Finite Group Databasebeta

← C5×#1843⋊C3 #14510690

Subgroups — C5×#1843⋊C3 #14510690

Order 1920.

122 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 26 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⋊C3C211yesmaximal, characteristic
2C5×#1843C311yesmaximal, characteristic, complemented, Hall
3C5×C8×A4—41nomaximal
4C5×#95⋊C3C411yescharacteristic
5#1843⋊C3C511yesmaximal, characteristic, direct product factor, Hall
6C2×C5×C4⋊C8—31no—
7C2×C5×C4⋊C8—31no—
8C5×#376C2×C311yescharacteristic
9C4×C5×A4—41no—
10#376⋊C3C2×C511yescharacteristic
11C22×C5×C8—31no—
12C22×C5×C8A411yescharacteristic
13C2×C42×C5—31no—
14C5×C4⋊C8—62no—
15C5×C4⋊C8—62no—
16C5×#95—31no—
17C5×#95C3×C411yescharacteristic
18#1843C3×C511yescharacteristic, complemented, Sylow
19C2×C5×A4—41no—
20C3×C5×C8—161no—
21C8×A4—41no—
22#95⋊C3C4×C511yescharacteristic
23C22×C4×C5—31no—
24C22×C4×C5—31no—
25C22×C4×C5C2×A411yescharacteristic
26C2×C5×C8—61no—
27C2×C5×C8—61no—
28C2×C5×C8—62no—
29C42×C5—32no—
30C42×C5—32no—
31C2×C4⋊C8—31no—
32C2×C4⋊C8—31no—
33#376C2×C3×C511yescharacteristic
34C5×A4—41no—
35C3×C4×C5—161no—
36C4×A4—41no—
37C23×C5C4×A411yescharacteristic
38C2×C4×C5—31no—
39C2×C4×C5—31no—
40C2×C4×C5—32no—
41C2×C4×C5—32no—
42C2×C4×C5—61no—
43C2×C4×C5—62no—
44C2×C4×C5—61no—
45C5×C8—41no—
46C5×C8—121no—
47C22×C8—31no—
48C22×C8C5×A411yescharacteristic
49C2×C42—31no—
50C4⋊C8—62no—
51C4⋊C8—62no—
52#95—31no—
53#95C3×C4×C511yescharacteristic
54C2×C3×C5—161no—
55C2×A4—41no—
56C3×C8—161no—
57C22×C5—31no—
58C22×C5—31no—
59C22×C5#131⋊C311yescharacteristic
60C4×C5—31no—
61C4×C5—62no—
62C4×C5—62no—
63C4×C5#127⋊C311yescharacteristic
64C22×C4—31no—
65C22×C4—31no—
66C22×C4C2×C5×A411yescharacteristic
67C2×C8—61no—
68C2×C8—61no—
69C2×C8—62no—
70C42—32no—
71C42—32no—
72C3×C5—161noHall
73A4—41no—
74C3×C4—161no—
75C2×C5—31no—
76C2×C5—31no—
77C2×C5#384⋊C311yescharacteristic
78C23C4×C5×A411yescharacteristic
79C2×C4—31no—
80C2×C4—31no—
81C2×C4—32no—
82C2×C4—32no—
83C2×C4—62no—
84C2×C4—61no—
85C2×C4—61no—
86C8—41no—
87C8—121no—
88C2×C3—161no—
89C5#1843⋊C311yescharacteristic, direct product factor, Sylow
90C22—31no—
91C22—31no—
92C22C5×#131⋊C311yescharacteristic
93C4—31no—
94C4—62no—
95C4—62no—
96C4C5×#127⋊C311yescharacteristic
97C3—161noSylow
98C2—31no—
99C2—31no—
100C2C5×#384⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4×C5#127⋊C3
commutator, hypocenter#95C3×C4×C5
FrattiniC22×C4C2×C5×A4
FittingC5×#1843C3
socleC23×C5C4×A4
prime radicalC5×#95⋊C3C4
cosocle#376C2×C3×C5
LCSG ▷ #95
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
2. C5×#1843C3semidirect
5. #1843⋊C3C5direct (N × H)
18. #1843C3×C5semidirect
89. C5#1843⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#376⋊C32
C5×#18433
C5×C8×A44
#1843⋊C35