Finite Group Databasebeta

← #10606198

Subgroups — #10606198

Order 640.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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×#385C211yesmaximal, characteristic
2C4×C22⋊Dic5C212yesmaximal
3#65270C212yesmaximal, complemented
4#65267C212yesmaximal, complemented
5#65242C211yesmaximal, characteristic
6#65241C212yesmaximal
7#65238C211yesmaximal, characteristic
8#64944C212yesmaximal, complemented
9#64939C212yesmaximal, complemented
10C23×C4×C5C2211yescharacteristic
11C2×C5×C4⋊C4C2212yes—
12C2×C5×C22⋊C4C2211yescharacteristic
13C2×C5×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic5C2212yes—
15C2×C22⋊Dic5C2212yes—
16C2×C4⋊Dic5C2211yescharacteristic
17C2×C4⋊Dic5C2211yescharacteristic
18C2×#683C2212yes—
19C2×#683C2212yes—
20C2×C4×Dic5C2212yes—
21C2×C4×Dic5C2212yes—
22C5×#95C2212yes—
23#3963C2211yescharacteristic
24#3963C2212yes—
25#3963C2212yes—
26#3963C2212yes—
27#3963C2212yes—
28#3963C2212yes—
29#3963C2211yescharacteristic
30#3963C2212yes—
31#2517—51nomaximal, Sylow
32C24×C5C2311yescharacteristic
33C22×C4×C5—24no—
34C22×C4×C5—41no—
35C22×C4×C5C2311yescharacteristic
36C22×C4×C5C2312yes—
37C22×C4×C5C2311yescharacteristic
38C22×C4×C5C2312yes—
39C22×Dic5C2312yes—
40C22×Dic5C2312yes—
41C22×Dic5C2312yes—
42C22×Dic5C2312yes—
43C5×C4⋊C4—24no—
44C5×C22⋊C4—22no—
45C5×C22⋊C4—41no—
46C22⋊Dic5—24no—
47C22⋊Dic5—24no—
48C4⋊Dic5—41no—
49C4⋊Dic5—41no—
50#683—24no—
51#683—24no—
52C4×Dic5—24no—
53C4×Dic5—42no—
54#399—51no—
55#397—52no—
56#397—51no—
57#387—52no—
58#387—52no—
59#387—52no—
60#385D511yescharacteristic
61#382—52no—
62C4×C22⋊C4—52no—
63C23×C5—22no—
64C23×C5—22no—
65C23×C5—21no—
66C23×C5—21no—
67C23×C5#4112yes—
68C23×C5C2411yescharacteristic
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—22no—
76C2×C4×C5—21no—
77C2×C4×C5—21no—
78C2×C4×C5—44no—
79C2×C4×C5#4114yes—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—22no—
88C2×Dic5—22no—
89C2×Dic5—22no—
90C2×Dic5—22no—
91C2×Dic5#4114yes—
92C23×C4C2×D511yescharacteristic
93C2×C4⋊C4—52no—
94C2×C4⋊C4—52no—
95C2×C4⋊C4—51no—
96C2×C4⋊C4—51no—
97C2×C4⋊C4C2×D512yes—
98C2×C22⋊C4—52no—
99C2×C22⋊C4—52no—
100C2×C22⋊C4C2×D511yescharacteristic
101C2×C22⋊C4C2×D511yescharacteristic
102C2×C42—52no—
103C2×C42—52no—
104#95—52no—
105#95—52no—
106#95—51no—
107#95—52no—
108#95—52no—
109#95—52no—
110#95—52no—
111#95—51no—
112#95C2×D512yes—
113C22×C5—24no—
114C22×C5—22no—
115C22×C5—41no—
116C22×C5—42no—
117C22×C5—41no—
118C22×C5C2×#4111yescharacteristic
119C22×C5C2×#4112yes—
120C22×C5C2×#4112yes—
121C22×C5H(5,𝔽2)11yescharacteristic
122C22×C52−1+411yescharacteristic
123C4×C5—24no—
124C4×C5—42no—
125C4×C5—41no—
126C4×C5—41no—
127Dic5—24no—
128Dic5—42no—
129Dic5—42no—
130Dic5—42no—
131C24C22×D511yescharacteristic
132C22×C4—24no—
133C22×C4—41no—
134C22×C4—52no—
135C22×C4—52no—
136C22×C4—52no—
137C22×C4—52no—
138C22×C4C22×D512yes—
139C22×C4C22×D511yescharacteristic
140C22×C4C22×D511yescharacteristic
141C22×C4C22×D512yes—
142C4⋊C4—24no—
143C4⋊C4—104no—
144C4⋊C4—104no—
145C4⋊C4—201no—
146C4⋊C4—201no—
147C22⋊C4—22no—
148C22⋊C4—41no—
149C22⋊C4—104no—
150C22⋊C4—104no—
151C42—104no—
152C42—202no—
153C2×C5—42no—
154C2×C5#52912yes—
155C2×C5#53911yescharacteristic
156C2×C5#55111yescharacteristic
157C2×C5#55212yes—
158C2×C5#55911yescharacteristic
159C23—22no—
160C23—21no—
161C23—21no—
162C23—22no—
163C23#70912yes—
164C23C23×D511yescharacteristic
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—54no—
176C2×C4—102no—
177C2×C4—102no—
178C2×C4—102no—
179C2×C4—102no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—102no—
186C2×C4—102no—
187C2×C4#71114yes—
188C5#251711yescharacteristic, complemented, Sylow
189C22—22no—
190C22—24no—
191C22—41no—
192C22—42no—
193C22—41no—
194C22C2×#70911yescharacteristic
195C22C2×#71112yes—
196C22#414411yescharacteristic
197C22#414711yescharacteristic
198C22D5×#4112yes—
199C4—24no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—104no—
204C4—202no—
205C4—202no—
206C4—202no—
207C2—42no—
208C2#6584911yescharacteristic
209C2#6587212yes—
210C2#6592111yescharacteristic
211C2#6597312yes—
212C2#6599811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#385C2
prime radicalC24×C5C23
hypercenter#385D5
hypocenterC5#2517
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #65270C2semidirect
4. #65267C2semidirect
8. #64944C2semidirect
9. #64939C2semidirect
188. C5#2517semidirect

Maximal subgroups

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

subgroupindex
C5×#3852
C4×C22⋊Dic52
#652702
#652672
#652422
#652412
#652382
#649442
#649392
#25175