Finite Group Databasebeta

← C5×(C3⋊D3)⋊D95 #30685929

Subgroups — C5×(C3⋊D3)⋊D95 #30685929

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
1C52×C3⋊D3×C19C211yesmaximal, characteristic, complemented
2C3×C5×D285C212yesmaximal, complemented
3C5×D3×D95—32nomaximal
4C32×C52×C19C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D95C511yesmaximal, characteristic, direct product factor
6C5×(C3⋊D3)⋊D19—51nomaximal
7C5×D285D312yescomplemented
8C52×D3×C19—32no—
9C52×D3×C19—61no—
10C3×C5×D95—32no—
11C2×C5×D95—91noHall
12C5×C3⋊D3×C19—22no—
13C5×C3⋊D3×C19D511yescharacteristic, complemented
14C5×C3⋊D3×C19C2×C511yescharacteristic, complemented
15C3×D285C2×C512yescomplemented
16C3×C5×D57—52no—
17C3×C52×C19—21no—
18C3×C52×C19C2×D312yescomplemented
19D3×D95—32no—
20C5×D3×D19—152no—
21C2×C52×C19—91no—
22C5×D95—32no—
23C5×(C3⋊D3)⋊D5—191nomaximal, Hall
24C32×C5×C19—22no—
25C32×C5×C19C2×D511yescharacteristic, complemented
26C32×C5×C19C22×C511yescharacteristic, complemented
27(C3⋊D3)⋊D19—51noHall
28D285C5×D312yescomplemented
29C5×D57—52no—
30C5×D3×C19—32no—
31C5×D3×C19—32no—
32C5×D3×C19—61no—
33C5×D3×C19—61no—
34C5×D3×C19—64no—
35C5×D3×C19—64no—
36C3×D95—32no—
37C3×C5×D19—152no—
38C52×C19D3211yescharacteristic, complemented, Hall
39C52×C3⋊D3D1911yescharacteristic, complemented
40C3×C5×D15—192no—
41C2×D95—91no—
42C2×C5×D19—451no—
43C3⋊D3×C19C5×D511yescharacteristic, complemented
44C3×D57—52no—
45C5×D3×D5—572no—
46C3×C5×C19—24no—
47C3×C5×C19—24no—
48C3×C5×C19—21no—
49C3×C5×C19—21no—
50C3×C5×C19D3×D512yescomplemented
51C3×C5×C19C2×C5×D312yescomplemented
52D3×D19—152no—
53C32×C52C2×D1911yescharacteristic, complemented, Hall
54C2×C5×C19—91no—
55C2×C5×C19—91no—
56C2×C5×C19—182no—
57D95—32no—
58C5×D19—152no—
59(C3⋊D3)⋊D5—191no—
60C5×D32—951no—
61C32×C19C2×C5×D511yescharacteristic, complemented, Hall
62C5×D15—192no—
63C52×D3—32no—
64C52×D3—61no—
65C3×C5×D5—572no—
66D57—52no—
67C3×D19—152no—
68D3×C19—32no—
69D3×C19—61no—
70C2×C5×D5—1711noHall
71C5×C19—22no—
72C5×C19C5×D3211yescharacteristic, complemented
73C5×C19(C3⋊D3)⋊D511yescharacteristic, complemented
74C5×C3⋊D3—22no—
75C5×C3⋊D3C5×D1911yescharacteristic, complemented
76C5×C3⋊D3D9511yescharacteristic, complemented
77C3×D15—192no—
78C3×C5×D3—952no—
79C2×D19—451noHall
80C3×C52—21no—
81C3×C52D3×D1912yescomplemented
82C2×C5×D3—2852no—
83D3×D5—572no—
84C3×C19—21no—
85C3×C19C5×D3×D512yescomplemented
86C2×C52—91no—
87C5×D5—572no—
88C32×C5—22no—
89C32×C5C2×C5×D1911yescharacteristic, complemented
90C32×C5C2×D9511yescharacteristic, complemented
91C2×C19—91no—
92D19—152no—
93D32—951noHall
94C2×C3×C5—2852no—
95D15—192no—
96C3×D5—572no—
97C5×D3—32no—
98C5×D3—32no—
99C5×D3—64no—
100C5×D3—61no—
101C5×D3—61no—
102C5×D3—64no—
103C5×D3—952no—
104C52(C3⋊D3)⋊D1911yescharacteristic, complemented, Sylow
105C22×C5—8551no—
106C2×D5—1711no—
107C19C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
108C3⋊D3C5×D9511yescharacteristic, complemented
109C3×D3—952no—
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5C5×D3×D1912yescomplemented
115C3×C5D3×D9512yescomplemented
116C2×D3—2852no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—182no—
120C2×C5—2852no—
121D5—572no—
122C32C2×C5×D9511yescharacteristic, complemented, Sylow
123C2×C3—2852no—
124D3—32no—
125D3—61no—
126D3—952no—
127C5—22no—
128C5C5×(C3⋊D3)⋊D1911yescharacteristic, complemented
129C5(C3⋊D3)⋊D9511yescharacteristic, direct product factor
130C22—8551noSylow
131C3—21no—
132C3C5×D3×D9512yescomplemented
133C2—91no—
134C2—2852no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D95
commutator, cosocle, hypocenterC32×C5×C19C22×C5
FrattiniC1G
Fitting, socleC32×C52×C19C22
LCSG ▷ C32×C5×C19
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C52×C3⋊D3×C19C2semidirect
2. C3×C5×D285C2semidirect
4. C32×C52×C19C22semidirect
5. (C3⋊D3)⋊D95C5direct (N × H)
7. C5×D285D3semidirect
13. C5×C3⋊D3×C19D5semidirect
14. C5×C3⋊D3×C19C2×C5semidirect
15. C3×D285C2×C5semidirect
18. C3×C52×C19C2×D3semidirect
25. C32×C5×C19C2×D5semidirect
26. C32×C5×C19C22×C5semidirect
28. D285C5×D3semidirect
38. C52×C19D32semidirect
39. C52×C3⋊D3D19semidirect
43. C3⋊D3×C19C5×D5semidirect
50. C3×C5×C19D3×D5semidirect
51. C3×C5×C19C2×C5×D3semidirect
53. C32×C52C2×D19semidirect
61. C32×C19C2×C5×D5semidirect
72. C5×C19C5×D32semidirect
73. C5×C19(C3⋊D3)⋊D5semidirect
75. C5×C3⋊D3C5×D19semidirect
76. C5×C3⋊D3D95semidirect
81. C3×C52D3×D19semidirect
85. C3×C19C5×D3×D5semidirect
89. C32×C5C2×C5×D19semidirect
90. C32×C5C2×D95semidirect
104. C52(C3⋊D3)⋊D19semidirect
107. C19C5×(C3⋊D3)⋊D5semidirect
108. C3⋊D3C5×D95semidirect
114. C3×C5C5×D3×D19semidirect
115. C3×C5D3×D95semidirect
122. C32C2×C5×D95semidirect
128. C5C5×(C3⋊D3)⋊D19semidirect
129. C5(C3⋊D3)⋊D95direct (N × H)
132. C3C5×D3×D95semidirect

Maximal subgroups

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

subgroupindex
C52×C3⋊D3×C192
C3×C5×D2852
C5×D3×D953
(C3⋊D3)⋊D955
C5×(C3⋊D3)⋊D195
C5×(C3⋊D3)⋊D519