Finite Group Databasebeta

← C5×(C3⋊D3)⋊D119 #36339501

Subgroups — C5×(C3⋊D3)⋊D119 #36339501

Order 21420.

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

normal subgroups only

This group has 176 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
1C3×C5×D357C212yesmaximal, complemented
2C5×C7×C17×C3⋊D3C211yesmaximal, characteristic, complemented
3C5×D3×D119—32nomaximal
4C32×C5×C7×C17C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D119C511yesmaximal, characteristic, direct product factor, Hall
6C5×D357D312yescomplemented
7C5×D3×C7×C17—32no—
8C5×D3×C7×C17—61no—
9C3×C5×D119—32no—
10C5×(C3⋊D3)⋊D17—71nomaximal, Hall
11C2×C5×D119—91noHall
12C7×C17×C3⋊D3C2×C511yescharacteristic, complemented
13C3×D357C2×C512yescomplemented
14C3×C5×C7×C17—21no—
15C3×C5×C7×C17C2×D312yescomplemented
16C5×C17×C3⋊D3D711yescharacteristic, complemented
17C3×C5×D51—72no—
18D3×D119—32no—
19C5×(C3⋊D3)⋊D7—171nomaximal, Hall
20C2×C5×C7×C17—91no—
21C5×D119—32no—
22C32×C7×C17C22×C511yescharacteristic, complemented, Hall
23C5×D3×D17—212no—
24C32×C5×C17C2×D711yescharacteristic, complemented, Hall
25D357C5×D312yescomplemented
26D3×C7×C17—32no—
27D3×C7×C17—61no—
28C3×D119—32no—
29C5×C7×C3⋊D3D1711yescharacteristic, complemented
30C3×C5×D21—172no—
31(C3⋊D3)⋊D17—71noHall
32C5×C7×C17D3211yescharacteristic, complemented, Hall
33C5×D51—72no—
34C5×D3×C17—32no—
35C5×D3×C17—61no—
36C3×C5×D17—212no—
37C2×D119—91noHall
38C5×D3×D7—512no—
39C3×C7×C17—21no—
40C3×C7×C17C2×C5×D312yescomplemented
41C2×C5×D17—631noHall
42C32×C5×C7C2×D1711yescharacteristic, complemented, Hall
43C17×C3⋊D3C5×D711yescharacteristic, complemented
44C3×D51—72no—
45C3×C5×C17—21no—
46C3×C5×C17D3×D712yescomplemented
47(C3⋊D3)⋊D7—171noHall
48C2×C7×C17—91no—
49D119—32no—
50C5×D21—172no—
51C5×D3×C7—32no—
52C5×D3×C7—61no—
53C3×C5×D7—512no—
54D3×D17—212no—
55C5×D32—1191noHall
56C2×C5×C17—91no—
57C5×D17—212no—
58C32×C17C2×C5×D711yescharacteristic, complemented, Hall
59C2×C5×D7—1531noHall
60C7×C3⋊D3C5×D1711yescharacteristic, complemented
61C3×D21—172no—
62C7×C17C5×D3211yescharacteristic, complemented, Hall
63C3×C5×C7—21no—
64C3×C5×C7D3×D1712yescomplemented
65D51—72no—
66C3×D17—212no—
67D3×C17—32no—
68D3×C17—61no—
69C5×C3⋊D3D11911yescharacteristic, complemented
70C3×C5×D3—1192no—
71C5×C17(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
72D3×D7—512no—
73C2×C5×C7—91no—
74C5×D7—512no—
75C2×D17—631noHall
76C32×C7C2×C5×D1711yescharacteristic, complemented, Hall
77C2×C5×D3—3572no—
78C3×C17—21no—
79C3×C17C5×D3×D712yescomplemented
80C32×C5C2×D11911yescharacteristic, complemented, Hall
81D21—172no—
82C3×D7—512no—
83D3×C7—32no—
84D3×C7—61no—
85D32—1191noHall
86C5×C7(C3⋊D3)⋊D1711yescharacteristic, complemented, Hall
87C2×C17—91no—
88D17—212no—
89C2×C3×C5—3572no—
90C5×D3—32no—
91C5×D3—61no—
92C5×D3—1192no—
93C2×D7—1531noHall
94C3×C7—21no—
95C3×C7C5×D3×D1712yescomplemented
96C22×C5—10711noHall
97C3⋊D3C5×D11911yescharacteristic, complemented
98C3×D3—1192no—
99C17C5×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
100C3×C5—21no—
101C3×C5D3×D11912yescomplemented
102C2×C7—91no—
103D7—512no—
104C2×D3—3572no—
105C2×C5—91no—
106C2×C5—3572no—
107C32C2×C5×D11911yescharacteristic, complemented, Sylow
108C7C5×(C3⋊D3)⋊D1711yescharacteristic, complemented, Sylow
109C2×C3—3572no—
110D3—32no—
111D3—61no—
112D3—1192no—
113C5(C3⋊D3)⋊D11911yescharacteristic, direct product factor, Sylow
114C22—10711noSylow
115C3—21no—
116C3C5×D3×D11912yescomplemented
117C2—91no—
118C2—3572no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D119
commutator, cosocle, hypocenterC32×C7×C17C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C17C22
LCSG ▷ C32×C7×C17
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D357C2semidirect
2. C5×C7×C17×C3⋊D3C2semidirect
4. C32×C5×C7×C17C22semidirect
5. (C3⋊D3)⋊D119C5direct (N × H)
6. C5×D357D3semidirect
12. C7×C17×C3⋊D3C2×C5semidirect
13. C3×D357C2×C5semidirect
15. C3×C5×C7×C17C2×D3semidirect
16. C5×C17×C3⋊D3D7semidirect
22. C32×C7×C17C22×C5semidirect
24. C32×C5×C17C2×D7semidirect
25. D357C5×D3semidirect
29. C5×C7×C3⋊D3D17semidirect
32. C5×C7×C17D32semidirect
40. C3×C7×C17C2×C5×D3semidirect
42. C32×C5×C7C2×D17semidirect
43. C17×C3⋊D3C5×D7semidirect
46. C3×C5×C17D3×D7semidirect
58. C32×C17C2×C5×D7semidirect
60. C7×C3⋊D3C5×D17semidirect
62. C7×C17C5×D32semidirect
64. C3×C5×C7D3×D17semidirect
69. C5×C3⋊D3D119semidirect
71. C5×C17(C3⋊D3)⋊D7semidirect
76. C32×C7C2×C5×D17semidirect
79. C3×C17C5×D3×D7semidirect
80. C32×C5C2×D119semidirect
86. C5×C7(C3⋊D3)⋊D17semidirect
95. C3×C7C5×D3×D17semidirect
97. C3⋊D3C5×D119semidirect
99. C17C5×(C3⋊D3)⋊D7semidirect
101. C3×C5D3×D119semidirect
107. C32C2×C5×D119semidirect
108. C7C5×(C3⋊D3)⋊D17semidirect
113. C5(C3⋊D3)⋊D119direct (N × H)
116. C3C5×D3×D119semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3572
C5×C7×C17×C3⋊D32
C5×D3×D1193
(C3⋊D3)⋊D1195
C5×(C3⋊D3)⋊D177
C5×(C3⋊D3)⋊D717