Finite Group Databasebeta

← #10603784⋊C3 #14511592

Subgroups — #10603784⋊C3 #14511592

Order 1920.

122 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 19 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⋊(#376⋊C3)C211yesmaximal, characteristic
2#10603784C311yesmaximal, characteristic, complemented, Hall
3A4×#170—41nomaximal
4C5×#95⋊C3C411yescharacteristic
5#1843⋊C3—51nomaximal, Hall
6C2×#4004—31no—
7C2×C4⋊#170—31no—
8#64937C2×C311yescharacteristic
9A4×Dic5—41no—
10#376⋊C3—51no—
11C22×#170—31no—
12C22×#170A411yescharacteristic
13C2×C4×Dic5—31no—
14#4004—62no—
15C4⋊#170—62no—
16C5×#95C3×C411yescharacteristic
17#3963—31no—
18#1843—51noSylow
19C2×C5×A4—41no—
20C3×#170—161no—
21C8×A4—201no—
22#95⋊C3AGL(1,𝔽5)11yescharacteristic
23C22×C4×C5—31no—
24C22×Dic5—31no—
25C22×Dic5C2×A411yescharacteristic
26C2×#170—61no—
27C2×#170—62no—
28C2×#170—61no—
29C4×Dic5—32no—
30C4×Dic5—32no—
31C2×C4⋊C8—151no—
32C2×C4⋊C8—151no—
33#376—51no—
34C5×A4—41no—
35C3×Dic5—161no—
36C4×A4—201no—
37C23×C5C4×A411yescharacteristic
38C2×C4×C5—32no—
39C2×C4×C5—62no—
40C2×Dic5—31no—
41C2×Dic5—31no—
42C2×Dic5—32no—
43C2×Dic5—61no—
44C2×Dic5—61no—
45#170—41no—
46#170—121no—
47C22×C8—51no—
48C22×C8—151no—
49C2×C42—151no—
50C4⋊C8—302no—
51C4⋊C8—302no—
52#95—151no—
53#95C3×AGL(1,𝔽5)11yescharacteristic
54C2×C3×C5—161no—
55C2×A4—41no—
56C3×C8—801no—
57C22×C5—31no—
58C22×C5—31no—
59C22×C5#131⋊C311yescharacteristic
60C4×C5—62no—
61Dic5—31no—
62Dic5—62no—
63Dic5#127⋊C311yescharacteristic
64C22×C4—31no—
65C22×C4—51no—
66C22×C4—151no—
67C2×C8—301no—
68C2×C8—302no—
69C2×C8—301no—
70C42—152no—
71C42—152no—
72C3×C5—161noHall
73A4—41no—
74C3×C4—801no—
75C2×C5—31no—
76C2×C5—31no—
77C2×C5#384⋊C311yescharacteristic
78C23A4×AGL(1,𝔽5)11yescharacteristic
79C2×C4—32no—
80C2×C4—62no—
81C2×C4—151no—
82C2×C4—151no—
83C2×C4—152no—
84C2×C4—301no—
85C2×C4—301no—
86C8—201no—
87C8—601no—
88C2×C3—161no—
89C5#1843⋊C311yescharacteristic, complemented, Sylow
90C22—31no—
91C22—31no—
92C22#4133⋊C311yescharacteristic
93C4—51no—
94C4—62no—
95C4—151no—
96C4—302no—
97C3—161noSylow
98C2—31no—
99C2—31no—
100C2#65688⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2#65688⋊C3
commutator, Fitting, hypocenterC5×#95C3×C4
FrattiniC23A4×AGL(1,𝔽5)
socleC23×C5C4×A4
prime radicalC5×#95⋊C3C4
cosocle#64937C2×C3
LCSG ▷ C5×#95
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #10603784C3semidirect
89. C5#1843⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5⋊(#376⋊C3)2
#106037843
A4×#1704
#1843⋊C35