Finite Group Databasebeta

← C23×C5×C42⋊C3 #14511306

Subgroups — C23×C5×C42⋊C3 #14511306

Order 1920.

1160 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C22×C5×C42⋊C3C217yesmaximal, direct product factor
2C23×C42×C5C311yesmaximal, characteristic, complemented, Hall
3C23×C5×A4—41nomaximal
4C2×C5×C42⋊C3C2217yesdirect product factor
5C23×C42⋊C3C511yesmaximal, characteristic, direct product factor, Hall
6C24×C4×C5—31no—
7C22×C42×C5—37no—
8C22×C42×C5C2×C317yescomplemented
9C22×C5×A4—47no—
10C5×C42⋊C3C2311yescharacteristic, direct product factor
11C22×C42⋊C3C2×C517yesdirect product factor
12C25×C5A411yescharacteristic
13C23×C4×C5—314no—
14C23×C4×C5—32no—
15C23×C4×C5—37no—
16C23×C4×C5—37no—
17C2×C42×C5—321no—
18C2×C42×C5—314no—
19C2×C42×C5C22×C317yescomplemented
20C23×C42C3×C511yescharacteristic, complemented, Sylow
21C23×C3×C5—161no—
22C2×C5×A4—47no—
23C23×A4—41no—
24C2×C42⋊C3C22×C517yesdirect product factor
25C24×C5—37no—
26C24×C5—31no—
27C24×C5C2×A417yes—
28C22×C4×C5—342no—
29C22×C4×C5—342no—
30C22×C4×C5—314no—
31C22×C4×C5—314no—
32C22×C4×C5—37no—
33C22×C4×C5—321no—
34C42×C5—37no—
35C42×C5—314no—
36C42×C5C23×C311yescharacteristic, complemented
37C24×C4—31no—
38C22×C42—37no—
39C22×C42C2×C3×C517yescomplemented
40C22×C3×C5—167no—
41C5×A4—41no—
42C22×A4—47no—
43C42⋊C3C23×C511yescharacteristic, direct product factor
44C23×C5—321no—
45C23×C5—314no—
46C23×C5—37no—
47C23×C5—37no—
48C23×C5C42⋊C311yescharacteristic, direct product factor
49C23×C5C22×A417yes—
50C2×C4×C5—314no—
51C2×C4×C5—342no—
52C2×C4×C5—314no—
53C2×C4×C5—342no—
54C2×C4×C5—31no—
55C2×C4×C5—37no—
56C25C5×A411yescharacteristic
57C23×C4—314no—
58C23×C4—32no—
59C23×C4—37no—
60C23×C4—37no—
61C2×C42—321no—
62C2×C42—314no—
63C2×C42C22×C3×C517yescomplemented
64C2×C3×C5—167no—
65C23×C3—161no—
66C2×A4—47no—
67C22×C5—37no—
68C22×C5—314no—
69C22×C5—37no—
70C22×C5—321no—
71C22×C5C2×C42⋊C317yesdirect product factor
72C22×C5C23×A411yescharacteristic
73C4×C5—32no—
74C4×C5—314no—
75C24—37no—
76C24—31no—
77C24C2×C5×A417yes—
78C22×C4—342no—
79C22×C4—342no—
80C22×C4—314no—
81C22×C4—314no—
82C22×C4—37no—
83C22×C4—321no—
84C42—37no—
85C42—314no—
86C42C23×C3×C511yescharacteristic, complemented
87C3×C5—161noHall
88C22×C3—167no—
89A4—41no—
90C2×C5—31no—
91C2×C5—37no—
92C2×C5C22×C42⋊C317yesdirect product factor
93C23—321no—
94C23—314no—
95C23—37no—
96C23—37no—
97C23C5×C42⋊C311yescharacteristic, direct product factor
98C23C22×C5×A417yes—
99C2×C4—314no—
100C2×C4—342no—
101C2×C4—314no—
102C2×C4—342no—
103C2×C4—31no—
104C2×C4—37no—
105C2×C3—167no—
106C5C23×C42⋊C311yescharacteristic, direct product factor, Sylow
107C22—37no—
108C22—314no—
109C22—37no—
110C22—321no—
111C22C2×C5×C42⋊C317yesdirect product factor
112C22C23×C5×A411yescharacteristic
113C4—32no—
114C4—314no—
115C3—161noSylow
116C2—31no—
117C2—37no—
118C2C22×C5×C42⋊C317yesdirect product factor
subgroupG/H
center, hypercenterC23×C5C42⋊C3
commutator, cosocle, hypocenterC42C23×C3×C5
FrattiniC22C23×C5×A4
FittingC23×C42×C5C3
socleC25×C5A4
LCSG ▷ C42
UCSC1 ◁ C23×C5

Complements

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

NH ≅ G/Ntype
1. C22×C5×C42⋊C3C2direct (N × H)
2. C23×C42×C5C3semidirect
4. C2×C5×C42⋊C3C22direct (N × H)
5. C23×C42⋊C3C5direct (N × H)
8. C22×C42×C5C2×C3semidirect
10. C5×C42⋊C3C23direct (N × H)
11. C22×C42⋊C3C2×C5direct (N × H)
19. C2×C42×C5C22×C3semidirect
20. C23×C42C3×C5semidirect
24. C2×C42⋊C3C22×C5direct (N × H)
36. C42×C5C23×C3semidirect
39. C22×C42C2×C3×C5semidirect
43. C42⋊C3C23×C5direct (N × H)
48. C23×C5C42⋊C3direct (N × H)
63. C2×C42C22×C3×C5semidirect
71. C22×C5C2×C42⋊C3direct (N × H)
86. C42C23×C3×C5semidirect
92. C2×C5C22×C42⋊C3direct (N × H)
97. C23C5×C42⋊C3direct (N × H)
106. C5C23×C42⋊C3direct (N × H)
111. C22C2×C5×C42⋊C3direct (N × H)
118. C2C22×C5×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C42⋊C32
C23×C42×C53
C23×C5×A44
C23×C42⋊C35