Finite Group Databasebeta

← #10613913

Subgroups — #10613913

Order 640.

596 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#4076C211yesmaximal, characteristic
3#65502C212yesmaximal, complemented
4#65502C212yesmaximal, complemented
5C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
6#65280C212yesmaximal, complemented
7#65279C214yesmaximal, complemented
8#65275C212yesmaximal, complemented
9C23×C4×C5C2211yescharacteristic
10C23×C4×C5C2211yescharacteristic
11C23×C4×C5C2211yescharacteristic
12C22×C22⋊D5C2212yes—
13C22×D20C2211yescharacteristic
14C2×C5×C4⋊C4—24no—
15C2×C5×C4⋊C4C2212yes—
16C2×C5×C4⋊C4C2212yes—
17C2×C22⋊Dic5C2212yes—
18#4076—24no—
19C2×#685C2214yes—
20C2×#685C2212yes—
21C2×#685C2214yes—
22C2×C4⋊Dic5C2211yescharacteristic
23C2×C4×Dic5C2212yes—
24#3963C2212yes—
25#3963C2214yes—
26#3963C2214yes—
27#2591—51nomaximal, Sylow
28C24×C5C2311yescharacteristic
29C23×D5C2312yes—
30C22×C4×C5—22no—
31C22×C4×C5—24no—
32C22×C4×C5—22no—
33C22×C4×C5—42no—
34C22×C4×C5—42no—
35C22×C4×C5D414yes—
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C2×C22⋊D5—24no—
41C2×C22⋊D5—28no—
42C22×Dic5C2314yes—
43C22×Dic5C2312yes—
44C2×D20—22no—
45C2×D20—42no—
46C5×C4⋊C4—24no—
47C5×C4⋊C4—24no—
48C22⋊Dic5—24no—
49#685—24no—
50#685—28no—
51#685—44no—
52C4⋊Dic5—22no—
53C4×Dic5—42no—
54C2×#121—51no—
55C22×C4⋊C4D511yescharacteristic, complemented
56#400—52no—
57#394—52no—
58#388—54no—
59#386—52no—
60#386—52no—
61C4×C22⋊C4—51no—
62C23×C5—22no—
63C23×C5—22no—
64C23×C5C2×D412yes—
65C23×C5#4114yes—
66C23×C5C2411yescharacteristic
67C22×D5—22no—
68C22×D5—24no—
69C22×D5—24no—
70C22×D5—24no—
71C2×C4×C5—28no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—22no—
77C2×C4×C5—24no—
78C2×C4×C5—44no—
79C2×C4×C5—44no—
80C2×C4×C5C2×D412yes—
81C2×C4×C5C2×D412yes—
82C2×C4×C5#4114yes—
83C22⋊D5—48no—
84C2×Dic5—22no—
85C2×Dic5—24no—
86C2×Dic5—24no—
87C2×Dic5—24no—
88C2×Dic5—24no—
89D20—44no—
90C22×D4—52no—
91C22×D4—51no—
92C23×C4C2×D511yescharacteristic
93C23×C4C2×D511yescharacteristic
94C23×C4C2×D511yescharacteristic
95#121—104no—
96C2×C4⋊C4—24no—
97C2×C4⋊C4—51no—
98C2×C4⋊C4C2×D512yes—
99C2×C4⋊C4C2×D512yes—
100C2×C22⋊C4—52no—
101C2×C22⋊C4—52no—
102C2×C22⋊C4—54no—
103C2×C22⋊C4—54no—
104C2×C42—52no—
105#95—52no—
106#95—54no—
107#95—54no—
108C22×C5—22no—
109C22×C5—22no—
110C22×C5—28no—
111C22×C5#12414yes—
112C22×C5C22×D411yescharacteristic
113C22×C5C2×#4112yes—
114C22×C5C2×#4112yes—
115C22×C5H(5,𝔽2)12yes—
116C2×D5—42no—
117C2×D5—42no—
118C2×D5—42no—
119C2×D5—48no—
120C4×C5—24no—
121C4×C5—22no—
122C4×C5—22no—
123C4×C5—42no—
124Dic5—42no—
125Dic5—44no—
126C24—52no—
127C24C22×D511yescharacteristic
128C2×D4—108no—
129C2×D4—104no—
130C2×D4—102no—
131C2×D4—202no—
132C22×C4—22no—
133C22×C4—24no—
134C22×C4—22no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—52no—
138C22×C4—54no—
139C22×C4C22⋊D514yes—
140C22×C4C22×D512yes—
141C22×C4C22×D512yes—
142C22×C4C22×D511yescharacteristic
143C22×C4C22×D511yescharacteristic
144C4⋊C4—24no—
145C4⋊C4—24no—
146C4⋊C4—102no—
147C22⋊C4—104no—
148C22⋊C4—108no—
149C22⋊C4—104no—
150C22⋊C4—204no—
151C42—202no—
152C2×C5—24no—
153C2×C5#52511yescharacteristic
154C2×C5C2×#12411yescharacteristic
155C2×C5#53411yescharacteristic
156C2×C5#55314yes—
157D5—82no—
158C23—22no—
159C23—22no—
160C23—104no—
161C23—104no—
162C23—104no—
163C23—102no—
164C23#71314yes—
165C23C2×C22⋊D512yes—
166C23C23×D511yescharacteristic
167D4—204no—
168D4—208no—
169C2×C4—28no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—44no—
178C2×C4—104no—
179C2×C4—104no—
180C2×C4—104no—
181C2×C4—104no—
182C2×C4—102no—
183C2×C4#70914yes—
184C2×C4C2×C22⋊D512yes—
185C2×C4C2×C22⋊D512yes—
186C5#259111yescharacteristic, complemented, Sylow
187C22—28no—
188C22—22no—
189C22—22no—
190C22—208no—
191C22—202no—
192C22—202no—
193C22—202no—
194C22#409314yes—
195C22C2×#70912yes—
196C22#414412yes—
197C22C2×#71312yes—
198C22C22×C22⋊D511yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—204no—
204C4—202no—
205C2—24no—
206C2—402no—
207C2#6584814yes—
208C2#6612511yescharacteristic
209C2#6613811yescharacteristic
210C2C2×#409311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC22×C5×C4⋊C4C2
prime radicalC2×#4076C2
hypercenterC22×C4⋊C4D5
hypocenterC5#2591
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×C4⋊C4C2semidirect
3. #65502C2semidirect
4. #65502C2semidirect
5. C4×C22⋊Dic5C2semidirect
6. #65280C2semidirect
7. #65279C2semidirect
8. #65275C2semidirect
55. C22×C4⋊C4D5semidirect
186. C5#2591semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C4⋊C42
C2×#40762
#655022
C4×C22⋊Dic52
#652802
#652792
#652752
#25915