Finite Group Databasebeta

← C5×#67149 #14268279

Subgroups — C5×#67149 #14268279

Order 1800.

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 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
2C3×C5×Dic15C211yesmaximal, characteristic, complemented
3C3×C52×Dic3C211yesmaximal, characteristic, complemented
4C4×C5×D15—31nomaximal
5C5×#1200—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C5×C3⋊D15C412yescomplemented
8#67149C511yesmaximal, characteristic, direct product factor
9C5×#624—51nomaximal
10C2×C5×D15—31no—
11C2×C5×D15—31no—
12C2×C5×D15—61no—
13C3×C4×C52—31no—
14C5×Dic15D311yescharacteristic, complemented
15C52×Dic3D311yescharacteristic, complemented
16C3×C5×Dic5—31no—
17C32×C52C2×C411yescharacteristic, complemented, Hall
18C4×C5×D5—91noHall
19C2×C3⋊D15C2×C511yescharacteristic
20C2×C5×C3⋊D3—51no—
21C3×Dic15C2×C511yescharacteristic, complemented
22C3×C5×Dic3—22no—
23C3×C5×Dic3—51no—
24C3×C5×Dic3D511yescharacteristic, complemented
25C3×C5×Dic3C2×C511yescharacteristic, complemented
26C2×C3×C52—21no—
27C2×C3×C52C2×D311yescharacteristic
28C2×C3×C52C2×D311yescharacteristic
29C5×D15—32no—
30C5×D15—32no—
31C5×D15—62no—
32C4×D15—31no—
33C4×C5×D3—151no—
34C4×C5×D3—151no—
35#1200—31no—
36C2×C5×D5—91no—
37C4×C52—31no—
38C5×Dic5—31no—
39C2×C32×C5—22no—
40C2×C32×C5C2×D511yescharacteristic
41C2×C32×C5C22×C511yescharacteristic
42C3⋊D15C4×C512yescomplemented
43C5×C3⋊D3—52no—
44C3×C52—21no—
45C3×C52C4×D311yescharacteristic, complemented
46C3×C52C4×D311yescharacteristic, complemented
47#624—51noHall
48C2×D15—31no—
49C2×D15—31no—
50C2×D15—61no—
51C2×C5×D3—151no—
52C2×C5×D3—151no—
53C2×C5×D3—301no—
54C3×C4×C5—31no—
55C3×C4×C5—31no—
56C3×C4×C5—62no—
57C3×C4×C5—151no—
58Dic15C5×D311yescharacteristic, complemented
59C3×Dic5—31no—
60C5×Dic3—22no—
61C5×Dic3—51no—
62C5×Dic3C5×D311yescharacteristic, complemented
63C5×Dic3D1511yescharacteristic, complemented
64C2×C52D3211yescharacteristic
65C5×D5—92no—
66C32×C5—22no—
67C32×C5C4×D511yescharacteristic, complemented
68C32×C5C2×C4×C511yescharacteristic, complemented
69C2×C4×C5—451no—
70C4×D5—91no—
71C2×C3⋊D3—51no—
72C3×Dic3—51no—
73C3×Dic3C5×D511yescharacteristic, complemented
74C2×C3×C5—21no—
75C2×C3×C5—21no—
76C2×C3×C5—22no—
77C2×C3×C5—22no—
78C2×C3×C5—42no—
79C2×C3×C5D3×D511yescharacteristic
80C2×C3×C5C2×C5×D311yescharacteristic
81C2×C3×C5C2×C5×D311yescharacteristic
82C2×C3×C5C2×D1511yescharacteristic
83D15—32no—
84D15—32no—
85D15—62no—
86C5×D3—152no—
87C5×D3—152no—
88C5×D3—302no—
89C52#62411yescharacteristic, complemented, Sylow
90C4×D3—151no—
91C4×D3—151no—
92C22×C5—451no—
93C2×D5—91no—
94C4×C5—31no—
95C4×C5—31no—
96C4×C5—62no—
97C4×C5—151no—
98Dic5—31no—
99C2×C32C2×C5×D511yescharacteristic
100C3⋊D3—52no—
101C3×C5—21no—
102C3×C5—21no—
103C3×C5—22no—
104C3×C5—22no—
105C3×C5—42no—
106C3×C5#120011yescharacteristic, complemented
107C3×C5C4×C5×D311yescharacteristic, complemented
108C3×C5C4×C5×D311yescharacteristic, complemented
109C3×C5C4×D1511yescharacteristic, complemented
110C2×D3—151no—
111C2×D3—151no—
112C2×D3—301no—
113C3×C4—31no—
114C3×C4—151no—
115Dic3—51no—
116Dic3C5×D1511yescharacteristic, complemented
117C2×C5—22no—
118C2×C5—452no—
119C2×C5C5×D3211yescharacteristic
120C2×C5D3×D1511yescharacteristic
121D5—92no—
122C32C4×C5×D511yescharacteristic, complemented, Sylow
123C2×C4—451noSylow
124C2×C3—21no—
125C2×C3C5×D3×D511yescharacteristic
126C2×C3C2×C5×D1511yescharacteristic
127D3—152no—
128D3—152no—
129D3—302no—
130C5—22no—
131C5C5×#62411yescharacteristic, complemented
132C5#6714911yescharacteristic, direct product factor
133C22—451no—
134C4—31no—
135C4—151no—
136C3—21no—
137C3C5×#120011yescharacteristic, complemented
138C3C4×C5×D1511yescharacteristic, complemented
139C2—452no—
140C2C5×D3×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C5D3×D15
commutator, hypocenterC32×C5C2×C4×C5
FrattiniC2C5×D3×D15
Fitting, socleC2×C32×C52C22
prime radicalC2×C5×C3⋊D15C2
cosocleC2×C32×C5C22×C5
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C3×C5×Dic15C2semidirect
3. C3×C52×Dic3C2semidirect
7. C5×C3⋊D15C4semidirect
8. #67149C5direct (N × H)
14. C5×Dic15D3semidirect
15. C52×Dic3D3semidirect
17. C32×C52C2×C4semidirect
21. C3×Dic15C2×C5semidirect
24. C3×C5×Dic3D5semidirect
25. C3×C5×Dic3C2×C5semidirect
42. C3⋊D15C4×C5semidirect
45. C3×C52C4×D3semidirect
46. C3×C52C4×D3semidirect
58. Dic15C5×D3semidirect
62. C5×Dic3C5×D3semidirect
63. C5×Dic3D15semidirect
67. C32×C5C4×D5semidirect
68. C32×C5C2×C4×C5semidirect
73. C3×Dic3C5×D5semidirect
89. C52#624semidirect
106. C3×C5#1200semidirect
107. C3×C5C4×C5×D3semidirect
108. C3×C5C4×C5×D3semidirect
109. C3×C5C4×D15semidirect
116. Dic3C5×D15semidirect
122. C32C4×C5×D5semidirect
131. C5C5×#624semidirect
132. C5#67149direct (N × H)
137. C3C5×#1200semidirect
138. C3C4×C5×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C3⋊D152
C3×C5×Dic152
C3×C52×Dic32
C4×C5×D153
C5×#12003
#671495
C5×#6245