Finite Group Databasebeta

← #13086873

Subgroups — #13086873

Order 1440.

468 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 116 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×#67139C211yesmaximal, characteristic
2C2×D5×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#10623908C211yesmaximal, characteristic, complemented
4C5×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C32×#685C211yesmaximal, characteristic, complemented
6#10623773C211yesmaximal, characteristic, complemented
7#10623772C211yesmaximal, characteristic, complemented
8#91413—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C32×D5C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16#67139—22no—
17D5×C3⋊Dic3—22no—
18#64095—51nomaximal, Hall
19C2×#1202—34no—
20C2×D5×Dic3—34no—
21#6714—34no—
22C5×C4⋊Dic3—34no—
23C3×#685D314yescomplemented
24#6668—34no—
25#6667—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×D5D412yes—
33C32×C4×C5—21no—
34C3⋊Dic15—21no—
35C5×C3⋊Dic3—21no—
36C5×C3⋊Dic3—21no—
37C32×Dic5—21no—
38#4040—91noHall
39C2×#638—51no—
40C22×C3⋊Dic3—51no—
41C32×C22⋊C4—51no—
42#3752—51no—
43#3752—51no—
44C4⋊(C3⋊Dic3)—51no—
45C4⋊(C3⋊Dic3)D511yescharacteristic, complemented
46C22×D15—34no—
47C22×C3×D5C2×D314yes—
48C2×C3×C4×C5C2×D314yes—
49C2×Dic15—34no—
50C2×C5×Dic3—34no—
51C2×C5×Dic3—34no—
52C2×C3×Dic5C2×D314yes—
53#1202—68no—
54D5×Dic3—68no—
55#886—154no—
56C2×C32×C5C2×D411yescharacteristic
57C2×C32×C5#4111yescharacteristic
58C2×C32×C5#4111yescharacteristic
59C3⋊D15—41no—
60C32×D5—22no—
61C2×D20—91no—
62C2×C4×D5—91no—
63C5×C4⋊C4—91no—
64#685—91no—
65#685—91no—
66#685C3⋊D311yescharacteristic, complemented
67#683—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⋊Dic3—102no—
75C2×C3⋊Dic3C2×D511yescharacteristic
76C2×C3⋊Dic3C2×D511yescharacteristic
77C22×C3×C5C22×D314yes—
78C2×D15—64no—
79C2×D15—64no—
80C2×D15—64no—
81C2×C3×D5—24no—
82C2×C3×D5—24no—
83C2×C3×D5D1218yes—
84C3×C4×C5—24no—
85Dic15—64no—
86C3×Dic5—24no—
87C5×Dic3—64no—
88C5×Dic3—64no—
89C2×#67—154no—
90C22×Dic3—154no—
91C3×C22⋊C4—54no—
92(C2×D3)⋊C4—154no—
93(C2×D3)⋊C4—154no—
94C4⋊Dic3—34no—
95C4⋊Dic3—154no—
96C32×C5#12311yescharacteristic, complemented, Hall
97C22×D5—91no—
98C22×D5C2×C3⋊D311yescharacteristic
99C2×C4×C5—91no—
100C2×C4×C5—91no—
101C2×C4×C5C2×C3⋊D311yescharacteristic
102C2×Dic5—91no—
103C2×Dic5C2×C3⋊D311yescharacteristic
104D20—182no—
105C4×D5—182no—
106C22×C32—52no—
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—21no—
117C3⋊Dic3—101no—
118#123—451noSylow
119C2×C3×C5C2×D1214yes—
120C2×C3×C5#23714yes—
121C2×C3×C5#23714yes—
122D15—124no—
123C3×D5—28no—
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—
132C2×Dic3—308no—
133C22×C5C22×C3⋊D311yescharacteristic
134C2×D5—21no—
135C2×D5—21no—
136C2×D5—181no—
137C2×D5—181no—
138C2×D5—181no—
139C2×D5C4⋊(C3⋊D3)12yes—
140C4×C5—21no—
141C4×C5—181no—
142C4×C5—181no—
143Dic5—21no—
144Dic5—181no—
145C2×C32—102no—
146C2×C32#70911yescharacteristic
147C2×C32D4×D511yescharacteristic
148C2×C32#71311yescharacteristic
149C3⋊D3—201no—
150C2×D4—451no—
151C22×C4—451no—
152C4⋊C4—91no—
153C4⋊C4—451no—
154C22⋊C4—51no—
155C22⋊C4—451no—
156C22⋊C4—451no—
157C3×C5#88614yescomplemented
158C22×C3—58no—
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—64no—
168Dic3—64no—
169Dic3—304no—
170C2×C5C2×C4⋊(C3⋊D3)11yescharacteristic
171C2×C5#383011yescharacteristic
172C2×C5#383011yescharacteristic
173D5—22no—
174D5—361no—
175C32#404011yescharacteristic, complemented, Sylow
176C23—51no—
177C23—451no—
178D4—902no—
179C2×C4—51no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—451no—
183C2×C4—902no—
184C2×C4D5×C3⋊D311yescharacteristic
185C2×C3—108no—
186C2×C3#676614yes—
187C2×C3D5×D1214yes—
188C2×C3#677914yes—
189D3—604no—
190C5#6409511yescharacteristic, complemented, Sylow
191C22—52no—
192C22—101no—
193C22—101no—
194C22—901no—
195C22—901no—
196C22—901no—
197C22C2×D5×C3⋊D311yescharacteristic
198C4—21no—
199C4—101no—
200C4—181no—
201C4—181no—
202C4—901no—
203C3#9141314yescomplemented
204C2—102no—
205C2—1801no—
206C2#1062414911yescharacteristic
207C2D5×C4⋊(C3⋊D3)11yescharacteristic
208C2#1062416211yescharacteristic
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#123
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D5×C3⋊Dic3C2semidirect
3. #10623908C2semidirect
4. C5×C4⋊(C3⋊Dic3)C2semidirect
5. C32×#685C2semidirect
6. #10623773C2semidirect
7. #10623772C2semidirect
23. C3×#685D3semidirect
45. C4⋊(C3⋊Dic3)D5semidirect
66. #685C3⋊D3semidirect
96. C32×C5#123semidirect
157. C3×C5#886semidirect
175. C32#4040semidirect
190. C5#64095semidirect
203. C3#91413semidirect

Maximal subgroups

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

subgroupindex
C2×#671392
C2×D5×C3⋊Dic32
#106239082
C5×C4⋊(C3⋊Dic3)2
C32×#6852
#106237732
#106237722
#914133
#640955