Finite Group Databasebeta

← #10608923

Subgroups — #10608923

Order 640.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×Q8×Dic5C211yesmaximal, characteristic
2C2×#4035C211yesmaximal, characteristic
3C5×#395C211yesmaximal, characteristic
4#65518C211yesmaximal, characteristic
5#65274C212yesmaximal
6#65272C211yesmaximal, characteristic
7#65261C212yesmaximal
8#64950C211yesmaximal, characteristic
9#64938C211yesmaximal, characteristic
10#64936C212yesmaximal
11#64936C212yesmaximal
12C22×C5×Q8C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C4⋊C4C2212yes—
15Q8×Dic5—24no—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2212yes—
18C2×C4⋊Dic5C2211yescharacteristic
19C2×C4⋊Dic5C2212yes—
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×#683C2211yescharacteristic
23C2×#683C2211yescharacteristic
24C2×#683C2212yes—
25C2×#683C2212yes—
26C2×#683C2212yes—
27C2×C4×Dic5C2212yes—
28C2×C4×Dic5C2212yes—
29C2×C4×Dic5C2211yescharacteristic
30#4035—24no—
31C5×#95C2212yes—
32C5×#95C2211yescharacteristic
33#3963C2212yes—
34#3963C2212yes—
35#3963C2211yescharacteristic
36#3963C2212yes—
37#2584—51nomaximal, Sylow
38C2×C5×Q8—22no—
39C2×C5×Q8—24no—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2312yes—
44C22×C4×C5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C22×Dic5C2312yes—
50C22×Dic5C2311yescharacteristic
51C5×C4⋊C4—22no—
52C5×C4⋊C4—24no—
53C4⋊Dic5—22no—
54C4⋊Dic5—22no—
55C4⋊Dic5—24no—
56C4⋊Dic5—42no—
57#683—22no—
58#683—24no—
59#683—22no—
60#683—22no—
61#683—22no—
62#683—42no—
63#683Q818yescomplemented
64C4×Dic5—24no—
65C4×Dic5—42no—
66C4×Dic5D414yes—
67C2×#125—51no—
68C2×C4×Q8—51no—
69#398—51no—
70#398—51no—
71#395—51no—
72#395D511yescharacteristic
73#389—52no—
74#389—52no—
75#389—52no—
76#389—52no—
77C4×C4⋊C4—51no—
78C23×C5C2411yescharacteristic
79C5×Q8—28no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—22no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—22no—
88C2×C4×C5—21no—
89C2×C4×C5—21no—
90C2×C4×C5C2×D412yes—
91C2×C4×C5C2×Q814yes—
92C2×C4×C5#4114yes—
93C2×Dic5—22no—
94C2×Dic5—21no—
95C2×Dic5—22no—
96C2×Dic5—21no—
97C2×Dic5—22no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—22no—
102C2×Dic5—21no—
103C2×Dic5—22no—
104C2×Dic5—21no—
105C2×Dic5C2×D412yes—
106C2×Dic5C2×D412yes—
107C2×Dic5C2×Q814yes—
108C2×Dic5C2×Q814yes—
109C22×Q8C2×D511yescharacteristic
110#125—104no—
111C4×Q8—104no—
112C2×C4⋊C4—52no—
113C2×C4⋊C4—52no—
114C2×C4⋊C4—51no—
115C2×C4⋊C4—51no—
116C2×C4⋊C4—51no—
117C2×C4⋊C4—51no—
118C2×C4⋊C4—51no—
119C2×C4⋊C4—51no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—52no—
122C2×C4⋊C4—52no—
123C2×C4⋊C4C2×D511yescharacteristic
124C2×C4⋊C4C2×D512yes—
125C2×C42—51no—
126C2×C42—52no—
127C2×C42—52no—
128#95—51no—
129#95—52no—
130#95—52no—
131#95—52no—
132#95C2×D511yescharacteristic
133#95C2×D512yes—
134C22×C5C22×D411yescharacteristic
135C22×C5C22×Q812yes—
136C22×C5C2×#4112yes—
137C22×C5H(5,𝔽2)11yescharacteristic
138C22×C52−1+411yescharacteristic
139C4×C5—22no—
140C4×C5—24no—
141C4×C5—24no—
142C4×C5—41no—
143C4×C5—41no—
144Dic5—22no—
145Dic5—24no—
146Dic5—41no—
147Dic5—42no—
148Dic5—41no—
149Dic5C4⋊Q814yes—
150C2×Q8—22no—
151C2×Q8—24no—
152C22×C4—51no—
153C22×C4—52no—
154C22×C4—51no—
155C22×C4—52no—
156C22×C4—51no—
157C22×C4—51no—
158C22×C4C22×D511yescharacteristic
159C22×C4C22×D511yescharacteristic
160C22×C4C22×D511yescharacteristic
161C22×C4C22×D512yes—
162C22×C4C22×D512yes—
163C4⋊C4—22no—
164C4⋊C4—24no—
165C4⋊C4—58no—
166C4⋊C4—104no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4—102no—
173C4⋊C4—104no—
174C4⋊C4—202no—
175C4⋊C4—202no—
176C42—54no—
177C42—104no—
178C42—202no—
179C2×C5#52511yescharacteristic
180C2×C5C2×C4⋊Q811yescharacteristic
181C2×C5#53711yescharacteristic
182C2×C5#55412yes—
183C2×C5#55712yes—
184C23C23×D511yescharacteristic
185Q8—28no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—52no—
197C2×C4—54no—
198C2×C4—52no—
199C2×C4—54no—
200C2×C4—102no—
201C2×C4—101no—
202C2×C4—101no—
203C2×C4—102no—
204C2×C4—102no—
205C2×C4—101no—
206C2×C4—101no—
207C2×C4—102no—
208C2×C4—102no—
209C2×C4—101no—
210C2×C4—102no—
211C2×C4—101no—
212C2×C4D4×D512yes—
213C2×C4#71114yes—
214C2×C4Q8×D514yes—
215C5#258411yescharacteristic, complemented, Sylow
216C22C2×D4×D511yescharacteristic
217C22C2×#71112yes—
218C22C2×Q8×D512yes—
219C22#414711yescharacteristic
220C22#414911yescharacteristic
221C4—22no—
222C4—24no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—54no—
227C4—102no—
228C4—104no—
229C4—201no—
230C4—202no—
231C4—201no—
232C2#6592011yescharacteristic
233C2#6596311yescharacteristic
234C2#6596912yes—
235C2#6605512yes—
236C2D5×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#395C2
hypercenter#395D5
hypocenterC5#2584
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
63. #683Q8semidirect
215. C5#2584semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic52
C2×#40352
C5×#3952
#655182
#652742
#652722
#652612
#649502
#649382
#649362
#25845