Finite Group Databasebeta

← C2×C5×C31×C3⋊D15 #42124993

Subgroups — C2×C5×C31×C3⋊D15 #42124993

Order 27900.

288 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 108 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×C31×C3⋊D15C212yesmaximal, direct product factor
2C2×C32×C52×C31C211yesmaximal, characteristic, complemented
3C2×C5×D15×C31—34nomaximal
4C32×C52×C31C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D3×C31—51nomaximal
6C2×C31×C3⋊D15C511yesmaximal, characteristic, direct product factor
7C5×D15×C31—38no—
8C2×C3×C52×C31D314yescomplemented
9C2×C5×D5×C31—91noHall
10C31×C3⋊D15C2×C512yesdirect product factor
11C5×C3⋊D3×C31—52no—
12C2×C32×C5×C31—22no—
13C2×C32×C5×C31D511yescharacteristic, complemented
14C2×C32×C5×C31C2×C511yescharacteristic, complemented
15C3×C52×C31C2×D314yescomplemented
16C2×D15×C31—34no—
17C2×C5×D3×C31—154no—
18C2×C52×C31C3⋊D311yescharacteristic, complemented
19C5×D5×C31—92no—
20C32×C5×C31—22no—
21C32×C5×C31C2×D511yescharacteristic, complemented
22C32×C5×C31C22×C511yescharacteristic, complemented
23C2×C3⋊D3×C31—51noHall
24C2×C3×C5×C31—28no—
25C2×C3×C5×C31C5×D314yescomplemented
26C2×C3×C5×C31D1514yescomplemented
27D15×C31—38no—
28C5×D3×C31—158no—
29C2×C5×C3⋊D15C3111yesmaximal, characteristic, direct product factor, Hall
30C52×C31C2×C3⋊D311yescharacteristic, complemented, Hall
31C22×C5×C31—451no—
32C2×D5×C31—91no—
33C2×C32×C31C5×D511yescharacteristic, complemented
34C3⋊D3×C31—52no—
35C3×C5×C31—28no—
36C3×C5×C31C2×C5×D314yescomplemented
37C3×C5×C31C2×D1514yescomplemented
38C2×C32×C52C2×C3111yescharacteristic, complemented
39C5×C3⋊D15C2×C3112yesdirect product factor
40C2×D3×C31—154no—
41C2×C5×C31—22no—
42C2×C5×C31—452no—
43C2×C5×C31C5×C3⋊D311yescharacteristic, complemented
44C2×C5×C31C3⋊D1511yescharacteristic, direct product factor
45D5×C31—92no—
46C2×C5×D15—34no—
47C32×C31C2×C5×D511yescharacteristic, complemented, Hall
48C32×C52C22×C3111yescharacteristic, complemented, Hall
49C2×C3×C31C5×D1514yescomplemented
50D3×C31—158no—
51C2×C3⋊D15C5×C3111yescharacteristic, direct product factor
52C2×C5×C3⋊D3—51no—
53C5×C31—22no—
54C5×C31C2×C5×C3⋊D311yescharacteristic, complemented
55C5×C31C2×C3⋊D1511yescharacteristic, direct product factor
56C2×C3×C52D3×C3114yescomplemented
57C5×D15—38no—
58C22×C31—451noHall
59C2×C5×D5—91noHall
60C3×C31C2×C5×D1514yescomplemented
61C2×C32×C5—22no—
62C2×C32×C5D5×C3111yescharacteristic, complemented
63C2×C32×C5C2×C5×C3111yescharacteristic, complemented
64C3⋊D15C2×C5×C3112yesdirect product factor
65C5×C3⋊D3—52no—
66C3×C52C2×D3×C3114yescomplemented
67C2×C31—452no—
68C2×C31C5×C3⋊D1511yescharacteristic, direct product factor
69C2×D15—34no—
70C2×C5×D3—154no—
71C2×C52C3⋊D3×C3111yescharacteristic, complemented
72C5×D5—92no—
73C32×C5—22no—
74C32×C5C2×D5×C3111yescharacteristic, complemented
75C32×C5C22×C5×C3111yescharacteristic, complemented
76C2×C3⋊D3—51noHall
77C31C2×C5×C3⋊D1511yescharacteristic, direct product factor, Sylow
78C2×C3×C5—28no—
79C2×C3×C5C5×D3×C3114yescomplemented
80C2×C3×C5D15×C3114yescomplemented
81D15—38no—
82C5×D3—158no—
83C52C2×C3⋊D3×C3111yescharacteristic, complemented, Sylow
84C22×C5—451no—
85C2×D5—91no—
86C2×C32C5×D5×C3111yescharacteristic, complemented
87C3⋊D3—52no—
88C3×C5—28no—
89C3×C5C2×C5×D3×C3114yescomplemented
90C3×C5C2×D15×C3114yescomplemented
91C2×D3—154no—
92C2×C5—22no—
93C2×C5—452no—
94C2×C5C5×C3⋊D3×C3111yescharacteristic, complemented
95C2×C5C31×C3⋊D1511yescharacteristic, direct product factor
96D5—92no—
97C32C2×C5×D5×C3111yescharacteristic, complemented, Sylow
98C2×C3C5×D15×C3114yescomplemented
99D3—158no—
100C5—22no—
101C5C2×C31×C3⋊D1511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D3×C3111yescharacteristic, complemented
103C22—451noSylow
104C3C2×C5×D15×C3114yescomplemented
105C2—452no—
106C2C5×C31×C3⋊D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C31C3⋊D15
commutator, cosocle, hypocenterC32×C5C22×C5×C31
FrattiniC1G
Fitting, socleC2×C32×C52×C31C2
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C31

Complements

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

NH ≅ G/Ntype
1. C5×C31×C3⋊D15C2direct (N × H)
2. C2×C32×C52×C31C2semidirect
4. C32×C52×C31C22semidirect
6. C2×C31×C3⋊D15C5direct (N × H)
8. C2×C3×C52×C31D3semidirect
10. C31×C3⋊D15C2×C5direct (N × H)
13. C2×C32×C5×C31D5semidirect
14. C2×C32×C5×C31C2×C5semidirect
15. C3×C52×C31C2×D3semidirect
18. C2×C52×C31C3⋊D3semidirect
21. C32×C5×C31C2×D5semidirect
22. C32×C5×C31C22×C5semidirect
25. C2×C3×C5×C31C5×D3semidirect
26. C2×C3×C5×C31D15semidirect
29. C2×C5×C3⋊D15C31direct (N × H)
30. C52×C31C2×C3⋊D3semidirect
33. C2×C32×C31C5×D5semidirect
36. C3×C5×C31C2×C5×D3semidirect
37. C3×C5×C31C2×D15semidirect
38. C2×C32×C52C2×C31semidirect
39. C5×C3⋊D15C2×C31direct (N × H)
43. C2×C5×C31C5×C3⋊D3semidirect
44. C2×C5×C31C3⋊D15direct (N × H)
47. C32×C31C2×C5×D5semidirect
48. C32×C52C22×C31semidirect
49. C2×C3×C31C5×D15semidirect
51. C2×C3⋊D15C5×C31direct (N × H)
54. C5×C31C2×C5×C3⋊D3semidirect
55. C5×C31C2×C3⋊D15direct (N × H)
56. C2×C3×C52D3×C31semidirect
60. C3×C31C2×C5×D15semidirect
62. C2×C32×C5D5×C31semidirect
63. C2×C32×C5C2×C5×C31semidirect
64. C3⋊D15C2×C5×C31direct (N × H)
66. C3×C52C2×D3×C31semidirect
68. C2×C31C5×C3⋊D15direct (N × H)
71. C2×C52C3⋊D3×C31semidirect
74. C32×C5C2×D5×C31semidirect
75. C32×C5C22×C5×C31semidirect
77. C31C2×C5×C3⋊D15direct (N × H)
79. C2×C3×C5C5×D3×C31semidirect
80. C2×C3×C5D15×C31semidirect
83. C52C2×C3⋊D3×C31semidirect
86. C2×C32C5×D5×C31semidirect
89. C3×C5C2×C5×D3×C31semidirect
90. C3×C5C2×D15×C31semidirect
94. C2×C5C5×C3⋊D3×C31semidirect
95. C2×C5C31×C3⋊D15direct (N × H)
97. C32C2×C5×D5×C31semidirect
98. C2×C3C5×D15×C31semidirect
101. C5C2×C31×C3⋊D15direct (N × H)
102. C5C2×C5×C3⋊D3×C31semidirect
104. C3C2×C5×D15×C31semidirect
106. C2C5×C31×C3⋊D15direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C31×C3⋊D152
C2×C32×C52×C312
C2×C5×D15×C313
C2×C5×C3⋊D3×C315
C2×C31×C3⋊D155
C2×C5×C3⋊D1531