Finite Group Databasebeta

← #14279471

Subgroups — #14279471

Order 1920.

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

normal subgroups only

This group has 208 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#11746726C212yesmaximal, complemented
3#10598520—31nomaximal, Hall
4C2×C3×#677—22no—
5C3×#4020C411yescharacteristic
6C3×#4015C2211yescharacteristic
7#91234—22no—
8C3×C4×C5×C8C411yescharacteristic
9#67789—51nomaximal, Hall
10#64982D311yescharacteristic
11#64855—32no—
12C2×C3×D20—21no—
13C2×C3×D20—41no—
14C2×C3×Dic10D412yes—
15#6762—42no—
16C2×C3×C5×C8—21no—
17C3×C42×C5C2×C411yescharacteristic
18C3×C4⋊Dic5—41no—
19C3×#677—44no—
20C3×#492—51no—
21#4548—52no—
22C2×#677—22no—
23#4020Dic311yescharacteristic
24#4015C2×D311yescharacteristic
25#4005—62no—
26C4×C5×C8Dic311yescharacteristic
27#1410—151noSylow
28C22×C3×D5—41no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C22⋊C411yescharacteristic
31C2×C3×Dic5—22no—
32C3×D20—42no—
33C3×D20—82no—
34C3×Dic10—42no—
35C3⋊#170—82no—
36C3×C5×C8—22no—
37C2×C3×SD16—102no—
38C3×C4⋊Q8—51no—
39C3×#127—51no—
40C3×C4×C8AGL(1,𝔽5)11yescharacteristic
41#836—102no—
42C2×D20—21no—
43C2×D20—41no—
44C2×Dic10#6712yes—
45#704—122no—
46C2×C5×C8—21no—
47C42×C5C2×Dic311yescharacteristic
48C4⋊Dic5—41no—
49#677—44no—
50#492—51no—
51#356—152no—
52C22×C3×C5#9911yescharacteristic
53C2×C3×D5—82no—
54C2×C3×D5—81no—
55C3×C4×C5—22no—
56C3×C4×C5—21no—
57C3×Dic5—42no—
58C2×C3×Q8—52no—
59C2×C3×D4—101no—
60C2×C3×D4—201no—
61C3×SD16—204no—
62C2×C3×C8—21no—
63C3×C4⋊C4—201no—
64C3×C42C2×AGL(1,𝔽5)11yescharacteristic
65#208—202no—
66C22×D5—41no—
67C2×C4×C5—21no—
68C2×C4×C5#21711yescharacteristic
69C2×Dic5—22no—
70D20—42no—
71D20—82no—
72Dic10—42no—
73#170—242no—
74C5×C8—22no—
75C2×SD16—102no—
76C4⋊Q8—51no—
77#127—51no—
78#101—302no—
79C4×C8ΓL(1,𝔽16)11yescharacteristic
80C2×C3×C5—21no—
81C2×C3×C5#35311yescharacteristic
82C3×D5—161no—
83C23×C3—201no—
84C3×Q8—202no—
85C3×D4—202no—
86C3×D4—402no—
87C2×C3×C4—21no—
88C2×C3×C4—102no—
89C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
90C3×C8—22no—
91C3⋊C8—402no—
92C22×C5#83411yescharacteristic
93C2×D5—82no—
94C2×D5—81no—
95C4×C5—22no—
96C4×C5—21no—
97Dic5—42no—
98C2×Q8—52no—
99C2×D4—101no—
100C2×D4—201no—
101SD16—204no—
102M16—602no—
103C2×C8—21no—
104C4⋊C4—201no—
105C42C2×ΓL(1,𝔽16)11yescharacteristic
106C3×C5#141011yescharacteristic, complemented, Hall
107C22×C3—402no—
108C22×C3—401no—
109C22×C3#399911yescharacteristic
110C3×C4—22no—
111C3×C4—21no—
112C3×C4—202no—
113C2×C5—21no—
114C2×C5#454511yescharacteristic
115D5—161no—
116C23—201no—
117Q8—202no—
118D4—202no—
119D4—402no—
120C2×C4—21no—
121C2×C4—102no—
122C2×C4#676311yescharacteristic
123C8—22no—
124C8—1202no—
125C2×C3—21no—
126C2×C3—801no—
127C2×C3#6485311yescharacteristic
128C5#6778911yescharacteristic, complemented, Sylow
129C22—402no—
130C22—401no—
131C22#9122811yescharacteristic
132C4—22no—
133C4—21no—
134C4—202no—
135C3#1059852011yescharacteristic, complemented, Sylow
136C2—21no—
137C2—801no—
138C2#1174672411yescharacteristic
subgroupG/H
centerC2#11746724
commutatorC3×C42×C5C2×C4
FrattiniC42C2×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC2×C3×C5#353
prime radicalC3×#4020C4
cosocleC3×#4015C22
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5#1410
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
2. #11746726C2semidirect
106. C3×C5#1410semidirect
128. C5#67789semidirect
135. C3#10598520semidirect

Maximal subgroups

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

subgroupindex
C3×#649822
#117467262
#105985203
#677895