Finite Group Databasebeta

← #10608922

Subgroups — #10608922

Order 640.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#4033C211yesmaximal, characteristic
3C5×#395C211yesmaximal, characteristic
4#65518C211yesmaximal, characteristic
5#65275C211yesmaximal, characteristic
6#65270C212yesmaximal
7#65261C212yesmaximal
8#64948C211yesmaximal, characteristic
9#64944C212yesmaximal
10#64939C211yesmaximal, characteristic
11#64935C212yesmaximal
12C22×C5×Q8C2211yescharacteristic
13C22×Dic10C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2212yes—
16Q8×Dic5—24no—
17C2×C4⋊Dic5C2212yes—
18C2×C4⋊Dic5C2211yescharacteristic
19C2×#683C2211yescharacteristic
20C2×#683C2211yescharacteristic
21C2×#683C2212yes—
22C2×#683C2212yes—
23C2×C4×Dic5C2211yescharacteristic
24C2×C4×Dic5C2211yescharacteristic
25C2×C4×Dic5C2212yes—
26C2×C4×Dic5C2211yescharacteristic
27#4033—24no—
28C5×#95C2212yes—
29C5×#95C2211yescharacteristic
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2212yes—
34#3963C2211yescharacteristic
35#3963C2212yes—
36#3963C2212yes—
37#2581—51nomaximal, Sylow
38C2×C5×Q8—22no—
39C2×C5×Q8—24no—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×C4×C5C2311yescharacteristic
44C22×C4×C5C2312yes—
45C22×Dic5C2312yes—
46C22×Dic5C2312yes—
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C22×Dic5C2311yescharacteristic
50C22×Dic5C2311yescharacteristic
51C2×Dic10—22no—
52C2×Dic10—22no—
53C2×Dic10Q814yescomplemented
54C5×C4⋊C4—22no—
55C5×C4⋊C4—24no—
56C4⋊Dic5—22no—
57C4⋊Dic5—24no—
58#683—22no—
59#683—24no—
60#683—22no—
61#683—24no—
62C4×Dic5—22no—
63C4×Dic5—22no—
64C4×Dic5—24no—
65C4×Dic5D414yes—
66C2×C4×Q8—51no—
67C2×C4×Q8—51no—
68#400—51no—
69#400—51no—
70#395—51no—
71#395D511yescharacteristic
72#391—52no—
73#389—52no—
74#387—52no—
75#387—52no—
76#382—51no—
77C23×C5C2411yescharacteristic
78C5×Q8—28no—
79C2×C4×C5—22no—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—21no—
85C2×C4×C5—22no—
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—22no—
89C2×C4×C5C2×D412yes—
90C2×C4×C5C2×Q812yes—
91C2×C4×C5#4114yes—
92C2×Dic5—21no—
93C2×Dic5—21no—
94C2×Dic5—22no—
95C2×Dic5—21no—
96C2×Dic5—22no—
97C2×Dic5—22no—
98C2×Dic5—22no—
99C2×Dic5—22no—
100C2×Dic5—24no—
101C2×Dic5—22no—
102C2×Dic5C2×D412yes—
103C2×Dic5C2×D412yes—
104C2×Dic5C2×Q812yes—
105C2×Dic5C2×Q812yes—
106C2×Dic5#4112yes—
107Dic10—28no—
108C22×Q8—51no—
109C22×Q8C2×D511yescharacteristic
110C4×Q8—104no—
111C4×Q8—104no—
112C2×C4⋊C4—52no—
113C2×C4⋊C4—51no—
114C2×C4⋊C4—51no—
115C2×C4⋊C4—51no—
116C2×C4⋊C4—52no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4C2×D511yescharacteristic
119C2×C4⋊C4C2×D512yes—
120C2×C42—51no—
121C2×C42—51no—
122C2×C42—51no—
123C2×C42—52no—
124#95—52no—
125#95—51no—
126#95—52no—
127#95—52no—
128#95—52no—
129#95—52no—
130#95—52no—
131#95C2×D511yescharacteristic
132#95C2×D512yes—
133C22×C5C22×D411yescharacteristic
134C22×C5C22×Q811yescharacteristic
135C22×C5C2×#4112yes—
136C22×C5C2×#4111yescharacteristic
137C22×C52−1+412yes—
138C4×C5—22no—
139C4×C5—22no—
140C4×C5—24no—
141C4×C5—41no—
142C4×C5—42no—
143Dic5—22no—
144Dic5—22no—
145Dic5—41no—
146Dic5—42no—
147Dic5—42no—
148Dic5C22⋊Q814yes—
149C2×Q8—22no—
150C2×Q8—24no—
151C2×Q8—54no—
152C2×Q8—102no—
153C2×Q8—102no—
154C22×C4—51no—
155C22×C4—51no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4—52no—
159C22×C4—51no—
160C22×C4C22×D512yes—
161C22×C4C22×D511yescharacteristic
162C22×C4C22×D511yescharacteristic
163C22×C4C22×D512yes—
164C22×C4C22×D511yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—24no—
167C4⋊C4—102no—
168C4⋊C4—104no—
169C4⋊C4—104no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4—104no—
173C42—54no—
174C42—102no—
175C42—104no—
176C42—102no—
177C2×C5C2×C22⋊Q811yescharacteristic
178C2×C5#52511yescharacteristic
179C2×C5#53611yescharacteristic
180C2×C5#55612yes—
181C2×C5#55712yes—
182C23C23×D511yescharacteristic
183Q8—28no—
184Q8—108no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—52no—
196C2×C4—52no—
197C2×C4—52no—
198C2×C4—52no—
199C2×C4—52no—
200C2×C4—101no—
201C2×C4—102no—
202C2×C4—101no—
203C2×C4—102no—
204C2×C4—101no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4—104no—
208C2×C4—102no—
209C2×C4—102no—
210C2×C4D4×D512yes—
211C2×C4#71114yes—
212C2×C4Q8×D512yes—
213C5#258111yescharacteristic, complemented, Sylow
214C22C2×D4×D511yescharacteristic
215C22C2×#71112yes—
216C22C2×Q8×D511yescharacteristic
217C22#414712yes—
218C22D5×#4111yescharacteristic
219C4—22no—
220C4—24no—
221C4—22no—
222C4—41no—
223C4—42no—
224C4—54no—
225C4—102no—
226C4—102no—
227C4—202no—
228C4—201no—
229C4—202no—
230C2#6592011yescharacteristic
231C2D5×C22⋊Q811yescharacteristic
232C2#6597512yes—
233C2#6605512yes—
234C2#6605811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#395C2
hypercenter#395D5
hypocenterC5#2581
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
53. C2×Dic10Q8semidirect
213. C5#2581semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic52
C2×#40332
C5×#3952
#655182
#652752
#652702
#652612
#649482
#649442
#649392
#649352
#25815