Finite Group Databasebeta

← #19152888⋊C3 #30685782

Subgroups — #19152888⋊C3 #30685782

Order 17100.

224 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 40 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×C3⋊(C5⋊(D19⋊C3))C212yesmaximal, complemented
2C3×C5⋊D5×C19⋊C3C211yesmaximal, characteristic, complemented
3#19152888C311yesmaximal, characteristic, complemented
4(C5⋊(D19⋊C3))⋊D5—31nomaximal
5C3×C52×C19⋊C3C2211yescharacteristic, complemented, Hall
6D5×C3⋊(D19⋊C3)—52nomaximal
7C5×D285C2×C312yescomplemented
8C3×C19×C5⋊D5C2×C311yescharacteristic, complemented
9C5⋊D5×C19⋊C3—21no—
10C5⋊D5×C19⋊C3D311yescharacteristic, complemented
11C5×C5⋊(D19⋊C3)—32no—
12(C5⋊D5)⋊D19—31noHall
13C3⋊(C5⋊(D19⋊C3))D512yescomplemented
14C5×C3⋊(D19⋊C3)—52no—
15C3×D5×C19⋊C3—52no—
16C3×D5×C19⋊C3—102no—
17C3×C52×C19C22×C311yescharacteristic, complemented
18C52×C19⋊C3—21no—
19C52×C19⋊C3C2×D311yescharacteristic, complemented
20D5×D57—52no—
21D5×D19⋊C3—152no—
22C19×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D95—32no—
24C3×D15⋊D5—191nomaximal, Hall
25C3×C5×C19⋊C3—22no—
26C3×C5×C19⋊C3C2×D512yescomplemented
27C2×C3⋊(D19⋊C3)—251noHall
28D285C3×D512yescomplemented
29C5×D57—52no—
30C3×D5×C19—52no—
31C3×D5×C19—102no—
32C5⋊(D19⋊C3)—32no—
33D5×C19⋊C3—52no—
34D5×C19⋊C3—102no—
35D5×C19⋊C3—102no—
36D5×C19⋊C3—104no—
37C5×D19⋊C3—152no—
38C52×C19C2×C3×D311yescharacteristic, complemented, Hall
39C3×C5×D15—192no—
40C32×C5⋊D5—381no—
41D5×D19—152no—
42C2×C3×C19⋊C3—251no—
43C3⋊(D19⋊C3)—52no—
44D15⋊D5—191no—
45C3×D52—571no—
46C3×C5×C19—22no—
47C3×C5×C19C2×C3×D512yescomplemented
48C5×C19⋊C3—24no—
49C5×C19⋊C3—22no—
50C5×C19⋊C3—22no—
51C5×C19⋊C3D3×D512yescomplemented
52C2×D57—251no—
53C2×D19⋊C3—751no—
54C32×C52—381noHall
55D95—32no—
56C5×D19—152no—
57D5×C19—52no—
58D5×C19—102no—
59C3×D3×D5—952no—
60C3×C19⋊C3D5211yescharacteristic, complemented, Hall
61C5×D15—192no—
62C3×C5⋊D5—381no—
63C3×C5⋊D5—381no—
64C3×C5⋊D5D19⋊C311yescharacteristic, complemented
65C3×C5×D5—572no—
66C2×C3×C19—251no—
67D57—52no—
68C2×C19⋊C3—251no—
69C2×C19⋊C3—501no—
70D19⋊C3—152no—
71D52—571noHall
72C5×C19—22no—
73C5×C19C3×D3×D512yescomplemented
74C3×D15—192no—
75C3×C5×D3—952no—
76C32×D5—1902no—
77C32×D5—1902no—
78C2×D19—751noHall
79C3×C52—381no—
80C3×C52—381no—
81C3×C52C2×D19⋊C311yescharacteristic, complemented
82C2×C3×D5—2852no—
83D3×D5—952no—
84C3×C19C3×D5211yescharacteristic, complemented
85C19⋊C3—21no—
86C19⋊C3D15⋊D511yescharacteristic, complemented
87C5⋊D5C3⋊(D19⋊C3)11yescharacteristic, complemented
88C5×D5—572no—
89C32×C5—382no—
90C32×C5—382no—
91C2×C19—251no—
92D19—152no—
93C2×C3×D3—4751noHall
94C2×C3×C5—2852no—
95D15—192no—
96C3×D5—52no—
97C3×D5—102no—
98C3×D5—572no—
99C3×D5—1902no—
100C3×D5—1902no—
101C3×D5—1902no—
102C3×D5—1904no—
103C5×D3—952no—
104C52C2×C3⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
105C2×D5—2852no—
106C19C3×D15⋊D511yescharacteristic, complemented, Sylow
107C2×C32—9501no—
108C3×D3—952no—
109C3×C5—22no—
110C3×C5—382no—
111C3×C5—384no—
112C3×C5—382no—
113C3×C5—382no—
114C3×C5D5×D19⋊C312yescomplemented
115C22×C3—14251no—
116C2×D3—4751no—
117C2×C5—2852no—
118D5—52no—
119D5—102no—
120D5—572no—
121C32—381noSylow
122C2×C3—251no—
123C2×C3—2852no—
124C2×C3—9501no—
125C2×C3—9501no—
126D3—952no—
127C5—22no—
128C5D5×C3⋊(D19⋊C3)12yescomplemented
129C22—14251noSylow
130C3—381no—
131C3—381no—
132C3(C5⋊(D19⋊C3))⋊D511yescharacteristic, complemented
133C2—251no—
134C2—2852no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C19C22×C3
LCSG ▷ C3×C52×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊(C5⋊(D19⋊C3))C2semidirect
2. C3×C5⋊D5×C19⋊C3C2semidirect
3. #19152888C3semidirect
5. C3×C52×C19⋊C3C22semidirect
7. C5×D285C2×C3semidirect
8. C3×C19×C5⋊D5C2×C3semidirect
10. C5⋊D5×C19⋊C3D3semidirect
13. C3⋊(C5⋊(D19⋊C3))D5semidirect
17. C3×C52×C19C22×C3semidirect
19. C52×C19⋊C3C2×D3semidirect
22. C19×C5⋊D5C3×D3semidirect
26. C3×C5×C19⋊C3C2×D5semidirect
28. D285C3×D5semidirect
38. C52×C19C2×C3×D3semidirect
47. C3×C5×C19C2×C3×D5semidirect
51. C5×C19⋊C3D3×D5semidirect
60. C3×C19⋊C3D52semidirect
64. C3×C5⋊D5D19⋊C3semidirect
73. C5×C19C3×D3×D5semidirect
81. C3×C52C2×D19⋊C3semidirect
84. C3×C19C3×D52semidirect
86. C19⋊C3D15⋊D5semidirect
87. C5⋊D5C3⋊(D19⋊C3)semidirect
104. C52C2×C3⋊(D19⋊C3)semidirect
106. C19C3×D15⋊D5semidirect
114. C3×C5D5×D19⋊C3semidirect
128. C5D5×C3⋊(D19⋊C3)semidirect
132. C3(C5⋊(D19⋊C3))⋊D5semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊(C5⋊(D19⋊C3))2
C3×C5⋊D5×C19⋊C32
#191528883
(C5⋊(D19⋊C3))⋊D53
D5×C3⋊(D19⋊C3)5
C3×D15⋊D519