Finite Group Databasebeta

← #13086923

Subgroups — #13086923

Order 1440.

564 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4×C5×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#67140C211yesmaximal, characteristic, complemented
3C2×#67139C211yesmaximal, characteristic, complemented
4C2×#67138C211yesmaximal, characteristic, complemented
5#10623908C211yesmaximal, characteristic, complemented
6C32×#685C211yesmaximal, characteristic, complemented
7#10623775C211yesmaximal, characteristic, complemented
8#91454—34nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C32×D5C2211yescharacteristic
12C2×C32×C4×C5C2211yescharacteristic
13C2×C3⋊Dic15C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C4×C5×C3⋊D3—22no—
16C2×C32×Dic5C2211yescharacteristic
17#67140—22no—
18#67139—22no—
19#67138—22no—
20#64093—51nomaximal, Hall
21C2×C4×C5×D3—34no—
22C2×#1203—34no—
23C2×#1202—34no—
24C2×#1201—34no—
25#6714—34no—
26C3×#685D314yescomplemented
27Dic3⋊Dic5—34no—
28C22×C32×C5C2311yescharacteristic
29C2×C3⋊D15—21no—
30C2×C3⋊D15—21no—
31C2×C3⋊D15—21no—
32C2×C5×C3⋊D3—21no—
33C2×C5×C3⋊D3—21no—
34C2×C5×C3⋊D3D412yescomplemented
35C2×C32×D5—21no—
36C2×C32×D5—21no—
37C2×C32×D5—21no—
38C32×C4×C5—21no—
39C3⋊Dic15—21no—
40C5×C3⋊Dic3D412yescomplemented
41C32×Dic5—21no—
42#4076—91noHall
43C2×#638—51no—
44C2×#638—51no—
45C2×C4⋊(C3⋊D3)—51no—
46C2×C4×C3⋊D3D511yescharacteristic, complemented
47C32×C22⋊C4—51no—
48#3752—51no—
49#3750—51no—
50C22×D15—34no—
51C22×C5×D3—34no—
52C22×C3×D5C2×D314yes—
53C2×C3×C4×C5C2×D314yes—
54C2×Dic15—34no—
55C2×C5×Dic3—34no—
56C4×C5×D3—68no—
57C2×C3×Dic5C2×D314yes—
58#1203—68no—
59#1202—68no—
60#1201—68no—
61#884—154no—
62C2×C32×C5C2×D411yescharacteristic
63C2×C32×C5C2×D411yescharacteristic
64C2×C32×C5#4111yescharacteristic
65C3⋊D15—41no—
66C5×C3⋊D3—22no—
67C32×D5—41no—
68C22×C4×C5—91no—
69C2×C22⋊D5—91no—
70C2×C22⋊D5—91no—
71C2×D20—91no—
72#685—91no—
73#685C3⋊D311yescharacteristic, complemented
74C4⋊Dic5—91no—
75C23×C32—51no—
76C22×C3⋊D3—51no—
77C22×C3⋊D3C2×D511yescharacteristic
78C2×C32×C4—51no—
79C2×C32×C4C2×D511yescharacteristic
80#638—102no—
81#638—102no—
82C2×C3⋊Dic3—51no—
83C2×C3⋊Dic3C2×D511yescharacteristic
84C4⋊(C3⋊D3)—102no—
85C4×C3⋊D3—22no—
86C22×C3×C5C22×D314yes—
87C2×D15—64no—
88C2×D15—64no—
89C2×D15—64no—
90C2×C5×D3—38no—
91C2×C5×D3—64no—
92C2×C5×D3—64no—
93C2×C3×D5—24no—
94C2×C3×D5—24no—
95C2×C3×D5—24no—
96C3×C4×C5—24no—
97Dic15—64no—
98C3×Dic5—24no—
99C5×Dic3—38no—
100C2×#67—154no—
101C2×#67—154no—
102C2×D12—154no—
103C2×C4×D3—34no—
104C3×C22⋊C4—54no—
105(C2×D3)⋊C4—154no—
106Dic3⋊C4—154no—
107C32×C5#12111yescharacteristic, complemented, Hall
108C23×C5—91no—
109C22×D5—91no—
110C22×D5C2×C3⋊D311yescharacteristic
111C2×C4×C5—91no—
112C2×C4×C5—182no—
113C2×C4×C5C2×C3⋊D311yescharacteristic
114C22⋊D5—182no—
115C22⋊D5—182no—
116C2×Dic5—91no—
117C2×Dic5C2×C3⋊D311yescharacteristic
118D20—182no—
119C22×C32—101no—
120C22×C32—101no—
121C22×C32—101no—
122C22×C32C22×D511yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—101no—
126C2×C3⋊D3—101no—
127C2×C3⋊D3—101no—
128C2×C3⋊D3D2012yescomplemented
129C32×C4—21no—
130C32×C4—101no—
131C3⋊Dic3—101no—
132C3⋊Dic3C22⋊D512yescomplemented
133#121—451noSylow
134C2×C3×C5#23514yes—
135C2×C3×C5D3×D414yes—
136C2×C3×C5D3×D414yes—
137D15—124no—
138C3×D5—44no—
139C5×D3—68no—
140C23×C3—54no—
141C22×D3—34no—
142C22×D3—154no—
143C2×C3×C4—54no—
144C2×C3×C4D3×D514yes—
145#67—308no—
146#67—308no—
147C2×Dic3—34no—
148C2×Dic3—154no—
149D12—308no—
150C4×D3—68no—
151C22×C5—92no—
152C22×C5—181no—
153C22×C5—181no—
154C22×C5C22×C3⋊D311yescharacteristic
155C2×D5—21no—
156C2×D5—21no—
157C2×D5—21no—
158C2×D5—181no—
159C2×D5—181no—
160C2×D5—181no—
161C4×C5—21no—
162C4×C5—92no—
163Dic5—21no—
164Dic5—181no—
165C2×C32—201no—
166C2×C32C2×D2011yescharacteristic
167C2×C32#70911yescharacteristic
168C2×C32C2×C22⋊D511yescharacteristic
169C3⋊D3—22no—
170C3⋊D3—201no—
171C2×D4—451no—
172C2×D4—451no—
173C2×D4—451no—
174C22×C4—91no—
175C4⋊C4—451no—
176C22⋊C4—51no—
177C22⋊C4—451no—
178C3×C5#88414yescomplemented
179C22×C3—104no—
180C22×C3—104no—
181C22×C3—104no—
182C22×C3C2×D3×D514yes—
183C2×D3—38no—
184C2×D3—64no—
185C2×D3—64no—
186C2×D3—304no—
187C2×D3—304no—
188C2×D3—304no—
189C3×C4—24no—
190C3×C4—104no—
191Dic3—38no—
192Dic3—304no—
193C2×C5—182no—
194C2×C5#382811yescharacteristic
195C2×C5D4×C3⋊D311yescharacteristic
196C2×C5D4×C3⋊D311yescharacteristic
197D5—41no—
198D5—361no—
199C32#407611yescharacteristic, complemented, Sylow
200C23—51no—
201C23—91no—
202C23—451no—
203D4—902no—
204D4—902no—
205D4—902no—
206C2×C4—51no—
207C2×C4—91no—
208C2×C4—182no—
209C2×C4—451no—
210C2×C4D5×C3⋊D311yescharacteristic
211C2×C3—204no—
212C2×C3#677114yes—
213C2×C3D3×D2014yes—
214C2×C3D3×C22⋊D514yes—
215D3—68no—
216D3—604no—
217C5#6409311yescharacteristic, complemented, Sylow
218C22—92no—
219C22—101no—
220C22—101no—
221C22—101no—
222C22—181no—
223C22—181no—
224C22—901no—
225C22—901no—
226C22—901no—
227C22C2×D5×C3⋊D311yescharacteristic
228C4—21no—
229C4—92no—
230C4—101no—
231C4—901no—
232C3#9145414yescomplemented
233C2—182no—
234C2—201no—
235C2—1801no—
236C2#1062415411yescharacteristic
237C2C3⋊D3×D2011yescharacteristic
238C2C3⋊D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5#121
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×C4×C5×C3⋊D3C2semidirect
2. C2×#67140C2semidirect
3. C2×#67139C2semidirect
4. C2×#67138C2semidirect
5. #10623908C2semidirect
6. C32×#685C2semidirect
7. #10623775C2semidirect
26. C3×#685D3semidirect
34. C2×C5×C3⋊D3D4semidirect
40. C5×C3⋊Dic3D4semidirect
46. C2×C4×C3⋊D3D5semidirect
73. #685C3⋊D3semidirect
107. C32×C5#121semidirect
128. C2×C3⋊D3D20semidirect
132. C3⋊Dic3C22⋊D5semidirect
178. C3×C5#884semidirect
199. C32#4076semidirect
217. C5#64093semidirect
232. C3#91454semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊D32
C2×#671402
C2×#671392
C2×#671382
#106239082
C32×#6852
#106237752
#914543
#640935