Finite Group Databasebeta

← C2×C5×C3⋊D285 #30685967

Subgroups — C2×C5×C3⋊D285 #30685967

Order 17100.

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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×C3⋊D285C212yesmaximal, direct product factor
2C2×C32×C52×C19C211yesmaximal, characteristic, complemented
3C2×C5×D285—34nomaximal
4C32×C52×C19C2211yescharacteristic, complemented, Hall
5C2×C5×C3⋊D57—51nomaximal
6C2×C3⋊D285C511yesmaximal, characteristic, direct product factor
7C5×D285—38no—
8C2×C3×C52×C19D314yescomplemented
9C2×C5×D95—91noHall
10C2×C32×C5×C19—22no—
11C2×C32×C5×C19D511yescharacteristic, complemented
12C2×C32×C5×C19C2×C511yescharacteristic, complemented
13C3⋊D285C2×C512yesdirect product factor
14C5×C3⋊D57—52no—
15C3×C52×C19C2×D314yescomplemented
16C2×D285—34no—
17C2×C5×D57—154no—
18C2×C52×C19C3⋊D311yescharacteristic, complemented
19C5×D95—92no—
20C2×C5×C3⋊D15—191nomaximal, Hall
21C32×C5×C19—22no—
22C32×C5×C19C2×D511yescharacteristic, complemented
23C32×C5×C19C22×C511yescharacteristic, complemented
24C2×C3⋊D57—51noHall
25C2×C3×C5×C19—28no—
26C2×C3×C5×C19C5×D314yescomplemented
27C2×C3×C5×C19D1514yescomplemented
28D285—38no—
29C5×D57—158no—
30C52×C19C2×C3⋊D311yescharacteristic, complemented, Hall
31C2×C32×C52D1911yescharacteristic, complemented
32C5×C3⋊D15—192no—
33C2×D95—91no—
34C2×C5×D19—451no—
35C2×C32×C19C5×D511yescharacteristic, complemented
36C3⋊D57—52no—
37C2×C5×D15—574no—
38C3×C5×C19—28no—
39C3×C5×C19C2×C5×D314yescomplemented
40C3×C5×C19C2×D1514yescomplemented
41C2×D57—154no—
42C32×C52C2×D1911yescharacteristic, complemented, Hall
43C2×C5×C19—22no—
44C2×C5×C19C5×C3⋊D311yescharacteristic, complemented
45C2×C5×C19C3⋊D1511yescharacteristic, complemented
46D95—92no—
47C5×D19—452no—
48C2×C3⋊D15—191no—
49C2×C5×C3⋊D3—951no—
50C32×C19C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52D5714yescomplemented
52C5×D15—578no—
53C2×C3×C19C5×D1514yescomplemented
54D57—158no—
55C2×C5×D5—1711noHall
56C5×C19—22no—
57C5×C19C2×C5×C3⋊D311yescharacteristic, complemented
58C5×C19C2×C3⋊D1511yescharacteristic, complemented
59C2×C32×C5—22no—
60C2×C32×C5C5×D1911yescharacteristic, complemented
61C2×C32×C5D9511yescharacteristic, complemented
62C3⋊D15—192no—
63C5×C3⋊D3—952no—
64C2×D19—451noHall
65C3×C52C2×D5714yescomplemented
66C2×D15—574no—
67C2×C5×D3—2854no—
68C3×C19C2×C5×D1514yescomplemented
69C2×C52C3⋊D5711yescharacteristic, complemented
70C5×D5—1712no—
71C32×C5—22no—
72C32×C5C2×C5×D1911yescharacteristic, complemented
73C32×C5C2×D9511yescharacteristic, complemented
74C2×C19C5×C3⋊D1511yescharacteristic, complemented
75D19—452no—
76C2×C3⋊D3—951noHall
77C2×C3×C5—28no—
78C2×C3×C5C5×D5714yescomplemented
79C2×C3×C5D28514yescomplemented
80D15—578no—
81C5×D3—2858no—
82C52C2×C3⋊D5711yescharacteristic, complemented, Sylow
83C22×C5—8551no—
84C2×D5—1711no—
85C19C2×C5×C3⋊D1511yescharacteristic, complemented, Sylow
86C2×C32C5×D9511yescharacteristic, complemented
87C3⋊D3—952no—
88C3×C5—28no—
89C3×C5C2×C5×D5714yescomplemented
90C3×C5C2×D28514yescomplemented
91C2×D3—2854no—
92C2×C5—22no—
93C2×C5—8552no—
94C2×C5C5×C3⋊D5711yescharacteristic, complemented
95C2×C5C3⋊D28511yescharacteristic, direct product factor
96D5—1712no—
97C32C2×C5×D9511yescharacteristic, complemented, Sylow
98C2×C3C5×D28514yescomplemented
99D3—2858no—
100C5—22no—
101C5C2×C3⋊D28511yescharacteristic, direct product factor
102C5C2×C5×C3⋊D5711yescharacteristic, complemented
103C22—8551noSylow
104C3C2×C5×D28514yescomplemented
105C2—8552no—
106C2C5×C3⋊D28511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊D285
commutator, cosocle, hypocenterC32×C5×C19C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C19C2
LCSG ▷ C32×C5×C19
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D285C2direct (N × H)
2. C2×C32×C52×C19C2semidirect
4. C32×C52×C19C22semidirect
6. C2×C3⋊D285C5direct (N × H)
8. C2×C3×C52×C19D3semidirect
11. C2×C32×C5×C19D5semidirect
12. C2×C32×C5×C19C2×C5semidirect
13. C3⋊D285C2×C5direct (N × H)
15. C3×C52×C19C2×D3semidirect
18. C2×C52×C19C3⋊D3semidirect
22. C32×C5×C19C2×D5semidirect
23. C32×C5×C19C22×C5semidirect
26. C2×C3×C5×C19C5×D3semidirect
27. C2×C3×C5×C19D15semidirect
30. C52×C19C2×C3⋊D3semidirect
31. C2×C32×C52D19semidirect
35. C2×C32×C19C5×D5semidirect
39. C3×C5×C19C2×C5×D3semidirect
40. C3×C5×C19C2×D15semidirect
42. C32×C52C2×D19semidirect
44. C2×C5×C19C5×C3⋊D3semidirect
45. C2×C5×C19C3⋊D15semidirect
50. C32×C19C2×C5×D5semidirect
51. C2×C3×C52D57semidirect
53. C2×C3×C19C5×D15semidirect
57. C5×C19C2×C5×C3⋊D3semidirect
58. C5×C19C2×C3⋊D15semidirect
60. C2×C32×C5C5×D19semidirect
61. C2×C32×C5D95semidirect
65. C3×C52C2×D57semidirect
68. C3×C19C2×C5×D15semidirect
69. C2×C52C3⋊D57semidirect
72. C32×C5C2×C5×D19semidirect
73. C32×C5C2×D95semidirect
74. C2×C19C5×C3⋊D15semidirect
78. C2×C3×C5C5×D57semidirect
79. C2×C3×C5D285semidirect
82. C52C2×C3⋊D57semidirect
85. C19C2×C5×C3⋊D15semidirect
86. C2×C32C5×D95semidirect
89. C3×C5C2×C5×D57semidirect
90. C3×C5C2×D285semidirect
94. C2×C5C5×C3⋊D57semidirect
95. C2×C5C3⋊D285direct (N × H)
97. C32C2×C5×D95semidirect
98. C2×C3C5×D285semidirect
101. C5C2×C3⋊D285direct (N × H)
102. C5C2×C5×C3⋊D57semidirect
104. C3C2×C5×D285semidirect
106. C2C5×C3⋊D285direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C3⋊D2852
C2×C32×C52×C192
C2×C5×D2853
C2×C5×C3⋊D575
C2×C3⋊D2855
C2×C5×C3⋊D1519