Finite Group Databasebeta

← #14279503

Subgroups — #14279503

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×#65002C211yesmaximal, characteristic
2#11746724C212yesmaximal
3#10598539—31nomaximal, Hall
4C3×#4020C2211yescharacteristic
5C3×#4016C411yescharacteristic, complemented
6#91228—22no—
7C3×C5×#97C411yescharacteristic, complemented
8C3×#3953—22no—
9#67784—51nomaximal, Hall
10#65002D311yescharacteristic
11#64853—32no—
12C2×C3×D20—41no—
13C2×C3×D20D412yes—
14#6763—42no—
15C2×C3×C5×C8—21no—
16C3×C42×C5C2×C411yescharacteristic
17C3×C4⋊Dic5—21no—
18C3×#683—41no—
19C3×#490—51no—
20#4545—52no—
21#4020C2×D311yescharacteristic
22#4016Dic311yescharacteristic, complemented
23#3999—62no—
24C5×#97Dic311yescharacteristic, complemented
25#3953—22no—
26#1412—151noSylow
27C22×C3×D5—22no—
28C2×ΓL(1,𝔽16)—82no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C22⋊C411yescharacteristic
31C2×C3×Dic5—41no—
32C3×D20—42no—
33C3×D20—82no—
34C3×C5×C8—41no—
35C3×#127—51no—
36C3×#125—51no—
37C3×#102—102no—
38C3×#97AGL(1,𝔽5)11yescharacteristic, complemented
39#834—102no—
40C2×D20—41no—
41C2×D20#6712yes—
42C22⋊AGL(1,𝔽5)—122no—
43C2×C5×C8—21no—
44C42×C5C2×Dic311yescharacteristic
45C4⋊Dic5—21no—
46#683—41no—
47#490—51no—
48#353—152no—
49C22×C3×C5#9911yescharacteristic
50C2×C3×D5—42no—
51C2×C3×D5—82no—
52ΓL(1,𝔽16)—162no—
53C3×C4×C5—21no—
54C3×C4×C5—41no—
55C3×Dic5—81no—
56C2×C3×D4—52no—
57C2×C3×D4—201no—
58C2×C3×C8—21no—
59C3×C4⋊C4—101no—
60C3×C4⋊C4—201no—
61C3×C42C2×AGL(1,𝔽5)11yescharacteristic
62#217—202no—
63C22×D5—22no—
64C2×AGL(1,𝔽5)—242no—
65C2×C4×C5—21no—
66C2×C4×C5#21711yescharacteristic
67C2×Dic5—41no—
68D20—42no—
69D20—82no—
70C5×C8—41no—
71#127—51no—
72#125—51no—
73#102—102no—
74#99—302no—
75#97ΓL(1,𝔽16)11yescharacteristic, complemented
76C2×C3×C5—21no—
77C2×C3×C5#35411yescharacteristic
78C3×D5—82no—
79C23×C3—102no—
80C3×D4—202no—
81C3×D4—402no—
82C2×C3×C4—21no—
83C2×C3×C4—201no—
84C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
85C2×Dic3—402no—
86C3×C8—41no—
87C22×C5#83411yescharacteristic
88C2×D5—42no—
89C2×D5—82no—
90AGL(1,𝔽5)—482no—
91C4×C5—21no—
92C4×C5—41no—
93Dic5—81no—
94C2×D4—52no—
95C2×D4—201no—
96C2×C8—21no—
97C4⋊C4—101no—
98C4⋊C4—201no—
99C22⋊C4—602no—
100C42C2×ΓL(1,𝔽16)11yescharacteristic
101C3×C5#141211yescharacteristic, complemented, Hall
102C22×C3—202no—
103C22×C3—402no—
104C22×C3#399911yescharacteristic
105C3×C4—21no—
106C3×C4—41no—
107C3×C4—401no—
108Dic3—802no—
109C2×C5—21no—
110C2×C5#454111yescharacteristic
111D5—82no—
112C23—102no—
113D4—202no—
114D4—402no—
115C2×C4—21no—
116C2×C4—201no—
117C2×C4—1202no—
118C2×C4#676311yescharacteristic
119C8—41no—
120C2×C3—21no—
121C2×C3—402no—
122C2×C3#6485411yescharacteristic
123C5#6778411yescharacteristic, complemented, Sylow
124C22—202no—
125C22—402no—
126C22#9122811yescharacteristic
127C4—21no—
128C4—41no—
129C4—401no—
130C4—2402no—
131C3#1059853911yescharacteristic, complemented, Sylow
132C2—21no—
133C2—402no—
134C2#1174672511yescharacteristic
subgroupG/H
centerC2#11746725
commutatorC3×C42×C5C2×C4
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C5×#97C4
socleC2×C3×C5#354
prime radical, cosocleC3×#4020C22
hypercenter#97ΓL(1,𝔽16)
hypocenterC3×C5#1412
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
5. C3×#4016C4semidirect
7. C3×C5×#97C4semidirect
22. #4016Dic3semidirect
24. C5×#97Dic3semidirect
38. C3×#97AGL(1,𝔽5)semidirect
75. #97ΓL(1,𝔽16)semidirect
101. C3×C5#1412semidirect
123. C5#67784semidirect
131. C3#10598539semidirect

Maximal subgroups

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

subgroupindex
C3×#650022
#117467242
#105985393
#677845