Finite Group Databasebeta

← #11754115

Subgroups — #11754115

Order 960.

536 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 126 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#92035C212yesmaximal, complemented
2#91808C211yesmaximal, characteristic, complemented
3C5×#919C211yesmaximal, characteristic, complemented
4C3×#4065C211yesmaximal, characteristic, complemented
5#91506C212yesmaximal, complemented
6#91504C212yesmaximal, complemented
7#91502C212yesmaximal, complemented
8#91265C211yesmaximal, characteristic, complemented
9#91256C211yesmaximal, characteristic, complemented
10D3×D40C211yesmaximal, characteristic, complemented
11D5×D24C211yesmaximal, characteristic, complemented
12#66103—31nomaximal, Hall
13#6821C2212yescomplemented
14C5×#239C2212yescomplemented
15C3×#713C2212yescomplemented
16#6777—22no—
17#6777C2212yescomplemented
18D3×D20—22no—
19D3×D20C2212yescomplemented
20D5×D12—22no—
21D5×D12C2212yescomplemented
22#6771—22no—
23#6771C2211yescharacteristic
24C3×C5×Q16C2211yescharacteristic, complemented
25#6717C2212yescomplemented
26D120C2211yescharacteristic, complemented
27C8×D15C2211yescharacteristic, complemented
28C5×#215C2212yescomplemented
29C5×D24C2211yescharacteristic, complemented
30C5×D3×C8C2211yescharacteristic, complemented
31C3×#688C2212yescomplemented
32C3×D40C2211yescharacteristic, complemented
33C3×C8×D5C2211yescharacteristic, complemented
34#6654C2212yescomplemented
35#6653C2212yescomplemented
36#6652C2212yescomplemented
37#6651C2211yescharacteristic, complemented
38#6650C2211yescharacteristic, complemented
39#6649C2211yescharacteristic, complemented
40#5769—51nomaximal, Hall
41#4149—32no—
42C5×#135—31no—
43#4095—32no—
44#4065—31no—
45#4065D311yescharacteristic, complemented
46#4060—32no—
47#4060—32no—
48D5×D8—31no—
49D5×D8—31no—
50C2×D40—31no—
51#4047—31no—
52C2×D3×D5—22no—
53C2×D3×D5—22no—
54C2×D3×D5—22no—
55C3×C5×Q8C2312yes—
56D60—22no—
57D60C2312yes—
58C4×D15—22no—
59C4×D15C2311yescharacteristic
60C5×D12—22no—
61C5×D12C2312yes—
62C4×C5×D3—22no—
63C4×C5×D3C2311yescharacteristic
64C3×D20—22no—
65C3×D20C2312yes—
66C3×C4×D5—22no—
67C3×C4×D5C2311yescharacteristic
68#1204D411yescharacteristic
69#1203—22no—
70#1203D411yescharacteristic
71#1202—22no—
72#1202D411yescharacteristic
73#1201—22no—
74#1201D411yescharacteristic
75C3×C5×C8C2311yescharacteristic
76C3⋊#168C2311yescharacteristic
77C3×#168C2311yescharacteristic
78C5×C3⋊C8C2311yescharacteristic
79#1009—52no—
80C3×#135—51no—
81#949—52no—
82#919—51no—
83#919D511yescharacteristic, complemented
84#914—52no—
85#914—52no—
86D3×D8—51no—
87D3×D8—51no—
88C2×D24—51no—
89#901—51no—
90C5×#41—32no—
91#713—32no—
92#713C2×D312yescomplemented
93D4×D5—32no—
94D4×D5—32no—
95D4×D5—62no—
96D4×D5—62no—
97#709—31no—
98#709—62no—
99C2×D20—32no—
100C2×D20—62no—
101C5×Q16C2×D311yescharacteristic, complemented
102C5×SD16—32no—
103C5×D8—31no—
104C2×C5×C8—31no—
105#688—32no—
106#688C2×D312yescomplemented
107#686—32no—
108#686—32no—
109#681—31no—
110D40—32no—
111D40—31no—
112D40C2×D311yescharacteristic, complemented
113#676—31no—
114#676—31no—
115C8×D5—31no—
116C8×D5C2×D311yescharacteristic, complemented
117#576—151noSylow
118C2×D15—22no—
119C2×D15C2×D411yescharacteristic
120C2×C5×D3—22no—
121C2×C5×D3C2×D411yescharacteristic
122C2×C3×D5—22no—
123C2×C3×D5C2×D411yescharacteristic
124D3×D5—82no—
125D3×D5—82no—
126D3×D5—82no—
127C3×C4×C5—22no—
128C3×C4×C5C2411yescharacteristic
129Dic15C2×D411yescharacteristic
130C3×Dic5C2×D411yescharacteristic
131C5×Dic3C2×D411yescharacteristic
132C3×#41—52no—
133#239—52no—
134#239C2×D512yescomplemented
135D3×D4—52no—
136D3×D4—52no—
137D3×D4—102no—
138D3×D4—102no—
139#235—51no—
140#235—102no—
141C2×D12—52no—
142C2×D12—102no—
143C3×Q16C2×D511yescharacteristic, complemented
144C3×SD16—52no—
145C3×D8—51no—
146C2×C3×C8—51no—
147#215—52no—
148#215C2×D512yescomplemented
149#213—52no—
150#213—52no—
151#208—51no—
152D24—52no—
153D24—51no—
154D24C2×D511yescharacteristic, complemented
155ΓL(1,𝔽25)—51no—
156ΓL(1,𝔽25)—51no—
157D3×C8—51no—
158D3×C8C2×D511yescharacteristic, complemented
159C22×D5—62no—
160C22×D5—62no—
161C22×D5—62no—
162C5×Q8C22×D312yes—
163C5×D4—32no—
164C5×D4—62no—
165C2×C4×C5—31no—
166C2×C4×C5—62no—
167C22⋊D5—31no—
168C22⋊D5—31no—
169C22⋊D5—62no—
170C22⋊D5—62no—
171D20—22no—
172D20—31no—
173D20—32no—
174D20—62no—
175D20—62no—
176D20C22×D312yes—
177C4×D5—22no—
178C4×D5—31no—
179C4×D5—62no—
180C4×D5C22×D311yescharacteristic
181Dic10—31no—
182C5×C8—31no—
183C5×C8C22×D311yescharacteristic
184#168—31no—
185#168C22×D311yescharacteristic
186H(5,𝔽2)—152no—
187AGL(1,ℤ/8)—152no—
188AGL(1,ℤ/8)—152no—
189AGL(1,ℤ/8)—152no—
190#135—31no—
191#135—51no—
192#135—151no—
193C2×D8—151no—
194C2×D8—151no—
195C2×D8—151no—
196#131—151no—
197C2×C3×C5C22×D411yescharacteristic
198D15—21no—
199D15—42no—
200C3×D5—21no—
201C3×D5—42no—
202C5×D3—21no—
203C5×D3—42no—
204C22×D3—102no—
205C22×D3—102no—
206C22×D3—102no—
207C3×Q8C22×D512yes—
208C3×D4—52no—
209C3×D4—102no—
210C2×C3×C4—51no—
211C2×C3×C4—102no—
212#67—51no—
213#67—51no—
214#67—102no—
215#67—102no—
216D12—22no—
217D12—51no—
218D12—52no—
219D12—102no—
220D12—102no—
221D12C22×D512yes—
222C4×D3—22no—
223C4×D3—51no—
224C4×D3—102no—
225C4×D3C22×D511yescharacteristic
226Dic6—51no—
227C3×C8—51no—
228C3×C8C22×D511yescharacteristic
229C3⋊C8—51no—
230C3⋊C8C22×D511yescharacteristic
231C22×C5—31no—
232C22×C5—62no—
233C2×D5—22no—
234C2×D5—31no—
235C2×D5—62no—
236C2×D5—242no—
237C2×D5—242no—
238C2×D5—242no—
239C2×D5D3×D411yescharacteristic
240C4×C5—22no—
241C4×C5—31no—
242C4×C5C23×D311yescharacteristic
243Dic5—31no—
244Dic5D3×D411yescharacteristic
245#41—32no—
246#41—52no—
247#41—151no—
248#41—152no—
249#41—302no—
250C2×D4—152no—
251C2×D4—152no—
252C2×D4—152no—
253C2×D4—302no—
254C2×D4—302no—
255C2×D4—302no—
256Q16D3×D511yescharacteristic, complemented
257SD16—32no—
258SD16—52no—
259SD16—152no—
260D8—31no—
261D8—51no—
262D8—152no—
263D8—152no—
264D8—152no—
265D8—151no—
266M16—151no—
267M16—151no—
268M16—151no—
269C2×C8—31no—
270C2×C8—51no—
271C2×C8—151no—
272C3×C5#57611yescharacteristic, complemented, Hall
273C22×C3—51no—
274C22×C3—102no—
275C2×D3—22no—
276C2×D3—51no—
277C2×D3—102no—
278C2×D3—402no—
279C2×D3—402no—
280C2×D3—402no—
281C2×D3D4×D511yescharacteristic
282C3×C4—22no—
283C3×C4—51no—
284C3×C4C23×D511yescharacteristic
285Dic3—51no—
286Dic3D4×D511yescharacteristic
287C2×C5—61no—
288C2×C5—122no—
289C2×C5C2×D3×D411yescharacteristic
290D5—21no—
291D5—42no—
292D5—61no—
293D5—122no—
294C23—302no—
295C23—302no—
296C23—302no—
297Q8—151no—
298Q8C2×D3×D512yes—
299D4—32no—
300D4—52no—
301D4—62no—
302D4—102no—
303D4—151no—
304D4—151no—
305D4—151no—
306D4—152no—
307D4—302no—
308D4—302no—
309D4—302no—
310D4—302no—
311C2×C4—31no—
312C2×C4—51no—
313C2×C4—62no—
314C2×C4—102no—
315C2×C4—151no—
316C2×C4—302no—
317C8—31no—
318C8—51no—
319C8—151no—
320C8C2×D3×D511yescharacteristic
321C2×C3—101no—
322C2×C3—202no—
323C2×C3C2×D4×D511yescharacteristic
324D3—21no—
325D3—42no—
326D3—101no—
327D3—202no—
328C5#576911yescharacteristic, complemented, Sylow
329C22—31no—
330C22—51no—
331C22—62no—
332C22—102no—
333C22—151no—
334C22—302no—
335C22—1202no—
336C22—1202no—
337C22—1202no—
338C4—22no—
339C4—31no—
340C4—51no—
341C4—151no—
342C4C22×D3×D511yescharacteristic
343C3#6610311yescharacteristic, complemented, Sylow
344C2—61no—
345C2—101no—
346C2—122no—
347C2—202no—
348C2—301no—
349C2—602no—
350C2D3×D4×D511yescharacteristic
subgroupG/H
centerC2D3×D4×D5
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC3×C5×Q16C22
socleC2×C3×C5C22×D4
hypercenterQ16D3×D5
hypocenterC3×C5#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. #92035C2semidirect
2. #91808C2semidirect
3. C5×#919C2semidirect
4. C3×#4065C2semidirect
5. #91506C2semidirect
6. #91504C2semidirect
7. #91502C2semidirect
8. #91265C2semidirect
9. #91256C2semidirect
10. D3×D40C2semidirect
11. D5×D24C2semidirect
13. #6821C22semidirect
14. C5×#239C22semidirect
15. C3×#713C22semidirect
17. #6777C22semidirect
19. D3×D20C22semidirect
21. D5×D12C22semidirect
24. C3×C5×Q16C22semidirect
25. #6717C22semidirect
26. D120C22semidirect
27. C8×D15C22semidirect
28. C5×#215C22semidirect
29. C5×D24C22semidirect
30. C5×D3×C8C22semidirect
31. C3×#688C22semidirect
32. C3×D40C22semidirect
33. C3×C8×D5C22semidirect
34. #6654C22semidirect
35. #6653C22semidirect
36. #6652C22semidirect
37. #6651C22semidirect
38. #6650C22semidirect
39. #6649C22semidirect
45. #4065D3semidirect
83. #919D5semidirect
92. #713C2×D3semidirect
101. C5×Q16C2×D3semidirect
106. #688C2×D3semidirect
112. D40C2×D3semidirect
116. C8×D5C2×D3semidirect
134. #239C2×D5semidirect
143. C3×Q16C2×D5semidirect
148. #215C2×D5semidirect
154. D24C2×D5semidirect
158. D3×C8C2×D5semidirect
256. Q16D3×D5semidirect
272. C3×C5#576semidirect
328. C5#5769semidirect
343. C3#66103semidirect

Maximal subgroups

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

subgroupindex
#920352
#918082
C5×#9192
C3×#40652
#915062
#915042
#915022
#912652
#912562
D3×D402
D5×D242
#661033
#57695