Finite Group Databasebeta

← #10604920

Subgroups — #10604920

Order 640.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#66139C211yesmaximal, characteristic
2#65761C212yesmaximal, complemented
3#64923C214yesmaximal, complemented
4C22×C5×D4C411yescharacteristic
5C2×#709C2211yescharacteristic
6D5⋊M16—22no—
7#4099—22no—
8#4086C412yes—
9#4084—22no—
10#4082C2212yes—
11#4072C411yescharacteristic
12#4013—22no—
13#4005C2214yescomplemented
14#2134—51nomaximal, Sylow
15C24×C5—21no—
16C2×C5×D4—21no—
17C2×C5×D4—42no—
18C2×C5×D4C2×C412yes—
19C22×C4×C5C2×C411yescharacteristic
20C2×C22⋊D5—24no—
21C2×C22⋊D5D412yes—
22#709—42no—
23C2×D20C2×C411yescharacteristic
24C2×C4×D5D412yes—
25C2×Dic10C2311yescharacteristic
26#704—24no—
27#700—42no—
28D5⋊C8—42no—
29C22⋊Dic5—21no—
30C22⋊Dic5—24no—
31C4⋊Dic5—21no—
32C4×Dic5C2×C412yes—
33#535—51no—
34#413—52no—
35#355—54no—
36C23×C5—22no—
37C23×C5—42no—
38C23×C5—82no—
39C23×C5C22⋊C411yescharacteristic
40C22×D5C22⋊C412yes—
41C5×D4—42no—
42C5×D4—42no—
43C2×C4×C5—22no—
44C2×C4×C5C22⋊C411yescharacteristic
45C2×C4×C5C22×C411yescharacteristic
46C22⋊D5—42no—
47C22⋊D5—84no—
48C2×Dic5—22no—
49C2×Dic5C2×D412yes—
50D20—41no—
51C4×D5—22no—
52C4×D5—22no—
53Dic10—41no—
54#170—44no—
55C2×#41—51no—
56C22×D4AGL(1,𝔽5)11yescharacteristic
57C2×M16—102no—
58#127—52no—
59#124—52no—
60#121—102no—
61#120—102no—
62#117—51no—
63#101—54no—
64#100—102no—
65C22×C5—21no—
66C22×C5—41no—
67C22×C5—44no—
68C22×C5—42no—
69C22×C5—84no—
70C22×C5C2×C22⋊C411yescharacteristic
71C2×D5—22no—
72C2×D5—42no—
73C4×C5—21no—
74C4×C5#9912yes—
75Dic5—22no—
76Dic5—42no—
77C24—21no—
78#41—202no—
79C2×Q8—51no—
80C2×D4—21no—
81C2×D4—42no—
82C2×D4—52no—
83C2×D4—51no—
84C2×D4—104no—
85C2×D4C2×AGL(1,𝔽5)12yes—
86C22×C4—52no—
87C22×C4C2×AGL(1,𝔽5)11yescharacteristic
88M16—104no—
89M16—202no—
90C2×C8—202no—
91C4⋊C4—101no—
92C22⋊C4—104no—
93C22⋊C4—101no—
94C42—52no—
95C2×C5—21no—
96C2×C5—41no—
97C2×C5—82no—
98C2×C5C2×#9911yescharacteristic
99D5—42no—
100C23—22no—
101C23—42no—
102C23—52no—
103C23—82no—
104C23C22⋊AGL(1,𝔽5)11yescharacteristic
105Q8—201no—
106D4—42no—
107D4—42no—
108D4—201no—
109D4—202no—
110D4—404no—
111C2×C4—22no—
112C2×C4—52no—
113C2×C4—102no—
114C2×C4—102no—
115C2×C4—102no—
116C2×C4C22⋊AGL(1,𝔽5)11yescharacteristic
117C2×C4C22×AGL(1,𝔽5)11yescharacteristic
118C8—204no—
119C5#213411yescharacteristic, complemented, Sylow
120C22—21no—
121C22—41no—
122C22—44no—
123C22—42no—
124C22—84no—
125C22—102no—
126C22—202no—
127C22C2×C22⋊AGL(1,𝔽5)11yescharacteristic
128C4—21no—
129C4—102no—
130C4—202no—
131C4#401112yes—
132C2—21no—
133C2—41no—
134C2—82no—
135C2—202no—
136C2C2×#401111yescharacteristic
subgroupG/H
centerC2C2×#4011
commutatorC2×C4×C5C22×C4
FrattiniC2×C4C22×AGL(1,𝔽5)
FittingC22×C5×D4C4
socleC2×C5C2×#99
prime radical#66139C2
cosocleC2×Dic10C23
hypercenterC22×D4AGL(1,𝔽5)
hypocenterC5#2134
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #65761C2semidirect
3. #64923C2semidirect
13. #4005C22semidirect
119. C5#2134semidirect

Maximal subgroups

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

subgroupindex
#661392
#657612
#649232
#21345