Finite Group Databasebeta

← #13025025

Subgroups — #13025025

Order 1280.

258 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 64 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#10614746C211yesmaximal, characteristic
2#10604155C212yesmaximal
3#10598745C214yesmaximal, complemented
4C2×C5×#125C411yescharacteristic
5#65804C411yescharacteristic
6#65354—22no—
7#65353C412yes—
8#65353C2212yes—
9#65253—22no—
10C4×#681C2211yescharacteristic
11#64912—22no—
12#64861C2214yes—
13#64860—22no—
14#11994—51nomaximal, Sylow
15C5×#125—21no—
16C5×#125—41no—
17C5×#125C2×C412yes—
18C2×C5×C4⋊C4—21no—
19C2×C5×C4⋊C4—41no—
20C2×C42×C5C2×C411yescharacteristic
21#4072—21no—
22#4070—41no—
23C2×#681D412yes—
24#4016C2×C412yes—
25#4015—21no—
26C4×Dic10—41no—
27#3998—24no—
28#3940—22no—
29#3940—22no—
30#3939—22no—
31#3939—22no—
32#3935D412yes—
33C4×#168C2×C411yescharacteristic
34C4×#168C2311yescharacteristic
35#3166—51no—
36#2165—52no—
37#1366—54no—
38C22×C4×C5—21no—
39C22×C4×C5—41no—
40C22×C4×C5C22⋊C411yescharacteristic
41C2×Dic10—41no—
42C5×C4⋊C4—22no—
43C5×C4⋊C4—42no—
44C5×C4⋊C4—42no—
45C5×C4⋊C4—41no—
46C42×C5—21no—
47C42×C5C22⋊C411yescharacteristic
48C42×C5C22×C411yescharacteristic
49C22⋊Dic5—41no—
50C4⋊Dic5—22no—
51C4⋊Dic5—41no—
52#683—42no—
53C4×Dic5—41no—
54#681—24no—
55C2×#168C22⋊C412yes—
56C2×#168C2×D412yes—
57#674—44no—
58#533—51no—
59C2×#125AGL(1,𝔽5)11yescharacteristic
60#501—102no—
61#499—52no—
62#499—52no—
63#428—102no—
64C4×M16—51no—
65#364—54no—
66#349—102no—
67#347—102no—
68C23×C5#10011yescharacteristic
69C2×C4×C5—22no—
70C2×C4×C5—21no—
71C2×C4×C5—21no—
72C2×C4×C5—42no—
73C2×C4×C5—81no—
74C2×C4×C5—82no—
75C2×C4×C5#10011yescharacteristic
76C2×C4×C5C2×C22⋊C411yescharacteristic
77C2×Dic5—42no—
78Dic10—82no—
79#168—22no—
80#168#13714yes—
81C2×M16—52no—
82C4⋊Q8—101no—
83#125—21no—
84#125—41no—
85#125—52no—
86#125C2×AGL(1,𝔽5)12yes—
87C22⋊Q8—201no—
88C4×Q8—201no—
89#117—101no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—41no—
92C2×C42C2×AGL(1,𝔽5)11yescharacteristic
93M32—104no—
94#107—102no—
95#107—102no—
96#106—102no—
97#106—102no—
98#97—52no—
99C4×C8—51no—
100C4×C8—51no—
101C22×C5—21no—
102C22×C5—41no—
103C22×C5C2×#10011yescharacteristic
104C4×C5—21no—
105C4×C5—41no—
106C4×C5—41no—
107C4×C5—82no—
108C4×C5#41912yes—
109Dic5—82no—
110C2×Q8—201no—
111C22×C4—21no—
112C22×C4—41no—
113C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
114M16—104no—
115C2×C8—52no—
116C2×C8—52no—
117C4⋊C4—22no—
118C4⋊C4—42no—
119C4⋊C4—42no—
120C4⋊C4—41no—
121C4⋊C4—102no—
122C4⋊C4—202no—
123C4⋊C4—201no—
124C22⋊C4—201no—
125C42—21no—
126C42—201no—
127C42C22⋊AGL(1,𝔽5)11yescharacteristic
128C42C22×AGL(1,𝔽5)11yescharacteristic
129C16—204no—
130C2×C5—21no—
131C2×C5—41no—
132C2×C5#155811yescharacteristic
133C23#401311yescharacteristic
134Q8—402no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—81no—
140C2×C4—82no—
141C2×C4—202no—
142C2×C4#401311yescharacteristic
143C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
144C8—54no—
145C8—102no—
146C5#1199411yescharacteristic, complemented, Sylow
147C22—21no—
148C22—41no—
149C22C2×#401311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—402no—
155C4#6578212yes—
156C2—21no—
157C2—41no—
158C2#1060497211yescharacteristic
subgroupG/H
centerC2#10604972
commutatorC42×C5C22×C4
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C5×#125C4
socleC2×C5#1558
prime radicalC23×C5#100
cosocleC4×#168C23
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#11994
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #10598745C2semidirect
146. C5#11994semidirect

Maximal subgroups

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

subgroupindex
#106147462
#106041552
#105987452
#119945