Finite Group Databasebeta

← #13014120

Subgroups — #13014120

Order 1280.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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#10600767C211yesmaximal, characteristic
2#10598818C212yesmaximal
3C2×#4072C411yescharacteristic
4C5×#407C411yescharacteristic
5#65496C2211yescharacteristic
6#64912—22no—
7#64774—22no—
8#7351—51nomaximal, Sylow
9C23×C4×C5C2×C411yescharacteristic
10C2×C5×M16—21no—
11C2×C22⋊Dic5C812yes—
12#4072—41no—
13#4072—41no—
14C2×C4⋊Dic5—21no—
15C2×C4×Dic5—21no—
16C2×#681D412yes—
17#3998—42no—
18C5×C22⋊C8—41no—
19C22⋊#168—41no—
20#1822—51no—
21#1320—52no—
22C24×C5C2×C811yescharacteristic
23C22×C4×C5—21no—
24C22×C4×C5—21no—
25C22×C4×C5—42no—
26C22×C4×C5C22⋊C411yescharacteristic
27C22×C4×C5M1611yescharacteristic
28C22×Dic5—22no—
29C5×M16—42no—
30C2×C5×C8—41no—
31C22⋊Dic5—42no—
32C4⋊Dic5—41no—
33C4⋊Dic5—41no—
34C4×Dic5—42no—
35#681—42no—
36C2×#168—22no—
37#674—82no—
38C2×#117—51no—
39#407—51no—
40#407AGL(1,𝔽5)11yescharacteristic
41#349—102no—
42#343—102no—
43C23×C5—21no—
44C23×C5—41no—
45C23×C5—81no—
46C23×C5C22⋊C811yescharacteristic
47C2×C4×C5—22no—
48C2×C4×C5—21no—
49C2×C4×C5—42no—
50C2×C4×C5—42no—
51C2×C4×C5—41no—
52C2×C4×C5#9911yescharacteristic
53C2×C4×C5#10011yescharacteristic
54C2×Dic5—42no—
55C2×Dic5—82no—
56C5×C8—81no—
57#168—42no—
58C23×C4C2×AGL(1,𝔽5)11yescharacteristic
59C2×M16—21no—
60C2×M16—52no—
61#117—201no—
62#117—201no—
63C2×C4⋊C4—101no—
64C2×C22⋊C4—52no—
65C2×C42—101no—
66M32—202no—
67C22⋊C8—41no—
68C22⋊C8—201no—
69C22×C5—21no—
70C22×C5—41no—
71C22×C5—42no—
72C22×C5—41no—
73C22×C5—82no—
74C22×C5#32311yescharacteristic
75C4×C5—21no—
76C4×C5—41no—
77C4×C5#35212yes—
78Dic5—82no—
79C24D5⋊C811yescharacteristic
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—42no—
83C22×C4—102no—
84C22×C4#70011yescharacteristic
85C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
86M16—42no—
87M16—202no—
88C2×C8—41no—
89C2×C8—102no—
90C4⋊C4—201no—
91C4⋊C4—201no—
92C22⋊C4—202no—
93C42—202no—
94C16—402no—
95C2×C5—21no—
96C2×C5—41no—
97C2×C5—81no—
98C2×C5#131711yescharacteristic
99C23—21no—
100C23—41no—
101C23—81no—
102C23#400311yescharacteristic
103C2×C4—22no—
104C2×C4—21no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4—41no—
108C2×C4—202no—
109C2×C4—402no—
110C2×C4#399911yescharacteristic
111C2×C4#401311yescharacteristic
112C8—81no—
113C8—202no—
114C5#735111yescharacteristic, complemented, Sylow
115C22—21no—
116C22—41no—
117C22—42no—
118C22—41no—
119C22—82no—
120C22#6491511yescharacteristic
121C4—21no—
122C4—41no—
123C4—402no—
124C4#6486512yes—
125C2—21no—
126C2—41no—
127C2—81no—
128C2#1059870311yescharacteristic
subgroupG/H
centerC2#10598703
commutator, prime radicalC24×C5C2×C8
FrattiniC23×C4C2×AGL(1,𝔽5)
FittingC5×#407C4
socleC2×C5#1317
cosocle#65496C22
hypercenter#407AGL(1,𝔽5)
hypocenterC5#7351
LCSG ▷ C24×C5 ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
114. C5#7351semidirect

Maximal subgroups

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

subgroupindex
#106007672
#105988182
#73515