Finite Group Databasebeta

← C3×(C19⋊C3)⋊#1042 #30685741

Subgroups — C3×(C19⋊C3)⋊#1042 #30685741

Order 17100.

156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 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×D5×C19⋊C3C211yesmaximal, characteristic
2C3×C19⋊#1042C311yesmaximal, characteristic, complemented
3(C19⋊C3)⋊#1042C313yesmaximal, direct product factor
4C3×C52×C19⋊C3C411yescharacteristic, complemented, Hall
5C3×(C19⋊C3)⋊AGL(1,𝔽5)—51nomaximal
6C3×(C19⋊C3)⋊Dic5—51nomaximal
7C3×C5×D5×C19C2×C311yescharacteristic
8C5×D5×C19⋊C3C2×C313yes—
9C19⋊#1042C3211yescharacteristic, complemented, Hall
10C2×C3×C5×C19⋊C3—51no—
11C3×D5×C19⋊C3D511yescharacteristic
12C3×C52×C19C3×C411yescharacteristic, complemented
13C52×C19⋊C3C3×C413yescomplemented
14C3×C19⋊AGL(1,𝔽5)—51no—
15(C19⋊C3)⋊AGL(1,𝔽5)—53no—
16C3×Dic95—51no—
17(C19⋊C3)⋊Dic5—53no—
18C5×D5×C19C2×C3211yescharacteristic
19C32×#1042—191nomaximal, Hall
20C3×C5×C19⋊C3—41no—
21C3×C5×C19⋊C3Dic511yescharacteristic, complemented
22C3×C5×C19⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
23C3×(C19⋊C3)⋊C4—251noHall
24C2×C3×C5×C19—51no—
25C3×D5×C19C3×D511yescharacteristic
26C2×C5×C19⋊C3—53no—
27D5×C19⋊C3C3×D513yes—
28C52×C19C32×C411yescharacteristic, complemented, Hall
29C32×C5×D5—191no—
30C19⋊AGL(1,𝔽5)—51no—
31Dic95—51no—
32C2×C3×C19⋊C3—51no—
33C3×#1042—193no—
34C3×#1042—571no—
35C3×C5×C19—41no—
36C3×C5×C19C3×Dic511yescharacteristic, complemented
37C3×C5×C19C3×AGL(1,𝔽5)11yescharacteristic, complemented
38C5×C19⋊C3—43no—
39C5×C19⋊C3C3×Dic513yescomplemented
40C5×C19⋊C3C3×AGL(1,𝔽5)13yescomplemented
41C3×Dic19—251no—
42(C19⋊C3)⋊C4—253no—
43C32×C52—191noHall
44C2×C5×C19—51no—
45D5×C19C32×D511yescharacteristic
46C32×AGL(1,𝔽5)—951no—
47C32×Dic5—951no—
48C3×C19⋊C3#104211yescharacteristic, complemented, Hall
49C3×C5×D5—193no—
50C3×C5×D5D19⋊C311yescharacteristic
51C2×C3×C19—51no—
52C2×C19⋊C3—53no—
53#1042—571noHall
54C5×C19—41no—
55C5×C19C32×Dic511yescharacteristic, complemented
56C5×C19C32×AGL(1,𝔽5)11yescharacteristic, complemented
57C2×C32×C5—951no—
58C32×D5—191no—
59Dic19—251noHall
60C3×C52—193no—
61C3×C52(C19⋊C3)⋊C411yescharacteristic, complemented
62C3×AGL(1,𝔽5)—2851no—
63C3×AGL(1,𝔽5)—953no—
64C3×Dic5—2851no—
65C3×Dic5—953no—
66C3×C19C3×#104211yescharacteristic, complemented
67C19⋊C3C3×#104213yescomplemented
68C5×D5C3×D19⋊C311yescharacteristic
69C32×C5—191no—
70C32×C5—191no—
71C32×C5—761no—
72C2×C19—51no—
73C32×C4—4751noHall
74C2×C3×C5—51no—
75C2×C3×C5—953no—
76C3×D5—193no—
77C3×D5C5⋊(D19⋊C3)11yescharacteristic
78C52C3×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
79AGL(1,𝔽5)—2851no—
80Dic5—2851no—
81C19C32×#104211yescharacteristic, complemented, Sylow
82C2×C32—951no—
83C3×C5—41no—
84C3×C5—193no—
85C3×C5—193no—
86C3×C5—763no—
87C3×C5(C19⋊C3)⋊Dic511yescharacteristic, complemented
88C3×C5(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
89C3×C4—14251no—
90C3×C4—4753no—
91C2×C5—51no—
92D5C3×C5⋊(D19⋊C3)11yescharacteristic
93C32—191noSylow
94C2×C3—51no—
95C2×C3—953no—
96C5—41no—
97C5C3×(C19⋊C3)⋊Dic511yescharacteristic, complemented
98C5C3×(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
99C4—14251noSylow
100C3—193no—
101C3(C19⋊C3)⋊#104211yescharacteristic, direct product factor
102C2—51no—
subgroupG/H
center, hypercenterC3(C19⋊C3)⋊#1042
commutator, hypocenterC52×C19C32×C4
FrattiniC1G
Fitting, socleC3×C52×C19C3×C4
prime radicalC3×C5×D5×C19⋊C3C2
cosocleC5×D5×C19C2×C32
LCSG ▷ C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×C19⋊#1042C3semidirect
3. (C19⋊C3)⋊#1042C3direct (N × H)
4. C3×C52×C19⋊C3C4semidirect
9. C19⋊#1042C32semidirect
12. C3×C52×C19C3×C4semidirect
13. C52×C19⋊C3C3×C4semidirect
21. C3×C5×C19⋊C3Dic5semidirect
22. C3×C5×C19⋊C3AGL(1,𝔽5)semidirect
28. C52×C19C32×C4semidirect
36. C3×C5×C19C3×Dic5semidirect
37. C3×C5×C19C3×AGL(1,𝔽5)semidirect
39. C5×C19⋊C3C3×Dic5semidirect
40. C5×C19⋊C3C3×AGL(1,𝔽5)semidirect
48. C3×C19⋊C3#1042semidirect
55. C5×C19C32×Dic5semidirect
56. C5×C19C32×AGL(1,𝔽5)semidirect
61. C3×C52(C19⋊C3)⋊C4semidirect
66. C3×C19C3×#1042semidirect
67. C19⋊C3C3×#1042semidirect
78. C52C3×(C19⋊C3)⋊C4semidirect
81. C19C32×#1042semidirect
87. C3×C5(C19⋊C3)⋊Dic5semidirect
88. C3×C5(C19⋊C3)⋊AGL(1,𝔽5)semidirect
97. C5C3×(C19⋊C3)⋊Dic5semidirect
98. C5C3×(C19⋊C3)⋊AGL(1,𝔽5)semidirect
101. C3(C19⋊C3)⋊#1042direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D5×C19⋊C32
C3×C19⋊#10423
(C19⋊C3)⋊#10423
C3×(C19⋊C3)⋊AGL(1,𝔽5)5
C3×(C19⋊C3)⋊Dic55
C32×#104219