Finite Group Databasebeta

← #10607834

Subgroups — #10607834

Order 640.

352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C5×#389C211yesmaximal, characteristic
2#65275C212yesmaximal
3#65274C211yesmaximal, characteristic
4#65271C212yesmaximal
5#65263C211yesmaximal, characteristic
6#65263C211yesmaximal, characteristic
7#65262C211yesmaximal, characteristic
8#65221C211yesmaximal, characteristic
9#65218C211yesmaximal, characteristic
10C5⋊#401C212yesmaximal
11#64949C212yesmaximal
12C22×Dic10C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15C2×C5×C4⋊C4C2212yes—
16C2×C42×C5C2211yescharacteristic
17C2×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊Dic5C2212yes—
19C2×#683C2212yes—
20C2×C4×Dic5C2211yescharacteristic
21C2×C4×Dic5C2211yescharacteristic
22C5×#95C2212yes—
23#3963C2211yescharacteristic
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2211yescharacteristic
28#3963C2212yes—
29#3963C2212yes—
30#3963C2212yes—
31#3963C2212yes—
32#3963C2212yes—
33#3963C2211yescharacteristic
34#3963C2211yescharacteristic
35#2645—51nomaximal, Sylow
36C22×C4×C5C2311yescharacteristic
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2312yes—
39C22×C4×C5C2312yes—
40C22×C4×C5C2311yescharacteristic
41C22×Dic5C2312yes—
42C22×Dic5C2311yescharacteristic
43C22×Dic5C2311yescharacteristic
44C22×Dic5C2311yescharacteristic
45C22×Dic5C2311yescharacteristic
46C22×Dic5C2312yes—
47C2×Dic10—22no—
48C2×Dic10—22no—
49C2×Dic10—22no—
50C5×C4⋊C4—22no—
51C5×C4⋊C4—22no—
52C5×C4⋊C4—42no—
53C42×C5—22no—
54C4⋊Dic5—22no—
55C4⋊Dic5—42no—
56#683—42no—
57C4×Dic5—22no—
58C4×Dic5—22no—
59#401—52no—
60#400—52no—
61#400—52no—
62#400—52no—
63#391—51no—
64#391—51no—
65#391—51no—
66#389—51no—
67#389—51no—
68#389D511yescharacteristic
69#376—51no—
70C23×C5C2411yescharacteristic
71C2×C4×C5—21no—
72C2×C4×C5—21no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—22no—
77C2×C4×C5—21no—
78C2×C4×C5—21no—
79C2×C4×C5—21no—
80C2×C4×C5—21no—
81C2×C4×C5—22no—
82C2×C4×C5—22no—
83C2×C4×C5#4112yes—
84C2×C4×C5#4112yes—
85C2×C4×C5#4112yes—
86C2×Dic5—21no—
87C2×Dic5—21no—
88C2×Dic5—21no—
89C2×Dic5—21no—
90C2×Dic5—22no—
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5—22no—
94C2×Dic5—21no—
95C2×Dic5—22no—
96C2×Dic5—21no—
97C2×Dic5—21no—
98C2×Dic5—21no—
99C2×Dic5—22no—
100C2×Dic5—21no—
101C2×Dic5—21no—
102C2×Dic5—21no—
103C2×Dic5—21no—
104Dic10—44no—
105C22×Q8—51no—
106C2×C4⋊C4—51no—
107C2×C4⋊C4—52no—
108C2×C4⋊C4—52no—
109C2×C4⋊C4C2×D511yescharacteristic
110C2×C4⋊C4C2×D511yescharacteristic
111C2×C4⋊C4C2×D512yes—
112C2×C42—51no—
113C2×C42—51no—
114C2×C42C2×D511yescharacteristic
115#95—51no—
116#95—51no—
117#95—51no—
118#95—51no—
119#95—52no—
120#95—52no—
121#95—52no—
122#95—52no—
123#95—52no—
124#95—52no—
125#95—52no—
126#95—52no—
127#95C2×D512yes—
128C22×C5C2×#4111yescharacteristic
129C22×C5C2×#4111yescharacteristic
130C22×C5C2×#4111yescharacteristic
131C22×C5H(5,𝔽2)11yescharacteristic
132C22×C52−1+411yescharacteristic
133C22×C52−1+411yescharacteristic
134C22×C52−1+411yescharacteristic
135C4×C5—41no—
136C4×C5—42no—
137C4×C5—41no—
138C4×C5—42no—
139C4×C5#12614yes—
140Dic5—42no—
141Dic5—41no—
142Dic5—41no—
143Dic5—41no—
144Dic5—42no—
145Dic5—41no—
146C2×Q8—102no—
147C2×Q8—102no—
148C2×Q8—102no—
149C22×C4—51no—
150C22×C4—51no—
151C22×C4—52no—
152C22×C4—51no—
153C22×C4—51no—
154C22×C4—52no—
155C22×C4C22×D511yescharacteristic
156C22×C4C22×D511yescharacteristic
157C22×C4C22×D512yes—
158C22×C4C22×D512yes—
159C22×C4C22×D511yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—102no—
164C4⋊C4—202no—
165C4⋊C4—202no—
166C42—22no—
167C42—102no—
168C42—102no—
169C2×C5C2×#12611yescharacteristic
170C2×C5#54111yescharacteristic
171C2×C5#54111yescharacteristic
172C2×C5#54111yescharacteristic
173C2×C5#54211yescharacteristic
174C2×C5#54211yescharacteristic
175C2×C5#54211yescharacteristic
176C23C23×D511yescharacteristic
177Q8—204no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4—102no—
193C2×C4—102no—
194C2×C4—102no—
195C2×C4—101no—
196C2×C4—101no—
197C2×C4—101no—
198C2×C4—101no—
199C2×C4—102no—
200C2×C4—102no—
201C2×C4—101no—
202C2×C4—102no—
203C2×C4—101no—
204C2×C4—101no—
205C2×C4—101no—
206C2×C4—101no—
207C2×C4—101no—
208C2×C4#70912yes—
209C2×C4#71112yes—
210C2×C4#71312yes—
211C5#264511yescharacteristic, complemented, Sylow
212C22C2×#70911yescharacteristic
213C22C2×#71111yescharacteristic
214C22#414411yescharacteristic
215C22C2×#71311yescharacteristic
216C22#414711yescharacteristic
217C22#415011yescharacteristic
218C22#415011yescharacteristic
219C4—42no—
220C4—41no—
221C4—42no—
222C4—41no—
223C4—201no—
224C4—202no—
225C4—202no—
226C4—201no—
227C4—201no—
228C4—201no—
229C4#404414yes—
230C2C2×#404411yescharacteristic
231C2#6589511yescharacteristic
232C2#6591711yescharacteristic
233C2#6593711yescharacteristic
234C2#6595911yescharacteristic
235C2#6603111yescharacteristic
236C2#6606711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#389C2
hypercenter#389D5
hypocenterC5#2645
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
211. C5#2645semidirect

Maximal subgroups

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

subgroupindex
C5×#3892
#652752
#652742
#652712
#652632
#652622
#652212
#652182
C5⋊#4012
#649492
#26455