Finite Group Databasebeta

← C3×#19152888 #30685892

Subgroups — C3×#19152888 #30685892

Order 17100.

224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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×D285C212yesmaximal, complemented
2C32×C19×C5⋊D5C211yesmaximal, characteristic, complemented
3#19152888C311yesmaximal, characteristic, direct product factor
4C3×(C5⋊D5)⋊D19—31nomaximal
5C32×C52×C19C2211yescharacteristic, complemented, Hall
6C3×D5×D57—52nomaximal
7C5×D285C2×C312yescomplemented
8C3×C19×C5⋊D5—21no—
9C3×C19×C5⋊D5D311yescharacteristic, complemented
10C3×C19×C5⋊D5C2×C311yescharacteristic, complemented
11C3×C5×D95—32no—
12(C5⋊D5)⋊D19—31noHall
13C3×D285D512yescomplemented
14C3×C5×D57—52no—
15C32×D5×C19—52no—
16C32×D5×C19—102no—
17C3×C52×C19—21no—
18C3×C52×C19C2×D311yescharacteristic, complemented
19C3×C52×C19C22×C311yescharacteristic, complemented
20D5×D57—52no—
21C3×D5×D19—152no—
22C19×C5⋊D5C3×D311yescharacteristic, complemented
23C5×D95—32no—
24C3×D15⋊D5—191nomaximal, Hall
25C32×C5×C19—22no—
26C32×C5×C19C2×D512yescomplemented
27C2×C3×D57—251noHall
28D285C3×D512yescomplemented
29C5×D57—52no—
30C3×D95—32no—
31C3×D5×C19—52no—
32C3×D5×C19—52no—
33C3×D5×C19—102no—
34C3×D5×C19—102no—
35C3×D5×C19—102no—
36C3×D5×C19—104no—
37C3×C5×D19—152no—
38C52×C19C2×C3×D311yescharacteristic, complemented, Hall
39C3×C5×D15—192no—
40C32×C5⋊D5D1911yescharacteristic, complemented
41D5×D19—152no—
42C2×C32×C19—251no—
43C3×D57—52no—
44D15⋊D5—191no—
45C3×D52—571no—
46C3×C5×C19—24no—
47C3×C5×C19—22no—
48C3×C5×C19—22no—
49C3×C5×C19—22no—
50C3×C5×C19D3×D512yescomplemented
51C3×C5×C19C2×C3×D512yescomplemented
52C2×D57—251no—
53C2×C3×D19—751no—
54C32×C52C2×D1911yescharacteristic, complemented, Hall
55D95—32no—
56C5×D19—152no—
57D5×C19—52no—
58D5×C19—102no—
59C3×D3×D5—952no—
60C32×C19D5211yescharacteristic, complemented, Hall
61C5×D15—192no—
62C3×C5⋊D5—21no—
63C3×C5⋊D5C3×D1911yescharacteristic, complemented
64C3×C5⋊D5D5711yescharacteristic, complemented
65C3×C5×D5—572no—
66C2×C3×C19—251no—
67C2×C3×C19—251no—
68C2×C3×C19—501no—
69D57—52no—
70C3×D19—152no—
71D52—571noHall
72C5×C19—22no—
73C5×C19C3×D3×D512yescomplemented
74C3×D15—192no—
75C3×C5×D3—952no—
76C32×D5—52no—
77C32×D5—102no—
78C2×D19—751noHall
79C3×C52—21no—
80C3×C52C2×C3×D1911yescharacteristic, complemented
81C3×C52C2×D5711yescharacteristic, complemented
82C2×C3×D5—2852no—
83D3×D5—952no—
84C3×C19—21no—
85C3×C19C3×D5211yescharacteristic, complemented
86C3×C19D15⋊D511yescharacteristic, complemented
87C5⋊D5C3×D5711yescharacteristic, complemented
88C5×D5—572no—
89C32×C5—22no—
90C32×C5D5×D1912yescomplemented
91C2×C19—251no—
92D19—152no—
93C2×C3×D3—4751noHall
94C2×C3×C5—2852no—
95D15—192no—
96C3×D5—52no—
97C3×D5—52no—
98C3×D5—102no—
99C3×D5—102no—
100C3×D5—102no—
101C3×D5—104no—
102C3×D5—572no—
103C5×D3—952no—
104C52C2×C3×D5711yescharacteristic, complemented, Sylow
105C2×D5—2852no—
106C19C3×D15⋊D511yescharacteristic, complemented, Sylow
107C2×C32—251no—
108C3×D3—952no—
109C3×C5—24no—
110C3×C5—22no—
111C3×C5—22no—
112C3×C5—22no—
113C3×C5C3×D5×D1912yescomplemented
114C3×C5D5×D5712yescomplemented
115C22×C3—14251no—
116C2×D3—4751no—
117C2×C5—2852no—
118D5—52no—
119D5—102no—
120D5—572no—
121C32(C5⋊D5)⋊D1911yescharacteristic, complemented, Sylow
122C2×C3—251no—
123C2×C3—251no—
124C2×C3—2852no—
125C2×C3—501no—
126D3—952no—
127C5—22no—
128C5C3×D5×D5712yescomplemented
129C22—14251noSylow
130C3—21no—
131C3C3×(C5⋊D5)⋊D1911yescharacteristic, complemented
132C3#1915288811yescharacteristic, direct product factor
133C2—251no—
134C2—2852no—
subgroupG/H
center, hypercenterC3#19152888
commutator, cosocle, hypocenterC3×C52×C19C22×C3
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C3×C52×C19
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×D285C2semidirect
2. C32×C19×C5⋊D5C2semidirect
3. #19152888C3direct (N × H)
5. C32×C52×C19C22semidirect
7. C5×D285C2×C3semidirect
9. C3×C19×C5⋊D5D3semidirect
10. C3×C19×C5⋊D5C2×C3semidirect
13. C3×D285D5semidirect
18. C3×C52×C19C2×D3semidirect
19. C3×C52×C19C22×C3semidirect
22. C19×C5⋊D5C3×D3semidirect
26. C32×C5×C19C2×D5semidirect
28. D285C3×D5semidirect
38. C52×C19C2×C3×D3semidirect
40. C32×C5⋊D5D19semidirect
50. C3×C5×C19D3×D5semidirect
51. C3×C5×C19C2×C3×D5semidirect
54. C32×C52C2×D19semidirect
60. C32×C19D52semidirect
63. C3×C5⋊D5C3×D19semidirect
64. C3×C5⋊D5D57semidirect
73. C5×C19C3×D3×D5semidirect
80. C3×C52C2×C3×D19semidirect
81. C3×C52C2×D57semidirect
85. C3×C19C3×D52semidirect
86. C3×C19D15⋊D5semidirect
87. C5⋊D5C3×D57semidirect
90. C32×C5D5×D19semidirect
104. C52C2×C3×D57semidirect
106. C19C3×D15⋊D5semidirect
113. C3×C5C3×D5×D19semidirect
114. C3×C5D5×D57semidirect
121. C32(C5⋊D5)⋊D19semidirect
128. C5C3×D5×D57semidirect
131. C3C3×(C5⋊D5)⋊D19semidirect
132. C3#19152888direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×D2852
C32×C19×C5⋊D52
#191528883
C3×(C5⋊D5)⋊D193
C3×D5×D575
C3×D15⋊D519