Finite Group Databasebeta

← C5×(C3⋊D3)⋊D155 #42124932

Subgroups — C5×(C3⋊D3)⋊D155 #42124932

Order 27900.

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×D465C212yesmaximal, complemented
2C52×C3⋊D3×C31C211yesmaximal, characteristic, complemented
3C5×D3×D155—32nomaximal
4C32×C52×C31C2211yescharacteristic, complemented, Hall
5(C3⋊D3)⋊D155C511yesmaximal, characteristic, direct product factor
6C5×(C3⋊D3)⋊D31—51nomaximal
7C5×D465D312yescomplemented
8C52×D3×C31—32no—
9C52×D3×C31—61no—
10C3×C5×D155—32no—
11C2×C5×D155—91noHall
12C5×C3⋊D3×C31—22no—
13C5×C3⋊D3×C31D511yescharacteristic, complemented
14C5×C3⋊D3×C31C2×C511yescharacteristic, complemented
15C3×D465C2×C512yescomplemented
16C3×C5×D93—52no—
17C3×C52×C31—21no—
18C3×C52×C31C2×D312yescomplemented
19D3×D155—32no—
20C5×D3×D31—152no—
21C2×C52×C31—91no—
22C5×D155—32no—
23C32×C5×C31—22no—
24C32×C5×C31C2×D511yescharacteristic, complemented
25C32×C5×C31C22×C511yescharacteristic, complemented
26(C3⋊D3)⋊D31—51noHall
27D465C5×D312yescomplemented
28C5×D93—52no—
29C5×D3×C31—32no—
30C5×D3×C31—32no—
31C5×D3×C31—64no—
32C5×D3×C31—61no—
33C5×D3×C31—61no—
34C5×D3×C31—64no—
35C3×D155—32no—
36C3×C5×D31—152no—
37C5×(C3⋊D3)⋊D5—311nomaximal, Hall
38C52×C31D3211yescharacteristic, complemented, Hall
39C2×D155—91no—
40C2×C5×D31—451no—
41C3⋊D3×C31C5×D511yescharacteristic, complemented
42C3×D93—52no—
43C3×C5×C31—24no—
44C3×C5×C31—21no—
45C3×C5×C31—21no—
46C3×C5×C31—24no—
47C3×C5×C31D3×D512yescomplemented
48C3×C5×C31C2×C5×D312yescomplemented
49C52×C3⋊D3D3111yescharacteristic, complemented
50C3×C5×D15—312no—
51D3×D31—152no—
52C2×C5×C31—91no—
53C2×C5×C31—91no—
54C2×C5×C31—182no—
55D155—32no—
56C5×D31—152no—
57C5×D3×D5—932no—
58C32×C31C2×C5×D511yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60D93—52no—
61C3×D31—152no—
62D3×C31—32no—
63D3×C31—61no—
64(C3⋊D3)⋊D5—311no—
65C5×D32—1551no—
66C5×C31—22no—
67C5×C31C5×D3211yescharacteristic, complemented
68C5×C31(C3⋊D3)⋊D511yescharacteristic, complemented
69C5×D15—312no—
70C52×D3—32no—
71C52×D3—61no—
72C3×C5×D5—932no—
73C2×D31—451noHall
74C2×C5×D5—2791noHall
75C3×C31—21no—
76C3×C31C5×D3×D512yescomplemented
77C5×C3⋊D3—22no—
78C5×C3⋊D3C5×D3111yescharacteristic, complemented
79C5×C3⋊D3D15511yescharacteristic, complemented
80C3×D15—312no—
81C3×C5×D3—1552no—
82C3×C52—21no—
83C3×C52D3×D3112yescomplemented
84C2×C31—91no—
85D31—152no—
86C2×C5×D3—4652no—
87D3×D5—932no—
88C2×C52—91no—
89C5×D5—932no—
90C32×C5—22no—
91C32×C5C2×C5×D3111yescharacteristic, complemented
92C32×C5C2×D15511yescharacteristic, complemented
93D32—1551noHall
94C31C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
95C2×C3×C5—4652no—
96D15—312no—
97C3×D5—932no—
98C5×D3—32no—
99C5×D3—32no—
100C5×D3—64no—
101C5×D3—61no—
102C5×D3—61no—
103C5×D3—64no—
104C5×D3—1552no—
105C52(C3⋊D3)⋊D3111yescharacteristic, complemented, Sylow
106C22×C5—13951no—
107C2×D5—2791no—
108C3⋊D3C5×D15511yescharacteristic, complemented
109C3×D3—1552no—
110C3×C5—24no—
111C3×C5—21no—
112C3×C5—21no—
113C3×C5—24no—
114C3×C5C5×D3×D3112yescomplemented
115C3×C5D3×D15512yescomplemented
116C2×D3—4652no—
117C2×C5—91no—
118C2×C5—91no—
119C2×C5—182no—
120C2×C5—4652no—
121D5—932no—
122C32C2×C5×D15511yescharacteristic, complemented, Sylow
123C2×C3—4652no—
124D3—32no—
125D3—61no—
126D3—1552no—
127C5—22no—
128C5C5×(C3⋊D3)⋊D3111yescharacteristic, complemented
129C5(C3⋊D3)⋊D15511yescharacteristic, direct product factor
130C22—13951noSylow
131C3—21no—
132C3C5×D3×D15512yescomplemented
133C2—91no—
134C2—4652no—
subgroupG/H
center, hypercenterC5(C3⋊D3)⋊D155
commutator, cosocle, hypocenterC32×C5×C31C22×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C32×C5×C31
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D465C2semidirect
2. C52×C3⋊D3×C31C2semidirect
4. C32×C52×C31C22semidirect
5. (C3⋊D3)⋊D155C5direct (N × H)
7. C5×D465D3semidirect
13. C5×C3⋊D3×C31D5semidirect
14. C5×C3⋊D3×C31C2×C5semidirect
15. C3×D465C2×C5semidirect
18. C3×C52×C31C2×D3semidirect
24. C32×C5×C31C2×D5semidirect
25. C32×C5×C31C22×C5semidirect
27. D465C5×D3semidirect
38. C52×C31D32semidirect
41. C3⋊D3×C31C5×D5semidirect
47. C3×C5×C31D3×D5semidirect
48. C3×C5×C31C2×C5×D3semidirect
49. C52×C3⋊D3D31semidirect
58. C32×C31C2×C5×D5semidirect
59. C32×C52C2×D31semidirect
67. C5×C31C5×D32semidirect
68. C5×C31(C3⋊D3)⋊D5semidirect
76. C3×C31C5×D3×D5semidirect
78. C5×C3⋊D3C5×D31semidirect
79. C5×C3⋊D3D155semidirect
83. C3×C52D3×D31semidirect
91. C32×C5C2×C5×D31semidirect
92. C32×C5C2×D155semidirect
94. C31C5×(C3⋊D3)⋊D5semidirect
105. C52(C3⋊D3)⋊D31semidirect
108. C3⋊D3C5×D155semidirect
114. C3×C5C5×D3×D31semidirect
115. C3×C5D3×D155semidirect
122. C32C2×C5×D155semidirect
128. C5C5×(C3⋊D3)⋊D31semidirect
129. C5(C3⋊D3)⋊D155direct (N × H)
132. C3C5×D3×D155semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4652
C52×C3⋊D3×C312
C5×D3×D1553
(C3⋊D3)⋊D1555
C5×(C3⋊D3)⋊D315
C5×(C3⋊D3)⋊D531