Finite Group Databasebeta

← C5×#63930 #13087202

Subgroups — C5×#63930 #13087202

Order 1440.

326 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C5×D4×C3⋊D3C211yesmaximal, characteristic
2C5×#3797C211yesmaximal, characteristic, complemented
3C3×C5×#214C212yesmaximal, complemented
4C5×#3717C212yesmaximal, complemented
5C5×#3710C211yesmaximal, characteristic, complemented
6C5×D3×SD16—32nomaximal
7C22×C5×C3⋊D3—21no—
8C32×C5×D4C2211yescharacteristic
9C5×#638—21no—
10C5×C4⋊(C3⋊D3)C2211yescharacteristic
11C4×C5×C3⋊D3C2211yescharacteristic
12C3×C5×Dic6C2212yescomplemented
13C5×#627—21no—
14C5×#624—21no—
15C3×C5×C3⋊C8C2212yescomplemented
16#63930C511yesmaximal, characteristic, direct product factor, Hall
17C5×D3×Q8—32no—
18C5×D3×D4—32no—
19C5×D3×D4—61no—
20C3×C5×SD16—32no—
21C5×#215—32no—
22C5×#214D312yescomplemented
23C5×#204—32no—
24C5×D3×C8—32no—
25C22×C32×C5—21no—
26C2×C5×C3⋊D3—21no—
27C2×C5×C3⋊D3—42no—
28C2×C5×C3⋊D3D411yescharacteristic
29C32×C4×C5C2311yescharacteristic
30C5×C3⋊Dic3D411yescharacteristic
31C3×C5×Dic3—22no—
32C2×C5×SD16—91noHall
33D4×C3⋊D3C2×C511yescharacteristic
34#3797C2×C511yescharacteristic, complemented
35C3×#214C2×C512yescomplemented
36#3717C2×C512yescomplemented
37#3710C2×C511yescharacteristic, complemented
38C22×C5×D3—62no—
39C22×C5×D3—62no—
40C3×C5×Q8—32no—
41C3×C5×D4—21no—
42C3×C5×D4C2×D312yes—
43C5×#67—62no—
44C5×#67—62no—
45C5×D12—32no—
46C5×D12—61no—
47C4×C5×D3—32no—
48C4×C5×D3—62no—
49C4×C5×D3—61no—
50C5×Dic6—62no—
51C5×Dic6C2×D312yescomplemented
52C3×C5×C8—32no—
53C5×C3⋊C8C2×D312yescomplemented
54D3×SD16—32no—
55C2×C32×C5—41no—
56C2×C32×C5C2×D411yescharacteristic
57C5×C3⋊D3—41no—
58C5×C3⋊D3SD1612yescomplemented
59C2×C5×Q8—91no—
60C2×C5×D4—91no—
61C5×SD16—32no—
62C5×SD16—92no—
63C2×C5×C8—91no—
64C22×C3⋊D3—21no—
65C32×D4C22×C511yescharacteristic
66#638—21no—
67C4⋊(C3⋊D3)C22×C511yescharacteristic
68C4×C3⋊D3C22×C511yescharacteristic
69C3×Dic6C22×C512yescomplemented
70#627—21no—
71#624—21no—
72C3×C3⋊C8C22×C512yescomplemented
73C22×C3×C5—22no—
74C22×C3×C5—22no—
75C2×C5×D3—32no—
76C2×C5×D3—61no—
77C2×C5×D3—62no—
78C2×C5×D3—62no—
79C2×C5×D3—124no—
80C2×C5×D3—124no—
81C3×C4×C5—21no—
82C3×C4×C5—62no—
83C3×C4×C5C22×D312yes—
84C5×Dic3—22no—
85C5×Dic3—32no—
86C5×Dic3—61no—
87D3×Q8—32no—
88D3×D4—32no—
89D3×D4—61no—
90C3×SD16—32no—
91#215—32no—
92#214C5×D312yescomplemented
93#204—32no—
94D3×C8—32no—
95C32×C5C2×SD1611yescharacteristic, complemented, Hall
96C23×C5—181no—
97C5×Q8—32no—
98C5×Q8—181no—
99C5×D4—91no—
100C5×D4—181no—
101C5×D4D3211yescharacteristic
102C2×C4×C5—91no—
103C2×C4×C5—181no—
104C5×C8—32no—
105C22×C32—21no—
106C2×C3⋊D3—21no—
107C2×C3⋊D3—42no—
108C2×C3⋊D3C5×D411yescharacteristic
109C32×C4C23×C511yescharacteristic
110C3⋊Dic3C5×D411yescharacteristic
111C3×Dic3—22no—
112C2×SD16—91noSylow
113C2×C3×C5—21no—
114C2×C3×C5—42no—
115C2×C3×C5—42no—
116C2×C3×C5D3×D412yes—
117C5×D3—34no—
118C5×D3—62no—
119C5×D3—122no—
120C5×D3—122no—
121C22×D3—62no—
122C22×D3—62no—
123C3×Q8—32no—
124C3×D4—21no—
125C3×D4C2×C5×D312yes—
126#67—62no—
127#67—62no—
128D12—32no—
129D12—61no—
130C4×D3—32no—
131C4×D3—61no—
132C4×D3—62no—
133Dic6—62no—
134Dic6C2×C5×D312yescomplemented
135C3×C8—32no—
136C3⋊C8C2×C5×D312yescomplemented
137C22×C5—21no—
138C22×C5—91no—
139C22×C5—181no—
140C22×C5—362no—
141C4×C5—62no—
142C4×C5—91no—
143C4×C5C2×D3211yescharacteristic
144C2×C32—41no—
145C2×C32C2×C5×D411yescharacteristic
146C3⋊D3—41no—
147C3⋊D3C5×SD1612yescomplemented
148C2×Q8—91no—
149C2×D4—91no—
150SD16—32no—
151SD16—92no—
152C2×C8—91no—
153C3×C5—21no—
154C3×C5D3×SD1612yescomplemented
155C22×C3—22no—
156C22×C3—22no—
157C2×D3—32no—
158C2×D3—61no—
159C2×D3—62no—
160C2×D3—62no—
161C2×D3—124no—
162C2×D3—124no—
163C3×C4—21no—
164C3×C4—62no—
165C3×C4C22×C5×D312yes—
166Dic3—22no—
167Dic3—32no—
168Dic3—61no—
169C2×C5—41no—
170C2×C5—92no—
171C2×C5—361no—
172C2×C5#381111yescharacteristic
173C32C2×C5×SD1611yescharacteristic, complemented, Sylow
174C23—181no—
175Q8—32no—
176Q8—181no—
177D4—91no—
178D4—181no—
179D4C5×D3211yescharacteristic
180C2×C4—91no—
181C2×C4—181no—
182C8—32no—
183C2×C3—21no—
184C2×C3—42no—
185C2×C3—42no—
186C2×C3C5×D3×D412yes—
187D3—34no—
188D3—62no—
189D3—122no—
190D3—122no—
191C5#6393011yescharacteristic, direct product factor, Sylow
192C22—21no—
193C22—91no—
194C22—181no—
195C22—362no—
196C4—62no—
197C4—91no—
198C4C2×C5×D3211yescharacteristic
199C3—21no—
200C3C5×D3×SD1612yescomplemented
201C2—41no—
202C2—92no—
203C2—361no—
204C2C5×#381111yescharacteristic
subgroupG/H
centerC2×C5#3811
commutator, cosocleC32×C4C23×C5
FrattiniC4C2×C5×D32
FittingC32×C5×D4C22
socleC2×C32×C5C2×D4
prime radicalC5×D4×C3⋊D3C2
hypercenterC5×D4D32
hypocenterC32C2×C5×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D4

Complements

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

NH ≅ G/Ntype
2. C5×#3797C2semidirect
3. C3×C5×#214C2semidirect
4. C5×#3717C2semidirect
5. C5×#3710C2semidirect
12. C3×C5×Dic6C22semidirect
15. C3×C5×C3⋊C8C22semidirect
16. #63930C5direct (N × H)
22. C5×#214D3semidirect
34. #3797C2×C5semidirect
35. C3×#214C2×C5semidirect
36. #3717C2×C5semidirect
37. #3710C2×C5semidirect
51. C5×Dic6C2×D3semidirect
53. C5×C3⋊C8C2×D3semidirect
58. C5×C3⋊D3SD16semidirect
69. C3×Dic6C22×C5semidirect
72. C3×C3⋊C8C22×C5semidirect
92. #214C5×D3semidirect
95. C32×C5C2×SD16semidirect
134. Dic6C2×C5×D3semidirect
136. C3⋊C8C2×C5×D3semidirect
147. C3⋊D3C5×SD16semidirect
154. C3×C5D3×SD16semidirect
173. C32C2×C5×SD16semidirect
191. C5#63930direct (N × H)
200. C3C5×D3×SD16semidirect

Maximal subgroups

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

subgroupindex
C5×D4×C3⋊D32
C5×#37972
C3×C5×#2142
C5×#37172
C5×#37102
C5×D3×SD163
#639305