Finite Group Databasebeta

← #10602024

Subgroups — #10602024

Order 640.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#66068C211yesmaximal, characteristic
2C5×#487C211yesmaximal, characteristic, complemented
3#65376C211yesmaximal, characteristic, complemented
4#65372C211yesmaximal, characteristic, complemented
5#64766C211yesmaximal, characteristic, complemented
6#64679C211yesmaximal, characteristic, complemented
7#64679C211yesmaximal, characteristic, complemented
8C5×C4⋊Q8C2211yescharacteristic
9C5×C4⋊Q8C2211yescharacteristic
10#4093—22no—
11C2×#688—21no—
12#4041—21no—
13#4041—21no—
14#4038—21no—
15#4038—21no—
16C4×D20C2211yescharacteristic
17C4×D20C2211yescharacteristic
18C5×#103—22no—
19C4×C5×C8C2211yescharacteristic
20#3967—21no—
21#3941—21no—
22#3939—21no—
23C4⋊#168C2211yescharacteristic
24C4⋊#168C2211yescharacteristic
25#1646—51nomaximal, Sylow
26C2×C5×Q8—21no—
27C2×C5×Q8D412yes—
28C2×D20—22no—
29C2×D20D411yescharacteristic
30C2×D20D411yescharacteristic
31C2×C4×D5—21no—
32C2×C4×D5—21no—
33C2×C5×C8—21no—
34C5×C4⋊C4—21no—
35C5×C4⋊C4—21no—
36C5×C4⋊C4—21no—
37C5×C4⋊C4—21no—
38C42×C5C2311yescharacteristic
39#688—42no—
40#685—22no—
41#685—22no—
42#685—21no—
43#685—21no—
44C4⋊Dic5D411yescharacteristic
45C4⋊Dic5D411yescharacteristic
46C4×Dic5—22no—
47C2×#168—21no—
48C2×#168—21no—
49#555—51no—
50#487D511yescharacteristic, complemented
51#474—51no—
52#461—51no—
53#333—51no—
54D4⋊C8—51no—
55D4⋊C8—51no—
56C22×D5—21no—
57C22×D5—21no—
58C5×Q8—42no—
59C5×Q8—41no—
60C5×Q8—41no—
61C2×C4×C5—22no—
62C2×C4×C5—41no—
63C2×C4×C5C2×D411yescharacteristic
64C2×C4×C5C2×D411yescharacteristic
65C2×C4×C5C2×D411yescharacteristic
66C2×Dic5—21no—
67C2×Dic5—21no—
68D20—21no—
69D20—21no—
70D20—21no—
71D20—21no—
72D20—82no—
73C4×D5—41no—
74C4×D5—41no—
75C4×D5—41no—
76C4×D5—41no—
77C5×C8—41no—
78#168—41no—
79#168—41no—
80C2×SD16—101no—
81C4⋊Q8C2×D511yescharacteristic
82C4⋊Q8C2×D511yescharacteristic
83#124—102no—
84#121—101no—
85#121—101no—
86C4×D4—51no—
87C4×D4—51no—
88#117—101no—
89#117—101no—
90#107—101no—
91C4⋊C8—51no—
92C4⋊C8—51no—
93#103—22no—
94#103—101no—
95#102—101no—
96C4×C8C2×D511yescharacteristic
97C22×C5#12011yescharacteristic
98C2×D5—41no—
99C2×D5—41no—
100C2×D5—41no—
101C2×D5—41no—
102C2×D5—41no—
103C2×D5—41no—
104C4×C5—21no—
105C4×C5—42no—
106C4×C5—81no—
107C4×C5#13511yescharacteristic
108C4×C5#13511yescharacteristic
109C4×C5AGL(1,ℤ/8)11yescharacteristic
110C4×C5#13711yescharacteristic
111Dic5—41no—
112Dic5—41no—
113C2×Q8—21no—
114C2×Q8C22⋊D512yes—
115C2×D4—51no—
116C2×D4—51no—
117C2×D4—102no—
118C22×C4—101no—
119C22×C4—101no—
120SD16—202no—
121C2×C8—21no—
122C2×C8—101no—
123C2×C8—101no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—51no—
129C4⋊C4—51no—
130C22⋊C4—102no—
131C22⋊C4—102no—
132C22⋊C4—101no—
133C22⋊C4—101no—
134C42—102no—
135C42C22×D511yescharacteristic
136C2×C5#44911yescharacteristic
137C2×C5#45211yescharacteristic
138C2×C5#45511yescharacteristic
139D5—81no—
140D5—81no—
141C23—101no—
142C23—101no—
143Q8—42no—
144Q8—41no—
145Q8—41no—
146D4—101no—
147D4—101no—
148D4—101no—
149D4—101no—
150D4—402no—
151C2×C4—22no—
152C2×C4—41no—
153C2×C4—101no—
154C2×C4—101no—
155C2×C4—201no—
156C2×C4—201no—
157C2×C4—201no—
158C2×C4—201no—
159C2×C4D4×D511yescharacteristic
160C2×C4D4×D511yescharacteristic
161C2×C4C2×C22⋊D511yescharacteristic
162C8—41no—
163C8—201no—
164C8—201no—
165C5#164611yescharacteristic, complemented, Sylow
166C22—201no—
167C22—201no—
168C22—201no—
169C22—201no—
170C22—201no—
171C22—201no—
172C22#408311yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—201no—
177C4—201no—
178C4#406011yescharacteristic
179C4#406211yescharacteristic
180C4#406411yescharacteristic
181C4#406511yescharacteristic
182C2—401no—
183C2—401no—
184C2#6535011yescharacteristic
185C2#6546111yescharacteristic
186C2#6547611yescharacteristic
subgroupG/H
centerC22#4083
commutator, cosocleC42×C5C23
FrattiniC42C22×D5
FittingC5×#487C2
socleC22×C5#120
prime radical#66068C2
hypercenter#487D5
hypocenterC5#1646
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. #65376C2semidirect
4. #65372C2semidirect
5. #64766C2semidirect
6. #64679C2semidirect
7. #64679C2semidirect
50. #487D5semidirect
165. C5#1646semidirect

Maximal subgroups

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

subgroupindex
#660682
C5×#4872
#653762
#653722
#647662
#646792
#16465