Finite Group Databasebeta

← C2×C5×#15690151 #44477705

Subgroups — C2×C5×#15690151 #44477705

Order 30420.

136 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 66 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×C5×#13095201C211yesmaximal, characteristic, complemented
2C5×#15690151C212yesmaximal, direct product factor
3C2×C3×C5×C13×D13C311yesmaximal, characteristic
4C5×#13095201C2211yescharacteristic, complemented, Hall
5C2×#15690151C511yesmaximal, characteristic, direct product factor, Hall
6C3×C5×C13×D13C2×C312yes—
7C2×C3×C5×C132C2×C311yescharacteristic
8C2×C5×C13×D13C911yescharacteristic, complemented, Hall
9C2×#13095201C2×C511yescharacteristic, complemented
10#15690151C2×C512yesdirect product factor
11C3×C5×C132C22×C311yescharacteristic
12C22×C5×C13⋊C9—131nomaximal
13C2×C5×D13⋊C9—131nomaximal
14C2×C3×C13×D13C3×C511yescharacteristic
15C2×C5×C132C2×C911yescharacteristic, complemented
16C5×C13×D13C2×C912yescomplemented
17#13095201C22×C511yescharacteristic, complemented, Hall
18C2×C5×C13⋊C9—132no—
19C2×C5×C13⋊C9—131no—
20C2×C5×C13⋊C9—131no—
21C5×D13⋊C9—132no—
22C2×C3×C132C2×C3×C511yescharacteristic
23C3×C13×D13C2×C3×C512yes—
24C5×C132C22×C911yescharacteristic, complemented, Hall
25C22×C3×C5×C13—391no—
26C2×C3×C5×D13C13⋊C311yescharacteristic
27C2×C13×D13C5×C911yescharacteristic, complemented, Hall
28C5×C13⋊C9—131no—
29C5×C13⋊C9—131no—
30C3×C132C22×C3×C511yescharacteristic
31C22×C13⋊C9—131no—
32C2×D13⋊C9—131no—
33C2×C3×C5×C13—62no—
34C2×C3×C5×C13—392no—
35C2×C3×C5×C13D13⋊C311yescharacteristic
36C2×C3×C5×C13C2×C13⋊C311yescharacteristic
37C3×C5×D13C2×C13⋊C312yes—
38C2×C132C2×C5×C911yescharacteristic, complemented
39C13×D13C2×C5×C912yescomplemented
40C22×C5×C13—391no—
41C2×C5×D13C13⋊C911yescharacteristic, complemented
42C2×C13⋊C9—132no—
43C2×C13⋊C9—131no—
44C2×C13⋊C9—131no—
45D13⋊C9—132no—
46C3×C5×C13—62no—
47C3×C5×C13C2×D13⋊C311yescharacteristic
48C3×C5×C13C22×C13⋊C311yescharacteristic
49C22×C5×C9—1691noHall
50C132C22×C5×C911yescharacteristic, complemented, Sylow
51C22×C3×C13—391no—
52C2×C3×D13C5×C13⋊C311yescharacteristic
53C2×C5×C13—62no—
54C2×C5×C13—392no—
55C2×C5×C13D13⋊C911yescharacteristic, complemented
56C2×C5×C13C2×C13⋊C911yescharacteristic, complemented
57C5×D13C2×C13⋊C912yescomplemented
58C13⋊C9—131no—
59C13⋊C9—131no—
60C2×C5×C9—1692no—
61C2×C5×C9—1691no—
62C2×C3×C13—62no—
63C2×C3×C13—392no—
64C2×C3×C13C5×D13⋊C311yescharacteristic
65C2×C3×C13C2×C5×C13⋊C311yescharacteristic
66C3×D13C2×C5×C13⋊C312yes—
67C5×C13—62no—
68C5×C13C2×D13⋊C911yescharacteristic, complemented
69C5×C13C22×C13⋊C911yescharacteristic, complemented
70C22×C3×C5—391no—
71C22×C13—391no—
72C2×D13C5×C13⋊C911yescharacteristic, complemented
73C5×C9—1691noHall
74C3×C13—62no—
75C3×C13C2×C5×D13⋊C311yescharacteristic
76C3×C13C22×C5×C13⋊C311yescharacteristic
77C22×C9—1691noHall
78C2×C3×C5—392no—
79C2×C3×C5#1175981811yescharacteristic
80C2×C13—62no—
81C2×C13—392no—
82C2×C13C5×D13⋊C911yescharacteristic, complemented
83C2×C13C2×C5×C13⋊C911yescharacteristic, complemented
84D13C2×C5×C13⋊C912yescomplemented
85C22×C5—391noHall
86C2×C9—1692no—
87C2×C9—1691no—
88C3×C5C2×#1175981811yescharacteristic
89C13—62no—
90C13C2×C5×D13⋊C911yescharacteristic, complemented
91C13C22×C5×C13⋊C911yescharacteristic, complemented
92C22×C3—391no—
93C2×C5—392no—
94C2×C5#1569015111yescharacteristic, direct product factor
95C9—1691noSylow
96C2×C3—392no—
97C2×C3C5×#1175981811yescharacteristic
98C5C2×#1569015111yescharacteristic, direct product factor, Sylow
99C22—391noSylow
100C3C2×C5×#1175981811yescharacteristic
101C2—392no—
102C2C5×#1569015111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5#11759818
commutator, hypocenterC132C22×C5×C9
FrattiniC3C2×C5×#11759818
Fitting, socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×C13×D13C3
cosocleC3×C132C22×C3×C5
LCSG ▷ C132
UCSC1 ◁ C2×C3×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×#13095201C2semidirect
2. C5×#15690151C2direct (N × H)
4. C5×#13095201C22semidirect
5. C2×#15690151C5direct (N × H)
8. C2×C5×C13×D13C9semidirect
9. C2×#13095201C2×C5semidirect
10. #15690151C2×C5direct (N × H)
15. C2×C5×C132C2×C9semidirect
16. C5×C13×D13C2×C9semidirect
17. #13095201C22×C5semidirect
24. C5×C132C22×C9semidirect
27. C2×C13×D13C5×C9semidirect
38. C2×C132C2×C5×C9semidirect
39. C13×D13C2×C5×C9semidirect
41. C2×C5×D13C13⋊C9semidirect
50. C132C22×C5×C9semidirect
55. C2×C5×C13D13⋊C9semidirect
56. C2×C5×C13C2×C13⋊C9semidirect
57. C5×D13C2×C13⋊C9semidirect
68. C5×C13C2×D13⋊C9semidirect
69. C5×C13C22×C13⋊C9semidirect
72. C2×D13C5×C13⋊C9semidirect
82. C2×C13C5×D13⋊C9semidirect
83. C2×C13C2×C5×C13⋊C9semidirect
84. D13C2×C5×C13⋊C9semidirect
90. C13C2×C5×D13⋊C9semidirect
91. C13C22×C5×C13⋊C9semidirect
94. C2×C5#15690151direct (N × H)
98. C5C2×#15690151direct (N × H)
102. C2C5×#15690151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#130952012
C5×#156901512
C2×C3×C5×C13×D133
C2×#156901515
C22×C5×C13⋊C913
C2×C5×D13⋊C913