Finite Group Databasebeta

← #13014136

Subgroups — #13014136

Order 1280.

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 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#10602533C211yesmaximal, characteristic
2#10598688C212yesmaximal
3C2×C5×#125C411yescharacteristic
4#65225C2211yescharacteristic
5C2×C4×#168C411yescharacteristic
6#64913—22no—
7#64749—22no—
8#7359—51nomaximal, Sylow
9C5×#125—21no—
10C5×#125—41no—
11C5×#125C812yescomplemented
12C2×C5×C4⋊C4—21no—
13C2×C5×C4⋊C4—41no—
14C2×C42×C5C2×C411yescharacteristic
15C2×C4⋊Dic5D412yes—
16C22×#168—21no—
17C22⋊#170—42no—
18#3963—41no—
19C4×#168—41no—
20#1991—51no—
21#1324—52no—
22C22×C4×C5—21no—
23C22×C4×C5—41no—
24C22×C4×C5C22⋊C411yescharacteristic
25C22×Dic5—22no—
26C2×#170—82no—
27C5×C4⋊C4—22no—
28C5×C4⋊C4—42no—
29C5×C4⋊C4—42no—
30C5×C4⋊C4—41no—
31C42×C5—21no—
32C42×C5C2×C811yescharacteristic
33C42×C5M1611yescharacteristic
34C4⋊Dic5—42no—
35C2×#168—22no—
36C2×#168—41no—
37C2×#168—41no—
38C2×#125AGL(1,𝔽5)11yescharacteristic
39C2×C4×C8—51no—
40#382—51no—
41#340—102no—
42#324—102no—
43C23×C5#9911yescharacteristic
44C2×C4×C5—21no—
45C2×C4×C5—21no—
46C2×C4×C5—21no—
47C2×C4×C5—21no—
48C2×C4×C5—42no—
49C2×C4×C5—42no—
50C2×C4×C5—82no—
51C2×C4×C5C22⋊C811yescharacteristic
52C2×C4×C5#10011yescharacteristic
53C2×Dic5—42no—
54C2×Dic5—82no—
55#170—162no—
56#168—42no—
57C22×C8—101no—
58#125—21no—
59#125—41no—
60#125#17012yescomplemented
61C2×C4⋊C4—21no—
62C2×C4⋊C4—41no—
63C2×C4⋊C4—52no—
64C2×C42C2×AGL(1,𝔽5)11yescharacteristic
65C22⋊C8—202no—
66C4×C8—201no—
67#95—201no—
68C22×C5—22no—
69C22×C5#32311yescharacteristic
70C22×C5#35411yescharacteristic
71C22×C5#35611yescharacteristic
72C4×C5—21no—
73C4×C5—21no—
74C4×C5—41no—
75C4×C5—41no—
76C4×C5—82no—
77Dic5—82no—
78C22×C4—21no—
79C22×C4—41no—
80C22×C4—102no—
81C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
82C2×C8—102no—
83C2×C8—201no—
84C2×C8—201no—
85C2×C8—402no—
86C4⋊C4—22no—
87C4⋊C4—42no—
88C4⋊C4—42no—
89C4⋊C4—41no—
90C4⋊C4—202no—
91C42—21no—
92C42C2×#17011yescharacteristic
93C42#70411yescharacteristic
94C2×C5—21no—
95C2×C5—21no—
96C2×C5#131911yescharacteristic
97C2×C5#141412yes—
98C23#401111yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—42no—
104C2×C4—42no—
105C2×C4—82no—
106C2×C4—202no—
107C2×C4—402no—
108C2×C4C22⋊#17011yescharacteristic
109C2×C4#401311yescharacteristic
110C8—202no—
111C8—802no—
112C5#735911yescharacteristic, complemented, Sylow
113C22—22no—
114C22#6492811yescharacteristic
115C22#6492911yescharacteristic
116C22#6493311yescharacteristic
117C4—21no—
118C4—21no—
119C4—41no—
120C4—41no—
121C4—82no—
122C4—402no—
123C2—21no—
124C2—21no—
125C2#1059874012yes—
126C2#1059882711yescharacteristic
subgroupG/H
centerC22#64928
commutatorC42×C5C2×C8
FrattiniC2×C42C2×AGL(1,𝔽5)
FittingC2×C5×#125C4
socleC22×C5#354
prime radicalC23×C5#99
cosocle#65225C22
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#7359
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
11. C5×#125C8semidirect
60. #125#170semidirect
112. C5#7359semidirect

Maximal subgroups

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

subgroupindex
#106025332
#105986882
#73595