Finite Group Databasebeta

← #13014112

Subgroups — #13014112

Order 1280.

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

normal subgroups only

This group has 200 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#10600327C211yesmaximal, characteristic
2#10598819C212yesmaximal
3C2×#4072C411yescharacteristic
4C5×#381C411yescharacteristic
5#65500C2211yescharacteristic
6#64933—22no—
7#64747—22no—
8#7348—51nomaximal, Sylow
9C23×C4×C5C2×C411yescharacteristic
10C2×C5×C22⋊C4—21no—
11C2×C22⋊Dic5—21no—
12C2×C22⋊Dic5D412yes—
13#4072—41no—
14#4072—41no—
15C2×C4⋊Dic5—21no—
16C2×C4×Dic5C812yescomplemented
17C22⋊#170—42no—
18C5×#95—41no—
19#3963—41no—
20#1820—51no—
21#1317—52no—
22C24×C5C22⋊C411yescharacteristic
23C22×C4×C5—21no—
24C22×C4×C5—21no—
25C22×C4×C5—42no—
26C22×C4×C5—41no—
27C22×C4×C5C2×C811yescharacteristic
28C22×C4×C5M1611yescharacteristic
29C22×Dic5—22no—
30C22×Dic5—22no—
31C2×#170—82no—
32C5×C22⋊C4—42no—
33C22⋊Dic5—41no—
34C22⋊Dic5—41no—
35C22⋊Dic5—42no—
36C4⋊Dic5—42no—
37C4×Dic5—42no—
38C2×#117—51no—
39#381—51no—
40#381AGL(1,𝔽5)11yescharacteristic
41#342—102no—
42#323—102no—
43C23×C5—22no—
44C23×C5—81no—
45C23×C5C22⋊C811yescharacteristic
46C23×C5#9911yescharacteristic
47C23×C5#10011yescharacteristic
48C2×C4×C5—21no—
49C2×C4×C5—21no—
50C2×C4×C5—42no—
51C2×C4×C5—42no—
52C2×C4×C5—41no—
53C2×C4×C5—41no—
54C2×C4×C5—81no—
55C2×C4×C5—82no—
56C2×Dic5—42no—
57C2×Dic5—42no—
58C2×Dic5—82no—
59C2×Dic5—82no—
60#170—162no—
61C23×C4C2×AGL(1,𝔽5)11yescharacteristic
62#117—201no—
63#117—201no—
64C2×C4⋊C4—101no—
65C2×C22⋊C4—21no—
66C2×C22⋊C4—52no—
67C2×C22⋊C4—101no—
68C2×C42—52no—
69C22⋊C8—202no—
70#95—41no—
71#95—201no—
72C22×C5—21no—
73C22×C5—21no—
74C22×C5—41no—
75C22×C5—41no—
76C22×C5—41no—
77C22×C5—82no—
78C22×C5#32311yescharacteristic
79C22×C5#35212yes—
80C4×C5—41no—
81C4×C5—41no—
82C4×C5—161no—
83Dic5—82no—
84Dic5—82no—
85C24C22⋊AGL(1,𝔽5)11yescharacteristic
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—42no—
89C22×C4—41no—
90C22×C4—102no—
91C22×C4—102no—
92C22×C4D5⋊C811yescharacteristic
93C22×C4#70011yescharacteristic
94C2×C8—402no—
95C4⋊C4—202no—
96C22⋊C4—42no—
97C22⋊C4—201no—
98C22⋊C4—201no—
99C22⋊C4—202no—
100C42—202no—
101C2×C5—21no—
102C2×C5—22no—
103C2×C5—41no—
104C2×C5—41no—
105C2×C5#131711yescharacteristic
106C23—22no—
107C23—81no—
108C23#399911yescharacteristic
109C23#400311yescharacteristic
110C23#401311yescharacteristic
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—42no—
114C2×C4—42no—
115C2×C4—41no—
116C2×C4—41no—
117C2×C4—81no—
118C2×C4—82no—
119C2×C4—202no—
120C2×C4—202no—
121C2×C4—402no—
122C2×C4—402no—
123C8—802no—
124C5#734811yescharacteristic, complemented, Sylow
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22#6486512yes—
132C22#6491511yescharacteristic
133C4—41no—
134C4—41no—
135C4—161no—
136C4—402no—
137C4—402no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2#1059870311yescharacteristic
subgroupG/H
centerC2#10598703
commutatorC22×C4×C5C2×C8
FrattiniC23×C4C2×AGL(1,𝔽5)
FittingC5×#381C4
socleC2×C5#1317
prime radicalC24×C5C22⋊C4
cosocle#65500C22
hypercenter#381AGL(1,𝔽5)
hypocenterC5#7348
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
16. C2×C4×Dic5C8semidirect
124. C5#7348semidirect

Maximal subgroups

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

subgroupindex
#106003272
#105988192
#73485