Finite Group Databasebeta

← #13085790

Subgroups — #13085790

Order 1440.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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#10624220C211yesmaximal, characteristic, complemented
2C3⋊D3×D20C211yesmaximal, characteristic, complemented
3#10623804C211yesmaximal, characteristic, complemented
4#10623799C211yesmaximal, characteristic, complemented
5C5×#3712C211yesmaximal, characteristic, complemented
6C3×#6657C211yesmaximal, characteristic, complemented
7C3×#6653C211yesmaximal, characteristic, complemented
8#91254—31nomaximal
9#91253—31nomaximal
10C2×D5×C3⋊D3—21no—
11C4⋊(C3⋊D15)C2211yescharacteristic
12C4×C5×C3⋊D3C2211yescharacteristic
13C3×D60C2211yescharacteristic, complemented
14C3×Dic30C2211yescharacteristic, complemented
15C32×D20C2211yescharacteristic
16#67156—21no—
17#67154—21no—
18#67139—21no—
19C3×C5×C3⋊C8C2211yescharacteristic, complemented
20C3×C5×C3⋊C8C2211yescharacteristic, complemented
21#63937—51nomaximal, Hall
22D3×D20—31no—
23D3×D20—31no—
24D3×D20—61no—
25#6769—31no—
26#6765—31no—
27D120—31no—
28#6706—31no—
29C5×ΓL(1,𝔽25)—31no—
30C5×ΓL(1,𝔽25)—31no—
31C3×D40—31no—
32C3×#677—31no—
33#6658—31no—
34#6657D311yescharacteristic, complemented
35#6653—31no—
36#6653D311yescharacteristic, complemented
37C2×C3⋊D15—21no—
38C2×C5×C3⋊D3D411yescharacteristic
39C2×C3×D15—21no—
40C2×C32×D5—21no—
41D5×C3⋊D3—42no—
42C32×C4×C5C2311yescharacteristic
43C5×C3⋊Dic3D411yescharacteristic
44C3×Dic15—21no—
45#4054—91noHall
46D4×C3⋊D3—51no—
47#3796—51no—
48C3×#214—51no—
49C3×#213—51no—
50#3717—51no—
51#3714—51no—
52#3712D511yescharacteristic, complemented
53C2×D3×D5—61no—
54C2×D3×D5—61no—
55C2×D3×D5—62no—
56D60—31no—
57D60—31no—
58D60—61no—
59D60C2×D311yescharacteristic, complemented
60Dic30C2×D311yescharacteristic, complemented
61C4×C5×D3—31no—
62C4×C5×D3—31no—
63C4×C5×D3—61no—
64C3×D20—21no—
65C3×D20—31no—
66C3×D20C2×D311yescharacteristic
67C3×D20C2×D311yescharacteristic
68C3×Dic10—31no—
69#1203—61no—
70#1202—61no—
71#1202—61no—
72#1202—62no—
73#1201—61no—
74#1200—61no—
75D5×Dic3—61no—
76C3×C5×C8—31no—
77C3×C5×C8—31no—
78C5×C3⋊C8C2×D311yescharacteristic, complemented
79C5×C3⋊C8C2×D311yescharacteristic, complemented
80#914—151no—
81#911—151no—
82C2×C32×C5C2×D411yescharacteristic
83C3⋊D15—41no—
84C5×C3⋊D3—21no—
85C3×D15—41no—
86C32×D5—41no—
87#709—91no—
88C2×D20—91no—
89C5×M16—91no—
90D40—31no—
91D40—91no—
92#677—31no—
93#677—91no—
94C22×C3⋊D3—101no—
95C32×D4—51no—
96#638—101no—
97C4⋊(C3⋊D3)—51no—
98C4×C3⋊D3C2×D511yescharacteristic
99C3×D12—51no—
100C3×Dic6—51no—
101#626—101no—
102D3×Dic3—101no—
103C3×C3⋊C8C2×D511yescharacteristic, complemented
104C3×C3⋊C8C2×D511yescharacteristic, complemented
105C2×D15—21no—
106C2×D15—62no—
107C2×D15—61no—
108C2×D15—61no—
109C2×C5×D3—31no—
110C2×C5×D3—31no—
111C2×C5×D3—61no—
112C2×C3×D5—22no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—61no—
116D3×D5—124no—
117D3×D5—122no—
118D3×D5—122no—
119C3×C4×C5—21no—
120C3×C4×C5C22×D311yescharacteristic
121C3×C4×C5C22×D311yescharacteristic
122Dic15—21no—
123C3×Dic5—61no—
124C5×Dic3—31no—
125C5×Dic3—31no—
126C5×Dic3—61no—
127#239—151no—
128#237—151no—
129D3×D4—151no—
130D3×D4—151no—
131D3×D4—301no—
132C3×SD16—151no—
133C3×D8—151no—
134#215—151no—
135#214—51no—
136#213—51no—
137#213—151no—
138D24—151no—
139#204—151no—
140ΓL(1,𝔽25)—31no—
141ΓL(1,𝔽25)—31no—
142C32×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
143C22×D5—181no—
144C2×C4×C5—91no—
145C22⋊D5—181no—
146D20—31no—
147D20—91no—
148D20—181no—
149D20D3211yescharacteristic
150C4×D5—181no—
151Dic10—31no—
152C5×C8—31no—
153C5×C8—31no—
154C22×C32—101no—
155C2×C3⋊D3—101no—
156C2×C3⋊D3—202no—
157C2×C3⋊D3D2011yescharacteristic
158C2×C3×D3—101no—
159C32×C4C22×D511yescharacteristic
160C3⋊Dic3D2011yescharacteristic
161C3×Dic3—101no—
162AGL(1,ℤ/8)—451noSylow
163C2×C3×C5—21no—
164C2×C3×C5D3×D411yescharacteristic
165C2×C3×C5D3×D411yescharacteristic
166D15—41no—
167D15—122no—
168D15—121no—
169D15—121no—
170C3×D5—42no—
171C3×D5—41no—
172C3×D5—41no—
173C3×D5—121no—
174C5×D3—62no—
175C5×D3—61no—
176C5×D3—61no—
177C22×D3—301no—
178C22×D3—301no—
179C22×D3—302no—
180C3×Q8—151no—
181C3×D4—51no—
182C3×D4—51no—
183C3×D4—101no—
184C3×D4—151no—
185#67—301no—
186#67—301no—
187#67—302no—
188#67—301no—
189C2×Dic3—301no—
190D12—51no—
191D12—151no—
192D12—151no—
193D12—301no—
194D12—301no—
195C4×D3—31no—
196C4×D3—31no—
197C4×D3—61no—
198C4×D3—301no—
199Dic6—51no—
200C3×C8—31no—
201C3×C8—31no—
202C3⋊C8D3×D511yescharacteristic, complemented
203C3⋊C8D3×D511yescharacteristic, complemented
204C22×C5—91no—
205C2×D5—21no—
206C2×D5—61no—
207C2×D5—181no—
208C2×D5—362no—
209C4×C5—91no—
210C4×C5C2×D3211yescharacteristic
211Dic5—61no—
212C2×C32—201no—
213C2×C32C2×D2011yescharacteristic
214C3⋊D3—21no—
215C3⋊D3—201no—
216C3×D3—201no—
217#41—451no—
218C2×D4—451no—
219SD16—151no—
220SD16—451no—
221D8—151no—
222D8—451no—
223M16—91no—
224C3×C5—21no—
225C3×C5#91111yescharacteristic, complemented
226C3×C5#91411yescharacteristic, complemented
227C22×C3—102no—
228C22×C3—101no—
229C22×C3—101no—
230C22×C3—301no—
231C2×D3—31no—
232C2×D3—31no—
233C2×D3—61no—
234C2×D3—101no—
235C2×D3—302no—
236C2×D3—301no—
237C2×D3—301no—
238C2×D3—604no—
239C2×D3—602no—
240C2×D3—602no—
241C3×C4—21no—
242C3×C4—301no—
243C3×C4C2×D3×D511yescharacteristic
244C3×C4C2×D3×D511yescharacteristic
245Dic3—31no—
246Dic3—31no—
247Dic3—61no—
248Dic3—101no—
249C2×C5—181no—
250C2×C5#381111yescharacteristic
251D5—41no—
252D5—121no—
253D5—361no—
254C32#405411yescharacteristic, complemented, Sylow
255C23—901no—
256Q8—151no—
257D4—51no—
258D4—151no—
259D4—451no—
260D4—901no—
261D4—901no—
262C2×C4—91no—
263C2×C4—901no—
264C8—31no—
265C8—31no—
266C2×C3—21no—
267C2×C3—202no—
268C2×C3—201no—
269C2×C3—201no—
270C2×C3—601no—
271C2×C3D3×D2011yescharacteristic
272C2×C3D3×D2011yescharacteristic
273D3—62no—
274D3—61no—
275D3—61no—
276D3—201no—
277D3—602no—
278D3—601no—
279D3—601no—
280C5#6393711yescharacteristic, complemented, Sylow
281C22—91no—
282C22—101no—
283C22—301no—
284C22—901no—
285C22—1802no—
286C4—91no—
287C4—301no—
288C4D32×D511yescharacteristic
289C3—21no—
290C3#9125311yescharacteristic, complemented
291C3#9125411yescharacteristic, complemented
292C2—181no—
293C2—201no—
294C2—601no—
295C2—1801no—
296C2#1062403111yescharacteristic
subgroupG/H
centerC2#10624031
commutator, Fitting, cosocleC32×C4×C5C23
Frattini, hypercenterC4D32×D5
socleC2×C32×C5C2×D4
hypocenterC32×C5AGL(1,ℤ/8)
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #10624220C2semidirect
2. C3⋊D3×D20C2semidirect
3. #10623804C2semidirect
4. #10623799C2semidirect
5. C5×#3712C2semidirect
6. C3×#6657C2semidirect
7. C3×#6653C2semidirect
13. C3×D60C22semidirect
14. C3×Dic30C22semidirect
19. C3×C5×C3⋊C8C22semidirect
20. C3×C5×C3⋊C8C22semidirect
34. #6657D3semidirect
36. #6653D3semidirect
52. #3712D5semidirect
59. D60C2×D3semidirect
60. Dic30C2×D3semidirect
78. C5×C3⋊C8C2×D3semidirect
79. C5×C3⋊C8C2×D3semidirect
103. C3×C3⋊C8C2×D5semidirect
104. C3×C3⋊C8C2×D5semidirect
142. C32×C5AGL(1,ℤ/8)semidirect
202. C3⋊C8D3×D5semidirect
203. C3⋊C8D3×D5semidirect
225. C3×C5#911semidirect
226. C3×C5#914semidirect
254. C32#4054semidirect
280. C5#63937semidirect
290. C3#91253semidirect
291. C3#91254semidirect

Maximal subgroups

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

subgroupindex
#106242202
C3⋊D3×D202
#106238042
#106237992
C5×#37122
C3×#66572
C3×#66532
#912543
#912533
#639375