Finite Group Databasebeta

← #13085550

Subgroups — #13085550

Order 1440.

200 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 23 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
1C2×#67138C211yesmaximal, characteristic
2#10624118C212yesmaximal, complemented
3C22×C5×C3⋊D3C411yescharacteristic
4C22×C32×D5C411yescharacteristic
5C2×C3⋊Dic15C2211yescharacteristic
6#67138—22no—
7#67127—22no—
8#63788—51nomaximal, Hall
9C2×#1201—62no—
10C22×C32×C5C2×C411yescharacteristic
11C2×C5×C3⋊D3—21no—
12C2×C5×C3⋊D3—41no—
13C2×C32×D5—21no—
14C2×C32×D5—41no—
15C3⋊Dic15D412yes—
16#4013—91nomaximal, Hall
17C2×#638—51no—
18#3792—52no—
19C22×C5×D3—62no—
20C22×C3×D5—22no—
21C2×Dic15—62no—
22#1201—68no—
23C2×C32×C5—21no—
24C2×C32×C5C22⋊C411yescharacteristic
25C5×C3⋊D3—41no—
26C32×D5—41no—
27C2×C22⋊D5—91no—
28#704—92no—
29C23×C32—51no—
30C22×C3⋊D3AGL(1,𝔽5)11yescharacteristic
31#638—102no—
32C2×C3⋊Dic3—51no—
33#622—102no—
34C22×C3×C5—22no—
35C2×C5×D3—64no—
36C2×C5×D3—124no—
37C2×C3×D5—24no—
38C2×C3×D5—44no—
39Dic15—64no—
40C2×#67—302no—
41C32×C5#10011yescharacteristic, complemented, Hall
42C23×C5—91no—
43C22×D5#15711yescharacteristic
44C22⋊D5—182no—
45C2×Dic5—91no—
46#170—182no—
47C22×C32—101no—
48C22×C32—201no—
49C22×C32C2×AGL(1,𝔽5)11yescharacteristic
50C2×C3⋊D3—21no—
51C2×C3⋊D3—41no—
52C3⋊Dic3—52no—
53#100—451noSylow
54C2×C3×C5—24no—
55C2×C3×C5—22no—
56C3×D5—44no—
57C5×D3—124no—
58C23×C3—102no—
59C22×D3—62no—
60#67—308no—
61C2×Dic3—302no—
62C22×C5—181no—
63C22×C5—361no—
64C22×C5C2×#15711yescharacteristic
65C2×D5—21no—
66C2×D5—41no—
67Dic5—92no—
68C2×C32—21no—
69C2×C32—201no—
70C2×C32C22⋊AGL(1,𝔽5)11yescharacteristic
71C3⋊D3—41no—
72C2×D4—451no—
73M16—452no—
74C3×C5—22no—
75C22×C3—22no—
76C22×C3—104no—
77C22×C3—204no—
78C2×D3—64no—
79C2×D3—124no—
80Dic3—304no—
81C2×C5—21no—
82C2×C5—361no—
83C2×C5C22⋊#15711yescharacteristic
84D5—41no—
85C32#401311yescharacteristic, complemented, Sylow
86C23—51no—
87C23—91no—
88D4—902no—
89C2×C4—451no—
90C8—902no—
91C2×C3—24no—
92C2×C3—22no—
93C2×C3—204no—
94D3—124no—
95C5#6378811yescharacteristic, complemented, Sylow
96C22—101no—
97C22—181no—
98C22—201no—
99C22—361no—
100C22D5⋊#15711yescharacteristic
101C4—452no—
102C3—22no—
103C2—21no—
104C2—201no—
105C2—361no—
106C2#1062399211yescharacteristic
subgroupG/H
centerC2#10623992
commutator, FittingC22×C32×C5C2×C4
Frattini, hypercenterC22D5⋊#157
socleC2×C32×C5C22⋊C4
prime radicalC2×#67138C2
cosocleC2×C3⋊Dic15C22
hypocenterC32×C5#100
LCSG ▷ C22×C32×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #10624118C2semidirect
41. C32×C5#100semidirect
85. C32#4013semidirect
95. C5#63788semidirect

Maximal subgroups

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

subgroupindex
C2×#671382
#106241182
#637885
#40139