Finite Group Databasebeta

← #11755331

Subgroups — #11755331

Order 960.

516 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#92101C211yesmaximal, characteristic, complemented
2#92017C211yesmaximal, characteristic, complemented
3C5×#950C211yesmaximal, characteristic, complemented
4C3×#4095C211yesmaximal, characteristic, complemented
5#91522C212yesmaximal, complemented
6#91505C212yesmaximal, complemented
7#91497C212yesmaximal, complemented
8#91482C212yesmaximal, complemented
9#91322C211yesmaximal, characteristic, complemented
10C2×#6657C211yesmaximal, characteristic, complemented
11#91291C211yesmaximal, characteristic, complemented
12#66104—31nomaximal, Hall
13C3×C5×#41C2211yescharacteristic, complemented
14Q8×D15C2212yescomplemented
15#6819—22no—
16#6819C2212yescomplemented
17#6817—21no—
18#6817C2211yescharacteristic
19C2×Dic30—21no—
20C2×Dic30C2211yescharacteristic, complemented
21C5×#235C2211yescharacteristic
22C2×C3×D20C2211yescharacteristic
23D5×#67—22no—
24#6777C2212yes—
25D3×D20—21no—
26#6766C2212yes—
27#6765—21no—
28C5×#216C2211yescharacteristic, complemented
29C5×#215C2211yescharacteristic, complemented
30C5×#214C2211yescharacteristic, complemented
31C5×#213C2211yescharacteristic, complemented
32C2×C5×C3⋊C8C2211yescharacteristic, complemented
33C3×#688C2212yescomplemented
34C3×#686C2212yescomplemented
35C3×#681C2211yescharacteristic, complemented
36#6663C2212yescomplemented
37#6659C2212yescomplemented
38#6657C2212yescomplemented
39#6657C2212yescomplemented
40#6651C2212yescomplemented
41#6648C2212yescomplemented
42#5775—51nomaximal, Hall
43#4150—31no—
44#4149—31no—
45C5×#135—31no—
46#4097—31no—
47#4095D311yescharacteristic, complemented
48#4064—32no—
49#4062—32no—
50D5×SD16—32no—
51#4057—32no—
52C2×#677—31no—
53#4047—31no—
54C22×C3×D5—21no—
55C2×D3×D5—22no—
56C3×C5×Q8C2311yescharacteristic
57C3×C5×D4—21no—
58C3×C5×D4C2311yescharacteristic
59C2×C3×C4×C5—21no—
60C2×C3×C4×C5C2311yescharacteristic
61#1220—22no—
62#1220D412yes—
63C2×Dic15—21no—
64C2×Dic15—22no—
65D60D411yescharacteristic
66C4×D15—22no—
67C4×D15C2312yes—
68Dic30—21no—
69Dic30—22no—
70Dic30D411yescharacteristic
71Dic30C2312yes—
72C5×#67—21no—
73C5×D12C2311yescharacteristic
74C4×C5×D3—21no—
75C5×Dic6C2311yescharacteristic
76C3×D20—21no—
77C3×D20C2312yes—
78#1202—22no—
79#1201—22no—
80D5×Dic3—22no—
81C3×#168C2312yes—
82C5×C3⋊C8C2311yescharacteristic
83C5×C3⋊C8C2311yescharacteristic
84#1010—51no—
85#1004—51no—
86C3×AGL(1,ℤ/8)—51no—
87#950D511yescharacteristic, complemented
88C2×#214—51no—
89#915—52no—
90D3×SD16—52no—
91#912—52no—
92#911—52no—
93#909—51no—
94#907—51no—
95C5×#41—31no—
96C5×#41C2×D311yescharacteristic, complemented
97#713—32no—
98Q8×D5—32no—
99#711—32no—
100#711—62no—
101D4×D5—32no—
102D4×D5—62no—
103#709—31no—
104#709—61no—
105#709—61no—
106C2×D20—61no—
107C2×D20C2×D311yescharacteristic
108C2×Dic10—31no—
109C2×Dic10—61no—
110C5×Q16—31no—
111C5×SD16—31no—
112C5×SD16—31no—
113C5×D8—31no—
114C2×C5×C8—31no—
115#689—32no—
116#688C2×D312yescomplemented
117#687—32no—
118#686C2×D312yescomplemented
119#681C2×D311yescharacteristic, complemented
120#677—32no—
121#677—32no—
122#676—32no—
123C8×D5—32no—
124#577—151noSylow
125C22×C3×C5—21no—
126C22×C3×C5C2×D411yescharacteristic
127C2×D15C2×D412yes—
128C2×C5×D3—21no—
129C2×C3×D5—22no—
130C2×C3×D5—81no—
131D3×D5—82no—
132C3×C4×C5—21no—
133C3×C4×C5C2×D411yescharacteristic
134C3×C4×C5C2411yescharacteristic
135Dic15—22no—
136Dic15C2×D412yes—
137C5×Dic3—21no—
138C3×#41C2×D511yescharacteristic, complemented
139C2×C3×D4—51no—
140C2×#67—102no—
141D3×Q8—52no—
142#237—52no—
143#237—52no—
144#237—101no—
145#237—102no—
146D3×D4—52no—
147D3×D4—101no—
148#235—51no—
149#235—101no—
150#235C2×D511yescharacteristic
151C2×Dic6—51no—
152C2×Dic6—101no—
153C3×SD16—52no—
154C3×D8—52no—
155C3×M16—51no—
156#216C2×D511yescharacteristic, complemented
157#215C2×D511yescharacteristic, complemented
158#214—52no—
159#214—52no—
160#214C2×D511yescharacteristic, complemented
161#213C2×D511yescharacteristic, complemented
162C2×C3⋊C8C2×D511yescharacteristic, complemented
163Dic12—52no—
164#204—52no—
165ΓL(1,𝔽25)—52no—
166D3×C8—52no—
167C22×D5—21no—
168C22×D5—62no—
169C5×Q8—31no—
170C5×Q8C22×D311yescharacteristic
171C5×D4—21no—
172C5×D4—31no—
173C5×D4—61no—
174C5×D4C22×D311yescharacteristic
175C2×C4×C5—21no—
176C2×C4×C5—61no—
177C2×C4×C5C22×D311yescharacteristic
178C22⋊D5—32no—
179C22⋊D5—62no—
180C22⋊D5—62no—
181C2×Dic5—62no—
182C2×Dic5—61no—
183D20—21no—
184D20—31no—
185D20—62no—
186D20C22×D312yes—
187C4×D5—32no—
188C4×D5—62no—
189C4×D5—62no—
190Dic10—31no—
191Dic10—32no—
192Dic10—62no—
193Dic10—61no—
194C5×C8—31no—
195C5×C8—31no—
196#168C22×D312yes—
1972−1+4—151no—
198H(5,𝔽2)—151no—
199#137—151no—
200#137—152no—
201AGL(1,ℤ/8)—51no—
202AGL(1,ℤ/8)—152no—
203#135—31no—
204#135—152no—
205C2×SD16—151no—
206C2×SD16—152no—
207#131—151no—
208C2×C3×C5—21no—
209C2×C3×C5—41no—
210C2×C3×C5C22×D411yescharacteristic
211D15—22no—
212C3×D5—42no—
213C5×D3—41no—
214C23×C3—101no—
215C22×D3—102no—
216C3×Q8C22×D511yescharacteristic
217C3×D4—21no—
218C3×D4—52no—
219C3×D4—101no—
220C3×D4C22×D511yescharacteristic
221C2×C3×C4—21no—
222C2×C3×C4C22×D511yescharacteristic
223#67—21no—
224#67—52no—
225#67—102no—
226#67—102no—
227#67—102no—
228C2×Dic3—102no—
229C2×Dic3—102no—
230C2×Dic3—101no—
231D12—51no—
232D12C22×D511yescharacteristic
233C4×D3—21no—
234C4×D3—52no—
235C4×D3—102no—
236Dic6—51no—
237Dic6—52no—
238Dic6—102no—
239Dic6—101no—
240Dic6C22×D511yescharacteristic
241C3×C8—52no—
242C3⋊C8C22×D511yescharacteristic
243C3⋊C8C22×D511yescharacteristic
244C22×C5—21no—
245C22×C5—61no—
246C22×C5D3×D411yescharacteristic
247C2×D5—22no—
248C2×D5—32no—
249C2×D5—81no—
250C2×D5—242no—
251C4×C5—21no—
252C4×C5—61no—
253C4×C5D3×D411yescharacteristic
254C4×C5C23×D311yescharacteristic
255Dic5—32no—
256Dic5—62no—
257#41—31no—
258#41—151no—
259#41—152no—
260#41—152no—
261#41—301no—
262#41—301no—
263#41—302no—
264#41D3×D511yescharacteristic, complemented
265C2×Q8—152no—
266C2×Q8—151no—
267C2×Q8—301no—
268C2×D4—51no—
269C2×D4—152no—
270C2×D4—301no—
271C2×D4—302no—
272Q16—31no—
273Q16—152no—
274SD16—31no—
275SD16—31no—
276SD16—52no—
277SD16—152no—
278SD16—152no—
279SD16—152no—
280D8—31no—
281D8—52no—
282M16—51no—
283M16—152no—
284C2×C8—31no—
285C2×C8—152no—
286C3×C5#57711yescharacteristic, complemented, Hall
287C22×C3—21no—
288C22×C3—102no—
289C22×C3—401no—
290C22×C3D4×D511yescharacteristic
291C2×D3—21no—
292C2×D3—52no—
293C2×D3—402no—
294C3×C4—21no—
295C3×C4D4×D511yescharacteristic
296C3×C4C23×D511yescharacteristic
297Dic3—21no—
298Dic3—52no—
299Dic3—102no—
300C2×C5—21no—
301C2×C5—41no—
302C2×C5—121no—
303C2×C5C2×D3×D411yescharacteristic
304D5—42no—
305D5—62no—
306C23—101no—
307C23—302no—
308Q8—31no—
309Q8—151no—
310Q8—152no—
311Q8—302no—
312Q8—301no—
313Q8C2×D3×D511yescharacteristic
314D4—21no—
315D4—31no—
316D4—52no—
317D4—61no—
318D4—101no—
319D4—152no—
320D4—151no—
321D4—302no—
322D4—302no—
323D4—302no—
324D4C2×D3×D511yescharacteristic
325C2×C4—21no—
326C2×C4—61no—
327C2×C4—152no—
328C2×C4—302no—
329C2×C4—302no—
330C2×C4—302no—
331C2×C4—301no—
332C2×C4C2×D3×D511yescharacteristic
333C8—31no—
334C8—31no—
335C8—52no—
336C2×C3—21no—
337C2×C3—41no—
338C2×C3—202no—
339C2×C3C2×D4×D511yescharacteristic
340D3—41no—
341D3—102no—
342C5#577511yescharacteristic, complemented, Sylow
343C22—21no—
344C22—61no—
345C22—102no—
346C22—152no—
347C22—401no—
348C22—1202no—
349C22#679011yescharacteristic
350C4—21no—
351C4—61no—
352C4—152no—
353C4—302no—
354C4#679011yescharacteristic
355C4C22×D3×D511yescharacteristic
356C3#6610411yescharacteristic, complemented, Sylow
357C2—21no—
358C2—41no—
359C2—121no—
360C2—202no—
361C2—302no—
362C2C2×#679011yescharacteristic
subgroupG/H
centerC2C2×#6790
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC3×C5×#41C22
socleC2×C3×C5C22×D4
hypercenter#41D3×D5
hypocenterC3×C5#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #92101C2semidirect
2. #92017C2semidirect
3. C5×#950C2semidirect
4. C3×#4095C2semidirect
5. #91522C2semidirect
6. #91505C2semidirect
7. #91497C2semidirect
8. #91482C2semidirect
9. #91322C2semidirect
10. C2×#6657C2semidirect
11. #91291C2semidirect
13. C3×C5×#41C22semidirect
14. Q8×D15C22semidirect
16. #6819C22semidirect
20. C2×Dic30C22semidirect
28. C5×#216C22semidirect
29. C5×#215C22semidirect
30. C5×#214C22semidirect
31. C5×#213C22semidirect
32. C2×C5×C3⋊C8C22semidirect
33. C3×#688C22semidirect
34. C3×#686C22semidirect
35. C3×#681C22semidirect
36. #6663C22semidirect
37. #6659C22semidirect
38. #6657C22semidirect
39. #6657C22semidirect
40. #6651C22semidirect
41. #6648C22semidirect
47. #4095D3semidirect
87. #950D5semidirect
96. C5×#41C2×D3semidirect
116. #688C2×D3semidirect
118. #686C2×D3semidirect
119. #681C2×D3semidirect
138. C3×#41C2×D5semidirect
156. #216C2×D5semidirect
157. #215C2×D5semidirect
160. #214C2×D5semidirect
161. #213C2×D5semidirect
162. C2×C3⋊C8C2×D5semidirect
264. #41D3×D5semidirect
286. C3×C5#577semidirect
342. C5#5775semidirect
356. C3#66104semidirect

Maximal subgroups

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

subgroupindex
#921012
#920172
C5×#9502
C3×#40952
#915222
#915052
#914972
#914822
#913222
C2×#66572
#912912
#661043
#57755