Finite Group Databasebeta

← #10603773⋊C3 #14511591

Subgroups — #10603773⋊C3 #14511591

Order 1920.

146 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 20 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#10603773C311yesmaximal, characteristic, complemented, Hall
3A4×#170—41nomaximal
4C5×#95⋊C3C411yescharacteristic
5#1726⋊C3—51nomaximal, Hall
6C2×#4002—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#4002—34no—
15C4×#170—32no—
16C4×#170—32no—
17C5×#95C3×C411yescharacteristic
18#3963—31no—
19#1726—51noSylow
20C2×C5×A4—41no—
21C3×#170—161no—
22C8×A4—201no—
23#95⋊C3AGL(1,𝔽5)11yescharacteristic
24C22×C4×C5—31no—
25C22×Dic5—31no—
26C22×Dic5C2×A411yescharacteristic
27C2×#170—32no—
28C2×#170—34no—
29C2×#170—31no—
30C2×#170—31no—
31C4×Dic5—32no—
32C4×Dic5—32no—
33C2×#97—151no—
34C2×C4×C8—151no—
35#376—51no—
36C5×A4—41no—
37C3×Dic5—161no—
38C4×A4—201no—
39C23×C5C4×A411yescharacteristic
40C2×C4×C5—32no—
41C2×C4×C5—62no—
42C2×Dic5—31no—
43C2×Dic5—31no—
44C2×Dic5—32no—
45C2×Dic5—61no—
46C2×Dic5—61no—
47#170—34no—
48#170—31no—
49#170C42⋊C311yescharacteristic
50C22×C8—51no—
51C22×C8—151no—
52C2×C42—151no—
53#97—154no—
54C4×C8—152no—
55C4×C8—152no—
56#95—151no—
57#95C3×AGL(1,𝔽5)11yescharacteristic
58C2×C3×C5—161no—
59C2×A4—41no—
60C3×C8—801no—
61C22×C5—31no—
62C22×C5—31no—
63C22×C5#131⋊C311yescharacteristic
64C4×C5—62no—
65Dic5—31no—
66Dic5—62no—
67Dic5C2×C42⋊C311yescharacteristic
68C22×C4—31no—
69C22×C4—51no—
70C22×C4—151no—
71C2×C8—151no—
72C2×C8—152no—
73C2×C8—154no—
74C2×C8—151no—
75C42—152no—
76C42—152no—
77C3×C5—161noHall
78A4—41no—
79C3×C4—801no—
80C2×C5—31no—
81C2×C5—31no—
82C2×C5C4×C42⋊C311yescharacteristic
83C23A4×AGL(1,𝔽5)11yescharacteristic
84C2×C4—32no—
85C2×C4—62no—
86C2×C4—151no—
87C2×C4—151no—
88C2×C4—152no—
89C2×C4—301no—
90C2×C4—301no—
91C8—51no—
92C8—151no—
93C8—154no—
94C2×C3—161no—
95C5#1726⋊C311yescharacteristic, complemented, Sylow
96C22—31no—
97C22—31no—
98C22#4133⋊C311yescharacteristic
99C4—51no—
100C4—62no—
101C4—151no—
102C4—302no—
103C3—161noSylow
104C2—31no—
105C2—31no—
106C2AGL(1,𝔽5)×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×C42⋊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. #10603773C3semidirect
95. C5#1726⋊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
#106037733
A4×#1704
#1726⋊C35