Finite Group Databasebeta

← #13088943

Subgroups — #13088943

Order 1440.

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

normal subgroups only

This group has 624 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
1#10624222C211yesmaximal, characteristic, complemented
2D3×Dic30C212yesmaximal, complemented
3C5×#3798C211yesmaximal, characteristic, complemented
4#10624148C211yesmaximal, characteristic, complemented
5C3×#6765C212yesmaximal, complemented
6#10624046C212yesmaximal, complemented
7#10624043C214yesmaximal, complemented
8D5×#627C212yesmaximal, complemented
9#92001—32nomaximal
10#67180C2211yescharacteristic
11C4×C5×C3⋊D3C2211yescharacteristic
12C3×Dic30C2212yes—
13C3×C4×C5×D3C2212yes—
14C32×D20C2211yescharacteristic
15#67158C2212yes—
16#67155C2212yes—
17#67153C2214yes—
18D3×Dic15C2214yes—
19C5×#627C2211yescharacteristic
20C5×#626C2212yes—
21C5×#625C2211yescharacteristic
22#67138C2212yes—
23D5×C3⋊Dic3C2212yes—
24C3×#1201C2214yes—
25C3×D5×Dic3C2214yes—
26#64309—51nomaximal, Hall
27C2×Dic30—32no—
28C5×#235—32no—
29C3×#709—32no—
30#6780—34no—
31#6780—34no—
32#6772—34no—
33D3×Dic10—32no—
34D3×Dic10—32no—
35#6765—32no—
36#6765—61no—
37#6765D312yescomplemented
38D5×Dic6—34no—
39C2×C5×C3⋊D3C2311yescharacteristic
40C2×C3×C5×D3C2312yes—
41C2×C32×D5C2312yes—
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15C2312yes—
44C5×C3⋊Dic3C2311yescharacteristic
45C3×Dic15C2314yes—
46C3×C5×Dic3C2312yes—
47#4150—91noHall
48#3830—51no—
49C3×#237—52no—
50C2×#627—52no—
51#3805—52no—
52#3804—54no—
53#3798D511yescharacteristic, complemented
54#3797—51no—
55D3×Dic6—52no—
56C2×C3×C4×C5—32no—
57C2×Dic15—34no—
58Dic30—32no—
59Dic30—34no—
60Dic30—61no—
61Dic30C2×D312yes—
62C5×#67—32no—
63C5×#67—32no—
64C5×D12—32no—
65C4×C5×D3—32no—
66C4×C5×D3—61no—
67C4×C5×D3C2×D312yes—
68C5×Dic6—32no—
69C3×C22⋊D5—34no—
70C3×D20—21no—
71C3×D20C2×D312yes—
72C3×C4×D5—34no—
73C3×Dic10—32no—
74#1204—34no—
75#1204—34no—
76#1201—34no—
77#1201—62no—
78#1201C2×D314yes—
79D3×Dic5—34no—
80D3×Dic5—34no—
81D5×Dic3—34no—
82D5×Dic3—62no—
83D5×Dic3C2×D314yes—
84#1010—152no—
85C2×C32×C5C2411yescharacteristic
86C5×C3⋊D3—21no—
87C3×C5×D3—22no—
88C32×D5—22no—
89C5×#41—91no—
90Q8×D5—92no—
91#711—94no—
92#711—92no—
93#709—32no—
94#709—91no—
95C2×Dic10—91no—
96C2×Dic10—92no—
97C32×D4—51no—
98#638—52no—
99C2×C3⋊Dic3—52no—
100C4×C3⋊D3C2×D511yescharacteristic
101#634—51no—
102C3×#67—54no—
103C2×C3×Dic3—54no—
104C3×C4×D3C2×D512yes—
105C3×Dic6—52no—
106#627—52no—
107#627—54no—
108#627C2×D511yescharacteristic
109#626C2×D512yes—
110#625C2×D511yescharacteristic
111#624—52no—
112D3×Dic3—54no—
113C22×C3×C5—32no—
114C2×C5×D3—32no—
115C2×C5×D3—61no—
116C2×C5×D3C22×D312yes—
117C2×C3×D5—22no—
118C2×C3×D5C22×D314yes—
119C3×C4×C5—21no—
120C3×C4×C5—32no—
121C3×C4×C5C22×D312yes—
122Dic15—34no—
123Dic15—62no—
124Dic15C22×D314yes—
125C3×Dic5—34no—
126C5×Dic3—32no—
127C5×Dic3—61no—
128C5×Dic3C22×D312yes—
129C3×#41—152no—
130D3×Q8—152no—
131D3×Q8—152no—
132#237—52no—
133#237—152no—
134#237—154no—
135#237—154no—
136#237—301no—
137#235—32no—
138#235—154no—
139C2×Dic6—154no—
140C2×Dic6—152no—
141C32×C52−1+411yescharacteristic, complemented, Hall
142C5×Q8—91no—
143C5×D4—92no—
144C5×D4—91no—
145C2×C4×C5—32no—
146C2×C4×C5—91no—
147C22⋊D5—34no—
148C22⋊D5—92no—
149C2×Dic5—92no—
150C2×Dic5—94no—
151D20D3211yescharacteristic
152C4×D5—34no—
153C4×D5—92no—
154Dic10—32no—
155Dic10—92no—
156Dic10—94no—
157Dic10—91no—
158C22×C32—52no—
159C2×C3⋊D3C22×D511yescharacteristic
160C2×C3×D3C22×D512yes—
161C32×C4C22×D511yescharacteristic
162C3⋊Dic3—52no—
163C3⋊Dic3C22×D511yescharacteristic
164C3×Dic3—54no—
165C3×Dic3C22×D512yes—
1662−1+4—451noSylow
167C2×C3×C5—21no—
168C2×C3×C5—62no—
169C2×C3×C5C23×D312yes—
170C3×D5—24no—
171C3×D5—42no—
172C5×D3—22no—
173C5×D3—62no—
174C5×D3—121no—
175C3×Q8—152no—
176C3×D4—52no—
177C3×D4—101no—
178C3×D4—154no—
179C2×C3×C4—32no—
180C2×C3×C4—154no—
181#67—32no—
182#67—32no—
183#67—54no—
184#67—154no—
185#67—302no—
186C2×Dic3—54no—
187C2×Dic3—154no—
188C2×Dic3—154no—
189C2×Dic3—302no—
190D12—32no—
191C4×D3—32no—
192C4×D3—61no—
193C4×D3—154no—
194C4×D3—154no—
195C4×D3D3×D512yes—
196Dic6—32no—
197Dic6—52no—
198Dic6—154no—
199Dic6—154no—
200Dic6—152no—
201Dic6—154no—
202Dic6—301no—
203C22×C5—32no—
204C22×C5—91no—
205C2×D5C2×D3212yes—
206C4×C5—32no—
207C4×C5—91no—
208C4×C5C2×D3211yescharacteristic
209Dic5—34no—
210Dic5—92no—
211C2×C32—102no—
212C2×C32C23×D511yescharacteristic
213C3⋊D3—21no—
214C3×D3—22no—
215#41—91no—
216#41—152no—
217#41—451no—
218#41—454no—
219#41—452no—
220C2×Q8—452no—
221C2×Q8—451no—
222C2×Q8—452no—
223C3×C5—21no—
224C3×C5#101012yescomplemented
225C22×C3—32no—
226C22×C3—54no—
227C22×C3—102no—
228C2×D3—32no—
229C2×D3—61no—
230C2×D3C2×D3×D512yes—
231C3×C4—21no—
232C3×C4—32no—
233C3×C4—154no—
234C3×C4C2×D3×D512yes—
235Dic3—32no—
236Dic3—54no—
237Dic3—61no—
238Dic3—154no—
239Dic3—302no—
240Dic3C2×D3×D512yes—
241C2×C5—62no—
242C2×C5—181no—
243C2×C5C22×D3211yescharacteristic
244D5—22no—
245C32#415011yescharacteristic, complemented, Sylow
246Q8—91no—
247Q8—152no—
248Q8—454no—
249Q8—452no—
250Q8—451no—
251D4—51no—
252D4—92no—
253D4—91no—
254D4—154no—
255D4—452no—
256C2×C4—32no—
257C2×C4—91no—
258C2×C4—154no—
259C2×C4—452no—
260C2×C4—452no—
261C2×C4—454no—
262C2×C3—21no—
263C2×C3—62no—
264C2×C3—104no—
265C2×C3—202no—
266C2×C3C22×D3×D512yes—
267D3—22no—
268D3—62no—
269D3—121no—
270C5#6430911yescharacteristic, complemented, Sylow
271C22—32no—
272C22—52no—
273C22—91no—
274C4—32no—
275C4—91no—
276C4—154no—
277C4—452no—
278C4D32×D511yescharacteristic
279C3—21no—
280C3#9200112yescomplemented
281C2—62no—
282C2—102no—
283C2—181no—
284C2C2×D32×D511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C4×C5C23
hypercenterC4D32×D5
hypocenterC32×C52−1+4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624222C2semidirect
2. D3×Dic30C2semidirect
3. C5×#3798C2semidirect
4. #10624148C2semidirect
5. C3×#6765C2semidirect
6. #10624046C2semidirect
7. #10624043C2semidirect
8. D5×#627C2semidirect
37. #6765D3semidirect
53. #3798D5semidirect
141. C32×C52−1+4semidirect
224. C3×C5#1010semidirect
245. C32#4150semidirect
270. C5#64309semidirect
280. C3#92001semidirect

Maximal subgroups

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

subgroupindex
#106242222
D3×Dic302
C5×#37982
#106241482
C3×#67652
#106240462
#106240432
D5×#6272
#920013
#643095