Finite Group Databasebeta

← #13014580

Subgroups — #13014580

Order 1280.

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

normal subgroups only

This group has 150 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#10602125C211yesmaximal, characteristic
2#10598520C211yesmaximal, characteristic
3#10598517C211yesmaximal, characteristic
4C5×#498C411yescharacteristic, complemented
5#65374—21no—
6#65368—21no—
7#64982C2211yescharacteristic
8#64855—21no—
9#64853—21no—
10C8×#168C411yescharacteristic, complemented
11#7535—51nomaximal, Sylow
12C5×C4⋊Q8—21no—
13C2×#688—42no—
14C2×#677—41no—
15#4020D411yescharacteristic
16#4015D411yescharacteristic
17#4005—41no—
18#3999—41no—
19C5×#106—41no—
20C4×C5×C8C2×C411yescharacteristic
21#3940—42no—
22C4×#168—21no—
23#1705—51no—
24#1410—51no—
25#1409—51no—
26C2×C5×Q8—41no—
27C2×D20—21no—
28C2×D20—41no—
29C2×Dic10—21no—
30C22⋊AGL(1,𝔽5)—81no—
31#704—81no—
32C2×C5×C8—21no—
33C5×C4⋊C4—41no—
34C5×C4⋊C4—41no—
35C42×C5C22⋊C411yescharacteristic
36#688—84no—
37C4⋊Dic5—41no—
38C2×#168—22no—
39#677—82no—
40#498—101no—
41#498AGL(1,𝔽5)11yescharacteristic, complemented
42#492—51no—
43#492—101no—
44#356—101no—
45#353—101no—
46C82—51no—
47C22×D5—41no—
48C2×AGL(1,𝔽5)—161no—
49C5×Q8—82no—
50C2×C4×C5—21no—
51C2×C4×C5—81no—
52C2×C4×C5#9911yescharacteristic
53C2×Dic5—41no—
54D20—81no—
55D20—82no—
56Dic10—81no—
57#170—161no—
58C5×C8—22no—
59#168—24no—
60C2×SD16—201no—
61C2×SD16—202no—
62C4⋊Q8—21no—
63C4⋊Q8—51no—
64#127—51no—
65#106—41no—
66#106—202no—
67#101—201no—
68#99—201no—
69C4×C8—101no—
70C4×C8C2×AGL(1,𝔽5)11yescharacteristic
71C22×C5#35311yescharacteristic
72C2×D5—81no—
73C2×D5—161no—
74AGL(1,𝔽5)—321no—
75C4×C5—22no—
76C4×C5—21no—
77C4×C5—161no—
78Dic5—81no—
79C2×Q8—41no—
80C2×Q8—101no—
81C2×D4—101no—
82C2×D4—201no—
83SD16—402no—
84SD16—404no—
85M16—401no—
86C2×C8—21no—
87C2×C8—102no—
88C4⋊C4—41no—
89C4⋊C4—41no—
90C4⋊C4—201no—
91C22⋊C4—401no—
92C42C22⋊AGL(1,𝔽5)11yescharacteristic
93C2×C5—21no—
94C2×C5#140911yescharacteristic
95D5—161no—
96C23—201no—
97Q8—82no—
98Q8—401no—
99D4—401no—
100D4—402no—
101C2×C4—21no—
102C2×C4—81no—
103C2×C4—201no—
104C2×C4—801no—
105C2×C4#401111yescharacteristic
106C8—22no—
107C8—104no—
108C8—801no—
109C5#753511yescharacteristic, complemented, Sylow
110C22—401no—
111C22—801no—
112C22#6492211yescharacteristic
113C4—22no—
114C4—21no—
115C4—161no—
116C4—401no—
117C4—1601no—
118C2—21no—
119C2—801no—
120C2#1059875311yescharacteristic
subgroupG/H
centerC2#10598753
commutatorC4×C5×C8C2×C4
FrattiniC4×C8C2×AGL(1,𝔽5)
FittingC5×#498C4
socleC2×C5#1409
prime radical#4020D4
cosocle#64982C22
hypercenter#498AGL(1,𝔽5)
hypocenterC5#7535
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
4. C5×#498C4semidirect
10. C8×#168C4semidirect
41. #498AGL(1,𝔽5)semidirect
109. C5#7535semidirect

Maximal subgroups

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

subgroupindex
#106021252
#105985202
#105985172
#75355