Finite Group Databasebeta

← C5×#2091⋊C3 #14510698

Subgroups — C5×#2091⋊C3 #14510698

Order 1920.

134 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 24 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×#338⋊C3C211yesmaximal, characteristic, complemented
2C5×#2091C311yesmaximal, characteristic, complemented, Hall
3C2×C4×C5×A4—41nomaximal
4#2091⋊C3C511yesmaximal, characteristic, direct product factor, Hall
5C5×#430—31no—
6C5×#407—31no—
7C5×#338C2×C311yescharacteristic, complemented
8C22×C5×A4—41no—
9C4×C5×A4—41no—
10C4×C5×A4—41no—
11#338⋊C3C2×C511yescharacteristic, complemented
12C23×C4×C5A411yescharacteristic
13C2×C5×M16—31no—
14C2×C5×M16—31no—
15C5×#108—62no—
16C5×C22⋊C8—62no—
17#2091C3×C511yescharacteristic, complemented, Sylow
18C2×C5×A4—42no—
19C2×C5×A4—41no—
20C2×C3×C4×C5—161no—
21C2×C4×A4—41no—
22C24×C5SL(2,𝔽3)11yescharacteristic
23C22×C4×C5—61no—
24C22×C4×C5—61no—
25C22×C4×C5SL(2,𝔽3)11yescharacteristic
26C22×C4×C5C2×A411yescharacteristic
27C5×M16—62no—
28C5×M16—62no—
29C2×C5×C8—32no—
30C2×C5×C8—61no—
31#430—31no—
32#407—31no—
33#338C2×C3×C511yescharacteristic, complemented
34C22×C3×C5—161no—
35C5×A4—41no—
36C3×C4×C5—161no—
37C3×C4×C5—161no—
38C22×A4—41no—
39C4×A4—41no—
40C4×A4—41no—
41C23×C5—42no—
42C23×C5—61no—
43C23×C5C2×SL(2,𝔽3)11yescharacteristic
44C2×C4×C5—31no—
45C2×C4×C5—31no—
46C2×C4×C5—41no—
47C2×C4×C5—61no—
48C2×C4×C5—121no—
49C5×C8—62no—
50C5×C8—121no—
51C23×C4C5×A411yescharacteristic
52C2×M16—31no—
53C2×M16—31no—
54#108—62no—
55C22⋊C8—62no—
56C2×C3×C5—162no—
57C2×C3×C5—161no—
58C2×A4—42no—
59C2×A4—41no—
60C2×C3×C4—161no—
61C22×C5—31no—
62C22×C5—41no—
63C22×C5—41no—
64C22×C5—62no—
65C22×C5—121no—
66C4×C5—31no—
67C4×C5—41no—
68C4×C5#127⋊C311yescharacteristic
69C24C5×SL(2,𝔽3)11yescharacteristic
70C22×C4—61no—
71C22×C4—61no—
72C22×C4C5×SL(2,𝔽3)11yescharacteristic
73C22×C4C2×C5×A411yescharacteristic
74M16—62no—
75M16—62no—
76C2×C8—32no—
77C2×C8—61no—
78C3×C5—161noHall
79C22×C3—161no—
80A4—41no—
81C3×C4—161no—
82C3×C4—161no—
83C2×C5—42no—
84C2×C5—61no—
85C2×C5#399⋊C311yescharacteristic
86C23—42no—
87C23—61no—
88C23C2×C5×SL(2,𝔽3)11yescharacteristic
89C2×C4—31no—
90C2×C4—31no—
91C2×C4—41no—
92C2×C4—61no—
93C2×C4—121no—
94C8—62no—
95C8—121no—
96C2×C3—162no—
97C2×C3—161no—
98C5#2091⋊C311yescharacteristic, direct product factor, Sylow
99C22—31no—
100C22—41no—
101C22—41no—
102C22—62no—
103C22—121no—
104C4—31no—
105C4—41no—
106C4C5×#127⋊C311yescharacteristic
107C3—161noSylow
108C2—42no—
109C2—61no—
110C2C5×#399⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4×C5#127⋊C3
commutator, cosocle, hypocenter#338C2×C3×C5
FrattiniC22×C4C2×C5×A4
FittingC5×#2091C3
socleC2×C5#399⋊C3
LCSG ▷ #338
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
1. C5×#338⋊C3C2semidirect
2. C5×#2091C3semidirect
4. #2091⋊C3C5direct (N × H)
7. C5×#338C2×C3semidirect
11. #338⋊C3C2×C5semidirect
17. #2091C3×C5semidirect
33. #338C2×C3×C5semidirect
98. C5#2091⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#338⋊C32
C5×#20913
C2×C4×C5×A44
#2091⋊C35