Finite Group Databasebeta

← #13100139

Subgroups — #13100139

Order 1600.

143 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 143 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C5×#4021C211yesmaximal, characteristic
2#11716848C212yesmaximal, complemented
3C2×C5×D20C411yescharacteristic
4C2×C5×Dic10C2211yescharacteristic
5#87853—22no—
6C42×C52C411yescharacteristic
7C5×#685—22no—
8#64856—51nomaximal
9#64762—51nomaximal
10C22×C5×D5—21no—
11C2×C4×C52—21no—
12C2×C4×C52C2×C411yescharacteristic
13C2×C5×Dic5D412yes—
14C5×D20—41no—
15C5×Dic10—41no—
16#6032—42no—
17C5×#124—51no—
18#4021D511yescharacteristic
19#4005—52no—
20#3968—52no—
21C22×C52C22⋊C411yescharacteristic
22C2×C5×D5—42no—
23C2×C5×D5—41no—
24C4×C52—21no—
25C4×C52—41no—
26C5×Dic5—22no—
27C2×C5×Q8—51no—
28C2×C5×D4—51no—
29C2×D20Dic511yescharacteristic
30C2×Dic10C2×D511yescharacteristic
31#704—102no—
32C5×C22⋊C4—102no—
33C42×C5—41no—
34C42×C5Dic511yescharacteristic
35C42×C5AGL(1,𝔽5)11yescharacteristic
36#685—22no—
37#681—102no—
38#355—251noSylow
39C2×C52—21no—
40C2×C52#9911yescharacteristic
41C5×D5—81no—
42C23×C5—101no—
43C22×D5—21no—
44C5×Q8—201no—
45C5×D4—201no—
46C2×C4×C5—21no—
47C2×C4×C5—21no—
48C2×C4×C5—42no—
49C2×C4×C5—41no—
50C2×C4×C5—52no—
51C2×C4×C5C2×Dic511yescharacteristic
52C2×C4×C5C2×AGL(1,𝔽5)11yescharacteristic
53C2×Dic5C22⋊D512yes—
54D20—41no—
55Dic10—41no—
56#170—202no—
57#168—202no—
58#124—51no—
59#101—252no—
60C52#35511yescharacteristic, complemented, Sylow
61C22×C5—41no—
62C22×C5—202no—
63C22×C5—201no—
64C22×C5C22⋊Dic511yescharacteristic
65C22×C5C22⋊AGL(1,𝔽5)11yescharacteristic
66C2×D5—42no—
67C2×D5—41no—
68C4×C5—21no—
69C4×C5—21no—
70C4×C5—42no—
71C4×C5—41no—
72C4×C5—41no—
73C4×C5—44no—
74C4×C5—102no—
75Dic5—22no—
76C2×Q8—51no—
77C2×D4—51no—
78M16—502no—
79C22⋊C4—102no—
80C42#104211yescharacteristic
81C2×C5—21no—
82C2×C5—21no—
83C2×C5—42no—
84C2×C5—41no—
85C2×C5—401no—
86C2×C5#396611yescharacteristic
87C2×C5#399911yescharacteristic
88D5—81no—
89C23—101no—
90Q8—201no—
91D4—201no—
92C2×C4—21no—
93C2×C4—52no—
94C2×C4C2×#104211yescharacteristic
95C8—1002no—
96C5—41no—
97C5#6476211yescharacteristic, complemented
98C5#6485611yescharacteristic, complemented
99C22—202no—
100C22—201no—
101C22C22⋊#104211yescharacteristic
102C4—21no—
103C4—41no—
104C4—102no—
105C2—21no—
106C2—401no—
107C2#1171684211yescharacteristic
subgroupG/H
centerC2#11716842
commutatorC2×C4×C52C2×C4
FrattiniC2×C4C2×#1042
FittingC42×C52C4
socleC2×C52#99
prime radicalC2×C5×D20C4
cosocleC2×C5×Dic10C22
hypercenterC42#1042
hypocenterC52#355
LCSG ▷ C2×C4×C52 ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11716848C2semidirect
60. C52#355semidirect
97. C5#64762semidirect
98. C5#64856semidirect

Maximal subgroups

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

subgroupindex
C5×#40212
#117168482
#648565
#647625