Finite Group Databasebeta

← #14278363

Subgroups — #14278363

Order 1920.

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 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
1#11746915C211yesmaximal, characteristic
2#11746731C211yesmaximal, characteristic, complemented
3C3×#64860C211yesmaximal, characteristic, complemented
4#10598734—31nomaximal, Hall
5#91763C411yescharacteristic
6C5×#870C411yescharacteristic
7#91227—21no—
8C3×#3998—21no—
9C3×#3935C2211yescharacteristic
10#90969—21no—
11#90969—21no—
12#67520—51nomaximal, Hall
13#65356—31no—
14#64860—31no—
15#64860D311yescharacteristic, complemented
16C2×D60—21no—
17C2×D60—41no—
18C3×C42×C5C2×C411yescharacteristic
19C5×C4⋊Dic3—21no—
20C5×Dic3⋊C4—41no—
21C2×C3×#168D411yescharacteristic
22C2×C3×#168D411yescharacteristic
23C3⋊#674—22no—
24C3×#674—22no—
25#4713—51no—
26C3×#347—51no—
27#4466—51no—
28C5×#125—31no—
29#4020—31no—
30#3998—21no—
31#3998—61no—
32#3941—61no—
33#3941—61no—
34#3935C2×D311yescharacteristic
35#1355—151noSylow
36C22×D15—41no—
37C2×C3×C4×C5—21no—
38C2×C3×C4×C5C22⋊C411yescharacteristic
39D60—41no—
40D60—41no—
41D60—82no—
42C2×C5×Dic3—41no—
43C3×#168—21no—
44C3×#168—21no—
45#874—51no—
46#870AGL(1,𝔽5)11yescharacteristic
47C3×M32—101no—
48C3×#97—51no—
49#821—101no—
50#821—101no—
51#812—101no—
52C2×D20—61no—
53C2×D20—121no—
54C5×C4⋊C4—61no—
55C5×C4⋊C4—121no—
56C42×C5C4×D311yescharacteristic
57C2×#168D1211yescharacteristic
58C2×#168#6711yescharacteristic
59#674—22no—
60#674—62no—
61#490—151no—
62#347—51no—
63#347—151no—
64C22×C3×C5#10011yescharacteristic
65C2×D15—82no—
66C2×D15—81no—
67C3×C4×C5—41no—
68C3×C4×C5#10411yescharacteristic
69C3×C4×C5#10411yescharacteristic
70C5×Dic3—81no—
71C2×D12—101no—
72C2×D12—201no—
73C2×C3×C8—51no—
74C2×C3×C8—51no—
75C3×C42C2×AGL(1,𝔽5)11yescharacteristic
76C4⋊Dic3—21no—
77Dic3⋊C4—41no—
78C3×C16—102no—
79C3⋊C16—102no—
80C22×D5—121no—
81C2×C4×C5—21no—
82C2×C4×C5—121no—
83C2×C4×C5(C2×D3)⋊C411yescharacteristic
84D20—121no—
85D20—121no—
86D20—242no—
87#168—21no—
88#168—21no—
89#127—151no—
90#125—31no—
91M32—101no—
92M32—301no—
93#102—301no—
94#102—301no—
95#97—51no—
96C2×C3×C5—21no—
97C2×C3×C5#32911yescharacteristic
98D15—161no—
99C22×D3—201no—
100C2×C3×C4—21no—
101C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
102C2×Dic3—41no—
103D12—201no—
104D12—201no—
105D12—402no—
106C3×C8—101no—
107C3×C8—101no—
108C22×C5#82311yescharacteristic
109C2×D5—242no—
110C2×D5—241no—
111C4×C5—41no—
112C4×C5—241no—
113C4×C5#80511yescharacteristic
114C4×C5#82511yescharacteristic
115C2×D4—301no—
116C2×D4—601no—
117C2×C8—51no—
118C2×C8—51no—
119C4⋊C4—61no—
120C4⋊C4—121no—
121C42D3×AGL(1,𝔽5)11yescharacteristic
122C16—102no—
123C16—302no—
124C3×C5#135511yescharacteristic, complemented, Hall
125C22×C3#401311yescharacteristic
126C2×D3—402no—
127C2×D3—401no—
128C3×C4—41no—
129C3×C4#401011yescharacteristic
130C3×C4#401011yescharacteristic
131Dic3—81no—
132C2×C5—21no—
133C2×C5#446411yescharacteristic
134D5—481no—
135C23—601no—
136D4—601no—
137D4—601no—
138D4—1202no—
139C2×C4—21no—
140C2×C4—121no—
141C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
142C8—101no—
143C8—101no—
144C2×C3—21no—
145C2×C3#6492711yescharacteristic
146D3—801no—
147C5#6752011yescharacteristic, complemented, Sylow
148C22—1202no—
149C22—1201no—
150C22#9117411yescharacteristic
151C4—41no—
152C4—241no—
153C4#9115711yescharacteristic
154C4#9115811yescharacteristic
155C3#1059873411yescharacteristic, complemented, Sylow
156C2—21no—
157C2—2401no—
158C2#1174650511yescharacteristic
subgroupG/H
centerC2#11746505
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#329
prime radical#91763C4
cosocleC3×#3935C22
hypocenterC3×C5#1355
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11746731C2semidirect
3. C3×#64860C2semidirect
15. #64860D3semidirect
124. C3×C5#1355semidirect
147. C5#67520semidirect
155. C3#10598734semidirect

Maximal subgroups

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

subgroupindex
#117469152
#117467312
C3×#648602
#105987343
#675205