Finite Group Databasebeta

← #10600187⋊C3 #14511554

Subgroups — #10600187⋊C3 #14511554

Order 1920.

140 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 27 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
1C4×C5×C42⋊C3C211yesmaximal, characteristic
2#10600187C311yesmaximal, characteristic, complemented, Hall
3C2×C5×C42⋊C3C411yescharacteristic
4A4×#168—41nomaximal
5#1842⋊C3—51nomaximal, Hall
6C43×C5C2×C311yescharacteristic
7C2×C4⋊#168—31no—
8C2×C4⋊#168—31no—
9C4×C5×A4—41no—
10C5×C42⋊C3C811yescharacteristic, complemented
11C4×C42⋊C3D511yescharacteristic
12C2×C42×C5—31no—
13C2×C42×C5—31no—
14C2×C42×C5C3×C411yescharacteristic
15C22×#168—31no—
16C22×#168A411yescharacteristic
17C4⋊#168—62no—
18C4⋊#168—62no—
19#1842—51noSylow
20C2×C5×A4—41no—
21C3×#168—161no—
22C8×A4—201no—
23C2×C42⋊C3Dic511yescharacteristic
24C22×C4×C5—31no—
25C22×C4×C5—31no—
26C22×C4×C5C2×A411yescharacteristic
27C42×C5—31no—
28C42×C5—32no—
29C42×C5—32no—
30C42×C5—62no—
31C42×C5C3×C811yescharacteristic, complemented
32C2×#168—61no—
33C2×#168—61no—
34C2×#168—62no—
35C2×C4⋊C8—151no—
36C2×C4⋊C8—151no—
37C43C3×D511yescharacteristic
38C5×A4—41no—
39C3×C4×C5—161no—
40C4×A4—41no—
41C42⋊C3#16811yescharacteristic, complemented
42C23×C5C4×A411yescharacteristic
43C2×C4×C5—32no—
44C2×C4×C5—32no—
45C2×C4×C5—31no—
46C2×C4×C5—31no—
47C2×C4×C5—31no—
48C2×C4×C5—31no—
49C2×C4×C5—32no—
50C2×C4×C5—62no—
51#168—41no—
52#168—121no—
53C22×C8—51no—
54C22×C8—151no—
55C2×C42—31no—
56C2×C42—31no—
57C2×C42C3×Dic511yescharacteristic
58C4⋊C8—302no—
59C4⋊C8—302no—
60C2×C3×C5—161no—
61C2×A4—41no—
62C3×C8—801no—
63C22×C5—31no—
64C22×C5—31no—
65C22×C5C8×A411yescharacteristic
66C4×C5—32no—
67C4×C5—32no—
68C4×C5—31no—
69C4×C5—62no—
70C4×C5#127⋊C311yescharacteristic
71C22×C4—31no—
72C22×C4—31no—
73C22×C4D5×A411yescharacteristic
74C2×C8—301no—
75C2×C8—301no—
76C2×C8—302no—
77C42—31no—
78C42—32no—
79C42—32no—
80C42—62no—
81C42C3×#16811yescharacteristic, complemented
82C3×C5—161noHall
83A4—41no—
84C3×C4—161no—
85C2×C5—31no—
86C2×C5—31no—
87C2×C5#384⋊C311yescharacteristic
88C23A4×Dic511yescharacteristic
89C2×C4—32no—
90C2×C4—32no—
91C2×C4—31no—
92C2×C4—31no—
93C2×C4—31no—
94C2×C4—31no—
95C2×C4—32no—
96C2×C4—62no—
97C8—201no—
98C8—601no—
99C2×C3—161no—
100C5#1842⋊C311yescharacteristic, complemented, Sylow
101C22—31no—
102C22—31no—
103C22A4×#16811yescharacteristic
104C4—32no—
105C4—32no—
106C4—31no—
107C4—62no—
108C4C5⋊(#127⋊C3)11yescharacteristic
109C3—161noSylow
110C2—31no—
111C2—31no—
112C2#65224⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4C5⋊(#127⋊C3)
commutator, hypocenterC42×C5C3×C8
FrattiniC22×C4D5×A4
Fitting, cosocleC43×C5C2×C3
socleC23×C5C4×A4
prime radicalC2×C5×C42⋊C3C4
LCSG ▷ C42×C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #10600187C3semidirect
10. C5×C42⋊C3C8semidirect
31. C42×C5C3×C8semidirect
41. C42⋊C3#168semidirect
81. C42C3×#168semidirect
100. C5#1842⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C42⋊C32
#106001873
A4×#1684
#1842⋊C35