Finite Group Databasebeta

← #14279486

Subgroups — #14279486

Order 1920.

188 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C3×#64988C211yesmaximal, characteristic
2#11746726C212yesmaximal
3#10598521—31nomaximal, Hall
4C2×C3×Dic20—22no—
5C3×#4015C411yescharacteristic
6C3×#4015C2211yescharacteristic
7#91234—22no—
8C3×C4×C5×C8C411yescharacteristic
9#67795—51nomaximal, Hall
10#64988D311yescharacteristic
11#64855—32no—
12C2×C3×Dic10—21no—
13C2×C3×Dic10D412yes—
14#6762—42no—
15C2×C3×C5×C8—21no—
16C3×C42×C5C2×C411yescharacteristic
17C3×C4⋊Dic5—41no—
18C3×C4⋊Dic5—41no—
19C3×Dic20—44no—
20C3×#494—51no—
21#4548—52no—
22C2×Dic20—22no—
23#4015Dic311yescharacteristic
24#4015C2×D311yescharacteristic
25#4005—62no—
26C4×C5×C8Dic311yescharacteristic
27#1411—151noSylow
28C2×C3×C4×C5—21no—
29C2×C3×C4×C5C22⋊C411yescharacteristic
30C2×C3×Dic5—22no—
31C2×C3×Dic5—41no—
32C3×Dic10—42no—
33C3×Dic10—42no—
34C3⋊#170—82no—
35C3×C5×C8—22no—
36C2×C3×Q16—102no—
37C3×C4⋊Q8—51no—
38C3×C4⋊Q8—51no—
39C3×C4×C8AGL(1,𝔽5)11yescharacteristic
40#836—102no—
41C2×Dic10—21no—
42C2×Dic10#6712yes—
43#704—122no—
44C2×C5×C8—21no—
45C42×C5C2×Dic311yescharacteristic
46C4⋊Dic5—41no—
47C4⋊Dic5—41no—
48Dic20—44no—
49#494—51no—
50#356—152no—
51C22×C3×C5#9911yescharacteristic
52C3×C4×C5—22no—
53C3×C4×C5—21no—
54C3×Dic5—42no—
55C3×Dic5—81no—
56C2×C3×Q8—52no—
57C2×C3×Q8—101no—
58C3×Q16—204no—
59C2×C3×C8—21no—
60C3×C4⋊C4—201no—
61C3×C4⋊C4—201no—
62C3×C42C2×AGL(1,𝔽5)11yescharacteristic
63#208—202no—
64C2×C4×C5—21no—
65C2×C4×C5#21711yescharacteristic
66C2×Dic5—22no—
67C2×Dic5—41no—
68Dic10—42no—
69Dic10—42no—
70#170—242no—
71C5×C8—22no—
72C2×Q16—102no—
73C4⋊Q8—51no—
74C4⋊Q8—51no—
75#101—302no—
76C4×C8ΓL(1,𝔽16)11yescharacteristic
77C2×C3×C5—21no—
78C2×C3×C5#35311yescharacteristic
79C3×Q8—202no—
80C3×Q8—202no—
81C2×C3×C4—21no—
82C2×C3×C4—102no—
83C2×C3×C4—201no—
84C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
85C3×C8—22no—
86C3⋊C8—402no—
87C22×C5#83411yescharacteristic
88C4×C5—22no—
89C4×C5—21no—
90Dic5—42no—
91Dic5—81no—
92C2×Q8—52no—
93C2×Q8—101no—
94Q16—204no—
95M16—602no—
96C2×C8—21no—
97C4⋊C4—201no—
98C4⋊C4—201no—
99C42C2×ΓL(1,𝔽16)11yescharacteristic
100C3×C5#141111yescharacteristic, complemented, Hall
101C22×C3#399911yescharacteristic
102C3×C4—22no—
103C3×C4—21no—
104C3×C4—202no—
105C3×C4—401no—
106C2×C5—21no—
107C2×C5#454511yescharacteristic
108Q8—202no—
109Q8—202no—
110C2×C4—21no—
111C2×C4—102no—
112C2×C4—201no—
113C2×C4#676311yescharacteristic
114C8—22no—
115C8—1202no—
116C2×C3—21no—
117C2×C3#6485311yescharacteristic
118C5#6779511yescharacteristic, complemented, Sylow
119C22#9122811yescharacteristic
120C4—22no—
121C4—21no—
122C4—202no—
123C4—401no—
124C3#1059852111yescharacteristic, complemented, Sylow
125C2—21no—
126C2#1174672411yescharacteristic
subgroupG/H
centerC2#11746724
commutatorC3×C42×C5C2×C4
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC2×C3×C5#353
prime radicalC22×C3×C5#99
cosocleC3×#4015C22
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5#1411
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
100. C3×C5#1411semidirect
118. C5#67795semidirect
124. C3#10598521semidirect

Maximal subgroups

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

subgroupindex
C3×#649882
#117467262
#105985213
#677955