Finite Group Databasebeta

← #13086924

Subgroups — #13086924

Order 1440.

456 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 108 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×#634C211yesmaximal, characteristic, complemented
2C2×#67139C211yesmaximal, characteristic
3#10623908C211yesmaximal, characteristic, complemented
4C32×#685C211yesmaximal, characteristic, complemented
5#10623772C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic, complemented
7Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#91455—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C32×D5C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C5×#634—22no—
16C2×C32×Dic5C2211yescharacteristic
17#67139—22no—
18#64094—51nomaximal, Hall
19C2×C5×Dic6—34no—
20C2×#1202—34no—
21#6714—34no—
22C3×#685D314yescomplemented
23#6667—34no—
24#6665—34no—
25Dic3×Dic5—34no—
26C22×C32×C5C2311yescharacteristic
27C2×C3⋊D15—21no—
28C2×C3⋊D15—21no—
29C2×C3⋊D15—21no—
30C2×C32×D5—21no—
31C2×C32×D5—21no—
32C2×C32×D5—21no—
33C32×C4×C5—21no—
34C3⋊Dic15—21no—
35C5×C3⋊Dic3—21no—
36C5×C3⋊Dic3D412yes—
37C32×Dic5—21no—
38#4093—91noHall
39C2×#638—51no—
40C2×#634D511yescharacteristic, complemented
41C32×C22⋊C4—51no—
42#3757—51no—
43#3752—51no—
44#3752—51no—
45C4×C3⋊Dic3—51no—
46C22×D15—34no—
47C22×C3×D5C2×D314yes—
48C2×C3×C4×C5C2×D314yes—
49C2×Dic15—34no—
50C2×C5×Dic3—34no—
51C2×C5×Dic3—34no—
52C5×Dic6—68no—
53C2×C3×Dic5C2×D314yes—
54#1202—68no—
55#885—154no—
56C2×C32×C5C2×D411yescharacteristic
57C2×C32×C5#4111yescharacteristic
58C2×C32×C5#4111yescharacteristic
59C3⋊D15—41no—
60C32×D5—41no—
61C2×C5×Q8—91no—
62C2×D20—91no—
63#685—91no—
64#685—91no—
65#685—91no—
66#685C3⋊D311yescharacteristic, complemented
67C4×Dic5—91no—
68C23×C32—51no—
69C22×C3⋊D3—51no—
70C2×C32×C4—51no—
71C2×C32×C4C2×D511yescharacteristic
72#638—102no—
73C2×C3⋊Dic3—51no—
74C2×C3⋊Dic3C2×D511yescharacteristic
75C2×C3⋊Dic3C2×D511yescharacteristic
76#634—22no—
77C22×C3×C5C22×D314yes—
78C2×D15—64no—
79C2×D15—64no—
80C2×D15—64no—
81C2×C3×D5—24no—
82C2×C3×D5—24no—
83C2×C3×D5—24no—
84C3×C4×C5—24no—
85Dic15—64no—
86C3×Dic5—24no—
87C5×Dic3—38no—
88C5×Dic3—64no—
89C2×#67—154no—
90C2×Dic6—34no—
91C3×C22⋊C4—54no—
92#217—154no—
93(C2×D3)⋊C4—154no—
94(C2×D3)⋊C4—154no—
95C4×Dic3—154no—
96C32×C5#12411yescharacteristic, complemented, Hall
97C22×D5—91no—
98C22×D5C2×C3⋊D311yescharacteristic
99C5×Q8—182no—
100C2×C4×C5—91no—
101C2×C4×C5—91no—
102C2×C4×C5C2×C3⋊D311yescharacteristic
103C2×Dic5—91no—
104C2×Dic5C2×C3⋊D311yescharacteristic
105D20—182no—
106C22×C32—101no—
107C22×C32—101no—
108C22×C32—101no—
109C22×C32C22×D511yescharacteristic
110C2×C3⋊D3—101no—
111C2×C3⋊D3—101no—
112C2×C3⋊D3—101no—
113C32×C4—21no—
114C32×C4—101no—
115C3⋊Dic3—21no—
116C3⋊Dic3—101no—
117C3⋊Dic3C22⋊D512yes—
118#124—451noSylow
119C2×C3×C5#23514yes—
120C2×C3×C5D3×D414yes—
121C2×C3×C5#23714yes—
122D15—124no—
123C3×D5—44no—
124C23×C3—54no—
125C22×D3—154no—
126C2×C3×C4—54no—
127C2×C3×C4D3×D514yes—
128#67—308no—
129C2×Dic3—34no—
130C2×Dic3—34no—
131C2×Dic3—154no—
132Dic6—68no—
133C22×C5C22×C3⋊D311yescharacteristic
134C2×D5—21no—
135C2×D5—21no—
136C2×D5—21no—
137C2×D5—181no—
138C2×D5—181no—
139C2×D5—181no—
140C4×C5—21no—
141C4×C5—92no—
142C4×C5—181no—
143Dic5—21no—
144Dic5—181no—
145C2×C32—201no—
146C2×C32#71311yescharacteristic
147C2×C32#71311yescharacteristic
148C2×C32C2×C22⋊D511yescharacteristic
149C3⋊D3—201no—
150C2×Q8—91no—
151C2×D4—451no—
152C22⋊C4—51no—
153C22⋊C4—451no—
154C22⋊C4—451no—
155C22⋊C4—451no—
156C42—451no—
157C3×C5#88514yescomplemented
158C22×C3—104no—
159C22×C3—104no—
160C22×C3—104no—
161C22×C3C2×D3×D514yes—
162C2×D3—304no—
163C2×D3—304no—
164C2×D3—304no—
165C3×C4—24no—
166C3×C4—104no—
167Dic3—38no—
168Dic3—64no—
169Dic3—304no—
170C2×C5#382811yescharacteristic
171C2×C5D4×C3⋊D311yescharacteristic
172C2×C5#383011yescharacteristic
173D5—41no—
174D5—361no—
175C32#409311yescharacteristic, complemented, Sylow
176C23—51no—
177C23—451no—
178Q8—182no—
179D4—902no—
180C2×C4—51no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—451no—
184C2×C4D5×C3⋊D311yescharacteristic
185C2×C3—204no—
186C2×C3#676614yes—
187C2×C3#677314yes—
188C2×C3D3×C22⋊D514yes—
189D3—604no—
190C5#6409411yescharacteristic, complemented, Sylow
191C22—101no—
192C22—101no—
193C22—101no—
194C22—901no—
195C22—901no—
196C22—901no—
197C22C2×D5×C3⋊D311yescharacteristic
198C4—21no—
199C4—92no—
200C4—101no—
201C4—181no—
202C4—901no—
203C3#9145514yescomplemented
204C2—201no—
205C2—1801no—
206C2#1062414911yescharacteristic
207C2#1062415611yescharacteristic
208C2C3⋊D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
prime radicalC2×#67139C2
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#124
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#634C2semidirect
3. #10623908C2semidirect
4. C32×#685C2semidirect
5. #10623772C2semidirect
6. #10623770C2semidirect
7. Dic5×C3⋊Dic3C2semidirect
22. C3×#685D3semidirect
40. C2×#634D5semidirect
66. #685C3⋊D3semidirect
96. C32×C5#124semidirect
157. C3×C5#885semidirect
175. C32#4093semidirect
190. C5#64094semidirect
203. C3#91455semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6342
C2×#671392
#106239082
C32×#6852
#106237722
#106237702
Dic5×C3⋊Dic32
#914553
#640945