Finite Group Databasebeta

← C3×(C19⋊C3)⋊#1044 #30685739

Subgroups — C3×(C19⋊C3)⋊#1044 #30685739

Order 17100.

192 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊#1044C311yesmaximal, characteristic, complemented
3(C19⋊C3)⋊#1044C313yesmaximal, direct product factor
4C3×C52×C19⋊C3C411yescharacteristic, complemented, Hall
5C3×(C19⋊C3)⋊AGL(1,𝔽5)—51nomaximal
6C3×(C19⋊C3)⋊AGL(1,𝔽5)—51nomaximal
7C3×C19×C5⋊D5C2×C311yescharacteristic
8C5⋊D5×C19⋊C3C2×C313yes—
9C19⋊#1044C3211yescharacteristic, complemented, Hall
10C3×D5×C19⋊C3—51no—
11C3×D5×C19⋊C3—51no—
12C3×D5×C19⋊C3—102no—
13C3×C52×C19C3×C411yescharacteristic, complemented
14C52×C19⋊C3C3×C413yescomplemented
15C3×C19⋊AGL(1,𝔽5)—51no—
16C3×C19⋊AGL(1,𝔽5)—51no—
17(C19⋊C3)⋊AGL(1,𝔽5)—53no—
18(C19⋊C3)⋊AGL(1,𝔽5)—53no—
19C19×C5⋊D5C2×C3211yescharacteristic
20C32×#1044—191nomaximal, Hall
21C3×C5×C19⋊C3—22no—
22C3×C5×C19⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
23C3×C5×C19⋊C3AGL(1,𝔽5)11yescharacteristic, complemented
24C3×(C19⋊C3)⋊C4—251noHall
25C3×D5×C19—51no—
26C3×D5×C19—51no—
27C3×D5×C19—102no—
28D5×C19⋊C3—53no—
29D5×C19⋊C3—53no—
30D5×C19⋊C3—106no—
31C52×C19C32×C411yescharacteristic, complemented, Hall
32C32×C5⋊D5—191no—
33C19⋊AGL(1,𝔽5)—51no—
34C19⋊AGL(1,𝔽5)—51no—
35C2×C3×C19⋊C3—251no—
36C3×#1044—193no—
37C3×#1044—571no—
38C3×C5×C19—22no—
39C3×C5×C19C3×AGL(1,𝔽5)11yescharacteristic, complemented
40C3×C5×C19C3×AGL(1,𝔽5)11yescharacteristic, complemented
41C5×C19⋊C3—26no—
42C5×C19⋊C3C3×AGL(1,𝔽5)13yescomplemented
43C5×C19⋊C3C3×AGL(1,𝔽5)13yescomplemented
44C3×Dic19—251no—
45(C19⋊C3)⋊C4—253no—
46C32×C52—191noHall
47D5×C19—51no—
48D5×C19—51no—
49D5×C19—102no—
50C32×AGL(1,𝔽5)—951no—
51C32×AGL(1,𝔽5)—951no—
52C3×C19⋊C3#104411yescharacteristic, complemented, Hall
53C3×C5⋊D5—193no—
54C3×C5⋊D5D19⋊C311yescharacteristic
55C2×C3×C19—251no—
56C2×C19⋊C3—253no—
57#1044—571noHall
58C5×C19—22no—
59C5×C19C32×AGL(1,𝔽5)11yescharacteristic, complemented
60C5×C19C32×AGL(1,𝔽5)11yescharacteristic, complemented
61C32×D5—951no—
62C32×D5—951no—
63C32×D5—1902no—
64Dic19—251noHall
65C3×C52—193no—
66C3×C52(C19⋊C3)⋊C411yescharacteristic, complemented
67C3×AGL(1,𝔽5)—2851no—
68C3×AGL(1,𝔽5)—951no—
69C3×AGL(1,𝔽5)—953no—
70C3×AGL(1,𝔽5)—953no—
71C3×C19C3×#104411yescharacteristic, complemented
72C19⋊C3C3×#104413yescomplemented
73C5⋊D5C3×D19⋊C311yescharacteristic
74C32×C5—191no—
75C32×C5—191no—
76C32×C5—382no—
77C2×C19—251no—
78C32×C4—4751noHall
79C3×D5—51no—
80C3×D5—51no—
81C3×D5—102no—
82C3×D5—953no—
83C3×D5—953no—
84C3×D5—1906no—
85C52C3×(C19⋊C3)⋊C411yescharacteristic, complemented, Sylow
86AGL(1,𝔽5)—2851no—
87AGL(1,𝔽5)—951no—
88C19C32×#104411yescharacteristic, complemented, Sylow
89C2×C32—4751no—
90C3×C5—22no—
91C3×C5—193no—
92C3×C5—193no—
93C3×C5—386no—
94C3×C5(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
95C3×C5(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
96C3×C4—14251no—
97C3×C4—4753no—
98D5—51no—
99D5—51no—
100D5—102no—
101C32—191noSylow
102C2×C3—251no—
103C2×C3—4753no—
104C5—22no—
105C5C3×(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
106C5C3×(C19⋊C3)⋊AGL(1,𝔽5)11yescharacteristic, complemented
107C4—14251noSylow
108C3—193no—
109C3(C19⋊C3)⋊#104411yescharacteristic, direct product factor
110C2—251no—
subgroupG/H
center, hypercenterC3(C19⋊C3)⋊#1044
commutator, hypocenterC52×C19C32×C4
FrattiniC1G
Fitting, socleC3×C52×C19C3×C4
prime radicalC3×C5⋊D5×C19⋊C3C2
cosocleC19×C5⋊D5C2×C32
LCSG ▷ C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3×C19⋊#1044C3semidirect
3. (C19⋊C3)⋊#1044C3direct (N × H)
4. C3×C52×C19⋊C3C4semidirect
9. C19⋊#1044C32semidirect
13. C3×C52×C19C3×C4semidirect
14. C52×C19⋊C3C3×C4semidirect
22. C3×C5×C19⋊C3AGL(1,𝔽5)semidirect
23. C3×C5×C19⋊C3AGL(1,𝔽5)semidirect
31. C52×C19C32×C4semidirect
39. C3×C5×C19C3×AGL(1,𝔽5)semidirect
40. C3×C5×C19C3×AGL(1,𝔽5)semidirect
42. C5×C19⋊C3C3×AGL(1,𝔽5)semidirect
43. C5×C19⋊C3C3×AGL(1,𝔽5)semidirect
52. C3×C19⋊C3#1044semidirect
59. C5×C19C32×AGL(1,𝔽5)semidirect
60. C5×C19C32×AGL(1,𝔽5)semidirect
66. C3×C52(C19⋊C3)⋊C4semidirect
71. C3×C19C3×#1044semidirect
72. C19⋊C3C3×#1044semidirect
85. C52C3×(C19⋊C3)⋊C4semidirect
88. C19C32×#1044semidirect
94. C3×C5(C19⋊C3)⋊AGL(1,𝔽5)semidirect
95. C3×C5(C19⋊C3)⋊AGL(1,𝔽5)semidirect
105. C5C3×(C19⋊C3)⋊AGL(1,𝔽5)semidirect
106. C5C3×(C19⋊C3)⋊AGL(1,𝔽5)semidirect
109. C3(C19⋊C3)⋊#1044direct (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⋊#10443
(C19⋊C3)⋊#10443
C3×(C19⋊C3)⋊AGL(1,𝔽5)5
C32×#104419