Finite Group Databasebeta

← #10610049

Subgroups — #10610049

Order 640.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#4036C211yesmaximal, characteristic
2C2×#4035C211yesmaximal, characteristic
3C5×#400C211yesmaximal, characteristic
4#65272C211yesmaximal, characteristic
5#65271C211yesmaximal, characteristic
6#64950C211yesmaximal, characteristic
7#64950C212yesmaximal
8#64947C212yesmaximal
9#64946C212yesmaximal
10#64946C212yesmaximal
11#64939C211yesmaximal, characteristic
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic5C2211yescharacteristic
15C2×C4⋊Dic5C2212yes—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2212yes—
18C2×#683C2211yescharacteristic
19C2×#683C2211yescharacteristic
20C2×#683C2211yescharacteristic
21C2×#683C2211yescharacteristic
22C2×#683C2212yes—
23C2×#683C2212yes—
24C2×#683C2212yes—
25C2×C4×Dic5C2211yescharacteristic
26#4036—24no—
27#4035—24no—
28C5×#95C2211yescharacteristic
29C5×#95C2212yes—
30C5×#95C2212yes—
31#3963C2212yes—
32#3963C2211yescharacteristic
33#3963C2212yes—
34#3963C2212yes—
35#3963C2212yes—
36#3963C2212yes—
37#2822—51nomaximal, Sylow
38C22×C4×C5C2311yescharacteristic
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×C4×C5C2312yes—
42C22×C4×C5C2311yescharacteristic
43C22×Dic5C2312yes—
44C22×Dic5C2311yescharacteristic
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2312yes—
47C22×Dic5C2311yescharacteristic
48C22×Dic5C2311yescharacteristic
49C5×C4⋊C4—22no—
50C5×C4⋊C4—22no—
51C4⋊Dic5—22no—
52C4⋊Dic5—22no—
53C4⋊Dic5—24no—
54C4⋊Dic5—42no—
55#683—22no—
56#683—22no—
57#683—22no—
58#683—22no—
59#683—24no—
60#683—42no—
61#683—42no—
62C4×Dic5D414yes—
63C2×#125—51no—
64C2×#125—51no—
65#400—51no—
66#400—52no—
67#400D511yescharacteristic
68#398—51no—
69#398—52no—
70#398—52no—
71#398—51no—
72#398—52no—
73#382—51no—
74C23×C5C2411yescharacteristic
75C2×C4×C5—22no—
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—22no—
79C2×C4×C5—21no—
80C2×C4×C5—22no—
81C2×C4×C5—21no—
82C2×C4×C5—22no—
83C2×C4×C5—24no—
84C2×C4×C5—22no—
85C2×C4×C5—22no—
86C2×C4×C5C2×D412yes—
87C2×Dic5—21no—
88C2×Dic5—21no—
89C2×Dic5—22no—
90C2×Dic5—21no—
91C2×Dic5—21no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—22no—
95C2×Dic5—21no—
96C2×Dic5—21no—
97C2×Dic5—22no—
98C2×Dic5—22no—
99C2×Dic5—22no—
100C2×Dic5—22no—
101C2×Dic5C2×D412yes—
102C2×Dic5C2×D412yes—
103#125—104no—
104#125—104no—
105C2×C4⋊C4—51no—
106C2×C4⋊C4—51no—
107C2×C4⋊C4—51no—
108C2×C4⋊C4—52no—
109C2×C4⋊C4—51no—
110C2×C4⋊C4—52no—
111C2×C4⋊C4—51no—
112C2×C4⋊C4—51no—
113C2×C4⋊C4—52no—
114C2×C4⋊C4—52no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4C2×D511yescharacteristic
117C2×C4⋊C4C2×D511yescharacteristic
118C2×C42—51no—
119#95—52no—
120#95—51no—
121#95—52no—
122#95—52no—
123#95—52no—
124#95—52no—
125#95C2×D511yescharacteristic
126#95C2×D512yes—
127#95C2×D512yes—
128C22×C5C22×D411yescharacteristic
129C22×C5H(5,𝔽2)11yescharacteristic
130C22×C52−1+411yescharacteristic
131C22×C52−1+412yes—
132C22×C52−1+412yes—
133C4×C5—22no—
134C4×C5—41no—
135C4×C5—42no—
136C4×C5—41no—
137C4×C5—42no—
138Dic5—22no—
139Dic5—22no—
140Dic5—41no—
141Dic5—41no—
142Dic5—42no—
143Dic5—42no—
144C22×C4—51no—
145C22×C4—51no—
146C22×C4—52no—
147C22×C4—51no—
148C22×C4—51no—
149C22×C4—52no—
150C22×C4C22×D512yes—
151C22×C4C22×D511yescharacteristic
152C22×C4C22×D512yes—
153C22×C4C22×D511yescharacteristic
154C22×C4C22×D511yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—102no—
158C4⋊C4—102no—
159C4⋊C4—104no—
160C4⋊C4—102no—
161C4⋊C4—102no—
162C4⋊C4—104no—
163C4⋊C4—102no—
164C4⋊C4—102no—
165C4⋊C4—202no—
166C4⋊C4—202no—
167C4⋊C4—202no—
168C42—54no—
169C2×C5#53611yescharacteristic
170C2×C5#53611yescharacteristic
171C2×C5#53711yescharacteristic
172C2×C5#56312yes—
173C2×C5#56412yes—
174C23C23×D511yescharacteristic
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—52no—
187C2×C4—52no—
188C2×C4—101no—
189C2×C4—101no—
190C2×C4—102no—
191C2×C4—101no—
192C2×C4—102no—
193C2×C4—101no—
194C2×C4—101no—
195C2×C4—102no—
196C2×C4—102no—
197C2×C4—101no—
198C2×C4—102no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4D4×D512yes—
203C5#282211yescharacteristic, complemented, Sylow
204C22C2×D4×D511yescharacteristic
205C22#414711yescharacteristic
206C22#414911yescharacteristic
207C22#415012yes—
208C22#415012yes—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—42no—
214C4—102no—
215C4—102no—
216C4—201no—
217C4—202no—
218C4—201no—
219C4—202no—
220C2#6596311yescharacteristic
221C2#6598211yescharacteristic
222C2#6600911yescharacteristic
223C2C5⋊#56412yes—
224C2#6604612yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#400C2
hypercenter#400D5
hypocenterC5#2822
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
203. C5#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#40362
C2×#40352
C5×#4002
#652722
#652712
#649502
#649472
#649462
#649392
#28225