Finite Group Databasebeta

← C5×#67151 #14268281

Subgroups — C5×#67151 #14268281

Order 1800.

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C2×C5×C3⋊D15C211yesmaximal, characteristic, complemented
2C2×C3×C5×D15C211yesmaximal, characteristic, complemented
3C3×C52×Dic3C211yesmaximal, characteristic, complemented
4C5×D60—31nomaximal
5C5×#1202—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C5×C3⋊D15—21no—
8C3×C5×D15—21no—
9#67151C511yesmaximal, characteristic, direct product factor
10C5×#626—51nomaximal
11C2×C5×D15—31no—
12C2×C5×D15—31no—
13C2×C5×D15—61no—
14C2×C5×D15D311yescharacteristic, complemented
15C2×C3×C5×D5—31no—
16C3×C4×C52—31no—
17C52×Dic3D311yescharacteristic, complemented
18C32×C52D411yescharacteristic, complemented, Hall
19C5×D20—91noHall
20C2×C3⋊D15C2×C511yescharacteristic, complemented
21C2×C5×C3⋊D3—51no—
22C2×C3×D15C2×C511yescharacteristic, complemented
23C2×C3×C5×D3—51no—
24C3×C5×Dic3—22no—
25C3×C5×Dic3D511yescharacteristic, complemented
26C3×C5×Dic3C2×C511yescharacteristic, complemented
27C2×C3×C52—21no—
28C2×C3×C52C2×D311yescharacteristic
29C2×C3×C52C2×D311yescharacteristic
30C5×D15—21no—
31C5×D15—62no—
32C5×D15—61no—
33C5×D15—61no—
34C3×C5×D5—61no—
35D60—31no—
36C5×#67—151no—
37C5×D12—151no—
38#1202—31no—
39C2×C5×D5—31no—
40C2×C5×D5—91no—
41C4×C52—31no—
42C2×C32×C5—22no—
43C2×C32×C5C2×D511yescharacteristic
44C2×C32×C5C22×C511yescharacteristic
45C3⋊D15—21no—
46C5×C3⋊D3—101no—
47C3×D15—21no—
48C3×C5×D3—101no—
49C3×C52—21no—
50C3×C52D1211yescharacteristic, complemented
51C3×C52#6711yescharacteristic, complemented
52#626—51noHall
53C22×C3×C5—151no—
54C2×D15—31no—
55C2×D15—31no—
56C2×D15—61no—
57C2×D15C5×D311yescharacteristic, complemented
58C2×C5×D3—51no—
59C2×C5×D3—151no—
60C2×C5×D3—151no—
61C2×C5×D3—301no—
62C2×C3×D5—31no—
63C3×C4×C5—31no—
64C3×C4×C5—31no—
65C3×C4×C5—62no—
66C5×Dic3—22no—
67C5×Dic3C5×D311yescharacteristic, complemented
68C5×Dic3D1511yescharacteristic, complemented
69C2×C52D3211yescharacteristic
70C5×D5—61no—
71C5×D5—181no—
72C32×C5—22no—
73C32×C5D2011yescharacteristic, complemented
74C32×C5C5×D411yescharacteristic, complemented
75C5×D4—451no—
76D20—91no—
77C2×C3⋊D3—51no—
78C2×C3×D3—51no—
79C3×Dic3C5×D511yescharacteristic, complemented
80C2×C3×C5—21no—
81C2×C3×C5—21no—
82C2×C3×C5—22no—
83C2×C3×C5—22no—
84C2×C3×C5—42no—
85C2×C3×C5—301no—
86C2×C3×C5D3×D511yescharacteristic
87C2×C3×C5C2×C5×D311yescharacteristic
88C2×C3×C5C2×C5×D311yescharacteristic
89C2×C3×C5C2×D1511yescharacteristic
90D15—21no—
91D15—62no—
92D15—61no—
93D15—61no—
94C3×D5—61no—
95C5×D3—101no—
96C5×D3—302no—
97C5×D3—301no—
98C5×D3—301no—
99C52#62611yescharacteristic, complemented, Sylow
100#67—151no—
101D12—151no—
102C22×C5—151no—
103C22×C5—451no—
104C2×D5—31no—
105C2×D5—91no—
106C4×C5—31no—
107C4×C5—31no—
108C4×C5—62no—
109C2×C32C2×C5×D511yescharacteristic
110C3⋊D3—101no—
111C3×D3—101no—
112C3×C5—21no—
113C3×C5—21no—
114C3×C5—22no—
115C3×C5—22no—
116C3×C5—42no—
117C3×C5#120211yescharacteristic, complemented
118C3×C5C5×D1211yescharacteristic, complemented
119C3×C5C5×#6711yescharacteristic, complemented
120C3×C5D6011yescharacteristic, complemented
121C22×C3—151no—
122C2×D3—51no—
123C2×D3—151no—
124C2×D3—151no—
125C2×D3—301no—
126C3×C4—31no—
127Dic3C5×D1511yescharacteristic, complemented
128C2×C5—22no—
129C2×C5—301no—
130C2×C5—901no—
131C2×C5C5×D3211yescharacteristic
132C2×C5D3×D1511yescharacteristic
133D5—61no—
134D5—181no—
135C32C5×D2011yescharacteristic, complemented, Sylow
136D4—451noSylow
137C2×C3—21no—
138C2×C3—301no—
139C2×C3C5×D3×D511yescharacteristic
140C2×C3C2×C5×D1511yescharacteristic
141D3—101no—
142D3—302no—
143D3—301no—
144D3—301no—
145C5—22no—
146C5C5×#62611yescharacteristic, complemented
147C5#6715111yescharacteristic, direct product factor
148C22—151no—
149C22—451no—
150C4—31no—
151C3—21no—
152C3C5×#120211yescharacteristic, complemented
153C3C5×D6011yescharacteristic, complemented
154C2—301no—
155C2—901no—
156C2C5×D3×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C5D3×D15
commutator, cosocleC2×C32×C5C22×C5
FrattiniC2C5×D3×D15
Fitting, socleC2×C32×C52C22
hypocenterC32×C5C5×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×C3⋊D15C2semidirect
2. C2×C3×C5×D15C2semidirect
3. C3×C52×Dic3C2semidirect
9. #67151C5direct (N × H)
14. C2×C5×D15D3semidirect
17. C52×Dic3D3semidirect
18. C32×C52D4semidirect
20. C2×C3⋊D15C2×C5semidirect
22. C2×C3×D15C2×C5semidirect
25. C3×C5×Dic3D5semidirect
26. C3×C5×Dic3C2×C5semidirect
50. C3×C52D12semidirect
51. C3×C52#67semidirect
57. C2×D15C5×D3semidirect
67. C5×Dic3C5×D3semidirect
68. C5×Dic3D15semidirect
73. C32×C5D20semidirect
74. C32×C5C5×D4semidirect
79. C3×Dic3C5×D5semidirect
99. C52#626semidirect
117. C3×C5#1202semidirect
118. C3×C5C5×D12semidirect
119. C3×C5C5×#67semidirect
120. C3×C5D60semidirect
127. Dic3C5×D15semidirect
135. C32C5×D20semidirect
146. C5C5×#626semidirect
147. C5#67151direct (N × H)
152. C3C5×#1202semidirect
153. C3C5×D60semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C3⋊D152
C2×C3×C5×D152
C3×C52×Dic32
C5×D603
C5×#12023
#671515
C5×#6265