Finite Group Databasebeta

← #13087398

Subgroups — #13087398

Order 1440.

422 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 100 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×C3⋊D15C211yesmaximal, characteristic
2C2×#67149C211yesmaximal, characteristic
3C2×#67149C211yesmaximal, characteristic
4C3×#6712C211yesmaximal, characteristic, complemented
5C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6Dic3⋊Dic15C211yesmaximal, characteristic, complemented
7#10623814C211yesmaximal, characteristic, complemented
8C4⋊C4×D15—31nomaximal
9#91404—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C4×C3⋊D15—22no—
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67149—22no—
19#67149C414yescomplemented
20#63883—51nomaximal, Hall
21C2×C4×D15—31no—
22C2×C4×D15—31no—
23C2×C4×D15—31no—
24C2×C4×D15—31no—
25C2×C4×D15—61no—
26C2×#1200—31no—
27C2×#1200—31no—
28C3×C5×C4⋊C4—31no—
29C4⋊Dic15—31no—
30#6712—31no—
31#6712D311yescharacteristic, complemented
32C5×Dic3⋊C4D311yescharacteristic, complemented
33C3×#683—31no—
34Dic3⋊Dic5—31no—
35#6668—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3⋊D15C2×C412yes—
38C2×C3⋊D15D412yes—
39C2×C3⋊D15Q812yes—
40C32×C4×C5—21no—
41C3⋊Dic15—21no—
42C3×Dic15—21no—
43C3×Dic15C2×C412yescomplemented
44C3×C5×Dic3—21no—
45C3×C5×Dic3C2×C412yescomplemented
46D5×C4⋊C4—91noHall
47C2×C4×C3⋊D3—51no—
48C2×#624—51no—
49C2×#624—51no—
50C3×Dic3⋊C4—51no—
51C3×Dic3⋊C4D511yescharacteristic, complemented
52Dic3⋊Dic3—51no—
53Dic3⋊Dic3—51no—
54C22×D15—31no—
55C22×D15—31no—
56C22×D15—61no—
57C2×C3×C4×C5—21no—
58C2×C3×C4×C5—31no—
59C2×C3×C4×C5—31no—
60C2×C3×C4×C5C2×D311yescharacteristic
61C2×C3×C4×C5C2×D311yescharacteristic
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—61no—
65C2×Dic15C2×D311yescharacteristic
66C2×Dic15C2×D311yescharacteristic
67C4×D15—34no—
68C4×D15—62no—
69C4×D15—62no—
70C4×D15—62no—
71C4×D15—64no—
72C2×C5×Dic3C2×D311yescharacteristic
73C2×C5×Dic3C2×D311yescharacteristic
74C2×C3×Dic5—31no—
75C2×C3×Dic5—31no—
76#1200—34no—
77#1200—62no—
78D3×C4⋊C4—151no—
79D3×C4⋊C4—151no—
80C2×C32×C5C22×C411yescharacteristic
81C2×C32×C5C2×D411yescharacteristic
82C2×C32×C5C2×Q811yescharacteristic
83C3⋊D15C4⋊C414yescomplemented
84C2×C4×D5—91no—
85C2×C4×D5—91no—
86C2×C4×D5—91no—
87C5×C4⋊C4—31no—
88C4⋊Dic5—91no—
89#683—31no—
90#683—91no—
91C22×C3⋊D3—51no—
92C2×C32×C4C2×D511yescharacteristic
93C2×C3⋊Dic3—51no—
94C4×C3⋊D3—102no—
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3C2×D511yescharacteristic
98C2×C3×Dic3C2×D511yescharacteristic
99#624—54no—
100#624—102no—
101C22×C3×C5—21no—
102C22×C3×C5C22×D311yescharacteristic
103C22×C3×C5C22×D311yescharacteristic
104C2×D15—32no—
105C2×D15—32no—
106C2×D15—32no—
107C2×D15—32no—
108C2×D15—32no—
109C2×D15—32no—
110C2×D15—62no—
111C2×D15—62no—
112C2×D15—62no—
113C3×C4×C5—22no—
114C3×C4×C5—21no—
115C3×C4×C5—21no—
116C3×C4×C5—32no—
117C3×C4×C5—61no—
118Dic15—21no—
119Dic15—62no—
120Dic15—61no—
121Dic15—61no—
122Dic15C4×D312yescomplemented
123C3×Dic5—32no—
124C3×Dic5—61no—
125C5×Dic3—21no—
126C5×Dic3C4×D312yescomplemented
127C2×C4×D3—151no—
128C2×C4×D3—151no—
129C2×C4×D3—151no—
130C2×C4×D3—151no—
131C2×C4×D3—151no—
132C2×C4×D3—151no—
133C2×C4×D3—301no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—151no—
136C4⋊Dic3—151no—
137C4⋊Dic3—151no—
138Dic3⋊C4—51no—
139Dic3⋊C4—151no—
140Dic3⋊C4—151no—
141Dic3⋊C4D1511yescharacteristic, complemented
142C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
143C22×D5—91no—
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5D3211yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—91no—
150C4×D5—94no—
151C4×D5—182no—
152C4×D5—182no—
153C22×C32C22×D511yescharacteristic
154C2×C3⋊D3—52no—
155C2×C3⋊D3—52no—
156C2×C3⋊D3—52no—
157C32×C4—21no—
158C3⋊Dic3—101no—
159C3×Dic3—21no—
160C3×Dic3—52no—
161C3×Dic3—101no—
162C3×Dic3C4×D512yescomplemented
163C2×C4⋊C4—451noSylow
164C2×C3×C5—21no—
165C2×C3×C5—21no—
166C2×C3×C5—21no—
167C2×C3×C5C2×C4×D311yescharacteristic
168C2×C3×C5C2×C4×D311yescharacteristic
169C2×C3×C5D3×D411yescharacteristic
170C2×C3×C5D3×D411yescharacteristic
171C2×C3×C5D3×Q811yescharacteristic
172C2×C3×C5D3×Q811yescharacteristic
173D15—34no—
174D15—34no—
175D15—64no—
176C22×D3—151no—
177C22×D3—151no—
178C22×D3—301no—
179C2×C3×C4—21no—
180C2×C3×C4—31no—
181C2×C3×C4—31no—
182C2×C3×C4—151no—
183C2×C3×C4—151no—
184C2×C3×C4D3×D511yescharacteristic
185C2×C3×C4C2×D1511yescharacteristic
186C2×Dic3—51no—
187C2×Dic3—51no—
188C2×Dic3—151no—
189C2×Dic3—151no—
190C2×Dic3—301no—
191C2×Dic3C2×D1511yescharacteristic
192C2×Dic3C2×D1511yescharacteristic
193C4×D3—154no—
194C4×D3—154no—
195C4×D3—302no—
196C4×D3—302no—
197C4×D3—302no—
198C4×D3—302no—
199C4×D3—304no—
200C22×C5C2×D3211yescharacteristic
201C2×D5—92no—
202C2×D5—92no—
203C2×D5—92no—
204C4×C5—21no—
205C4×C5—32no—
206C4×C5—61no—
207Dic5—32no—
208Dic5—61no—
209Dic5—181no—
210C2×C32C2×C4×D511yescharacteristic
211C2×C32D4×D511yescharacteristic
212C2×C32Q8×D511yescharacteristic
213C3⋊D3—54no—
214C22×C4—451no—
215C22×C4—451no—
216C22×C4—451no—
217C4⋊C4—31no—
218C4⋊C4—151no—
219C4⋊C4—451no—
220C4⋊C4—451no—
221C3×C5—21no—
222C3×C5D3×C4⋊C411yescharacteristic, complemented
223C3×C5D3×C4⋊C411yescharacteristic, complemented
224C22×C3—21no—
225C22×C3C2×D3×D511yescharacteristic
226C22×C3C22×D1511yescharacteristic
227C2×D3—152no—
228C2×D3—152no—
229C2×D3—152no—
230C2×D3—152no—
231C2×D3—152no—
232C2×D3—152no—
233C2×D3—302no—
234C2×D3—302no—
235C2×D3—302no—
236C3×C4—22no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—32no—
240C3×C4—61no—
241C3×C4—152no—
242C3×C4—301no—
243Dic3—21no—
244Dic3—52no—
245Dic3—101no—
246Dic3—302no—
247Dic3—301no—
248Dic3—301no—
249Dic3C4×D1512yescomplemented
250C2×C5#379711yescharacteristic
251C2×C5C4×D3211yescharacteristic
252C2×C5#381111yescharacteristic
253D5—94no—
254C32D5×C4⋊C411yescharacteristic, complemented, Sylow
255C23—451no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—151no—
259C2×C4—151no—
260C2×C4—454no—
261C2×C4—451no—
262C2×C4—902no—
263C2×C4—902no—
264C2×C4D3×D1511yescharacteristic
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3D15⋊Q811yescharacteristic
269C2×C3C4×D3×D511yescharacteristic
270C2×C3#679011yescharacteristic
271C2×C3C2×C4×D1511yescharacteristic
272C2×C3D4×D1511yescharacteristic
273C2×C3Q8×D1511yescharacteristic
274D3—154no—
275D3—154no—
276D3—304no—
277C5#6388311yescharacteristic, complemented, Sylow
278C22—452no—
279C22—452no—
280C22—452no—
281C22C2×D3×D1511yescharacteristic
282C4—21no—
283C4—32no—
284C4—61no—
285C4—152no—
286C4—301no—
287C4—901no—
288C3—21no—
289C3#9140411yescharacteristic, complemented
290C3C4⋊C4×D1511yescharacteristic, complemented
291C2—454no—
292C2#1062419811yescharacteristic
293C2C4×D3×D1511yescharacteristic
294C2#1062421811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC22×C3⋊D15C22
hypercenterC2×C4D3×D15
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. C3×#6712C2semidirect
5. C3×C5×Dic3⋊C4C2semidirect
6. Dic3⋊Dic15C2semidirect
7. #10623814C2semidirect
19. #67149C4semidirect
31. #6712D3semidirect
32. C5×Dic3⋊C4D3semidirect
43. C3×Dic15C2×C4semidirect
45. C3×C5×Dic3C2×C4semidirect
51. C3×Dic3⋊C4D5semidirect
83. C3⋊D15C4⋊C4semidirect
122. Dic15C4×D3semidirect
126. C5×Dic3C4×D3semidirect
141. Dic3⋊C4D15semidirect
142. C32×C5C2×C4⋊C4semidirect
162. C3×Dic3C4×D5semidirect
222. C3×C5D3×C4⋊C4semidirect
223. C3×C5D3×C4⋊C4semidirect
249. Dic3C4×D15semidirect
254. C32D5×C4⋊C4semidirect
277. C5#63883semidirect
289. C3#91404semidirect
290. C3C4⋊C4×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C2×#671492
C3×#67122
C3×C5×Dic3⋊C42
Dic3⋊Dic152
#106238142
C4⋊C4×D153
#914043
#638835