Finite Group Databasebeta

← #10609912

Subgroups — #10609912

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×#4034C211yesmaximal, characteristic
2C2×#4033C211yesmaximal, characteristic
3C5×#400C211yesmaximal, characteristic
4#65275C211yesmaximal, characteristic
5#65271C211yesmaximal, characteristic
6#64948C211yesmaximal, characteristic
7#64939C212yesmaximal
8#64938C211yesmaximal, characteristic
9#64935C212yesmaximal
10#64935C212yesmaximal
11#64935C212yesmaximal
12C22×Dic10C2212yes—
13C22×Dic10C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic5C2211yescharacteristic
17C2×#683C2211yescharacteristic
18C2×#683C2211yescharacteristic
19C2×#683C2212yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2211yescharacteristic
22C2×C4×Dic5C2211yescharacteristic
23C2×C4×Dic5C2212yes—
24C2×C4×Dic5C2211yescharacteristic
25#4034—24no—
26#4033—24no—
27C5×#95C2212yes—
28C5×#95C2212yes—
29C5×#95C2211yescharacteristic
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2212yes—
34#3963C2212yes—
35#3963C2212yes—
36#3963C2211yescharacteristic
37#2568—51nomaximal, Sylow
38C22×C4×C5C2312yes—
39C22×C4×C5C2311yescharacteristic
40C22×C4×C5C2312yes—
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2311yescharacteristic
43C22×Dic5C2312yes—
44C22×Dic5C2312yes—
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C2×Dic10—22no—
50C2×Dic10—22no—
51C2×Dic10—24no—
52C2×Dic10—28no—
53C2×Dic10Q814yescomplemented
54C5×C4⋊C4—22no—
55C5×C4⋊C4—22no—
56C4⋊Dic5—22no—
57#683—22no—
58#683—22no—
59#683—24no—
60#683—24no—
61C4×Dic5—22no—
62C4×Dic5—22no—
63C4×Dic5—24no—
64C4×Dic5D414yes—
65C2×C4⋊Q8—51no—
66C2×C4×Q8—51no—
67#400—51no—
68#400—51no—
69#400—51no—
70#400D511yescharacteristic
71#391—52no—
72#391—52no—
73#391—52no—
74#382—52no—
75C4×C4⋊C4—51no—
76C23×C5C2411yescharacteristic
77C2×C4×C5—21no—
78C2×C4×C5—21no—
79C2×C4×C5—22no—
80C2×C4×C5—21no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5—22no—
84C2×C4×C5—24no—
85C2×C4×C5—22no—
86C2×C4×C5—22no—
87C2×C4×C5C2×D412yes—
88C2×C4×C5C2×Q812yes—
89C2×Dic5—21no—
90C2×Dic5—21no—
91C2×Dic5—21no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—22no—
95C2×Dic5—24no—
96C2×Dic5—22no—
97C2×Dic5—22no—
98C2×Dic5C2×D412yes—
99C2×Dic5C2×D412yes—
100C2×Dic5C2×Q812yes—
101C2×Dic5C2×Q812yes—
102C2×Dic5#4112yes—
103C2×Dic5#4114yes—
104Dic10—28no—
105Dic10—48no—
106C22×Q8—51no—
107C22×Q8—52no—
108C4⋊Q8—104no—
109C4×Q8—104no—
110C2×C4⋊C4—51no—
111C2×C4⋊C4—51no—
112C2×C4⋊C4—52no—
113C2×C4⋊C4—51no—
114C2×C4⋊C4—52no—
115C2×C4⋊C4C2×D511yescharacteristic
116C2×C4⋊C4C2×D511yescharacteristic
117C2×C42—51no—
118C2×C42—51no—
119C2×C42—51no—
120C2×C42—52no—
121#95—51no—
122#95—52no—
123#95—52no—
124#95—52no—
125#95—52no—
126#95—52no—
127#95—52no—
128#95C2×D511yescharacteristic
129#95C2×D512yes—
130#95C2×D512yes—
131C22×C5C22×D411yescharacteristic
132C22×C5C22×Q811yescharacteristic
133C22×C5C2×#4111yescharacteristic
134C22×C5C2×#4112yes—
135C22×C52−1+412yes—
136C4×C5—22no—
137C4×C5—22no—
138C4×C5—42no—
139C4×C5—41no—
140C4×C5—42no—
141Dic5—22no—
142Dic5—42no—
143Dic5—41no—
144Dic5—42no—
145Dic5C22⋊Q814yes—
146Dic5#12414yes—
147C2×Q8—54no—
148C2×Q8—102no—
149C2×Q8—102no—
150C2×Q8—104no—
151C2×Q8—108no—
152C22×C4—51no—
153C22×C4—51no—
154C22×C4—51no—
155C22×C4—52no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4C22×D512yes—
159C22×C4C22×D511yescharacteristic
160C22×C4C22×D512yes—
161C22×C4C22×D511yescharacteristic
162C22×C4C22×D511yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—22no—
165C4⋊C4—102no—
166C4⋊C4—104no—
167C4⋊C4—104no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C42—54no—
171C42—102no—
172C42—102no—
173C42—104no—
174C2×C5C2×C22⋊Q811yescharacteristic
175C2×C5C2×#12411yescharacteristic
176C2×C5#53611yescharacteristic
177C2×C5#55612yes—
178C2×C5#55712yes—
179C23C23×D511yescharacteristic
180Q8—108no—
181Q8—208no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—52no—
193C2×C4—52no—
194C2×C4—52no—
195C2×C4—52no—
196C2×C4—54no—
197C2×C4—52no—
198C2×C4—101no—
199C2×C4—101no—
200C2×C4—101no—
201C2×C4—102no—
202C2×C4—102no—
203C2×C4—102no—
204C2×C4—104no—
205C2×C4—102no—
206C2×C4—102no—
207C2×C4D4×D512yes—
208C2×C4Q8×D512yes—
209C5#256811yescharacteristic, complemented, Sylow
210C22C2×D4×D511yescharacteristic
211C22C2×Q8×D511yescharacteristic
212C22D5×#4111yescharacteristic
213C22D5×#4112yes—
214C22#415012yes—
215C4—22no—
216C4—22no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—54no—
221C4—54no—
222C4—102no—
223C4—201no—
224C4—202no—
225C4—202no—
226C2D5×C22⋊Q811yescharacteristic
227C2#6598211yescharacteristic
228C2D5×#12411yescharacteristic
229C2#6601912yes—
230C2#6603612yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#400C2
hypercenter#400D5
hypocenterC5#2568
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
53. C2×Dic10Q8semidirect
209. C5#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#40342
C2×#40332
C5×#4002
#652752
#652712
#649482
#649392
#649382
#649352
#25685