Finite Group Databasebeta

← #10608273

Subgroups — #10608273

Order 640.

452 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 161 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×Q8×Dic5C211yesmaximal, characteristic
2C2×#4036C211yesmaximal, characteristic
3C5×#391C211yesmaximal, characteristic
4#65519C211yesmaximal, characteristic
5#65265C211yesmaximal, characteristic
6#65225C211yesmaximal, characteristic
7C4×#683C211yesmaximal, characteristic
8#64946C214yesmaximal
9#64944C214yesmaximal
10C22×C5×Q8C2211yescharacteristic
11C2×C5×C4⋊C4C2211yescharacteristic
12C2×C42×C5C2211yescharacteristic
13Q8×Dic5—24no—
14C2×C4⋊Dic5C2212yes—
15C2×C4⋊Dic5C2211yescharacteristic
16C2×C4⋊Dic5C2212yes—
17C2×C4⋊Dic5C2211yescharacteristic
18C2×#683C2212yes—
19C2×#683C2214yes—
20C2×#683C2212yes—
21C2×C4×Dic5C2212yes—
22C2×C4×Dic5C2211yescharacteristic
23C2×C4×Dic5C2211yescharacteristic
24#4036—24no—
25C5×#95C2214yes—
26#3963C2212yes—
27#3963C2214yes—
28#3963C2214yes—
29#2565—51nomaximal, Sylow
30C2×C5×Q8—22no—
31C2×C5×Q8—22no—
32C2×C5×Q8Q814yes—
33C22×C4×C5C2312yes—
34C22×C4×C5C2312yes—
35C22×C4×C5C2312yes—
36C22×C4×C5C2311yescharacteristic
37C22×Dic5C2312yes—
38C22×Dic5C2312yes—
39C22×Dic5C2311yescharacteristic
40C22×Dic5C2311yescharacteristic
41C22×Dic5C2312yes—
42C5×C4⋊C4—22no—
43C42×C5—22no—
44C4⋊Dic5—22no—
45C4⋊Dic5—22no—
46C4⋊Dic5—24no—
47C4⋊Dic5—24no—
48#683—24no—
49#683—24no—
50#683—28no—
51C4×Dic5—22no—
52C4×Dic5—24no—
53C4×Dic5D414yes—
54C2×#125—51no—
55C2×C4×Q8—51no—
56#398—54no—
57#391—51no—
58#391D511yescharacteristic
59#387—54no—
60#384—51no—
61#382—51no—
62C4×C4⋊C4—51no—
63C23×C5C2411yescharacteristic
64C5×Q8—28no—
65C2×C4×C5—22no—
66C2×C4×C5—22no—
67C2×C4×C5—22no—
68C2×C4×C5—24no—
69C2×C4×C5—22no—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5C2×D412yes—
73C2×C4×C5C2×Q814yes—
74C2×C4×C5C2×Q812yes—
75C2×C4×C5#4112yes—
76C2×Dic5—22no—
77C2×Dic5—22no—
78C2×Dic5—22no—
79C2×Dic5—22no—
80C2×Dic5—22no—
81C2×Dic5—22no—
82C2×Dic5—24no—
83C2×Dic5—24no—
84C2×Dic5C2×D412yes—
85C2×Dic5C2×D412yes—
86C2×Dic5#4114yes—
87C22×Q8C2×D511yescharacteristic
88#125—104no—
89C4×Q8—104no—
90C2×C4⋊C4—51no—
91C2×C4⋊C4—52no—
92C2×C4⋊C4—51no—
93C2×C4⋊C4—52no—
94C2×C4⋊C4—52no—
95C2×C4⋊C4—52no—
96C2×C4⋊C4—54no—
97C2×C4⋊C4C2×D511yescharacteristic
98C2×C42—51no—
99C2×C42—52no—
100C2×C42—51no—
101C2×C42C2×D511yescharacteristic
102#95—52no—
103#95—54no—
104#95—54no—
105#95C2×D514yes—
106C22×C5C22×D411yescharacteristic
107C22×C5C22×Q811yescharacteristic
108C22×C5C2×#4111yescharacteristic
109C22×C5C2×#4112yes—
110C22×C52−1+412yes—
111C4×C5—24no—
112C4×C5—42no—
113C4×C5—42no—
114C4×C5C22⋊Q814yes—
115Dic5—22no—
116Dic5—22no—
117Dic5—24no—
118Dic5—42no—
119Dic5—42no—
120C2×Q8—22no—
121C2×Q8—22no—
122C2×Q8Dic1014yes—
123C22×C4—52no—
124C22×C4—51no—
125C22×C4—51no—
126C22×C4—52no—
127C22×C4—52no—
128C22×C4C22×D512yes—
129C22×C4C22×D512yes—
130C22×C4C22×D512yes—
131C22×C4C22×D511yescharacteristic
132C4⋊C4—22no—
133C4⋊C4—104no—
134C4⋊C4—104no—
135C4⋊C4—104no—
136C4⋊C4—104no—
137C4⋊C4—108no—
138C4⋊C4—102no—
139C4⋊C4—102no—
140C42—22no—
141C42—54no—
142C42—104no—
143C42—102no—
144C2×C5C2×C22⋊Q811yescharacteristic
145C2×C5#53211yescharacteristic
146C2×C5#53611yescharacteristic
147C2×C5#55212yes—
148C2×C5#55712yes—
149C23C23×D511yescharacteristic
150Q8—28no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—52no—
159C2×C4—52no—
160C2×C4—54no—
161C2×C4—102no—
162C2×C4—102no—
163C2×C4—102no—
164C2×C4—102no—
165C2×C4—102no—
166C2×C4—102no—
167C2×C4—104no—
168C2×C4—104no—
169C2×C4C2×Dic1014yes—
170C2×C4C2×Dic1012yes—
171C2×C4D4×D512yes—
172C2×C4#71112yes—
173C5#256511yescharacteristic, complemented, Sylow
174C22C22×Dic1011yescharacteristic
175C22C2×D4×D511yescharacteristic
176C22C2×#71111yescharacteristic
177C22#414712yes—
178C22D5×#4112yes—
179C4—24no—
180C4—42no—
181C4—42no—
182C4—102no—
183C4—104no—
184C4—102no—
185C4—202no—
186C4—202no—
187C4#402414yes—
188C2C2×#402411yescharacteristic
189C2#6590312yes—
190C2#6597312yes—
191C2#6600211yescharacteristic
192C2#6605811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, prime radical, cosocleC23×C5C24
FittingC5×#391C2
hypercenter#391D5
hypocenterC5#2565
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
173. C5#2565semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic52
C2×#40362
C5×#3912
#655192
#652652
#652252
C4×#6832
#649462
#649442
#25655