Finite Group Databasebeta

← #13085928

Subgroups — #13085928

Order 1440.

402 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 94 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×#67157C211yesmaximal, characteristic
2C2×Dic3×D15C211yesmaximal, characteristic, complemented
3C2×C3×#1200C211yesmaximal, characteristic, complemented
4#10623811C211yesmaximal, characteristic, complemented
5C5×Dic32C211yesmaximal, characteristic, complemented
6#10623775C211yesmaximal, characteristic, complemented
7C3×#6667C211yesmaximal, characteristic, complemented
8C4×#1202—31nomaximal
9#91395—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C22×C3×D15C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67157C414yescomplemented
18Dic3×D15—22no—
19C3×#1200—22no—
20#63879—51nomaximal, Hall
21C2×C4×D15—31no—
22C2×C3×C4×D5—31no—
23C2×#1202—31no—
24C2×#1202—31no—
25C2×#1200D311yescharacteristic, complemented
26C2×D5×Dic3—31no—
27#6714—31no—
28C4×C5×Dic3—31no—
29C4×C5×Dic3—31no—
30C3×#685—31no—
31Dic3⋊Dic5—31no—
32Dic3⋊Dic5—31no—
33Dic3⋊Dic5—61no—
34#6667D311yescharacteristic, complemented
35#6665—31no—
36C22×C32×C5C2311yescharacteristic
37C2×C3×D15—21no—
38C2×C3×D15—21no—
39C2×C3×D15—21no—
40C2×C3×D15—21no—
41C2×C3×D15C2×C412yescomplemented
42C2×C3×D15C2×C412yescomplemented
43C3⋊Dic15—21no—
44C5×C3⋊Dic3C2×C412yescomplemented
45C3×C5×Dic3—21no—
46C3×C5×Dic3D412yescomplemented
47C32×Dic5—21no—
48C4×D20—91noHall
49C2×C3×C4×D3—51no—
50C2×#625—51no—
51C2×D3×Dic3—51no—
52#3750—51no—
53C3×(C2×D3)⋊C4—51no—
54(C2×D3)⋊Dic3—51no—
55Dic32D511yescharacteristic, complemented
56C22×D15C2×D311yescharacteristic
57C22×D15C2×D311yescharacteristic
58C22×C3×D5—31no—
59C22×C3×D5—31no—
60C2×C3×C4×C5—31no—
61C2×C3×C4×C5—31no—
62C2×Dic15—31no—
63C2×Dic15—31no—
64C2×Dic15—61no—
65C4×D15—62no—
66C2×C5×Dic3—31no—
67C2×C5×Dic3—31no—
68C2×C5×Dic3—61no—
69C2×C5×Dic3C2×D311yescharacteristic
70C2×C5×Dic3C2×D311yescharacteristic
71C2×C3×Dic5—21no—
72C2×C3×Dic5C2×D311yescharacteristic
73C2×C3×Dic5C2×D311yescharacteristic
74C3×C4×D5—62no—
75#1202—34no—
76#1202—34no—
77#1200—22no—
78D5×Dic3—62no—
79C4×#67—151no—
80#67⋊C4—151no—
81C2×C32×C5C22×C411yescharacteristic
82C2×C32×C5C2×D411yescharacteristic
83C2×C32×C5#4111yescharacteristic
84C3×D15—22no—
85C3×D15—22no—
86C2×D20—91no—
87C2×C4×D5—31no—
88C2×C4×D5—91no—
89C42×C5—91no—
90#685—31no—
91#685—91no—
92C4⋊Dic5—91no—
93C22×C3×D3—51no—
94C22×C3×D3—51no—
95C2×C32×C4—51no—
96C2×C3⋊Dic3—51no—
97C2×C3⋊Dic3C2×D511yescharacteristic
98C2×C3×Dic3C2×D511yescharacteristic
99C2×C3×Dic3C2×D511yescharacteristic
100C3×C4×D3—102no—
101#625—54no—
102D3×Dic3—102no—
103C22×C3×C5—21no—
104C22×C3×C5C22×D311yescharacteristic
105C22×C3×C5C22×D311yescharacteristic
106C2×D15—21no—
107C2×D15—21no—
108C2×D15—21no—
109C2×D15—21no—
110C2×D15C4×D312yescomplemented
111C2×D15C4×D312yescomplemented
112C2×C3×D5—32no—
113C2×C3×D5—32no—
114C2×C3×D5—61no—
115C2×C3×D5—61no—
116C2×C3×D5—61no—
117C2×C3×D5—61no—
118C3×C4×C5—32no—
119C3×C4×C5—61no—
120Dic15—61no—
121Dic15—61no—
122Dic15—121no—
123C3×Dic5—21no—
124C3×Dic5—21no—
125C3×Dic5—41no—
126C5×Dic3—21no—
127C5×Dic3—32no—
128C5×Dic3—32no—
129C5×Dic3—62no—
130C5×Dic3#6712yescomplemented
131C22×C3×C4—151no—
132C2×#67—151no—
133C2×#67—151no—
134C22×Dic3—151no—
135C2×C4×D3—51no—
136C2×C4×D3—151no—
137C3×C22⋊C4—151no—
138#217—151no—
139(C2×D3)⋊C4—51no—
140(C2×D3)⋊C4—151no—
141Dic3⋊C4—151no—
142Dic3⋊C4—151no—
143Dic3⋊C4—301no—
144C4×Dic3—31no—
145C4×Dic3—31no—
146C32×C5C4×D411yescharacteristic, complemented, Hall
147C22×D5—31no—
148C22×D5—31no—
149C2×C4×C5—31no—
150C2×C4×C5—31no—
151C2×C4×C5—91no—
152C2×Dic5—91no—
153C2×Dic5D3211yescharacteristic
154D20—94no—
155C4×D5—62no—
156C4×D5—182no—
157C22×C32C22×D511yescharacteristic
158C2×C3×D3—52no—
159C2×C3×D3—52no—
160C2×C3×D3—101no—
161C2×C3×D3—101no—
162C2×C3×D3—101no—
163C2×C3×D3—101no—
164C32×C4—101no—
165C3⋊Dic3—101no—
166C3⋊Dic3C4×D512yescomplemented
167C3×Dic3—21no—
168C3×Dic3D2012yescomplemented
169C4×D4—451noSylow
170C2×C3×C5—21no—
171C2×C3×C5—21no—
172C2×C3×C5—21no—
173C2×C3×C5C2×C4×D311yescharacteristic
174C2×C3×C5C2×C4×D311yescharacteristic
175C2×C3×C5#23511yescharacteristic
176C2×C3×C5D3×D411yescharacteristic
177C2×C3×C5#23711yescharacteristic
178C2×C3×C5C2×#6711yescharacteristic
179D15—22no—
180D15—22no—
181C3×D5—62no—
182C3×D5—62no—
183C23×C3—151no—
184C23×C3—151no—
185C22×D3—51no—
186C22×D3—51no—
187C2×C3×C4—31no—
188C2×C3×C4—31no—
189C2×C3×C4—51no—
190C2×C3×C4—51no—
191C2×C3×C4—101no—
192C2×C3×C4—302no—
193#67—154no—
194#67—154no—
195C2×Dic3—31no—
196C2×Dic3—31no—
197C2×Dic3—61no—
198C2×Dic3—151no—
199C2×Dic3—151no—
200C2×Dic3—301no—
201C2×Dic3—302no—
202C2×Dic3D3×D511yescharacteristic
203C2×Dic3D3×D511yescharacteristic
204C4×D3—102no—
205C4×D3—302no—
206C22×C5C2×D3211yescharacteristic
207C2×D5—32no—
208C2×D5—32no—
209C2×D5—61no—
210C2×D5—61no—
211C2×D5—61no—
212C2×D5—61no—
213C4×C5—32no—
214C4×C5—61no—
215C4×C5—92no—
216Dic5—21no—
217Dic5—181no—
218C2×C32C2×C4×D511yescharacteristic
219C2×C32C2×D2011yescharacteristic
220C2×C32#70911yescharacteristic
221C3×D3—102no—
222C3×D3—102no—
223C2×D4—451no—
224C22×C4—151no—
225C22×C4—451no—
226C4⋊C4—451no—
227C22⋊C4—151no—
228C22⋊C4—451no—
229C42—91no—
230C3×C5—21no—
231C3×C5#67⋊C411yescharacteristic, complemented
232C3×C5C4×#6711yescharacteristic, complemented
233C22×C3—21no—
234C22×C3—152no—
235C22×C3—152no—
236C22×C3—301no—
237C22×C3—301no—
238C22×C3—301no—
239C22×C3—301no—
240C22×C3C2×D3×D511yescharacteristic
241C22×C3C2×D3×D511yescharacteristic
242C2×D3—52no—
243C2×D3—52no—
244C2×D3—101no—
245C2×D3—101no—
246C2×D3—101no—
247C2×D3—101no—
248C3×C4—32no—
249C3×C4—61no—
250C3×C4—101no—
251C3×C4—101no—
252C3×C4—201no—
253Dic3—21no—
254Dic3—32no—
255Dic3—32no—
256Dic3—62no—
257Dic3—301no—
258Dic3—301no—
259Dic3—601no—
260Dic3#120212yescomplemented
261C2×C5#379511yescharacteristic
262C2×C5C4×D3211yescharacteristic
263C2×C5D3×#6711yescharacteristic
264D5—62no—
265D5—62no—
266C32C4×D2011yescharacteristic, complemented, Sylow
267C23—151no—
268C23—151no—
269D4—454no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—51no—
273C2×C4—91no—
274C2×C4—302no—
275C2×C4—451no—
276C2×C4—902no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—302no—
281C2×C3—302no—
282C2×C3#677111yescharacteristic
283C2×C3C4×D3×D511yescharacteristic
284C2×C3C4×D3×D511yescharacteristic
285C2×C3D3×D2011yescharacteristic
286C2×C3#677911yescharacteristic
287C2×C3C2×#120211yescharacteristic
288D3—102no—
289D3—102no—
290C5#6387911yescharacteristic, complemented, Sylow
291C22—152no—
292C22—152no—
293C22—301no—
294C22—301no—
295C22—301no—
296C22—301no—
297C22D32×D511yescharacteristic
298C4—32no—
299C4—61no—
300C4—92no—
301C4—101no—
302C4—901no—
303C3—21no—
304C3#9139511yescharacteristic, complemented
305C3C4×#120211yescharacteristic, complemented
306C2—302no—
307C2—302no—
308C2#1062402211yescharacteristic
309C2D3×#120211yescharacteristic
310C2#1062405311yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67157C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×D15C2semidirect
3. C2×C3×#1200C2semidirect
4. #10623811C2semidirect
5. C5×Dic32C2semidirect
6. #10623775C2semidirect
7. C3×#6667C2semidirect
17. #67157C4semidirect
25. C2×#1200D3semidirect
34. #6667D3semidirect
41. C2×C3×D15C2×C4semidirect
42. C2×C3×D15C2×C4semidirect
44. C5×C3⋊Dic3C2×C4semidirect
46. C3×C5×Dic3D4semidirect
55. Dic32D5semidirect
110. C2×D15C4×D3semidirect
111. C2×D15C4×D3semidirect
130. C5×Dic3#67semidirect
146. C32×C5C4×D4semidirect
166. C3⋊Dic3C4×D5semidirect
168. C3×Dic3D20semidirect
231. C3×C5#67⋊C4semidirect
232. C3×C5C4×#67semidirect
260. Dic3#1202semidirect
266. C32C4×D20semidirect
290. C5#63879semidirect
304. C3#91395semidirect
305. C3C4×#1202semidirect

Maximal subgroups

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

subgroupindex
C2×#671572
C2×Dic3×D152
C2×C3×#12002
#106238112
C5×Dic322
#106237752
C3×#66672
C4×#12023
#913953
#638795