Finite Group Databasebeta

← #10602023

Subgroups — #10602023

Order 640.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#66064C211yesmaximal, characteristic
2C5×#487C211yesmaximal, characteristic, complemented
3#65383C211yesmaximal, characteristic, complemented
4#65372C211yesmaximal, characteristic
5#64766C211yesmaximal, characteristic, complemented
6#64679C211yesmaximal, characteristic
7#64676C211yesmaximal, characteristic, complemented
8C5×C4⋊Q8C2211yescharacteristic
9C5×C4⋊Q8C2211yescharacteristic
10#4092—22no—
11C2×#688—21no—
12#4043—21no—
13#4039—21no—
14D5×C4⋊C4—21no—
15#4036—21no—
16C4×D20C2211yescharacteristic
17C4×Dic10C2211yescharacteristic
18C5×#103—22no—
19C4×C5×C8C2211yescharacteristic
20#3967—21no—
21#3942—21no—
22#3940—21no—
23C4⋊#168C2211yescharacteristic
24C4⋊#168C2211yescharacteristic
25#1643—51nomaximal, Sylow
26C2×C5×Q8—21no—
27C2×C5×Q8D412yes—
28C2×D20D411yescharacteristic
29C2×C4×D5—21no—
30C2×C4×D5—22no—
31C2×Dic10D411yescharacteristic
32C2×C5×C8—21no—
33C5×C4⋊C4—21no—
34C5×C4⋊C4—21no—
35C5×C4⋊C4—21no—
36C5×C4⋊C4—21no—
37C42×C5C2311yescharacteristic
38#688—42no—
39#685—22no—
40#685—21no—
41C4⋊Dic5—22no—
42C4⋊Dic5D411yescharacteristic
43C4⋊Dic5D411yescharacteristic
44#683—22no—
45#683—21no—
46C4×Dic5—21no—
47C2×#168—21no—
48C2×#168—21no—
49#554—51no—
50#487D511yescharacteristic, complemented
51#475—51no—
52#461—51no—
53#333—51no—
54Q8⋊C8—51no—
55D4⋊C8—51no—
56C22×D5—21no—
57C5×Q8—42no—
58C5×Q8—41no—
59C5×Q8—41no—
60C2×C4×C5—22no—
61C2×C4×C5—41no—
62C2×C4×C5C2×D411yescharacteristic
63C2×C4×C5C2×D411yescharacteristic
64C2×C4×C5C2×D411yescharacteristic
65C2×Dic5—21no—
66C2×Dic5—21no—
67C2×Dic5—21no—
68D20—21no—
69D20SD1612yes—
70C4×D5—41no—
71C4×D5—41no—
72C4×D5—82no—
73Dic10—21no—
74Dic10—21no—
75C5×C8—41no—
76#168—41no—
77#168—41no—
78C2×SD16—101no—
79C4⋊Q8C2×D511yescharacteristic
80C4⋊Q8C2×D511yescharacteristic
81#125—101no—
82C22⋊Q8—101no—
83C22⋊Q8—102no—
84C4×Q8—51no—
85C4×D4—51no—
86C4×D4—101no—
87C2×C4⋊C4—101no—
88#106—101no—
89C4⋊C8—51no—
90C4⋊C8—51no—
91#103—22no—
92#103—101no—
93#103—101no—
94C4×C8C2×D511yescharacteristic
95C22×C5#12011yescharacteristic
96C2×D5—22no—
97C2×D5—41no—
98C2×D5—41no—
99C4×C5—21no—
100C4×C5—42no—
101C4×C5—81no—
102C4×C5C2×SD1611yescharacteristic
103C4×C5#13511yescharacteristic
104C4×C5#13711yescharacteristic
105C4×C5#13711yescharacteristic
106Dic5—41no—
107Dic5—41no—
108Dic5—41no—
109C2×Q8—21no—
110C2×Q8—51no—
111C2×Q8C22⋊D512yes—
112C2×D4—51no—
113C22×C4—102no—
114C22×C4—101no—
115SD16—202no—
116C2×C8—21no—
117C2×C8—101no—
118C2×C8—101no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—51no—
124C4⋊C4—51no—
125C4⋊C4—102no—
126C4⋊C4—102no—
127C4⋊C4—101no—
128C22⋊C4—102no—
129C22⋊C4—101no—
130C42—101no—
131C42C22×D511yescharacteristic
132C2×C5#44811yescharacteristic
133C2×C5#45211yescharacteristic
134C2×C5#45511yescharacteristic
135D5—42no—
136C23—101no—
137Q8—42no—
138Q8—41no—
139Q8—41no—
140Q8—101no—
141Q8—101no—
142D4—52no—
143D4—101no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—101no—
147C2×C4—101no—
148C2×C4—101no—
149C2×C4—201no—
150C2×C4—201no—
151C2×C4—402no—
152C2×C4D4×D511yescharacteristic
153C2×C4D4×D511yescharacteristic
154C2×C4C2×C22⋊D511yescharacteristic
155C8—41no—
156C8—201no—
157C8—201no—
158C5#164311yescharacteristic, complemented, Sylow
159C22—102no—
160C22—201no—
161C22—201no—
162C22#408311yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—201no—
167C4—201no—
168C4—201no—
169C4D5×SD1611yescharacteristic
170C4#406111yescharacteristic
171C4#406411yescharacteristic
172C4#406511yescharacteristic
173C2—202no—
174C2#6535011yescharacteristic
175C2#6545911yescharacteristic
176C2#6547611yescharacteristic
subgroupG/H
centerC22#4083
commutator, cosocleC42×C5C23
FrattiniC42C22×D5
FittingC5×#487C2
socleC22×C5#120
prime radicalC2×D20D4
hypercenter#487D5
hypocenterC5#1643
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C5×#487C2semidirect
3. #65383C2semidirect
5. #64766C2semidirect
7. #64676C2semidirect
50. #487D5semidirect
158. C5#1643semidirect

Maximal subgroups

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

subgroupindex
#660642
C5×#4872
#653832
#653722
#647662
#646792
#646762
#16435