Finite Group Databasebeta

← #14279456

Subgroups — #14279456

Order 1920.

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

normal subgroups only

This group has 220 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×#64982C211yesmaximal, characteristic
2#11746724C212yesmaximal
3#10598517—31nomaximal, Hall
4C2×C3×#677—22no—
5C3×#4020C2211yescharacteristic
6C3×#4015C411yescharacteristic, complemented
7#91228—22no—
8C3×C4×C5×C8C411yescharacteristic, complemented
9#67788—51nomaximal, Hall
10#64982D311yescharacteristic
11#64853—32no—
12C2×C3×D20—41no—
13C2×C3×D20D412yes—
14C2×C3×Dic10—21no—
15#6763—42no—
16C2×C3×C5×C8—21no—
17C3×C42×C5C2×C411yescharacteristic
18C3×C4⋊Dic5—41no—
19C3×#677—44no—
20C3×#492—51no—
21#4545—52no—
22C2×#677—22no—
23#4020C2×D311yescharacteristic
24#4015Dic311yescharacteristic, complemented
25#3999—62no—
26C4×C5×C8Dic311yescharacteristic, complemented
27#1409—151noSylow
28C22×C3×D5—22no—
29C2×ΓL(1,𝔽16)—82no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C22⋊C411yescharacteristic
32C2×C3×Dic5—41no—
33C3×D20—42no—
34C3×D20—82no—
35C3×Dic10—42no—
36C3×C5×C8—22no—
37C2×C3×SD16—102no—
38C3×C4⋊Q8—51no—
39C3×#127—51no—
40C3×C4×C8AGL(1,𝔽5)11yescharacteristic, complemented
41#834—102no—
42C2×D20—41no—
43C2×D20#6712yes—
44C2×Dic10—21no—
45C22⋊AGL(1,𝔽5)—122no—
46C2×C5×C8—21no—
47C42×C5C2×Dic311yescharacteristic
48C4⋊Dic5—41no—
49#677—44no—
50#492—51no—
51#353—152no—
52C22×C3×C5#9911yescharacteristic
53C2×C3×D5—42no—
54C2×C3×D5—82no—
55ΓL(1,𝔽16)—162no—
56C3×C4×C5—22no—
57C3×C4×C5—21no—
58C3×Dic5—81no—
59C2×C3×Q8—101no—
60C2×C3×D4—52no—
61C2×C3×D4—201no—
62C3×SD16—204no—
63C2×C3×C8—21no—
64C3×C4⋊C4—201no—
65C3×C42C2×AGL(1,𝔽5)11yescharacteristic
66#217—202no—
67C22×D5—22no—
68C2×AGL(1,𝔽5)—242no—
69C2×C4×C5—21no—
70C2×C4×C5#21711yescharacteristic
71C2×Dic5—41no—
72D20—42no—
73D20—82no—
74Dic10—42no—
75C5×C8—22no—
76C2×SD16—102no—
77C4⋊Q8—51no—
78#127—51no—
79#99—302no—
80C4×C8ΓL(1,𝔽16)11yescharacteristic, complemented
81C2×C3×C5—21no—
82C2×C3×C5#35311yescharacteristic
83C3×D5—82no—
84C23×C3—102no—
85C3×Q8—202no—
86C3×D4—202no—
87C3×D4—402no—
88C2×C3×C4—21no—
89C2×C3×C4—201no—
90C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
91C2×Dic3—402no—
92C3×C8—22no—
93C22×C5#83411yescharacteristic
94C2×D5—42no—
95C2×D5—82no—
96AGL(1,𝔽5)—482no—
97C4×C5—22no—
98C4×C5—21no—
99Dic5—81no—
100C2×Q8—101no—
101C2×D4—52no—
102C2×D4—201no—
103SD16—204no—
104C2×C8—21no—
105C4⋊C4—201no—
106C22⋊C4—602no—
107C42C2×ΓL(1,𝔽16)11yescharacteristic
108C3×C5#140911yescharacteristic, complemented, Hall
109C22×C3—202no—
110C22×C3—402no—
111C22×C3#399911yescharacteristic
112C3×C4—22no—
113C3×C4—21no—
114C3×C4—401no—
115Dic3—802no—
116C2×C5—21no—
117C2×C5#454511yescharacteristic
118D5—82no—
119C23—102no—
120Q8—202no—
121D4—202no—
122D4—402no—
123C2×C4—21no—
124C2×C4—201no—
125C2×C4—1202no—
126C2×C4#676311yescharacteristic
127C8—22no—
128C2×C3—21no—
129C2×C3—402no—
130C2×C3#6485311yescharacteristic
131C5#6778811yescharacteristic, complemented, Sylow
132C22—202no—
133C22—402no—
134C22#9122811yescharacteristic
135C4—22no—
136C4—21no—
137C4—401no—
138C4—2402no—
139C3#1059851711yescharacteristic, complemented, Sylow
140C2—21no—
141C2—402no—
142C2#1174672411yescharacteristic
subgroupG/H
centerC2#11746724
commutatorC3×C42×C5C2×C4
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC2×C3×C5#353
prime radical, cosocleC3×#4020C22
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5#1409
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
6. C3×#4015C4semidirect
8. C3×C4×C5×C8C4semidirect
24. #4015Dic3semidirect
26. C4×C5×C8Dic3semidirect
40. C3×C4×C8AGL(1,𝔽5)semidirect
80. C4×C8ΓL(1,𝔽16)semidirect
108. C3×C5#1409semidirect
131. C5#67788semidirect
139. C3#10598517semidirect

Maximal subgroups

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

subgroupindex
C3×#649822
#117467242
#105985173
#677885