53C4×Dic5—42no—
54#400—51no—
55#400—52no—
56#398—52no—
57#395—51no—
58#391—52no—
59#391—52no—
60#391D511yescharacteristic
61#387—52no—
62#387—52no—
63C23×C5C2411yescharacteristic
64C5×Q8—44no—
65C2×C4×C5—22no—
66C2×C4×C5—22no—
67C2×C4×C5—21no—
68C2×C4×C5—21no—
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5—22no—
73C2×C4×C5—21no—
74C2×C4×C5—21no—
75C2×C4×C5—22no—
76C2×C4×C5C2×Q812yes—
77C2×C4×C5C2×Q814yes—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—24no—
88C2×Dic5#4114yes—
89Dic10—44no—
90C22×Q8—51no—
91C22×Q8C2×D511yescharacteristic
92C2×C4⋊C4—52no—
93C2×C4⋊C4—52no—
94C2×C4⋊C4—51no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4C2×D511yescharacteristic
98C2×C42—52no—
99C2×C42C2×D511yescharacteristic
100#95—52no—
101#95—52no—
102#95—52no—
103#95—52no—
104#95—52no—
105#95—52no—
106#95—52no—
107#95—51no—
108#95—51no—
109#95C2×D512yes—
110#95C2×D512yes—
111C22×C5C22×Q811yescharacteristic
112C22×C5C2×#4112yes—
113C22×C5H(5,𝔽2)11yescharacteristic
114C22×C5H(5,𝔽2)11yescharacteristic
115C22×C52−1+412yes—
116C4×C5—24no—
117C4×C5—22no—
118C4×C5—42no—
119C4×C5—41no—
120C4×C5—41no—
121Dic5—24no—
122Dic5—42no—
123Dic5—42no—
124Dic5—42no—
125C2×Q8—41no—
126C2×Q8—41no—
127C2×Q8—104no—
128C2×Q8—201no—
129C2×Q8Dic1014yescomplemented
130C22×C4—52no—
131C22×C4—52no—
132C22×C4—52no—
133C22×C4—52no—
134C22×C4C22×D511yescharacteristic
135C22×C4C22×D512yes—
136C22×C4C22×D511yescharacteristic
137C22×C4C22×D511yescharacteristic
138C22×C4C22×D512yes—
139C4⋊C4—41no—
140C4⋊C4—104no—
141C4⋊C4—104no—
142C4⋊C4—202no—
143C4⋊C4—202no—
144C4⋊C4—201no—
145C42—41no—
146C42—202no—
147C2×C5#54212yes—
148C2×C5#54311yescharacteristic
149C2×C5#55111yescharacteristic
150C2×C5#55712yes—
151C2×C5#56311yescharacteristic
152C23C23×D511yescharacteristic
153Q8—44no—
154Q8—204no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—54no—
167C2×C4—102no—
168C2×C4—102no—
169C2×C4—102no—
170C2×C4—102no—
171C2×C4—102no—
172C2×C4—104no—
173C2×C4—102no—
174C2×C4—102no—
175C2×C4—102no—
176C2×C4—102no—
177C2×C4C2×Dic1012yes—
178C2×C4C2×Dic1014yes—
179C5#279911yescharacteristic, complemented, Sylow
180C22C22×Dic1011yescharacteristic
181C22#414411yescharacteristic
182C22#414411yescharacteristic
183C22#414712yes—
184C22D5×#4112yes—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—104no—
191C4—202no—
192C4—202no—
193C4—202no—
194C2#6581711yescharacteristic
195C2#6590312yes—
196C2#6597412yes—
197C2#6601311yescharacteristic
198C2#6606911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2799
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
34. C2×C5×Q8Q8semidirect
129. C2×Q8Dic10semidirect
179. C5#2799semidirect

Maximal subgroups

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

subgroupindex
C5×#3912
#655192
#652752
#652682
#652222
#649492
#649462
#649442
#649352
#27995