Finite Group Databasebeta

← #13087667

Subgroups — #13087667

Order 1440.

394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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×C3×C4×D15C211yesmaximal, characteristic
2C2×#67154C211yesmaximal, characteristic
3C2×#67154C211yesmaximal, characteristic
4C5×#3750C211yesmaximal, characteristic, complemented
5C3×#6712C211yesmaximal, characteristic, complemented
6#10623832C211yesmaximal, characteristic, complemented
7#10623831C211yesmaximal, characteristic, complemented
8#91404—31nomaximal
9D5×Dic3⋊C4—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×Dic15C2211yescharacteristic
17C3×C4×D15—22no—
18#67154—22no—
19#67154C414yescomplemented
20D3×Dic3⋊C4—51nomaximal, Hall
21C2×C4×D15D311yescharacteristic
22C2×C3×C4×D5—31no—
23C2×#1200—31no—
24C2×#1200—31no—
25C2×D5×Dic3—31no—
26C2×D5×Dic3—31no—
27#6712D311yescharacteristic, complemented
28C5×Dic3⋊C4—31no—
29C5×Dic3⋊C4—31no—
30C5×Dic3⋊C4—61no—
31C3×#683—31no—
32Dic3⋊Dic5—31no—
33Dic3⋊Dic5—31no—
34#6669—31no—
35#6668—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3×D15C2×C412yes—
38C2×C3×D15D412yes—
39C2×C3×D15Q812yes—
40C32×C4×C5—21no—
41C5×C3⋊Dic3—21no—
42C5×C3⋊Dic3C2×C412yescomplemented
43C3×Dic15—21no—
44C3×Dic15—21no—
45C3×Dic15C2×C412yescomplemented
46D5×C4⋊C4—91noHall
47C2×C3×C4×D3—51no—
48C2×D3×Dic3—51no—
49C2×D3×Dic3—51no—
50#3750D511yescharacteristic, complemented
51C3×Dic3⋊C4—51no—
52#3724—51no—
53Dic3⋊Dic3—51no—
54C22×D15C2×D311yescharacteristic
55C22×C3×D5—31no—
56C2×C3×C4×C5—21no—
57C2×C3×C4×C5C2×D311yescharacteristic
58C2×C3×C4×C5C2×D311yescharacteristic
59C2×Dic15C2×D311yescharacteristic
60C2×Dic15C2×D311yescharacteristic
61C2×Dic15C2×D311yescharacteristic
62C4×D15—22no—
63C2×C5×Dic3—31no—
64C2×C5×Dic3—31no—
65C2×C5×Dic3—31no—
66C2×C5×Dic3—31no—
67C2×C5×Dic3—61no—
68C2×C5×Dic3—61no—
69C2×C3×Dic5—31no—
70C2×C3×Dic5—31no—
71C2×C3×Dic5—31no—
72C3×C4×D5—62no—
73#1200—34no—
74#1200—62no—
75D5×Dic3—34no—
76D5×Dic3—62no—
77C2×Dic3⋊C4—151no—
78D3×C4⋊C4—151no—
79C2×C32×C5C22×C411yescharacteristic
80C2×C32×C5C2×D411yescharacteristic
81C2×C32×C5C2×Q811yescharacteristic
82C3×D15C4⋊C414yescomplemented
83C2×C4×D5—31no—
84C2×C4×D5—91no—
85C2×C4×D5—91no—
86C5×C4⋊C4—91no—
87C4⋊Dic5—91no—
88#683—31no—
89#683—91no—
90C22×C3×D3—51no—
91C2×C32×C4C2×D511yescharacteristic
92C2×C3⋊Dic3C2×D511yescharacteristic
93C2×C3⋊Dic3C2×D511yescharacteristic
94C2×C3×Dic3—51no—
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C3×C4×D3—102no—
98D3×Dic3—54no—
99D3×Dic3—102no—
100C22×C3×C5—21no—
101C22×C3×C5C22×D311yescharacteristic
102C22×C3×C5C22×D311yescharacteristic
103C2×D15Dic612yes—
104C2×D15C4×D312yes—
105C2×D15#6712yes—
106C2×C3×D5—32no—
107C2×C3×D5—32no—
108C2×C3×D5—32no—
109C3×C4×C5—21no—
110C3×C4×C5—21no—
111C3×C4×C5—41no—
112Dic15—21no—
113Dic15—21no—
114Dic15C4×D312yescomplemented
115C3×Dic5—32no—
116C3×Dic5—61no—
117C3×Dic5—61no—
118C5×Dic3—32no—
119C5×Dic3—32no—
120C5×Dic3—62no—
121C5×Dic3—61no—
122C5×Dic3—61no—
123C5×Dic3—121no—
124C22×C3×C4—151no—
125C22×Dic3—151no—
126C22×Dic3—151no—
127C2×C4×D3—51no—
128C2×C4×D3—151no—
129C2×C4×D3—151no—
130C3×C4⋊C4—151no—
131C4⋊Dic3—151no—
132Dic3⋊C4—31no—
133Dic3⋊C4—31no—
134Dic3⋊C4—51no—
135Dic3⋊C4—61no—
136Dic3⋊C4—151no—
137Dic3⋊C4—151no—
138Dic3⋊C4—151no—
139C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
140C22×D5—31no—
141C2×C4×C5—91no—
142C2×C4×C5—91no—
143C2×C4×C5D3211yescharacteristic
144C2×Dic5—31no—
145C2×Dic5—31no—
146C2×Dic5—31no—
147C4×D5—62no—
148C4×D5—94no—
149C4×D5—182no—
150C22×C32C22×D511yescharacteristic
151C2×C3×D3—52no—
152C2×C3×D3—52no—
153C2×C3×D3—52no—
154C32×C4—21no—
155C3⋊Dic3—21no—
156C3⋊Dic3C4×D512yescomplemented
157C3×Dic3—52no—
158C3×Dic3—101no—
159C3×Dic3—101no—
160C2×C4⋊C4—451noSylow
161C2×C3×C5—21no—
162C2×C3×C5—21no—
163C2×C3×C5—21no—
164C2×C3×C5C2×Dic611yescharacteristic
165C2×C3×C5C2×C4×D311yescharacteristic
166C2×C3×C5C2×C4×D311yescharacteristic
167C2×C3×C5D3×D411yescharacteristic
168C2×C3×C5D3×Q811yescharacteristic
169C2×C3×C5C2×#6711yescharacteristic
170D15Dic3⋊C414yescomplemented
171C3×D5—34no—
172C23×C3—151no—
173C22×D3—51no—
174C2×C3×C4—21no—
175C2×C3×C4—151no—
176C2×C3×C4—151no—
177C2×C3×C4—151no—
178C2×C3×C4—302no—
179C2×C3×C4D3×D511yescharacteristic
180C2×C3×C4D3×D511yescharacteristic
181C2×Dic3—31no—
182C2×Dic3—31no—
183C2×Dic3—31no—
184C2×Dic3—31no—
185C2×Dic3—51no—
186C2×Dic3—51no—
187C2×Dic3—51no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—154no—
191C2×Dic3—302no—
192C4×D3—102no—
193C4×D3—154no—
194C4×D3—302no—
195C22×C5C2×D3211yescharacteristic
196C2×D5—32no—
197C2×D5—32no—
198C2×D5—32no—
199C4×C5—21no—
200C4×C5—92no—
201C4×C5—181no—
202Dic5—32no—
203Dic5—61no—
204Dic5—61no—
205C2×C32C2×C4×D511yescharacteristic
206C2×C32D4×D511yescharacteristic
207C2×C32Q8×D511yescharacteristic
208C3×D3—54no—
209C22×C4—151no—
210C22×C4—451no—
211C22×C4—451no—
212C4⋊C4—91no—
213C4⋊C4—151no—
214C4⋊C4—451no—
215C4⋊C4—451no—
216C3×C5—21no—
217C3×C5D3×C4⋊C411yescharacteristic, complemented
218C3×C5C2×Dic3⋊C411yescharacteristic, complemented
219C22×C3—21no—
220C22×C3—152no—
221C22×C3—152no—
222C22×C3—152no—
223C22×C3C2×D3×D511yescharacteristic
224C22×C3C2×D3×D511yescharacteristic
225C2×D3—52no—
226C2×D3—52no—
227C2×D3—52no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—41no—
231C3×C4—152no—
232C3×C4—301no—
233C3×C4—301no—
234Dic3—32no—
235Dic3—32no—
236Dic3—52no—
237Dic3—62no—
238Dic3—61no—
239Dic3—61no—
240Dic3—101no—
241Dic3—101no—
242Dic3—121no—
243C2×C5D3×Dic611yescharacteristic
244C2×C5C4×D3211yescharacteristic
245C2×C5D3×#6711yescharacteristic
246D5—34no—
247C32D5×C4⋊C411yescharacteristic, complemented, Sylow
248C23—151no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—151no—
252C2×C4—151no—
253C2×C4—151no—
254C2×C4—302no—
255C2×C4—454no—
256C2×C4—902no—
257C2×C4(C3⋊D3)⋊D511yescharacteristic
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—154no—
262C2×C3D5×Dic611yescharacteristic
263C2×C3D15⋊Q811yescharacteristic
264C2×C3C4×D3×D511yescharacteristic
265C2×C3C4×D3×D511yescharacteristic
266C2×C3D5×#6711yescharacteristic
267C2×C3#679011yescharacteristic
268D3—54no—
269C5D3×Dic3⋊C411yescharacteristic, complemented, Sylow
270C22—152no—
271C22—152no—
272C22—152no—
273C22C2×(C3⋊D3)⋊D511yescharacteristic
274C4—21no—
275C4—92no—
276C4—152no—
277C4—181no—
278C4—301no—
279C4—301no—
280C3—21no—
281C3D5×Dic3⋊C411yescharacteristic, complemented
282C3#9140411yescharacteristic, complemented
283C2—154no—
284C2#1062421911yescharacteristic
285C2C4×(C3⋊D3)⋊D511yescharacteristic
286C2#1062423511yescharacteristic
subgroupG/H
center, FrattiniC22C2×(C3⋊D3)⋊D5
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C3×D15C22
hypercenterC2×C4(C3⋊D3)⋊D5
hypocenterC32×C5C2×C4⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. C5×#3750C2semidirect
5. C3×#6712C2semidirect
6. #10623832C2semidirect
7. #10623831C2semidirect
19. #67154C4semidirect
27. #6712D3semidirect
42. C5×C3⋊Dic3C2×C4semidirect
45. C3×Dic15C2×C4semidirect
50. #3750D5semidirect
82. C3×D15C4⋊C4semidirect
114. Dic15C4×D3semidirect
139. C32×C5C2×C4⋊C4semidirect
156. C3⋊Dic3C4×D5semidirect
170. D15Dic3⋊C4semidirect
217. C3×C5D3×C4⋊C4semidirect
218. C3×C5C2×Dic3⋊C4semidirect
247. C32D5×C4⋊C4semidirect
269. C5D3×Dic3⋊C4semidirect
281. C3D5×Dic3⋊C4semidirect
282. C3#91404semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
C2×#671542
C5×#37502
C3×#67122
#106238322
#106238312
#914043
D5×Dic3⋊C43
D3×Dic3⋊C45