Finite Group Databasebeta

← #10609568

Subgroups — #10609568

Order 640.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#4035C211yesmaximal, characteristic
2C2×#4034C211yesmaximal, characteristic
3C5×#398C211yesmaximal, characteristic
4#65272C211yesmaximal, characteristic
5#65269C211yesmaximal, characteristic
6#65268C212yesmaximal
7#65265C212yesmaximal
8#64950C211yesmaximal, characteristic
9#64945C212yesmaximal
10#64939C212yesmaximal
11#64937C211yesmaximal, characteristic
12C22×Dic10C2212yes—
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2212yes—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊Dic5C2212yes—
19C2×#683C2212yes—
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×#683C2211yescharacteristic
23C2×#683C2211yescharacteristic
24C2×#683C2212yes—
25C2×#683C2212yes—
26C2×C4×Dic5C2211yescharacteristic
27C2×C4×Dic5C2212yes—
28#4035—24no—
29#4034—24no—
30C5×#95C2211yescharacteristic
31C5×#95C2212yes—
32#3963C2212yes—
33#3963C2211yescharacteristic
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2660—51nomaximal, Sylow
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2311yescharacteristic
42C22×C4×C5C2312yes—
43C22×Dic5C2312yes—
44C22×Dic5C2311yescharacteristic
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2311yescharacteristic
47C22×Dic5C2312yes—
48C22×Dic5C2311yescharacteristic
49C2×Dic10—24no—
50C2×Dic10—42no—
51C2×Dic10—42no—
52C5×C4⋊C4—22no—
53C5×C4⋊C4—22no—
54C5×C4⋊C4—42no—
55C4⋊Dic5—22no—
56C4⋊Dic5—22no—
57C4⋊Dic5—42no—
58#683—22no—
59#683—24no—
60#683—22no—
61#683—22no—
62#683—22no—
63#683—42no—
64#683—42no—
65C4×Dic5D414yes—
66C4×Dic5Q818yescomplemented
67C2×C4⋊Q8—51no—
68C2×#125—51no—
69#398—51no—
70#398—51no—
71#398—51no—
72#398D511yescharacteristic
73#395—52no—
74#395—52no—
75#384—52no—
76#382—52no—
77#376—51no—
78C23×C5C2411yescharacteristic
79C2×C4×C5—22no—
80C2×C4×C5—22no—
81C2×C4×C5—22no—
82C2×C4×C5—21no—
83C2×C4×C5—21no—
84C2×C4×C5—22no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—21no—
88C2×C4×C5—22no—
89C2×C4×C5—22no—
90C2×C4×C5C2×D412yes—
91C2×C4×C5C2×Q814yes—
92C2×Dic5—22no—
93C2×Dic5—21no—
94C2×Dic5—21no—
95C2×Dic5—22no—
96C2×Dic5—21no—
97C2×Dic5—21no—
98C2×Dic5—22no—
99C2×Dic5—21no—
100C2×Dic5—22no—
101C2×Dic5—21no—
102C2×Dic5—22no—
103C2×Dic5—22no—
104C2×Dic5C2×D412yes—
105C2×Dic5C2×D412yes—
106C2×Dic5C2×Q814yes—
107C2×Dic5C2×Q814yes—
108Dic10—48no—
109C22×Q8—52no—
110C4⋊Q8—104no—
111#125—104no—
112C2×C4⋊C4—51no—
113C2×C4⋊C4—51no—
114C2×C4⋊C4—51no—
115C2×C4⋊C4—51no—
116C2×C4⋊C4—51no—
117C2×C4⋊C4—52no—
118C2×C4⋊C4—51no—
119C2×C4⋊C4—52no—
120C2×C4⋊C4—52no—
121C2×C4⋊C4—52no—
122C2×C4⋊C4C2×D511yescharacteristic
123C2×C4⋊C4C2×D511yescharacteristic
124C2×C4⋊C4C2×D512yes—
125C2×C42—51no—
126C2×C42—52no—
127#95—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×C5H(5,𝔽2)11yescharacteristic
137C22×C5H(5,𝔽2)11yescharacteristic
138C22×C52−1+412yes—
139C4×C5—22no—
140C4×C5—24no—
141C4×C5—42no—
142C4×C5—41no—
143C4×C5—41no—
144Dic5—22no—
145Dic5—24no—
146Dic5—42no—
147Dic5—41no—
148Dic5—41no—
149Dic5C4⋊Q814yes—
150C2×Q8—104no—
151C2×Q8—202no—
152C2×Q8—202no—
153C22×C4—51no—
154C22×C4—52no—
155C22×C4—51no—
156C22×C4—51no—
157C22×C4—52no—
158C22×C4—51no—
159C22×C4C22×D511yescharacteristic
160C22×C4C22×D512yes—
161C22×C4C22×D511yescharacteristic
162C22×C4C22×D511yescharacteristic
163C22×C4C22×D512yes—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—42no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—104no—
172C4⋊C4—102no—
173C4⋊C4—102no—
174C4⋊C4—202no—
175C4⋊C4—202no—
176C4⋊C4—202no—
177C42—54no—
178C42—58no—
179C2×C5C2×C4⋊Q811yescharacteristic
180C2×C5#53511yescharacteristic
181C2×C5#53611yescharacteristic
182C2×C5#54412yes—
183C2×C5#54412yes—
184C23C23×D511yescharacteristic
185Q8—208no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—52no—
198C2×C4—54no—
199C2×C4—52no—
200C2×C4—54no—
201C2×C4—101no—
202C2×C4—102no—
203C2×C4—101no—
204C2×C4—102no—
205C2×C4—101no—
206C2×C4—101no—
207C2×C4—102no—
208C2×C4—101no—
209C2×C4—102no—
210C2×C4—101no—
211C2×C4—102no—
212C2×C4—102no—
213C2×C4D4×D512yes—
214C2×C4Q8×D514yes—
215C5#266011yescharacteristic, complemented, Sylow
216C22C2×D4×D511yescharacteristic
217C22#414411yescharacteristic
218C22C2×Q8×D512yes—
219C22#414911yescharacteristic
220C22#415012yes—
221C4—24no—
222C4—22no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—54no—
227C4—102no—
228C4—104no—
229C4—202no—
230C4—201no—
231C4—201no—
232C2#6594111yescharacteristic
233C2#6595712yes—
234C2#6598211yescharacteristic
235C2#6602312yes—
236C2D5×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#398C2
hypercenter#398D5
hypocenterC5#2660
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
66. C4×Dic5Q8semidirect
215. C5#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#40352
C2×#40342
C5×#3982
#652722
#652692
#652682
#652652
#649502
#649452
#649392
#649372
#26605