Finite Group Databasebeta

← C5×(C3⋊D3)⋊D85 #29506029

Subgroups — C5×(C3⋊D3)⋊D85 #29506029

Order 15300.

224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C52×C17×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×C5×D255C212yesmaximal, complemented
3C5×D3×D85—32nomaximal
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D85C511yesmaximal, characteristic, direct product factor
6C5×(C3⋊D3)⋊D17—51nomaximal
7C5×D255D312yescomplemented
8C52×D3×C17—32no—
9C52×D3×C17—61no—
10C3×C5×D85—32no—
11C2×C5×D85—91noHall
12C5×C17×C3⋊D3—22no—
13C5×C17×C3⋊D3D511yescharacteristic, complemented
14C5×C17×C3⋊D3C2×C511yescharacteristic, complemented
15C3×D255C2×C512yescomplemented
16C3×C5×D51—52no—
17C3×C52×C17—21no—
18C3×C52×C17C2×D312yescomplemented
19D3×D85—32no—
20C5×D3×D17—152no—
21C5×(C3⋊D3)⋊D5—171nomaximal, Hall
22C2×C52×C17—91no—
23C5×D85—32no—
24C32×C5×C17—22no—
25C32×C5×C17C2×D511yescharacteristic, complemented
26C32×C5×C17C22×C511yescharacteristic, complemented
27(C3⋊D3)⋊D17—51noHall
28D255C5×D312yescomplemented
29C5×D51—52no—
30C5×D3×C17—32no—
31C5×D3×C17—32no—
32C5×D3×C17—64no—
33C5×D3×C17—61no—
34C5×D3×C17—61no—
35C5×D3×C17—64no—
36C3×D85—32no—
37C3×C5×D17—152no—
38C52×C3⋊D3D1711yescharacteristic, complemented
39C3×C5×D15—172no—
40C52×C17D3211yescharacteristic, complemented, Hall
41C2×D85—91no—
42C2×C5×D17—451no—
43C17×C3⋊D3C5×D511yescharacteristic, complemented
44C3×D51—52no—
45C5×D3×D5—512no—
46C3×C5×C17—24no—
47C3×C5×C17—21no—
48C3×C5×C17—21no—
49C3×C5×C17—24no—
50C3×C5×C17D3×D512yescomplemented
51C3×C5×C17C2×C5×D312yescomplemented
52C32×C52C2×D1711yescharacteristic, complemented, Hall
53D3×D17—152no—
54(C3⋊D3)⋊D5—171no—
55C5×D32—851no—
56C2×C5×C17—91no—
57C2×C5×C17—91no—
58C2×C5×C17—182no—
59D85—32no—
60C5×D17—152no—
61C32×C17C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—172no—
63C52×D3—32no—
64C52×D3—61no—
65C3×C5×D5—512no—
66D51—52no—
67C3×D17—152no—
68D3×C17—32no—
69D3×C17—61no—
70C2×C5×D5—1531noHall
71C5×C3⋊D3—22no—
72C5×C3⋊D3C5×D1711yescharacteristic, complemented
73C5×C3⋊D3D8511yescharacteristic, complemented
74C3×D15—172no—
75C3×C5×D3—852no—
76C5×C17—22no—
77C5×C17C5×D3211yescharacteristic, complemented
78C5×C17(C3⋊D3)⋊D511yescharacteristic, complemented
79C3×C52—21no—
80C3×C52D3×D1712yescomplemented
81C2×D17—451noHall
82C2×C5×D3—2552no—
83D3×D5—512no—
84C3×C17—21no—
85C3×C17C5×D3×D512yescomplemented
86C2×C52—91no—
87C5×D5—512no—
88C32×C5—22no—
89C32×C5C2×C5×D1711yescharacteristic, complemented
90C32×C5C2×D8511yescharacteristic, complemented
91D32—851noHall
92C2×C17—91no—
93D17—152no—
94C2×C3×C5—2552no—
95D15—172no—
96C3×D5—512no—
97C5×D3—32no—
98C5×D3—32no—
99C5×D3—64no—
100C5×D3—61no—
101C5×D3—61no—
102C5×D3—64no—
103C5×D3—852no—
104C52(C3⋊D3)⋊D1711yescharacteristic, complemented, Sylow
105C22×C5—7651no—
106C2×D5—1531no—
107C3⋊D3C5×D8511yescharacteristic, complemented
108C3×D3—852no—
109C17C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5C5×D3×D1712yescomplemented
115C3×C5D3×D8512yescomplemented
116C2×D3—2552no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—182no—
120C2×C5—2552no—
121D5—512no—
122C32C2×C5×D8511yescharacteristic, complemented, Sylow
123C2×C3—2552no—
124D3—32no—
125D3—61no—
126D3—852no—
127C5—22no—
128C5C5×(C3⋊D3)⋊D1711yescharacteristic, complemented
129C5(C3⋊D3)⋊D8511yescharacteristic, direct product factor
130C22—7651noSylow
131C3—21no—
132C3C5×D3×D8512yescomplemented
133C2—91no—
134C2—2552no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D85
commutator, cosocle, hypocenterC32×C5×C17C22×C5
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C5×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C52×C17×C3⋊D3C2semidirect
2. C3×C5×D255C2semidirect
4. C32×C52×C17C22semidirect
5. (C3⋊D3)⋊D85C5direct (N × H)
7. C5×D255D3semidirect
13. C5×C17×C3⋊D3D5semidirect
14. C5×C17×C3⋊D3C2×C5semidirect
15. C3×D255C2×C5semidirect
18. C3×C52×C17C2×D3semidirect
25. C32×C5×C17C2×D5semidirect
26. C32×C5×C17C22×C5semidirect
28. D255C5×D3semidirect
38. C52×C3⋊D3D17semidirect
40. C52×C17D32semidirect
43. C17×C3⋊D3C5×D5semidirect
50. C3×C5×C17D3×D5semidirect
51. C3×C5×C17C2×C5×D3semidirect
52. C32×C52C2×D17semidirect
61. C32×C17C2×C5×D5semidirect
72. C5×C3⋊D3C5×D17semidirect
73. C5×C3⋊D3D85semidirect
77. C5×C17C5×D32semidirect
78. C5×C17(C3⋊D3)⋊D5semidirect
80. C3×C52D3×D17semidirect
85. C3×C17C5×D3×D5semidirect
89. C32×C5C2×C5×D17semidirect
90. C32×C5C2×D85semidirect
104. C52(C3⋊D3)⋊D17semidirect
107. C3⋊D3C5×D85semidirect
109. C17C5×(C3⋊D3)⋊D5semidirect
114. C3×C5C5×D3×D17semidirect
115. C3×C5D3×D85semidirect
122. C32C2×C5×D85semidirect
128. C5C5×(C3⋊D3)⋊D17semidirect
129. C5(C3⋊D3)⋊D85direct (N × H)
132. C3C5×D3×D85semidirect

Maximal subgroups

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

subgroupindex
C52×C17×C3⋊D32
C3×C5×D2552
C5×D3×D853
(C3⋊D3)⋊D855
C5×(C3⋊D3)⋊D175
C5×(C3⋊D3)⋊D517