Finite Group Databasebeta

← #13014583

Subgroups — #13014583

Order 1280.

138 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 22 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#10598852C211yesmaximal, characteristic
2#10598520C211yesmaximal, characteristic
3#10598517C211yesmaximal, characteristic
4#64983—21no—
5#64982C2211yescharacteristic
6#64970—21no—
7#64969C411yescharacteristic, complemented
8#64855—21no—
9#64853—21no—
10C5×C82C411yescharacteristic, complemented
11#7536—51nomaximal, Sylow
12C2×#677—41no—
13#4020D411yescharacteristic
14#4015—21no—
15#4015D411yescharacteristic
16#4005—41no—
17#3999—41no—
18C4×C5×C8—21no—
19C4×C5×C8C2×C411yescharacteristic
20#3953—42no—
21#3949—41no—
22#3948—42no—
23#1708—51no—
24#1410—51no—
25#1409—51no—
26C2×D20—21no—
27C2×D20—41no—
28C2×Dic10—21no—
29C2×Dic10—41no—
30C22⋊AGL(1,𝔽5)—81no—
31#704—81no—
32C2×C5×C8—21no—
33C2×C5×C8—22no—
34C42×C5C22⋊C411yescharacteristic
35C4⋊Dic5—41no—
36C4⋊Dic5—41no—
37C4⋊Dic5—41no—
38#677—82no—
39#498—51no—
40#492—51no—
41#487—101no—
42#486—101no—
43#356—101no—
44#353—101no—
45C82AGL(1,𝔽5)11yescharacteristic, complemented
46C22×D5—41no—
47C2×AGL(1,𝔽5)—161no—
48C2×C4×C5—21no—
49C2×C4×C5#9911yescharacteristic
50C2×Dic5—41no—
51C2×Dic5—81no—
52D20—81no—
53D20—82no—
54Dic10—81no—
55Dic10—82no—
56#170—161no—
57C5×C8—22no—
58C5×C8—42no—
59C2×SD16—201no—
60C4⋊Q8—51no—
61C4⋊Q8—101no—
62#127—51no—
63#106—201no—
64#103—202no—
65#102—202no—
66#101—201no—
67#99—201no—
68C4×C8—21no—
69C4×C8C2×AGL(1,𝔽5)11yescharacteristic
70C22×C5#35311yescharacteristic
71C2×D5—81no—
72C2×D5—161no—
73AGL(1,𝔽5)—321no—
74C4×C5—22no—
75C4×C5—21no—
76Dic5—81no—
77Dic5—161no—
78C2×Q8—101no—
79C2×Q8—201no—
80C2×D4—101no—
81C2×D4—201no—
82SD16—402no—
83M16—401no—
84C2×C8—21no—
85C2×C8—22no—
86C4⋊C4—201no—
87C4⋊C4—201no—
88C4⋊C4—201no—
89C22⋊C4—401no—
90C42C22⋊AGL(1,𝔽5)11yescharacteristic
91C2×C5—21no—
92C2×C5#140911yescharacteristic
93D5—161no—
94C23—201no—
95Q8—401no—
96Q8—402no—
97D4—401no—
98D4—402no—
99C2×C4—21no—
100C2×C4—201no—
101C2×C4—401no—
102C2×C4—801no—
103C2×C4#399911yescharacteristic
104C8—22no—
105C8—42no—
106C8—801no—
107C5#753611yescharacteristic, complemented, Sylow
108C22—401no—
109C22—801no—
110C22#6485311yescharacteristic
111C4—22no—
112C4—21no—
113C4—401no—
114C4—801no—
115C4—1601no—
116C2—21no—
117C2—801no—
118C2#1059851711yescharacteristic
subgroupG/H
centerC2#10598517
commutatorC4×C5×C8C2×C4
FrattiniC4×C8C2×AGL(1,𝔽5)
FittingC5×C82C4
socleC2×C5#1409
prime radical#4020D4
cosocle#64982C22
hypercenterC82AGL(1,𝔽5)
hypocenterC5#7536
LCSG ▷ C4×C5×C8 ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C82

Complements

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

NH ≅ G/Ntype
7. #64969C4semidirect
10. C5×C82C4semidirect
45. C82AGL(1,𝔽5)semidirect
107. C5#7536semidirect

Maximal subgroups

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

subgroupindex
#105988522
#105985202
#105985172
#75365