Finite Group Databasebeta

← (C3⋊D3)⋊D455 #30655749

Subgroups — (C3⋊D3)⋊D455 #30655749

Order 16380.

176 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 45 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×C7×C13×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×D1365C212yesmaximal, complemented
3D3×D455—32nomaximal
4C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D91—51nomaximal, Hall
6D1365D312yescomplemented
7C5×D3×C7×C13—32no—
8C5×D3×C7×C13—61no—
9C3×D455—32no—
10(C3⋊D3)⋊D65—71nomaximal, Hall
11C2×D455—91noHall
12C7×C13×C3⋊D3D511yescharacteristic, complemented
13C3×D273—52no—
14C3×C5×C7×C13—21no—
15C3×C5×C7×C13C2×D312yescomplemented
16(C3⋊D3)⋊D35—131nomaximal, Hall
17C5×C13×C3⋊D3D711yescharacteristic, complemented
18C3×D195—72no—
19D3×D91—152no—
20C2×C5×C7×C13—91no—
21D455—32no—
22C32×C7×C13C2×D511yescharacteristic, complemented, Hall
23D3×D65—212no—
24C5×C7×C3⋊D3D1311yescharacteristic, complemented
25C3×D105—132no—
26C32×C5×C13C2×D711yescharacteristic, complemented, Hall
27D273—52no—
28D3×C7×C13—32no—
29D3×C7×C13—61no—
30C3×D91—152no—
31(C3⋊D3)⋊D13—351noHall
32C5×C7×C13D3211yescharacteristic, complemented, Hall
33D3×D35—392no—
34D195—72no—
35C5×D3×C13—32no—
36C5×D3×C13—61no—
37C3×D65—212no—
38C2×D91—451noHall
39C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
40C3×C7×C13—21no—
41C3×C7×C13D3×D512yescomplemented
42C2×D65—631noHall
43(C3⋊D3)⋊D7—651noHall
44C13×C3⋊D3D3511yescharacteristic, complemented
45C3×D39—352no—
46D105—132no—
47C5×D3×C7—32no—
48C5×D3×C7—61no—
49C3×D35—392no—
50C3×C5×C13—21no—
51C3×C5×C13D3×D712yescomplemented
52C2×C7×C13—91no—
53D91—152no—
54(C3⋊D3)⋊D5—911noHall
55D3×D13—1052no—
56C2×D35—1171noHall
57C2×C5×C13—91no—
58D65—212no—
59C7×C3⋊D3D6511yescharacteristic, complemented
60C3×D21—652no—
61C32×C13C2×D3511yescharacteristic, complemented, Hall
62C3×C5×C7—21no—
63C3×C5×C7D3×D1312yescomplemented
64C7×C13(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
65C5×C3⋊D3D9111yescharacteristic, complemented
66C3×D15—912no—
67D3×D7—1952no—
68D39—352no—
69C3×D13—1052no—
70D3×C13—32no—
71D3×C13—61no—
72C2×C5×C7—91no—
73D35—392no—
74C5×C13(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
75C32×C7C2×D6511yescharacteristic, complemented, Hall
76D3×D5—2732no—
77C2×D13—3151noHall
78C32×C5C2×D9111yescharacteristic, complemented, Hall
79D21—652no—
80C3×D7—1952no—
81D3×C7—32no—
82D3×C7—61no—
83C3×C13—21no—
84C3×C13D3×D3512yescomplemented
85D32—4551noHall
86C5×C7(C3⋊D3)⋊D1311yescharacteristic, complemented, Hall
87D15—912no—
88C3×D5—2732no—
89C5×D3—32no—
90C5×D3—61no—
91C2×D7—5851noHall
92C2×C13—91no—
93D13—1052no—
94C3×C7—21no—
95C3×C7D3×D6512yescomplemented
96C2×D5—8191noHall
97C3⋊D3D45511yescharacteristic, complemented
98C3×D3—4552no—
99C3×C5—21no—
100C3×C5D3×D9112yescomplemented
101C2×C7—91no—
102D7—1952no—
103C13(C3⋊D3)⋊D3511yescharacteristic, complemented, Sylow
104C2×D3—13652no—
105C2×C5—91no—
106D5—2732no—
107C32C2×D45511yescharacteristic, complemented, Sylow
108C7(C3⋊D3)⋊D6511yescharacteristic, complemented, Sylow
109C2×C3—13652no—
110D3—32no—
111D3—61no—
112D3—4552no—
113C5(C3⋊D3)⋊D9111yescharacteristic, complemented, Sylow
114C22—40951noSylow
115C3—21no—
116C3D3×D45512yescomplemented
117C2—91no—
118C2—13652no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C13C22
LCSG ▷ C32×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C7×C13×C3⋊D3C2semidirect
2. C3×D1365C2semidirect
4. C32×C5×C7×C13C22semidirect
6. D1365D3semidirect
12. C7×C13×C3⋊D3D5semidirect
15. C3×C5×C7×C13C2×D3semidirect
17. C5×C13×C3⋊D3D7semidirect
22. C32×C7×C13C2×D5semidirect
24. C5×C7×C3⋊D3D13semidirect
26. C32×C5×C13C2×D7semidirect
32. C5×C7×C13D32semidirect
39. C32×C5×C7C2×D13semidirect
41. C3×C7×C13D3×D5semidirect
44. C13×C3⋊D3D35semidirect
51. C3×C5×C13D3×D7semidirect
59. C7×C3⋊D3D65semidirect
61. C32×C13C2×D35semidirect
63. C3×C5×C7D3×D13semidirect
64. C7×C13(C3⋊D3)⋊D5semidirect
65. C5×C3⋊D3D91semidirect
74. C5×C13(C3⋊D3)⋊D7semidirect
75. C32×C7C2×D65semidirect
78. C32×C5C2×D91semidirect
84. C3×C13D3×D35semidirect
86. C5×C7(C3⋊D3)⋊D13semidirect
95. C3×C7D3×D65semidirect
97. C3⋊D3D455semidirect
100. C3×C5D3×D91semidirect
103. C13(C3⋊D3)⋊D35semidirect
107. C32C2×D455semidirect
108. C7(C3⋊D3)⋊D65semidirect
113. C5(C3⋊D3)⋊D91semidirect
116. C3D3×D455semidirect

Maximal subgroups

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

subgroupindex
C5×C7×C13×C3⋊D32
C3×D13652
D3×D4553
(C3⋊D3)⋊D915
(C3⋊D3)⋊D657
(C3⋊D3)⋊D3513