Finite Group Databasebeta

← C5×#67150 #14268280

Subgroups — C5×#67150 #14268280

Order 1800.

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

normal subgroups only

This group has 184 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×C3×C5×D15C211yesmaximal, characteristic, complemented
2C2×C3×C52×D3C211yesmaximal, characteristic, complemented
3C5×C3⋊Dic15C211yesmaximal, characteristic, complemented
4C5×#1220—31nomaximal
5C5×#1201—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C3×C5×D15—21no—
8C3×C52×D3—21no—
9#67150C511yesmaximal, characteristic, direct product factor
10C5×#625—51nomaximal
11C22×C3×C52—31no—
12C2×C5×D15D311yescharacteristic, complemented
13C2×C52×D3D311yescharacteristic, complemented
14C2×C3×C5×D5—31no—
15C5×Dic15—31no—
16C5×Dic15—31no—
17C5×Dic15—61no—
18C32×C52D411yescharacteristic, complemented, Hall
19C5×C22⋊D5—91noHall
20C2×C3×D15C2×C511yescharacteristic, complemented
21C2×C3×C5×D3—22no—
22C2×C3×C5×D3—51no—
23C2×C3×C5×D3D511yescharacteristic, complemented
24C2×C3×C5×D3C2×C511yescharacteristic, complemented
25C3⋊Dic15C2×C511yescharacteristic, complemented
26C5×C3⋊Dic3—51no—
27C2×C3×C52—21no—
28C2×C3×C52—61no—
29C2×C3×C52C2×D311yescharacteristic
30C2×C3×C52C2×D311yescharacteristic
31C5×D15—21no—
32C52×D3—21no—
33C3×C5×D5—61no—
34#1220—31no—
35C5×#67—151no—
36C5×#67—151no—
37#1201—31no—
38C22×C52—31no—
39C2×C5×D5—31no—
40C5×Dic5—91no—
41C2×C32×C5—22no—
42C2×C32×C5C2×D511yescharacteristic
43C2×C32×C5C22×C511yescharacteristic
44C3×D15—21no—
45C3×C5×D3—24no—
46C3×C5×D3—21no—
47C3×C5×D3—21no—
48C3×C5×D3—101no—
49C3×C52—21no—
50C3×C52#6711yescharacteristic, complemented
51C3×C52#6711yescharacteristic, complemented
52#625—51noHall
53C22×C3×C5—31no—
54C22×C3×C5—31no—
55C22×C3×C5—62no—
56C22×C3×C5—151no—
57C2×D15C5×D311yescharacteristic, complemented
58C2×C5×D3—22no—
59C2×C5×D3—51no—
60C2×C5×D3C5×D311yescharacteristic, complemented
61C2×C5×D3D1511yescharacteristic, complemented
62C2×C3×D5—31no—
63Dic15—31no—
64Dic15—31no—
65Dic15—61no—
66C5×Dic3—151no—
67C5×Dic3—151no—
68C5×Dic3—301no—
69C2×C52—61no—
70C2×C52D3211yescharacteristic
71C5×D5—61no—
72C32×C5—22no—
73C32×C5C22⋊D511yescharacteristic, complemented
74C32×C5C5×D411yescharacteristic, complemented
75C5×D4—451no—
76C22⋊D5—91no—
77C2×C3×D3—51no—
78C2×C3×D3C5×D511yescharacteristic, complemented
79C3⋊Dic3—51no—
80C2×C3×C5—21no—
81C2×C3×C5—21no—
82C2×C3×C5—22no—
83C2×C3×C5—22no—
84C2×C3×C5—42no—
85C2×C3×C5—64no—
86C2×C3×C5—61no—
87C2×C3×C5—61no—
88C2×C3×C5—301no—
89C2×C3×C5D3×D511yescharacteristic
90C2×C3×C5C2×C5×D311yescharacteristic
91C2×C3×C5C2×C5×D311yescharacteristic
92C2×C3×C5C2×D1511yescharacteristic
93D15—21no—
94C3×D5—61no—
95C5×D3—24no—
96C5×D3—21no—
97C5×D3—21no—
98C5×D3—101no—
99C52#62511yescharacteristic, complemented, Sylow
100#67—151no—
101#67—151no—
102C22×C5—31no—
103C22×C5—31no—
104C22×C5—62no—
105C22×C5—151no—
106C2×D5—31no—
107C4×C5—451no—
108Dic5—91no—
109C2×C32C2×C5×D511yescharacteristic
110C3×D3—21no—
111C3×D3—101no—
112C3×C5—21no—
113C3×C5—21no—
114C3×C5—22no—
115C3×C5—22no—
116C3×C5—42no—
117C3×C5#120111yescharacteristic, complemented
118C3×C5C5×#6711yescharacteristic, complemented
119C3×C5C5×#6711yescharacteristic, complemented
120C3×C5#122011yescharacteristic, complemented
121C22×C3—31no—
122C22×C3—151no—
123C2×D3—51no—
124C2×D3C5×D1511yescharacteristic, complemented
125Dic3—151no—
126Dic3—151no—
127Dic3—301no—
128C2×C5—22no—
129C2×C5—64no—
130C2×C5—61no—
131C2×C5—61no—
132C2×C5—301no—
133C2×C5C5×D3211yescharacteristic
134C2×C5D3×D1511yescharacteristic
135D5—61no—
136C32C5×C22⋊D511yescharacteristic, complemented, Sylow
137D4—451noSylow
138C2×C3—21no—
139C2×C3—61no—
140C2×C3—301no—
141C2×C3C5×D3×D511yescharacteristic
142C2×C3C2×C5×D1511yescharacteristic
143D3—21no—
144D3—101no—
145C5—22no—
146C5C5×#62511yescharacteristic, complemented
147C5#6715011yescharacteristic, direct product factor
148C22—31no—
149C22—151no—
150C4—451no—
151C3—21no—
152C3C5×#120111yescharacteristic, complemented
153C3C5×#122011yescharacteristic, complemented
154C2—61no—
155C2—301no—
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×C3×C5×D15C2semidirect
2. C2×C3×C52×D3C2semidirect
3. C5×C3⋊Dic15C2semidirect
9. #67150C5direct (N × H)
12. C2×C5×D15D3semidirect
13. C2×C52×D3D3semidirect
18. C32×C52D4semidirect
20. C2×C3×D15C2×C5semidirect
23. C2×C3×C5×D3D5semidirect
24. C2×C3×C5×D3C2×C5semidirect
25. C3⋊Dic15C2×C5semidirect
50. C3×C52#67semidirect
51. C3×C52#67semidirect
57. C2×D15C5×D3semidirect
60. C2×C5×D3C5×D3semidirect
61. C2×C5×D3D15semidirect
73. C32×C5C22⋊D5semidirect
74. C32×C5C5×D4semidirect
78. C2×C3×D3C5×D5semidirect
99. C52#625semidirect
117. C3×C5#1201semidirect
118. C3×C5C5×#67semidirect
119. C3×C5C5×#67semidirect
120. C3×C5#1220semidirect
124. C2×D3C5×D15semidirect
136. C32C5×C22⋊D5semidirect
146. C5C5×#625semidirect
147. C5#67150direct (N × H)
152. C3C5×#1201semidirect
153. C3C5×#1220semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×D152
C2×C3×C52×D32
C5×C3⋊Dic152
C5×#12203
C5×#12013
#671505
C5×#6255