Finite Group Databasebeta

← #10605925

Subgroups — #10605925

Order 640.

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

normal subgroups only

This group has 488 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
1C2×#4018C211yesmaximal, characteristic
2C2×#4015C211yesmaximal, characteristic, complemented
3C5×#382C211yesmaximal, characteristic, complemented
4#65276C212yesmaximal
5#65274C212yesmaximal, complemented
6#64966C212yesmaximal
7#64962C212yesmaximal
8#64948C212yesmaximal, complemented
9#64945C212yesmaximal, complemented
10C22×C4×D5C2211yescharacteristic
11C22×Dic10C2212yes—
12C2×C5×C4⋊C4C2212yes—
13C2×C42×C5C2211yescharacteristic
14C2×#685C2211yescharacteristic
15C2×#685C2211yescharacteristic
16C2×#685C2214yes—
17C2×C4⋊Dic5C2212yes—
18C2×C4⋊Dic5C2212yes—
19C2×C4⋊Dic5C2214yes—
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×C4×Dic5C2211yescharacteristic
23#4018—24no—
24#4015—24no—
25C5×#95C2212yes—
26C5×#95C2212yes—
27#3963C2214yes—
28#3963C2214yes—
29#2628—51nomaximal, Sylow
30C23×D5C2311yescharacteristic
31C22×C4×C5C2314yes—
32C22×C4×C5C2311yescharacteristic
33C22×C4×C5C2311yescharacteristic
34C22×C4×C5C2311yescharacteristic
35C22×Dic5C2314yes—
36C22×Dic5C2311yescharacteristic
37C22×Dic5C2311yescharacteristic
38C22×Dic5C2311yescharacteristic
39C2×C4×D5—22no—
40C2×C4×D5—22no—
41C2×C4×D5Q814yescomplemented
42C2×Dic10—24no—
43C2×Dic10—44no—
44C5×C4⋊C4—24no—
45C42×C5D414yes—
46#685—22no—
47#685—22no—
48#685—44no—
49C4⋊Dic5—24no—
50C4⋊Dic5—24no—
51C4⋊Dic5—44no—
52#683—22no—
53#683—22no—
54C4×Dic5—22no—
55C2×C4⋊Q8—51no—
56C2×#117—51no—
57#400—52no—
58#399—52no—
59#395—52no—
60#393—52no—
61#389—52no—
62#382D511yescharacteristic, complemented
63#380—52no—
64C23×C5C2411yescharacteristic
65C22×D5—21no—
66C22×D5—21no—
67C22×D5—22no—
68C22×D5—22no—
69C22×D5C2×Q812yes—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5—24no—
73C2×C4×C5—24no—
74C2×C4×C5—24no—
75C2×C4×C5C2×D412yes—
76C2×C4×C5C2×D412yes—
77C2×C4×C5C2×D412yes—
78C2×C4×C5C2×Q812yes—
79C2×C4×C5#4112yes—
80C2×Dic5—21no—
81C2×Dic5—21no—
82C2×Dic5—21no—
83C2×Dic5—21no—
84C2×Dic5—24no—
85C2×Dic5—22no—
86C2×Dic5—24no—
87C2×Dic5—24no—
88C2×Dic5—22no—
89C2×Dic5C2×Q812yes—
90C4×D5—28no—
91Dic10—48no—
92C22×Q8—52no—
93C23×C4—51no—
94C4⋊Q8—104no—
95#117—104no—
96C2×C4⋊C4—51no—
97C2×C4⋊C4—51no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—52no—
100C2×C4⋊C4—54no—
101C2×C4⋊C4C2×D512yes—
102C2×C22⋊C4—51no—
103C2×C22⋊C4—51no—
104C2×C22⋊C4—54no—
105C2×C42—51no—
106C2×C42C2×D511yescharacteristic
107#95—54no—
108#95—54no—
109#95C2×D512yes—
110#95C2×D512yes—
111C22×C5C22×D411yescharacteristic
112C22×C5C22×Q811yescharacteristic
113C22×C5C2×#4111yescharacteristic
114C22×C5H(5,𝔽2)12yes—
115C22×C52−1+412yes—
116C2×D5—22no—
117C2×D5—24no—
118C2×D5—41no—
119C2×D5—41no—
120C2×D5—42no—
121C4×C5—22no—
122C4×C5—22no—
123C4×C5—44no—
124C4×C5C22⋊Q814yes—
125Dic5—22no—
126Dic5—44no—
127Dic5—41no—
128Dic5—41no—
129C24—51no—
130C2×Q8—104no—
131C2×Q8—204no—
132C22×C4—51no—
133C22×C4—54no—
134C22×C4—51no—
135C22×C4—54no—
136C22×C4—51no—
137C22×C4—102no—
138C22×C4—102no—
139C22×C4C22×D514yes—
140C22×C4C22×D511yescharacteristic
141C22×C4C22×D511yescharacteristic
142C22×C4C22×D511yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—102no—
145C4⋊C4—102no—
146C4⋊C4—104no—
147C4⋊C4—104no—
148C4⋊C4—204no—
149C22⋊C4—102no—
150C22⋊C4—102no—
151C22⋊C4—204no—
152C42—102no—
153C42D2014yes—
154C2×C5C2×C22⋊Q811yescharacteristic
155C2×C5#53511yescharacteristic
156C2×C5#53611yescharacteristic
157C2×C5#54212yes—
158C2×C5#54412yes—
159D5—42no—
160C23—52no—
161C23—101no—
162C23—101no—
163C23—102no—
164C23—102no—
165C23C23×D511yescharacteristic
166Q8—208no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—52no—
173C2×C4—101no—
174C2×C4—101no—
175C2×C4—108no—
176C2×C4—101no—
177C2×C4—101no—
178C2×C4—104no—
179C2×C4—104no—
180C2×C4—102no—
181C2×C4—104no—
182C2×C4—102no—
183C2×C4C2×D2012yes—
184C2×C4C2×D2012yes—
185C2×C4C2×D2012yes—
186C2×C4#71112yes—
187C2×C4Q8×D512yes—
188C5#262811yescharacteristic, complemented, Sylow
189C22—102no—
190C22—104no—
191C22—201no—
192C22—201no—
193C22—202no—
194C22C22×D2011yescharacteristic
195C22C2×#71111yescharacteristic
196C22C2×Q8×D511yescharacteristic
197C22#414912yes—
198C22#415012yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—102no—
203C4—204no—
204C4—201no—
205C4—201no—
206C4#404314yes—
207C2—202no—
208C2C2×#404311yescharacteristic
209C2#6585911yescharacteristic
210C2#6586011yescharacteristic
211C2#6601612yes—
212C2#6602312yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#382C2
prime radicalC23×D5C23
hypercenter#382D5
hypocenterC5#2628
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#4015C2semidirect
3. C5×#382C2semidirect
5. #65274C2semidirect
8. #64948C2semidirect
9. #64945C2semidirect
41. C2×C4×D5Q8semidirect
62. #382D5semidirect
188. C5#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#40182
C2×#40152
C5×#3822
#652762
#652742
#649662
#649622
#649482
#649452
#26285