Finite Group Databasebeta

← #10605867

Subgroups — #10605867

Order 640.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#4075C211yesmaximal, characteristic
2C22×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C5×#381C211yesmaximal, characteristic, complemented
4#65247C212yesmaximal
5#65239C212yesmaximal, complemented
6#64966C212yesmaximal, complemented
7#64963C212yesmaximal, complemented
8#64950C212yesmaximal, complemented
9#64948C212yesmaximal, complemented
10C23×C4×C5C2211yescharacteristic
11C22×C22⋊D5C2211yescharacteristic
12C23×Dic5C2212yes—
13C2×C5×C22⋊C4C2212yes—
14C2×C22⋊Dic5C2211yescharacteristic
15#4075—24no—
16C2×#685C2211yescharacteristic
17C2×#685C2211yescharacteristic
18C2×#685C2214yes—
19C2×C4⋊Dic5—24no—
20C2×C4⋊Dic5C2212yes—
21C2×C4⋊Dic5C2212yes—
22C2×C4⋊Dic5C2214yes—
23C2×#683C2211yescharacteristic
24C2×#683C2211yescharacteristic
25C5×#95C2212yes—
26C5×#95C2212yes—
27#3963C2214yes—
28#3963C2214yes—
29#2623—51nomaximal, Sylow
30C24×C5C2311yescharacteristic
31C23×D5C2311yescharacteristic
32C22×C4×C5—24no—
33C22×C4×C5D414yes—
34C22×C4×C5C2314yes—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2311yescharacteristic
37C2×C22⋊D5—22no—
38C2×C22⋊D5—24no—
39C22×Dic5—24no—
40C22×Dic5—44no—
41C22×Dic5C2311yescharacteristic
42C22×Dic5C2311yescharacteristic
43C22×Dic5C2314yes—
44C22×Dic5C2311yescharacteristic
45C5×C22⋊C4—24no—
46C22⋊Dic5—22no—
47#685—22no—
48#685—22no—
49#685—44no—
50C4⋊Dic5—24no—
51C4⋊Dic5—24no—
52C4⋊Dic5—44no—
53#683—22no—
54#683—22no—
55C2×#123—51no—
56C22×C4⋊C4—51no—
57#400—52no—
58#399—52no—
59#398—52no—
60#397—52no—
61#386—52no—
62#385—52no—
63#381D511yescharacteristic, complemented
64C23×C5—22no—
65C23×C5—22no—
66C23×C5C2×D412yes—
67C23×C5#4114yes—
68C23×C5C2411yescharacteristic
69C22×D5—21no—
70C22×D5—22no—
71C22×D5—22no—
72C22×D5—22no—
73C2×C4×C5—28no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—24no—
77C2×C4×C5—24no—
78C2×C4×C5—24no—
79C2×C4×C5C2×D412yes—
80C2×C4×C5C2×D412yes—
81C22⋊D5—44no—
82C2×Dic5—21no—
83C2×Dic5—21no—
84C2×Dic5—21no—
85C2×Dic5—24no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—24no—
89C2×Dic5—24no—
90C2×Dic5—22no—
91C2×Dic5—48no—
92C22×D4—51no—
93C23×C4—52no—
94C23×C4C2×D511yescharacteristic
95#123—104no—
96C2×C4⋊C4—52no—
97C2×C4⋊C4—52no—
98C2×C4⋊C4—51no—
99C2×C4⋊C4—51no—
100C2×C4⋊C4—54no—
101C2×C4⋊C4—104no—
102C2×C22⋊C4—51no—
103C2×C22⋊C4—51no—
104C2×C22⋊C4—51no—
105C2×C22⋊C4—54no—
106C2×C22⋊C4C2×D512yes—
107#95—54no—
108#95—54no—
109#95C2×D512yes—
110#95C2×D512yes—
111C22×C5—22no—
112C22×C5—22no—
113C22×C5—28no—
114C22×C5#12314yes—
115C22×C5C22×D411yescharacteristic
116C22×C5C2×#4112yes—
117C22×C5H(5,𝔽2)12yes—
118C22×C52−1+412yes—
119C2×D5—41no—
120C2×D5—41no—
121C2×D5—41no—
122C2×D5—44no—
123C4×C5—22no—
124C4×C5—22no—
125C4×C5—44no—
126Dic5—41no—
127Dic5—41no—
128Dic5—44no—
129Dic5—41no—
130C24—51no—
131C24C22×D511yescharacteristic
132C2×D4—102no—
133C2×D4—104no—
134C22×C4—24no—
135C22×C4—51no—
136C22×C4—51no—
137C22×C4—54no—
138C22×C4—51no—
139C22×C4—104no—
140C22×C4—204no—
141C22×C4D2014yes—
142C22×C4C22×D514yes—
143C22×C4C22×D511yescharacteristic
144C22×C4C22×D511yescharacteristic
145C4⋊C4—104no—
146C4⋊C4—104no—
147C4⋊C4—102no—
148C4⋊C4—102no—
149C4⋊C4—204no—
150C22⋊C4—24no—
151C22⋊C4—102no—
152C22⋊C4—102no—
153C22⋊C4—102no—
154C22⋊C4—204no—
155C2×C5—24no—
156C2×C5C2×#12311yescharacteristic
157C2×C5#53511yescharacteristic
158C2×C5#53611yescharacteristic
159C2×C5#53914yes—
160D5—81no—
161C23—22no—
162C23—22no—
163C23—101no—
164C23—102no—
165C23—102no—
166C23—102no—
167C23C2×D2012yes—
168C23#71114yes—
169C23C23×D511yescharacteristic
170D4—204no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—101no—
178C2×C4—101no—
179C2×C4—104no—
180C2×C4—101no—
181C2×C4—102no—
182C2×C4—104no—
183C2×C4—102no—
184C2×C4—104no—
185C2×C4—102no—
186C2×C4—208no—
187C2×C4C2×D2012yes—
188C2×C4C2×D2012yes—
189C5#262311yescharacteristic, complemented, Sylow
190C22—22no—
191C22—22no—
192C22—28no—
193C22—201no—
194C22—201no—
195C22—201no—
196C22—204no—
197C22#403214yes—
198C22C22×D2011yescharacteristic
199C22C2×#71112yes—
200C22#414912yes—
201C22#415012yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—201no—
206C4—204no—
207C4—201no—
208C4—201no—
209C2—24no—
210C2—401no—
211C2C2×#403211yescharacteristic
212C2#6585911yescharacteristic
213C2#6586011yescharacteristic
214C2#6599914yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#381C2
prime radicalC22×C22⋊D5C22
hypercenter#381D5
hypocenterC5#2623
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic5C2semidirect
3. C5×#381C2semidirect
5. #65239C2semidirect
6. #64966C2semidirect
7. #64963C2semidirect
8. #64950C2semidirect
9. #64948C2semidirect
63. #381D5semidirect
189. C5#2623semidirect

Maximal subgroups

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

subgroupindex
C2×#40752
C22×C4⋊Dic52
C5×#3812
#652472
#652392
#649662
#649632
#649502
#649482
#26235