Finite Group Databasebeta

← #13087045

Subgroups — #13087045

Order 1440.

564 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 140 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×#67184C211yesmaximal, characteristic, complemented
2C2×C5×#638C211yesmaximal, characteristic, complemented
3C22×C32×Dic5C211yesmaximal, characteristic, complemented
4C2×#67140C211yesmaximal, characteristic, complemented
5#10623773C211yesmaximal, characteristic, complemented
6#10623772C211yesmaximal, characteristic, complemented
7#10623771C211yesmaximal, characteristic, complemented
8#91566—34nomaximal
9C23×C32×C5C2211yescharacteristic
10C22×C3⋊D15C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic
12#67184—22no—
13C2×C3⋊Dic15C2211yescharacteristic
14C5×#638—22no—
15C2×C5×C3⋊Dic3C2211yescharacteristic
16C2×C32×Dic5—22no—
17C2×C32×Dic5C2211yescharacteristic
18C2×C32×Dic5C2211yescharacteristic
19#67140—22no—
20#64139—51nomaximal, Hall
21C2×#1220—34no—
22C2×C5×#67—34no—
23C22×C3×Dic5D314yescomplemented
24C2×#1203—34no—
25#6668—34no—
26#6667—34no—
27(C2×D3)⋊Dic5—34no—
28C22×C32×C5—21no—
29C22×C32×C5—21no—
30C22×C32×C5D412yescomplemented
31C22×C32×C5C2311yescharacteristic
32C2×C3⋊D15—21no—
33C2×C3⋊D15—21no—
34C2×C3⋊D15—21no—
35C2×C5×C3⋊D3—21no—
36C2×C5×C3⋊D3—21no—
37C2×C5×C3⋊D3—21no—
38C3⋊Dic15—21no—
39C5×C3⋊Dic3—21no—
40C32×Dic5—21no—
41C32×Dic5D412yescomplemented
42#4085—91noHall
43C22×C32×C4—51no—
44C2×#638—51no—
45C2×#638D511yescharacteristic, complemented
46C2×C4⋊(C3⋊D3)—51no—
47#3752—51no—
48#3752—51no—
49C4⋊(C3⋊Dic3)—51no—
50C23×C3×C5C2×D314yes—
51C22×D15—34no—
52C22×C5×D3—34no—
53#1220—68no—
54C2×Dic15—34no—
55C5×#67—68no—
56C2×C5×Dic3—34no—
57C2×C3×Dic5—28no—
58C2×C3×Dic5C2×D314yes—
59C2×C3×Dic5C2×D314yes—
60#1203—68no—
61#930—154no—
62C2×C32×C5—22no—
63C2×C32×C5C2×D411yescharacteristic
64C2×C32×C5C2×D411yescharacteristic
65C2×C32×C5#4111yescharacteristic
66C3⋊D15—41no—
67C5×C3⋊D3—41no—
68C2×C5×D4—91no—
69C2×C22⋊D5—91no—
70C2×C22⋊D5—91no—
71C22×Dic5C3⋊D311yescharacteristic, complemented
72C22⋊Dic5—91no—
73#685—91no—
74#683—91no—
75C23×C32C2×D511yescharacteristic
76C22×C3⋊D3—51no—
77C22×C3⋊D3C2×D511yescharacteristic
78C2×C32×C4—51no—
79C2×C32×C4—51no—
80C2×C32×C4—102no—
81#638—22no—
82#638—102no—
83C2×C3⋊Dic3—51no—
84C2×C3⋊Dic3C2×D511yescharacteristic
85C4⋊(C3⋊D3)—102no—
86C22×C3×C5—24no—
87C22×C3×C5—24no—
88C22×C3×C5D1218yescomplemented
89C22×C3×C5C22×D314yes—
90C2×D15—64no—
91C2×D15—64no—
92C2×D15—64no—
93C2×C5×D3—64no—
94C2×C5×D3—64no—
95C2×C5×D3—64no—
96Dic15—64no—
97C3×Dic5—24no—
98C3×Dic5#6718yescomplemented
99C5×Dic3—64no—
100C22×C3×C4—54no—
101C2×#67—34no—
102C2×#67—154no—
103C2×D12—154no—
104(C2×D3)⋊C4—154no—
105(C2×D3)⋊C4—154no—
106C4⋊Dic3—154no—
107C32×C5#12111yescharacteristic, complemented, Hall
108C23×C5—91no—
109C23×C5C2×C3⋊D311yescharacteristic
110C22×D5—91no—
111C5×D4—182no—
112C2×C4×C5—91no—
113C22⋊D5—182no—
114C22⋊D5—182no—
115C2×Dic5—22no—
116C2×Dic5—91no—
117C2×Dic5C2×C3⋊D311yescharacteristic
118C2×Dic5C2×C3⋊D311yescharacteristic
119C22×C32—21no—
120C22×C32—21no—
121C22×C32C22⋊D512yescomplemented
122C22×C32C22×D511yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3—101no—
127C2×C3⋊D3—101no—
128C2×C3⋊D3—101no—
129C32×C4—52no—
130C32×C4—101no—
131C3⋊Dic3—21no—
132C3⋊Dic3—101no—
133#121—451noSylow
134C2×C3×C5—28no—
135C2×C3×C5C2×D1214yes—
136C2×C3×C5#23514yes—
137C2×C3×C5C2×#6714yes—
138D15—124no—
139C5×D3—124no—
140C23×C3D3×D514yes—
141C22×D3—34no—
142C22×D3—154no—
143C2×C3×C4—54no—
144C2×C3×C4—54no—
145C2×C3×C4—108no—
146#67—68no—
147#67—308no—
148C2×Dic3—34no—
149C2×Dic3—154no—
150D12—308no—
151C22×C5—21no—
152C22×C5—21no—
153C22×C5—181no—
154C22×C5—181no—
155C22×C5—181no—
156C22×C5C4⋊(C3⋊D3)12yescomplemented
157C22×C5C22×C3⋊D311yescharacteristic
158C2×D5—181no—
159C2×D5—181no—
160C2×D5—181no—
161C4×C5—181no—
162Dic5—21no—
163Dic5—181no—
164Dic5#63812yescomplemented
165C2×C32—22no—
166C2×C32D4×D511yescharacteristic
167C2×C32#71111yescharacteristic
168C2×C32C2×C22⋊D511yescharacteristic
169C3⋊D3—41no—
170C3⋊D3—201no—
171C2×D4—91no—
172C2×D4—451no—
173C2×D4—451no—
174C22×C4—51no—
175C4⋊C4—451no—
176C22⋊C4—451no—
177C22⋊C4—451no—
178C3×C5#93014yescomplemented
179C22×C3—24no—
180C22×C3—24no—
181C22×C3#120318yescomplemented
182C22×C3C2×D3×D514yes—
183C2×D3—64no—
184C2×D3—64no—
185C2×D3—64no—
186C2×D3—304no—
187C2×D3—304no—
188C2×D3—304no—
189C3×C4—58no—
190C3×C4—104no—
191Dic3—64no—
192Dic3—304no—
193C2×C5—22no—
194C2×C5—361no—
195C2×C5C2×C4⋊(C3⋊D3)11yescharacteristic
196C2×C5#382811yescharacteristic
197C2×C5C2×#63811yescharacteristic
198D5—361no—
199C32#408511yescharacteristic, complemented, Sylow
200C23—91no—
201C23—451no—
202C23D5×C3⋊D311yescharacteristic
203D4—182no—
204D4—902no—
205D4—902no—
206C2×C4—51no—
207C2×C4—51no—
208C2×C4—91no—
209C2×C4—102no—
210C2×C4—451no—
211C2×C3—28no—
212C2×C3#678214yes—
213C2×C3C2×#120314yes—
214C2×C3D5×#6714yes—
215D3—124no—
216D3—604no—
217C5#6413911yescharacteristic, complemented, Sylow
218C22—21no—
219C22—21no—
220C22—181no—
221C22—181no—
222C22—181no—
223C22—901no—
224C22—901no—
225C22—901no—
226C22#6714012yescomplemented
227C22C2×D5×C3⋊D311yescharacteristic
228C4—52no—
229C4—101no—
230C4—181no—
231C4—901no—
232C3#9156614yescomplemented
233C2—22no—
234C2—361no—
235C2—1801no—
236C2#1062416511yescharacteristic
237C2C2×#6714011yescharacteristic
238C2D5×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D5×C3⋊D3
hypocenterC32×C5#121
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#67184C2semidirect
2. C2×C5×#638C2semidirect
3. C22×C32×Dic5C2semidirect
4. C2×#67140C2semidirect
5. #10623773C2semidirect
6. #10623772C2semidirect
7. #10623771C2semidirect
23. C22×C3×Dic5D3semidirect
30. C22×C32×C5D4semidirect
41. C32×Dic5D4semidirect
45. C2×#638D5semidirect
71. C22×Dic5C3⋊D3semidirect
88. C22×C3×C5D12semidirect
98. C3×Dic5#67semidirect
107. C32×C5#121semidirect
121. C22×C32C22⋊D5semidirect
156. C22×C5C4⋊(C3⋊D3)semidirect
164. Dic5#638semidirect
178. C3×C5#930semidirect
181. C22×C3#1203semidirect
199. C32#4085semidirect
217. C5#64139semidirect
226. C22#67140semidirect
232. C3#91566semidirect

Maximal subgroups

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

subgroupindex
C2×#671842
C2×C5×#6382
C22×C32×Dic52
C2×#671402
#106237732
#106237722
#106237712
#915663
#641395