Finite Group Databasebeta

← #10608290

Subgroups — #10608290

Order 640.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#4090C211yesmaximal, characteristic
2C2×#4036C211yesmaximal, characteristic
3C5×#391C211yesmaximal, characteristic
4#65519C211yesmaximal, characteristic
5#65263C211yesmaximal, characteristic
6#65221C211yesmaximal, characteristic
7#65218C211yesmaximal, characteristic
8#64949C214yesmaximal
9#64947C214yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C22×Dic10C2211yescharacteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C42×C5C2211yescharacteristic
14#4090—24no—
15C2×C4⋊Dic5C2212yes—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2212yes—
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×C4×Dic5C2211yescharacteristic
21C2×C4×Dic5C2211yescharacteristic
22#4036—24no—
23C5×#95C2214yes—
24#3963C2212yes—
25#3963C2214yes—
26#3963C2214yes—
27#3963C2214yes—
28#3963C2212yes—
29#2642—51nomaximal, Sylow
30C2×C5×Q8—22no—
31C2×C5×Q8—22no—
32C2×C5×Q8—22no—
33C22×C4×C5C2312yes—
34C22×C4×C5C2312yes—
35C22×C4×C5C2312yes—
36C22×C4×C5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2311yescharacteristic
41C22×Dic5C2311yescharacteristic
42C2×Dic10—22no—
43C2×Dic10—22no—
44C2×Dic10—22no—
45C5×C4⋊C4—22no—
46C42×C5—22no—
47C4⋊Dic5—22no—
48C4⋊Dic5—24no—
49#683—24no—
50#683—24no—
51#683—24no—
52C4×Dic5—22no—
53C4×Dic5D414yes—
54C2×C4⋊Q8—51no—
55C2×#125—51no—
56#400—54no—
57#400—54no—
58#391—51no—
59#391—51no—
60#391—51no—
61#391D511yescharacteristic
62#376—51no—
63C23×C5C2411yescharacteristic
64C5×Q8—44no—
65C2×C4×C5—22no—
66C2×C4×C5—22no—
67C2×C4×C5—22no—
68C2×C4×C5—22no—
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—24no—
72C2×C4×C5—22no—
73C2×C4×C5C2×D412yes—
74C2×C4×C5#4112yes—
75C2×C4×C5#4112yes—
76C2×Dic5—22no—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—24no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5C2×D412yes—
87C2×Dic5C2×D412yes—
88Dic10—44no—
89C22×Q8—51no—
90C22×Q8C2×D511yescharacteristic
91C4⋊Q8—104no—
92#125—104no—
93C2×C4⋊C4—51no—
94C2×C4⋊C4—52no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4C2×D511yescharacteristic
99C2×C42—51no—
100C2×C42—51no—
101C2×C42C2×D511yescharacteristic
102#95—52no—
103#95—52no—
104#95—54no—
105#95—54no—
106#95—54no—
107#95C2×D514yes—
108C22×C5C22×D411yescharacteristic
109C22×C5C2×#4111yescharacteristic
110C22×C5C2×#4111yescharacteristic
111C22×C52−1+412yes—
112C22×C52−1+412yes—
113C4×C5—42no—
114C4×C5—42no—
115C4×C5—42no—
116C4×C5#12414yes—
117Dic5—22no—
118Dic5—22no—
119Dic5—42no—
120Dic5—42no—
121Dic5—42no—
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—22no—
125C2×Q8—102no—
126C2×Q8—102no—
127C2×Q8—102no—
128C22×C4—51no—
129C22×C4—51no—
130C22×C4—52no—
131C22×C4—52no—
132C22×C4—52no—
133C22×C4C22×D512yes—
134C22×C4C22×D512yes—
135C22×C4C22×D512yes—
136C22×C4C22×D511yescharacteristic
137C4⋊C4—22no—
138C4⋊C4—104no—
139C4⋊C4—104no—
140C4⋊C4—104no—
141C4⋊C4—104no—
142C4⋊C4—102no—
143C42—22no—
144C42—54no—
145C42—102no—
146C2×C5C2×#12411yescharacteristic
147C2×C5#53611yescharacteristic
148C2×C5#53611yescharacteristic
149C2×C5#54112yes—
150C2×C5#54112yes—
151C23C23×D511yescharacteristic
152Q8—44no—
153Q8—204no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—24no—
162C2×C4—52no—
163C2×C4—52no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—102no—
168C2×C4—102no—
169C2×C4—102no—
170C2×C4—102no—
171C2×C4—104no—
172C2×C4—102no—
173C2×C4—102no—
174C2×C4#70912yes—
175C2×C4D4×D512yes—
176C2×C4#71112yes—
177C5#264211yescharacteristic, complemented, Sylow
178C22C2×#70911yescharacteristic
179C22C2×D4×D511yescharacteristic
180C22C2×#71111yescharacteristic
181C22#414712yes—
182C22#415012yes—
183C4—42no—
184C4—42no—
185C4—42no—
186C4—102no—
187C4—102no—
188C4—202no—
189C4—202no—
190C4—202no—
191C4#403114yes—
192C2C2×#403111yescharacteristic
193C2#6591712yes—
194C2#6595912yes—
195C2#6600911yescharacteristic
196C2#6605811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2642
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
177. C5#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#40902
C2×#40362
C5×#3912
#655192
#652632
#652212
#652182
#649492
#649472
#26425