Finite Group Databasebeta

← C3×C11×C19×Dic15 #49178490

Subgroups — C3×C11×C19×Dic15 #49178490

Order 37620.

112 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×C32×C5×C11×C19C211yesmaximal, characteristic
2C11×C19×Dic15C311yesmaximal, characteristic, direct product factor
3C3×C11×C19×Dic5—31nomaximal
4C32×C5×C11×C19C411yescharacteristic, complemented, Hall
5C3×C11×Dic3×C19—51nomaximal, Hall
6C2×C3×C5×C11×C19—21no—
7C2×C3×C5×C11×C19D311yescharacteristic
8C2×C3×C5×C11×C19C2×C311yescharacteristic
9C11×C19×Dic5—31noHall
10C2×C32×C11×C19D511yescharacteristic
11C3×C19×Dic15C1111yesmaximal, characteristic, direct product factor, Hall
12C3×C5×C11×C19—21no—
13C3×C5×C11×C19Dic311yescharacteristic, complemented
14C3×C5×C11×C19C3×C411yescharacteristic, complemented
15C11×Dic3×C19—51no—
16C3×C4×C11×C19—151no—
17C2×C5×C11×C19C3×D311yescharacteristic
18C3×C11×Dic15C1911yesmaximal, characteristic, direct product factor, Hall
19C32×C11×C19Dic511yescharacteristic, complemented, Hall
20C2×C32×C5×C19C2×C1111yescharacteristic
21C2×C3×C11×C19—21no—
22C2×C3×C11×C19C3×D511yescharacteristic
23C2×C3×C11×C19D1511yescharacteristic
24C19×Dic15C3×C1111yescharacteristic, direct product factor
25C3×C19×Dic5—31no—
26C5×C11×C19C3×Dic311yescharacteristic, complemented, Hall
27C2×C32×C5×C11C2×C1911yescharacteristic
28C32×C5×C19C4×C1111yescharacteristic, complemented, Hall
29C4×C11×C19—151noHall
30C3×Dic3×C19—51noHall
31C11×Dic15C3×C1911yescharacteristic, direct product factor
32C3×C11×Dic5—31no—
33C3×C11×C19—21no—
34C3×C11×C19C3×Dic511yescharacteristic, complemented
35C3×C11×C19Dic1511yescharacteristic, direct product factor
36C2×C3×C5×C19—21no—
37C2×C3×C5×C19D3×C1111yescharacteristic
38C2×C3×C5×C19C2×C3×C1111yescharacteristic
39C32×C5×C11C4×C1911yescharacteristic, complemented, Hall
40C2×C11×C19C3×D1511yescharacteristic
41C3×C11×Dic3—51noHall
42C19×Dic5—31noHall
43C2×C32×C19D5×C1111yescharacteristic
44C2×C3×C5×C11—21no—
45C2×C3×C5×C11D3×C1911yescharacteristic
46C2×C3×C5×C11C2×C3×C1911yescharacteristic
47C3×C5×C19—21no—
48C3×C5×C19C11×Dic311yescharacteristic, complemented
49C3×C5×C19C3×C4×C1111yescharacteristic, complemented
50C3×C4×C19—151no—
51Dic3×C19—51no—
52C11×Dic5—31noHall
53C11×C19C3×Dic1511yescharacteristic, direct product factor, Hall
54C2×C32×C11D5×C1911yescharacteristic
55C2×C5×C19C3×D3×C1111yescharacteristic
56C3×Dic15C11×C1911yescharacteristic, direct product factor, Hall
57C32×C19C11×Dic511yescharacteristic, complemented, Hall
58C3×C5×C11—21no—
59C3×C5×C11Dic3×C1911yescharacteristic, complemented
60C3×C5×C11C3×C4×C1911yescharacteristic, complemented
61C3×C4×C11—151no—
62C11×Dic3—51no—
63C2×C3×C19—21no—
64C2×C3×C19C3×D5×C1111yescharacteristic
65C2×C3×C19C11×D1511yescharacteristic
66C2×C5×C11C3×D3×C1911yescharacteristic
67C32×C11C19×Dic511yescharacteristic, complemented, Hall
68C5×C19C3×C11×Dic311yescharacteristic, complemented, Hall
69C2×C32×C5C2×C11×C1911yescharacteristic
70C4×C19—151noHall
71C2×C3×C11—21no—
72C2×C3×C11C3×D5×C1911yescharacteristic
73C2×C3×C11C19×D1511yescharacteristic
74Dic15C3×C11×C1911yescharacteristic, direct product factor
75C3×Dic5—31no—
76C3×C19—21no—
77C3×C19C3×C11×Dic511yescharacteristic, complemented
78C3×C19C11×Dic1511yescharacteristic, direct product factor
79C5×C11C3×Dic3×C1911yescharacteristic, complemented, Hall
80C32×C5C4×C11×C1911yescharacteristic, complemented, Hall
81C4×C11—151noHall
82C2×C19C3×C11×D1511yescharacteristic
83C3×Dic3—51noHall
84C3×C11—21no—
85C3×C11C3×C19×Dic511yescharacteristic, complemented
86C3×C11C19×Dic1511yescharacteristic, direct product factor
87C2×C3×C5—21no—
88C2×C3×C5D3×C11×C1911yescharacteristic
89C2×C3×C5C2×C3×C11×C1911yescharacteristic
90C2×C11C3×C19×D1511yescharacteristic
91Dic5—31noHall
92C19C3×C11×Dic1511yescharacteristic, direct product factor, Sylow
93C2×C32D5×C11×C1911yescharacteristic
94C3×C5—21no—
95C3×C5C3×C4×C11×C1911yescharacteristic, complemented
96C3×C5C11×Dic3×C1911yescharacteristic, complemented
97C3×C4—151no—
98Dic3—51no—
99C11C3×C19×Dic1511yescharacteristic, direct product factor, Sylow
100C2×C5C3×D3×C11×C1911yescharacteristic
101C32C11×C19×Dic511yescharacteristic, complemented, Sylow
102C2×C3—21no—
103C2×C3C3×D5×C11×C1911yescharacteristic
104C2×C3C11×C19×D1511yescharacteristic
105C5C3×C11×Dic3×C1911yescharacteristic, complemented, Sylow
106C4—151noSylow
107C3—21no—
108C3C3×C11×C19×Dic511yescharacteristic, complemented
109C3C11×C19×Dic1511yescharacteristic, direct product factor
110C2C3×C11×C19×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C11×C19D15
commutator, hypocenterC3×C5C3×C4×C11×C19
FrattiniC2C3×C11×C19×D15
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C3×C5C2×C3×C11×C19
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C11×C19

Complements

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

NH ≅ G/Ntype
2. C11×C19×Dic15C3direct (N × H)
4. C32×C5×C11×C19C4semidirect
11. C3×C19×Dic15C11direct (N × H)
13. C3×C5×C11×C19Dic3semidirect
14. C3×C5×C11×C19C3×C4semidirect
18. C3×C11×Dic15C19direct (N × H)
19. C32×C11×C19Dic5semidirect
24. C19×Dic15C3×C11direct (N × H)
26. C5×C11×C19C3×Dic3semidirect
28. C32×C5×C19C4×C11semidirect
31. C11×Dic15C3×C19direct (N × H)
34. C3×C11×C19C3×Dic5semidirect
35. C3×C11×C19Dic15direct (N × H)
39. C32×C5×C11C4×C19semidirect
48. C3×C5×C19C11×Dic3semidirect
49. C3×C5×C19C3×C4×C11semidirect
53. C11×C19C3×Dic15direct (N × H)
56. C3×Dic15C11×C19direct (N × H)
57. C32×C19C11×Dic5semidirect
59. C3×C5×C11Dic3×C19semidirect
60. C3×C5×C11C3×C4×C19semidirect
67. C32×C11C19×Dic5semidirect
68. C5×C19C3×C11×Dic3semidirect
74. Dic15C3×C11×C19direct (N × H)
77. C3×C19C3×C11×Dic5semidirect
78. C3×C19C11×Dic15direct (N × H)
79. C5×C11C3×Dic3×C19semidirect
80. C32×C5C4×C11×C19semidirect
85. C3×C11C3×C19×Dic5semidirect
86. C3×C11C19×Dic15direct (N × H)
92. C19C3×C11×Dic15direct (N × H)
95. C3×C5C3×C4×C11×C19semidirect
96. C3×C5C11×Dic3×C19semidirect
99. C11C3×C19×Dic15direct (N × H)
101. C32C11×C19×Dic5semidirect
105. C5C3×C11×Dic3×C19semidirect
108. C3C3×C11×C19×Dic5semidirect
109. C3C11×C19×Dic15direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×C11×C192
C11×C19×Dic153
C3×C11×C19×Dic53
C3×C11×Dic3×C195
C3×C19×Dic1511
C3×C11×Dic1519