Finite Group Databasebeta

← #13089412

Subgroups — #13089412

Order 1440.

624 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 143 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×#3830C211yesmaximal, characteristic, complemented
2C3×#6819C212yesmaximal, complemented
3C2×#67158C212yesmaximal, complemented
4#10624230C214yesmaximal, complemented
5#10624229C212yesmaximal, complemented
6#10624223C211yesmaximal, characteristic, complemented
7#10624222C211yesmaximal, characteristic, complemented
8#10624219C212yesmaximal, complemented
9#92020—32nomaximal
10C32×C5×D4C2211yescharacteristic
11C5×#638C2212yes—
12C2×C5×C3⋊Dic3C2212yes—
13C4×C5×C3⋊D3C2211yescharacteristic
14C5×#634C2211yescharacteristic
15C3×#1220C2214yes—
16C2×C3×Dic15C2214yes—
17C3×C4×D15C2212yes—
18C3×Dic30C2212yes—
19#67158C2214yes—
20#67158C2212yes—
21#67158C2211yescharacteristic
22#67157C2211yescharacteristic
23#67156C2212yes—
24#67155C2212yes—
25#67154C2214yes—
26#64309—51nomaximal, Hall
27#6819D312yescomplemented
28C5×#237—32no—
29C5×#237—61no—
30C3×#711—32no—
31C2×#1204—34no—
32#6782—34no—
33#6780—34no—
34#6779—34no—
35#6771—32no—
36D15⋊Q8—32no—
37D3×Dic10—32no—
38D5×Dic6—32no—
39C22×C32×C5C2312yes—
40C2×C5×C3⋊D3C2311yescharacteristic
41C2×C3×D15C2312yes—
42C32×C4×C5C2311yescharacteristic
43C5×C3⋊Dic3C2312yes—
44C5×C3⋊Dic3C2311yescharacteristic
45C3×Dic15C2314yes—
46C3×Dic15C2312yes—
47#4150—91noHall
48#3830D511yescharacteristic, complemented
49C3×#237—52no—
50C2×#627—52no—
51#3805—52no—
52#3804—54no—
53#3798—51no—
54#3797—51no—
55D3×Dic6—52no—
56C3×C5×D4—21no—
57C3×C5×D4C2×D312yes—
58#1220C2×D314yes—
59C2×Dic15C2×D314yes—
60C4×D15C2×D312yes—
61Dic30C2×D312yes—
62C5×#67—34no—
63C5×#67—62no—
64C2×C5×Dic3—34no—
65C2×C5×Dic3—62no—
66C4×C5×D3—32no—
67C4×C5×D3—61no—
68C5×Dic6—32no—
69C5×Dic6—61no—
70C3×C22⋊D5—34no—
71C2×C3×Dic5—34no—
72C3×C4×D5—32no—
73C3×Dic10—32no—
74#1204—34no—
75#1204—34no—
76#1204—34no—
77#1204—32no—
78#1203—32no—
79#1202—32no—
80#1201—32no—
81#1200—34no—
82D3×Dic5—34no—
83D5×Dic3—34no—
84#1010—152no—
85C2×C32×C5—22no—
86C2×C32×C5C2411yescharacteristic
87C5×C3⋊D3—21no—
88C3×D15—22no—
89C5×#41—91no—
90Q8×D5—92no—
91#711—32no—
92#711—94no—
93#709—91no—
94#709—92no—
95C2×Dic10—91no—
96C2×Dic10—92no—
97C32×D4C2×D511yescharacteristic
98#638C2×D512yes—
99C2×C3⋊Dic3C2×D512yes—
100C4×C3⋊D3C2×D511yescharacteristic
101#634C2×D511yescharacteristic
102C3×#67—54no—
103C2×C3×Dic3—54no—
104C3×C4×D3—52no—
105C3×Dic6—52no—
106#627—54no—
107#627—52no—
108#627—51no—
109#626—52no—
110#625—51no—
111#624—52no—
112D3×Dic3—54no—
113C22×C3×C5—22no—
114C22×C3×C5C22×D314yes—
115C2×D15C22×D312yes—
116C2×C5×D3—32no—
117C2×C5×D3—61no—
118C2×C3×D5—32no—
119C3×C4×C5—21no—
120C3×C4×C5C22×D312yes—
121Dic15C22×D314yes—
122Dic15C22×D312yes—
123C3×Dic5—34no—
124C3×Dic5—32no—
125C5×Dic3—34no—
126C5×Dic3—32no—
127C5×Dic3—62no—
128C5×Dic3—61no—
129C3×#41—152no—
130D3×Q8—152no—
131D3×Q8—152no—
132#237—32no—
133#237—52no—
134#237—61no—
135#237—154no—
136#237—154no—
137#235—152no—
138#235—154no—
139C2×Dic6—152no—
140C2×Dic6—154no—
141C32×C52−1+411yescharacteristic, complemented, Hall
142C5×Q8—91no—
143C5×D4—92no—
144C5×D4D3211yescharacteristic
145C2×C4×C5—92no—
146C2×C4×C5—91no—
147C22⋊D5—34no—
148C22⋊D5—92no—
149C2×Dic5—34no—
150C2×Dic5—92no—
151D20—91no—
152C4×D5—32no—
153C4×D5—94no—
154Dic10—32no—
155Dic10—92no—
156Dic10—91no—
157Dic10—94no—
158C22×C32C22×D512yes—
159C2×C3⋊D3C22×D511yescharacteristic
160C2×C3×D3—52no—
161C32×C4C22×D511yescharacteristic
162C3⋊Dic3C22×D512yes—
163C3⋊Dic3C22×D511yescharacteristic
164C3×Dic3—54no—
165C3×Dic3—52no—
1662−1+4—451noSylow
167C2×C3×C5—24no—
168C2×C3×C5—21no—
169C2×C3×C5—42no—
170C2×C3×C5C23×D312yes—
171D15—22no—
172C3×D5—62no—
173C5×D3—62no—
174C5×D3—121no—
175C3×Q8—152no—
176C3×D4—21no—
177C3×D4—154no—
178C3×D4D3×D512yes—
179C2×C3×C4—154no—
180C2×C3×C4—152no—
181#67—34no—
182#67—54no—
183#67—62no—
184#67—152no—
185#67—152no—
186C2×Dic3—34no—
187C2×Dic3—54no—
188C2×Dic3—62no—
189C2×Dic3—154no—
190D12—152no—
191C4×D3—32no—
192C4×D3—52no—
193C4×D3—61no—
194C4×D3—154no—
195C4×D3—154no—
196Dic6—32no—
197Dic6—52no—
198Dic6—61no—
199Dic6—154no—
200Dic6—152no—
201Dic6—154no—
202Dic6—154no—
203C22×C5—91no—
204C22×C5C2×D3212yes—
205C2×D5—32no—
206C4×C5—91no—
207C4×C5—92no—
208C4×C5C2×D3211yescharacteristic
209Dic5—34no—
210Dic5—32no—
211C2×C32—22no—
212C2×C32C23×D511yescharacteristic
213C3⋊D3—21no—
214C3×D3—102no—
215#41—91no—
216#41—152no—
217#41—451no—
218#41—452no—
219#41—454no—
220C2×Q8—452no—
221C2×Q8—451no—
222C2×Q8—452no—
223C3×C5—21no—
224C3×C5#101012yescomplemented
225C22×C3—22no—
226C22×C3—152no—
227C22×C3C2×D3×D514yes—
228C2×D3—32no—
229C2×D3—52no—
230C2×D3—61no—
231C3×C4—21no—
232C3×C4—152no—
233C3×C4—154no—
234C3×C4C2×D3×D512yes—
235Dic3—34no—
236Dic3—32no—
237Dic3—54no—
238Dic3—52no—
239Dic3—62no—
240Dic3—61no—
241C2×C5—22no—
242C2×C5—181no—
243C2×C5C22×D3211yescharacteristic
244D5—62no—
245C32#415011yescharacteristic, complemented, Sylow
246Q8—91no—
247Q8—152no—
248Q8—451no—
249Q8—452no—
250Q8—454no—
251D4—92no—
252D4—154no—
253D4—451no—
254D4—452no—
255D4(C3⋊D3)⋊D511yescharacteristic
256C2×C4—92no—
257C2×C4—91no—
258C2×C4—154no—
259C2×C4—152no—
260C2×C4—454no—
261C2×C4—452no—
262C2×C3—24no—
263C2×C3—21no—
264C2×C3—42no—
265C2×C3—302no—
266C2×C3C22×D3×D512yes—
267D3—62no—
268D3—102no—
269D3—121no—
270C5#6430911yescharacteristic, complemented, Sylow
271C22—91no—
272C22—152no—
273C22C2×(C3⋊D3)⋊D512yes—
274C4—91no—
275C4—92no—
276C4—152no—
277C4—154no—
278C4C2×(C3⋊D3)⋊D511yescharacteristic
279C3—21no—
280C3#9202012yescomplemented
281C2—22no—
282C2—181no—
283C2—302no—
284C2C22×(C3⋊D3)⋊D511yescharacteristic
subgroupG/H
center, FrattiniC2C22×(C3⋊D3)⋊D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C5×D4C22
hypercenterD4(C3⋊D3)⋊D5
hypocenterC32×C52−1+4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C5×#3830C2semidirect
2. C3×#6819C2semidirect
3. C2×#67158C2semidirect
4. #10624230C2semidirect
5. #10624229C2semidirect
6. #10624223C2semidirect
7. #10624222C2semidirect
8. #10624219C2semidirect
27. #6819D3semidirect
48. #3830D5semidirect
141. C32×C52−1+4semidirect
224. C3×C5#1010semidirect
245. C32#4150semidirect
270. C5#64309semidirect
280. C3#92020semidirect

Maximal subgroups

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

subgroupindex
C5×#38302
C3×#68192
C2×#671582
#106242302
#106242292
#106242232
#106242222
#106242192
#920203
#643095