Finite Group Databasebeta

← C2×C32×C5×D85 #29506085

Subgroups — C2×C32×C5×D85 #29506085

Order 15300.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C32×C5×D85C212yesmaximal, direct product factor
2C2×C32×C52×C17C211yesmaximal, characteristic, complemented
3C2×C3×C5×D85C314yesmaximal, direct product factor
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5C2×C32×C5×D17—51nomaximal
6C2×C32×D85C511yesmaximal, characteristic, direct product factor
7C3×C5×D85C2×C318yesdirect product factor
8C2×C3×C52×C17C2×C314yescomplemented
9C2×C5×D85C3211yescharacteristic, direct product factor, Hall
10C2×C32×C5×C17—22no—
11C2×C32×C5×C17D511yescharacteristic, complemented
12C2×C32×C5×C17C2×C511yescharacteristic, complemented
13C32×D85C2×C512yesdirect product factor
14C32×C5×D17—52no—
15C3×C52×C17C22×C314yescomplemented
16C2×C3×D85C3×C514yesdirect product factor
17C2×C3×C5×D17—54no—
18C2×C32×C5×D5—171nomaximal, Hall
19C2×C52×C17C2×C3211yescharacteristic, complemented
20C5×D85C2×C3212yesdirect product factor
21C32×C5×C17—22no—
22C32×C5×C17C2×D511yescharacteristic, complemented
23C32×C5×C17C22×C511yescharacteristic, complemented
24C2×C32×D17—51noHall
25C2×C3×C5×C17—28no—
26C2×C3×C5×C17C3×D514yescomplemented
27C2×C3×C5×C17C2×C3×C514yescomplemented
28C3×D85C2×C3×C518yesdirect product factor
29C3×C5×D17—58no—
30C2×C32×C52D1711yescharacteristic, complemented
31C32×C5×D5—172no—
32C52×C17C22×C3211yescharacteristic, complemented, Hall
33C2×D85C32×C511yescharacteristic, direct product factor
34C2×C5×D17—51no—
35C2×C32×C17C5×D511yescharacteristic, complemented
36C32×D17—52no—
37C2×C3×C5×D5—174no—
38C3×C5×C17—28no—
39C3×C5×C17C2×C3×D514yescomplemented
40C3×C5×C17C22×C3×C514yescomplemented
41C32×C52C2×D1711yescharacteristic, complemented, Hall
42C2×C3×D17—54no—
43C22×C32×C5—851no—
44C2×C32×D5—171no—
45C2×C5×C17—22no—
46C2×C5×C17C32×D511yescharacteristic, complemented
47C2×C5×C17C2×C32×C511yescharacteristic, complemented
48D85C2×C32×C512yesdirect product factor
49C5×D17—52no—
50C32×C17C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52C3×D1714yescomplemented
52C3×C5×D5—178no—
53C2×C3×C17C3×C5×D514yescomplemented
54C3×D17—58no—
55C2×C5×D5—171noHall
56C2×C32×C5—22no—
57C2×C32×C5—852no—
58C2×C32×C5C5×D1711yescharacteristic, complemented
59C2×C32×C5D8511yescharacteristic, direct product factor
60C32×D5—172no—
61C5×C17—22no—
62C5×C17C2×C32×D511yescharacteristic, complemented
63C5×C17C22×C32×C511yescharacteristic, complemented
64C3×C52C2×C3×D1714yescomplemented
65C2×D17—51noHall
66C22×C3×C5—854no—
67C2×C3×D5—174no—
68C3×C17C2×C3×C5×D514yescomplemented
69C2×C52C32×D1711yescharacteristic, complemented
70C5×D5—172no—
71C32×C5—22no—
72C32×C5C2×C5×D1711yescharacteristic, complemented
73C32×C5C2×D8511yescharacteristic, direct product factor
74C22×C32—851noHall
75C2×C17C32×C5×D511yescharacteristic, complemented
76D17—52no—
77C2×C3×C5—28no—
78C2×C3×C5—858no—
79C2×C3×C5C3×C5×D1714yescomplemented
80C2×C3×C5C3×D8514yesdirect product factor
81C3×D5—178no—
82C52C2×C32×D1711yescharacteristic, complemented, Sylow
83C22×C5—851no—
84C2×D5—171no—
85C2×C32—852no—
86C2×C32C5×D8511yescharacteristic, direct product factor
87C17C2×C32×C5×D511yescharacteristic, complemented, Sylow
88C3×C5—28no—
89C3×C5C2×C3×C5×D1714yescomplemented
90C3×C5C2×C3×D8514yesdirect product factor
91C22×C3—854no—
92C2×C5—22no—
93C2×C5—852no—
94C2×C5C32×C5×D1711yescharacteristic, complemented
95C2×C5C32×D8511yescharacteristic, direct product factor
96D5—172no—
97C32C2×C5×D8511yescharacteristic, direct product factor, Sylow
98C2×C3—858no—
99C2×C3C3×C5×D8514yesdirect product factor
100C5—22no—
101C5C2×C32×D8511yescharacteristic, direct product factor
102C5C2×C32×C5×D1711yescharacteristic, complemented
103C22—851noSylow
104C3C2×C3×C5×D8514yesdirect product factor
105C2—852no—
106C2C32×C5×D8511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5D85
commutator, cosocle, hypocenterC5×C17C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D85C2direct (N × H)
2. C2×C32×C52×C17C2semidirect
3. C2×C3×C5×D85C3direct (N × H)
4. C32×C52×C17C22semidirect
6. C2×C32×D85C5direct (N × H)
7. C3×C5×D85C2×C3direct (N × H)
8. C2×C3×C52×C17C2×C3semidirect
9. C2×C5×D85C32direct (N × H)
11. C2×C32×C5×C17D5semidirect
12. C2×C32×C5×C17C2×C5semidirect
13. C32×D85C2×C5direct (N × H)
15. C3×C52×C17C22×C3semidirect
16. C2×C3×D85C3×C5direct (N × H)
19. C2×C52×C17C2×C32semidirect
20. C5×D85C2×C32direct (N × H)
22. C32×C5×C17C2×D5semidirect
23. C32×C5×C17C22×C5semidirect
26. C2×C3×C5×C17C3×D5semidirect
27. C2×C3×C5×C17C2×C3×C5semidirect
28. C3×D85C2×C3×C5direct (N × H)
30. C2×C32×C52D17semidirect
32. C52×C17C22×C32semidirect
33. C2×D85C32×C5direct (N × H)
35. C2×C32×C17C5×D5semidirect
39. C3×C5×C17C2×C3×D5semidirect
40. C3×C5×C17C22×C3×C5semidirect
41. C32×C52C2×D17semidirect
46. C2×C5×C17C32×D5semidirect
47. C2×C5×C17C2×C32×C5semidirect
48. D85C2×C32×C5direct (N × H)
50. C32×C17C2×C5×D5semidirect
51. C2×C3×C52C3×D17semidirect
53. C2×C3×C17C3×C5×D5semidirect
58. C2×C32×C5C5×D17semidirect
59. C2×C32×C5D85direct (N × H)
62. C5×C17C2×C32×D5semidirect
63. C5×C17C22×C32×C5semidirect
64. C3×C52C2×C3×D17semidirect
68. C3×C17C2×C3×C5×D5semidirect
69. C2×C52C32×D17semidirect
72. C32×C5C2×C5×D17semidirect
73. C32×C5C2×D85direct (N × H)
75. C2×C17C32×C5×D5semidirect
79. C2×C3×C5C3×C5×D17semidirect
80. C2×C3×C5C3×D85direct (N × H)
82. C52C2×C32×D17semidirect
86. C2×C32C5×D85direct (N × H)
87. C17C2×C32×C5×D5semidirect
89. C3×C5C2×C3×C5×D17semidirect
90. C3×C5C2×C3×D85direct (N × H)
94. C2×C5C32×C5×D17semidirect
95. C2×C5C32×D85direct (N × H)
97. C32C2×C5×D85direct (N × H)
99. C2×C3C3×C5×D85direct (N × H)
101. C5C2×C32×D85direct (N × H)
102. C5C2×C32×C5×D17semidirect
104. C3C2×C3×C5×D85direct (N × H)
106. C2C32×C5×D85direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D852
C2×C32×C52×C172
C2×C3×C5×D853
C2×C32×C5×D175
C2×C32×D855
C2×C32×C5×D517