Finite Group Databasebeta

← C2×C5×Q8×C3⋊D3 #13089495

Subgroups — C2×C5×Q8×C3⋊D3 #13089495

Order 1440.

936 conjugacy classes of subgroups; only the 346 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 346 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
1C2×C32×C5×Q8C211yesmaximal, characteristic, complemented
2C5×Q8×C3⋊D3C218yesmaximal, direct product factor
3C2×C4×C5×C3⋊D3C213yesmaximal
4C2×C5×#634C213yesmaximal, complemented
5C2×C5×D3×Q8—34nomaximal
6C22×C5×C3⋊D3C2211yescharacteristic
7C32×C5×Q8C2214yescomplemented
8C2×C32×C4×C5C2213yes—
9C2×C5×C3⋊Dic3C2213yes—
10C4×C5×C3⋊D3C22112yes—
11C5×#634C22112yescomplemented
12C2×Q8×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×Q8D314yescomplemented
14C5×D3×Q8—332no—
15C2×C4×C5×D3—312no—
16C2×C5×Dic6—312no—
17C22×C32×C5C2311yescharacteristic
18C2×C5×C3⋊D3Q814yesdirect product factor
19C2×C5×C3⋊D3C2312yes—
20C32×C4×C5C2316yes—
21C5×C3⋊Dic3C2316yes—
22C22×C5×Q8—91noHall
23C2×C32×Q8C2×C511yescharacteristic, complemented
24Q8×C3⋊D3C2×C518yesdirect product factor
25C2×C4×C3⋊D3C2×C513yes—
26C2×#634C2×C513yescomplemented
27C22×C5×D3—34no—
28C3×C5×Q8C2×D3116yescomplemented
29C2×C3×C4×C5C2×D3112yes—
30C2×C5×Dic3—312no—
31C4×C5×D3—348no—
32C5×Dic6—348no—
33C2×D3×Q8—34no—
34C2×C32×C5C2×Q812yescomplemented
35C2×C32×C5C2411yescharacteristic
36C5×C3⋊D3C2×Q814yesdirect product factor
37C2×C5×Q8—98no—
38C2×C5×Q8—93no—
39C2×C5×Q8C3⋊D311yescharacteristic, direct product factor
40C22×C4×C5—93no—
41C22×C3⋊D3C22×C511yescharacteristic
42C32×Q8C22×C514yescomplemented
43C2×C32×C4C22×C513yes—
44C2×C3⋊Dic3C22×C513yes—
45C4×C3⋊D3C22×C5112yes—
46#634C22×C5112yescomplemented
47C22×C3×C5C22×D314yes—
48C2×C5×D3—316no—
49C2×C5×D3—38no—
50C3×C4×C5C22×D3124yes—
51C5×Dic3—324no—
52C2×C3×Q8C5×D314yescomplemented
53D3×Q8—332no—
54C2×C4×D3—312no—
55C2×Dic6—312no—
56C32×C5C22×Q811yescharacteristic, complemented, Hall
57C23×C5—91no—
58C5×Q8—912no—
59C5×Q8C2×C3⋊D314yesdirect product factor
60C2×C4×C5—93no—
61C2×C4×C5—912no—
62C2×C4×C5C2×C3⋊D313yes—
63C22×C32C23×C511yescharacteristic
64C2×C3⋊D3C5×Q814yesdirect product factor
65C2×C3⋊D3C23×C512yes—
66C32×C4C23×C516yes—
67C3⋊Dic3C23×C516yes—
68C22×Q8—91noSylow
69C2×C3×C5D3×Q818yescomplemented
70C2×C3×C5C23×D314yes—
71C5×D3—316no—
72C22×D3—34no—
73C3×Q8C2×C5×D3116yescomplemented
74C2×C3×C4C2×C5×D3112yes—
75C2×Dic3—312no—
76C4×D3—348no—
77Dic6—348no—
78C22×C5—92no—
79C22×C5—94no—
80C22×C5C22×C3⋊D311yescharacteristic
81C4×C5—96no—
82C4×C5C22×C3⋊D316yes—
83C2×C32C2×C5×Q812yescomplemented
84C2×C32C24×C511yescharacteristic
85C3⋊D3C2×C5×Q814yesdirect product factor
86C2×Q8—98no—
87C2×Q8—93no—
88C2×Q8C5×C3⋊D311yescharacteristic, direct product factor
89C22×C4—93no—
90C3×C5C2×D3×Q814yescomplemented
91C22×C3C22×C5×D314yes—
92C2×D3—316no—
93C2×D3—38no—
94C3×C4C22×C5×D3124yes—
95Dic3—324no—
96C2×C5—94no—
97C2×C5Q8×C3⋊D312yesdirect product factor
98C2×C5C23×C3⋊D311yescharacteristic
99C32C22×C5×Q811yescharacteristic, complemented, Sylow
100C23—91no—
101Q8—912no—
102Q8C2×C5×C3⋊D314yesdirect product factor
103C2×C4—93no—
104C2×C4—912no—
105C2×C4C2×C5×C3⋊D313yes—
106C2×C3C5×D3×Q818yescomplemented
107C2×C3C23×C5×D314yes—
108D3—316no—
109C5C2×Q8×C3⋊D311yescharacteristic, direct product factor, Sylow
110C22—94no—
111C22—92no—
112C22C22×C5×C3⋊D311yescharacteristic
113C4—96no—
114C4C22×C5×C3⋊D316yes—
115C3C2×C5×D3×Q814yescomplemented
116C2—94no—
117C2C5×Q8×C3⋊D312yesdirect product factor
118C2C23×C5×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C5C22×C3⋊D3
commutator, cosocleC2×C32C24×C5
FrattiniC2C23×C5×C3⋊D3
FittingC2×C32×C5×Q8C2
socleC22×C32×C5C23
prime radicalC22×C5×C3⋊D3C22
hypercenterC2×C5×Q8C3⋊D3
hypocenterC32C22×C5×Q8
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C5 ◁ C2×C5×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C5×Q8C2semidirect
2. C5×Q8×C3⋊D3C2direct (N × H)
4. C2×C5×#634C2semidirect
7. C32×C5×Q8C22semidirect
11. C5×#634C22semidirect
12. C2×Q8×C3⋊D3C5direct (N × H)
13. C2×C3×C5×Q8D3semidirect
18. C2×C5×C3⋊D3Q8direct (N × H)
23. C2×C32×Q8C2×C5semidirect
24. Q8×C3⋊D3C2×C5direct (N × H)
26. C2×#634C2×C5semidirect
28. C3×C5×Q8C2×D3semidirect
34. C2×C32×C5C2×Q8semidirect
36. C5×C3⋊D3C2×Q8direct (N × H)
39. C2×C5×Q8C3⋊D3direct (N × H)
42. C32×Q8C22×C5semidirect
46. #634C22×C5semidirect
52. C2×C3×Q8C5×D3semidirect
56. C32×C5C22×Q8semidirect
59. C5×Q8C2×C3⋊D3direct (N × H)
64. C2×C3⋊D3C5×Q8direct (N × H)
69. C2×C3×C5D3×Q8semidirect
73. C3×Q8C2×C5×D3semidirect
83. C2×C32C2×C5×Q8semidirect
85. C3⋊D3C2×C5×Q8direct (N × H)
88. C2×Q8C5×C3⋊D3direct (N × H)
90. C3×C5C2×D3×Q8semidirect
97. C2×C5Q8×C3⋊D3direct (N × H)
99. C32C22×C5×Q8semidirect
102. Q8C2×C5×C3⋊D3direct (N × H)
106. C2×C3C5×D3×Q8semidirect
109. C5C2×Q8×C3⋊D3direct (N × H)
115. C3C2×C5×D3×Q8semidirect
117. C2C5×Q8×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×Q82
C5×Q8×C3⋊D32
C2×C4×C5×C3⋊D32
C2×C5×#6342
C2×C5×D3×Q83
C2×Q8×C3⋊D35