Finite Group Databasebeta

← #13014578

Subgroups — #13014578

Order 1280.

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

normal subgroups only

This group has 128 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#10602131C211yesmaximal, characteristic
2#10598521C211yesmaximal, characteristic
3#10598521C211yesmaximal, characteristic
4C5×#498C411yescharacteristic
5#65370—21no—
6#65368—21no—
7#64988C2211yescharacteristic
8#64855—21no—
9#64855—21no—
10#64675C411yescharacteristic
11#7534—51nomaximal, Sylow
12C5×C4⋊Q8—21no—
13C2×Dic20—41no—
14#4015D411yescharacteristic
15#4015D411yescharacteristic
16#4005—41no—
17#4005—41no—
18C5×#106—41no—
19C4×C5×C8C2×C411yescharacteristic
20#3967—42no—
21#3940—42no—
22C4×#168—21no—
23#1716—51no—
24#1411—51no—
25#1411—51no—
26C2×C5×Q8—41no—
27C2×Dic10—21no—
28C2×Dic10—21no—
29#704—81no—
30#704—81no—
31C2×C5×C8—21no—
32C5×C4⋊C4—41no—
33C5×C4⋊C4—41no—
34C42×C5C22⋊C411yescharacteristic
35C4⋊Dic5—41no—
36C4⋊Dic5—41no—
37C2×#168—22no—
38Dic20—82no—
39#498—101no—
40#498AGL(1,𝔽5)11yescharacteristic
41#494—51no—
42#487—101no—
43#356—101no—
44#356—101no—
45#322—51no—
46C5×Q8—82no—
47C2×C4×C5—21no—
48C2×C4×C5—81no—
49C2×C4×C5#9911yescharacteristic
50C2×Dic5—41no—
51C2×Dic5—41no—
52Dic10—81no—
53Dic10—81no—
54#170—161no—
55#170—161no—
56C5×C8—22no—
57#168—42no—
58C2×Q16—201no—
59C4⋊Q8—21no—
60C4⋊Q8—51no—
61C4⋊Q8—51no—
62#106—41no—
63#106—202no—
64#103—202no—
65#101—201no—
66#101—201no—
67C4×C8—101no—
68C4×C8C2×AGL(1,𝔽5)11yescharacteristic
69C22×C5#35311yescharacteristic
70C4×C5—22no—
71C4×C5—21no—
72C4×C5—161no—
73Dic5—81no—
74Dic5—81no—
75C2×Q8—41no—
76C2×Q8—101no—
77C2×Q8—101no—
78Q16—402no—
79M16—401no—
80M16—401no—
81C2×C8—21no—
82C2×C8—102no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—201no—
86C4⋊C4—201no—
87C42C22⋊AGL(1,𝔽5)11yescharacteristic
88C2×C5—21no—
89C2×C5#140911yescharacteristic
90Q8—82no—
91Q8—401no—
92Q8—401no—
93C2×C4—21no—
94C2×C4—81no—
95C2×C4—201no—
96C2×C4—201no—
97C2×C4#401111yescharacteristic
98C8—22no—
99C8—202no—
100C8—801no—
101C8—801no—
102C5#753411yescharacteristic, complemented, Sylow
103C22#6492211yescharacteristic
104C4—22no—
105C4—21no—
106C4—161no—
107C4—401no—
108C4—401no—
109C2—21no—
110C2#1059875311yescharacteristic
subgroupG/H
centerC2#10598753
commutatorC4×C5×C8C2×C4
FrattiniC4×C8C2×AGL(1,𝔽5)
FittingC5×#498C4
socleC2×C5#1409
prime radicalC22×C5#353
cosocle#64988C22
hypercenter#498AGL(1,𝔽5)
hypocenterC5#7534
LCSG ▷ C4×C5×C8 ▷ C42×C5 ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
102. C5#7534semidirect

Maximal subgroups

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

subgroupindex
#106021312
#105985212
#75345