Finite Group Databasebeta

← #14511589

Subgroups — #14511589

Order 1920.

144 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 18 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
1C5⋊(#393⋊C3)C211yesmaximal, characteristic
2#10598829—31nomaximal, Hall
3C2×A4⋊AGL(1,𝔽5)—41nomaximal
4C5×C22⋊SL(2,𝔽3)C411yescharacteristic, complemented
5#68001—51nomaximal, Hall
6#65520D311yescharacteristic
7#64917—31no—
8#64915—31no—
9C2×D5×A4—41no—
10A4⋊AGL(1,𝔽5)—42no—
11#393⋊C3—51no—
12C22×C5×Q8Dic311yescharacteristic, complemented
13C2×C22⋊AGL(1,𝔽5)—61no—
14C2×#685—31no—
15C22⋊#170—61no—
16#3963—31no—
17#1351—151noSylow
18C2×C5×A4—41no—
19C2×ΓL(1,𝔽16)—161no—
20D5×A4—41no—
21D5×A4—41no—
22C5×SL(2,𝔽3)—161no—
23C22⋊SL(2,𝔽3)AGL(1,𝔽5)11yescharacteristic, complemented
24C2×SL(2,ℤ/4)—201no—
25C23×D5S411yescharacteristic
26C22×AGL(1,𝔽5)—121no—
27C2×C5×Q8—121no—
28C22×C4×C5—31no—
29C22×Dic5—31no—
30C22⋊AGL(1,𝔽5)—62no—
31C22⋊AGL(1,𝔽5)—121no—
32C2×#170—121no—
33#685—121no—
34#393—51no—
35#342—151no—
36#323—151no—
37C2×C3×D5—161no—
38C5×A4—41no—
39ΓL(1,𝔽16)—162no—
40C22×A4—201no—
41SL(2,ℤ/4)—202no—
42C23×C5SL(2,ℤ/4)11yescharacteristic
43C22×D5—61no—
44C22×D5—61no—
45C22×D5#22611yescharacteristic
46C22×D5GL(2,𝔽3)11yescharacteristic
47C2×AGL(1,𝔽5)—122no—
48C2×AGL(1,𝔽5)—241no—
49C2×AGL(1,𝔽5)—241no—
50C5×Q8—41no—
51C5×Q8—121no—
52C2×C4×C5—61no—
53C2×C4×C5—121no—
54C2×Dic5—61no—
55C2×Dic5—121no—
56#170—241no—
57C22×Q8ΓL(1,𝔽16)11yescharacteristic, complemented
58C2×C22⋊C4—151no—
59C2×C22⋊C4—301no—
60C22⋊C8—301no—
61#95—151no—
62C2×C3×C5—161no—
63C3×D5—161no—
64C3×D5—161no—
65C2×A4—41no—
66C2×A4—201no—
67C2×A4—201no—
68C2×Dic3—801no—
69SL(2,𝔽3)—161no—
70C22×C5—31no—
71C22×C5—31no—
72C22×C5#85911yescharacteristic
73C2×D5—41no—
74C2×D5—61no—
75C2×D5—61no—
76C2×D5—121no—
77AGL(1,𝔽5)—242no—
78C4×C5—121no—
79Dic5—121no—
80C24—51no—
81C2×Q8—121no—
82C22×C4—31no—
83C22×C4—151no—
84C22×C4—601no—
85C2×C8—601no—
86C22⋊C4—302no—
87C22⋊C4—601no—
88C22⋊C4—601no—
89C3×C5—161noHall
90C22×C3—801no—
91A4—41no—
92Dic3—802no—
93C2×C5—31no—
94C2×C5—31no—
95C2×C5#462511yescharacteristic
96D5—41no—
97D5—41no—
98C23—51no—
99C23—51no—
100C23—301no—
101C23—301no—
102C23A4⋊AGL(1,𝔽5)11yescharacteristic
103Q8—41no—
104Q8—121no—
105C2×C4—61no—
106C2×C4—121no—
107C2×C4—301no—
108C2×C4—601no—
109C2×C4—602no—
110C2×C4—1201no—
111C2×C4—1201no—
112C8—1201no—
113C2×C3—161no—
114C2×C3—801no—
115C2×C3—801no—
116C5#6800111yescharacteristic, complemented, Sylow
117C22—31no—
118C22—31no—
119C22—201no—
120C22—301no—
121C22—301no—
122C22—601no—
123C22#9188611yescharacteristic
124C4—121no—
125C4—601no—
126C4—1202no—
127C3—161noSylow
128C2—31no—
129C2—31no—
130C2—201no—
131C2—201no—
132C2#1175155911yescharacteristic
subgroupG/H
center, hypercenterC2#11751559
commutator, hypocenterC5×C22⋊SL(2,𝔽3)C4
FrattiniC23A4⋊AGL(1,𝔽5)
FittingC22×C5×Q8Dic3
socleC23×C5SL(2,ℤ/4)
prime radical, cosocleC5⋊(#393⋊C3)C2
LCSG ▷ C5×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
4. C5×C22⋊SL(2,𝔽3)C4semidirect
12. C22×C5×Q8Dic3semidirect
23. C22⋊SL(2,𝔽3)AGL(1,𝔽5)semidirect
57. C22×Q8ΓL(1,𝔽16)semidirect
116. C5#68001semidirect

Maximal subgroups

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

subgroupindex
C5⋊(#393⋊C3)2
#105988293
C2×A4⋊AGL(1,𝔽5)4
#680015