Finite Group Databasebeta

← #13014560

Subgroups — #13014560

Order 1280.

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

normal subgroups only

This group has 126 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#10602754C211yesmaximal, characteristic
2#10598742C211yesmaximal, characteristic
3#10598736C211yesmaximal, characteristic
4C5×#564C411yescharacteristic
5#65358C2211yescharacteristic
6#65354—21no—
7#64860—21no—
8#64855—21no—
9#64763—21no—
10#64763C411yescharacteristic
11#7526—51nomaximal, Sylow
12C5×#125—21no—
13C5×#125—41no—
14C5×#125—41no—
15C5×#125—41no—
16C5×#125C2×C411yescharacteristic
17#4015D411yescharacteristic
18#4005—41no—
19#3998—41no—
20#3942—41no—
21#3940—41no—
22#3939—41no—
23#3935—21no—
24#3935D411yescharacteristic
25#1663—51no—
26#1413—51no—
27#1356—51no—
28C2×Dic10—21no—
29#704—81no—
30C5×C4⋊C4—21no—
31C5×C4⋊C4—21no—
32C5×C4⋊C4—21no—
33C5×C4⋊C4—41no—
34C5×C4⋊C4—41no—
35C5×C4⋊C4—41no—
36C5×C4⋊C4—41no—
37C5×C4⋊C4—41no—
38C5×C4⋊C4—41no—
39C42×C5—41no—
40C42×C5C22⋊C411yescharacteristic
41C4⋊Dic5—41no—
42C2×#168—21no—
43C2×#168—41no—
44#674—42no—
45#564AGL(1,𝔽5)11yescharacteristic
46#501—101no—
47#491—51no—
48#356—101no—
49#347—101no—
50#330—51no—
51#330—101no—
52C2×C4×C5—21no—
53C2×C4×C5—41no—
54C2×C4×C5—41no—
55C2×C4×C5—41no—
56C2×C4×C5#9911yescharacteristic
57C2×Dic5—41no—
58Dic10—81no—
59#170—161no—
60#168—41no—
61#168—42no—
62C4⋊Q8—51no—
63#125—21no—
64#125—41no—
65#125—41no—
66#125—41no—
67#125C2×AGL(1,𝔽5)11yescharacteristic
68M32—201no—
69#107—201no—
70#106—201no—
71#103—201no—
72#101—201no—
73#97—51no—
74#97—101no—
75C22×C5AΣL(1,𝔽16)11yescharacteristic
76C4×C5—21no—
77C4×C5—41no—
78C4×C5—81no—
79C4×C5—81no—
80C4×C5—81no—
81Dic5—81no—
82C2×Q8—101no—
83M16—401no—
84C2×C8—101no—
85C2×C8—201no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—41no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—201no—
96C42—41no—
97C42C22⋊AGL(1,𝔽5)11yescharacteristic
98C16—202no—
99C2×C5—21no—
100C2×C5#140411yescharacteristic
101Q8—401no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—201no—
107C2×C4#401111yescharacteristic
108C8—201no—
109C8—202no—
110C8—801no—
111C5#752611yescharacteristic, complemented, Sylow
112C22#6493411yescharacteristic
113C4—21no—
114C4—41no—
115C4—81no—
116C4—81no—
117C4—81no—
118C4—401no—
119C2—21no—
120C2#1059883511yescharacteristic
subgroupG/H
centerC2#10598835
commutatorC5×#125C2×C4
Frattini#125C2×AGL(1,𝔽5)
FittingC5×#564C4
socleC2×C5#1404
prime radicalC22×C5AΣL(1,𝔽16)
cosocle#65358C22
hypercenter#564AGL(1,𝔽5)
hypocenterC5#7526
LCSG ▷ C5×#125 ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125 ◁ #564

Complements

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

NH ≅ G/Ntype
111. C5#7526semidirect

Maximal subgroups

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

subgroupindex
#106027542
#105987422
#105987362
#75265