Finite Group Databasebeta

← #11754704

Subgroups — #11754704

Order 960.

536 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 128 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#92095C211yesmaximal, characteristic, complemented
2#92018C211yesmaximal, characteristic, complemented
3C2×C5×#213C211yesmaximal, characteristic, complemented
4C3×#4078C211yesmaximal, characteristic, complemented
5#91500C212yesmaximal, complemented
6#91499C212yesmaximal, complemented
7#91482C212yesmaximal, complemented
8#91481C212yesmaximal, complemented
9#91311C211yesmaximal, characteristic, complemented
10#91304C211yesmaximal, characteristic, complemented
11#91291C211yesmaximal, characteristic, complemented
12#66091—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic, complemented
14C2×#1220—22no—
15#6819—21no—
16#6819C2212yescomplemented
17D4×D15—21no—
18D4×D15C2212yescomplemented
19#6817C2211yescharacteristic
20#6817C2211yescharacteristic, complemented
21C2×C5×D12C2211yescharacteristic, complemented
22C3×#709C2211yescharacteristic, complemented
23D3×C22⋊D5—22no—
24#6777C2212yescomplemented
25D5×D12—21no—
26#6772—21no—
27#6768C2212yescomplemented
28C5×#213C2212yescomplemented
29C5×#213C2212yescomplemented
30C2×C5×C3⋊C8C2211yescharacteristic, complemented
31C3×#687C2212yescomplemented
32C3×#686C2212yescomplemented
33C3×#681C2211yescharacteristic, complemented
34#6662C2211yescharacteristic, complemented
35#6659C2212yescomplemented
36#6658C2211yescharacteristic, complemented
37#6657C2211yescharacteristic, complemented
38#6654C2212yescomplemented
39#6653C2211yescharacteristic, complemented
40#6651C2212yescomplemented
41#6648C2212yescomplemented
42#5774—51nomaximal, Hall
43#4144—31no—
44#4144—31no—
45C2×C5×D8—31no—
46#4078—31no—
47#4078D311yescharacteristic, complemented
48#4058—32no—
49#4057—32no—
50#4057—32no—
51D5×D8—32no—
52#4050—31no—
53#4047—31no—
54C23×C3×C5—21no—
55C22×D15—22no—
56C22×C5×D3—21no—
57C2×D3×D5—22no—
58C3×C5×D4—21no—
59C3×C5×D4C2312yes—
60C2×C3×C4×C5C2311yescharacteristic
61#1220—21no—
62#1220—22no—
63#1220—22no—
64#1220D412yes—
65C2×Dic15—22no—
66D60D411yescharacteristic
67D60C2311yescharacteristic
68C4×D15—21no—
69C4×D15C2312yes—
70Dic30D411yescharacteristic
71Dic30C2311yescharacteristic
72C5×D12—21no—
73C5×D12C2312yes—
74C3×C22⋊D5—21no—
75C3×D20C2311yescharacteristic
76C3×C4×D5—21no—
77C3×Dic10C2311yescharacteristic
78#1203—22no—
79#1201—22no—
80D3×Dic5—22no—
81C3×#168C2312yes—
82C5×C3⋊C8C2311yescharacteristic
83C5×C3⋊C8C2311yescharacteristic
84#1009—51no—
85#1004—51no—
86C3×AGL(1,ℤ/8)—51no—
87#950—51no—
88C2×#213D511yescharacteristic, complemented
89#916—52no—
90#914—52no—
91#911—52no—
92D3×D8—52no—
93#908—51no—
94#907—51no—
95C2×C5×D4—31no—
96C2×C5×D4C2×D311yescharacteristic, complemented
97C2×C22⋊D5—62no—
98C2×C22⋊D5—62no—
99#711—32no—
100#711—32no—
101#711—61no—
102#711—61no—
103D4×D5—32no—
104D4×D5—32no—
105D4×D5—61no—
106D4×D5—61no—
107#709—31no—
108#709—31no—
109#709C2×D311yescharacteristic, complemented
110C5×D8—32no—
111C5×D8—32no—
112C2×C5×C8—31no—
113#687—32no—
114#687C2×D312yescomplemented
115#686—32no—
116#686C2×D312yescomplemented
117#681C2×D311yescharacteristic, complemented
118Dic20—31no—
119D40—31no—
120#677—31no—
121#677—31no—
122#676—32no—
123C8×D5—32no—
124#576—151noSylow
125C22×C3×C5—22no—
126C22×C3×C5—81no—
127C22×C3×C5C2×D411yescharacteristic
128C2×D15—21no—
129C2×D15—82no—
130C2×D15C2×D412yes—
131C2×C5×D3—22no—
132C2×C5×D3—81no—
133C2×C3×D5—21no—
134D3×D5—82no—
135C3×C4×C5C2×D411yescharacteristic
136C3×C4×C5C2411yescharacteristic
137Dic15—21no—
138Dic15C2×D412yes—
139C3×Dic5—21no—
140C3×#41—51no—
141C2×C3×D4C2×D511yescharacteristic, complemented
142C2×#67—102no—
143#239—52no—
144#237—52no—
145#237—101no—
146D3×D4—52no—
147D3×D4—52no—
148D3×D4—101no—
149D3×D4—102no—
150#235—51no—
151#235—51no—
152#235—101no—
153C2×D12—101no—
154C2×D12C2×D511yescharacteristic, complemented
155C3×SD16—52no—
156C3×D8—52no—
157C3×M16—51no—
158#216—51no—
159#215—51no—
160#214—51no—
161#213—51no—
162#213C2×D512yescomplemented
163#213C2×D512yescomplemented
164C2×C3⋊C8C2×D511yescharacteristic, complemented
165D24—52no—
166#204—52no—
167ΓL(1,𝔽25)—52no—
168D3×C8—52no—
169C23×C5—21no—
170C23×C5—61no—
171C22×D5—62no—
172C22×D5—62no—
173C5×D4—21no—
174C5×D4—32no—
175C5×D4—61no—
176C5×D4C22×D312yes—
177C2×C4×C5C22×D311yescharacteristic
178C22⋊D5—21no—
179C22⋊D5—32no—
180C22⋊D5—62no—
181C22⋊D5—62no—
182C22⋊D5—62no—
183C22⋊D5—62no—
184C22⋊D5—61no—
185C2×Dic5—62no—
186C2×Dic5—62no—
187D20—31no—
188D20—31no—
189D20C22×D311yescharacteristic
190C4×D5—21no—
191C4×D5—32no—
192C4×D5—61no—
193Dic10—31no—
194Dic10—31no—
195Dic10C22×D311yescharacteristic
196C5×C8—31no—
197C5×C8—31no—
198#168C22×D312yes—
199H(5,𝔽2)—151no—
200H(5,𝔽2)—151no—
201AGL(1,ℤ/8)—51no—
202AGL(1,ℤ/8)—151no—
203AGL(1,ℤ/8)—152no—
204AGL(1,ℤ/8)—152no—
205#135—151no—
206#135—152no—
207C2×D8—31no—
208C2×D8—152no—
209#131—151no—
210C2×C3×C5—21no—
211C2×C3×C5—42no—
212C2×C3×C5C22×D411yescharacteristic
213D15—22no—
214D15—41no—
215C3×D5—41no—
216C5×D3—42no—
217C23×C3—21no—
218C22×D3—21no—
219C22×D3—102no—
220C22×D3—102no—
221C3×Q8—51no—
222C3×D4—21no—
223C3×D4—51no—
224C3×D4—101no—
225C3×D4C22×D512yes—
226C2×C3×C4—101no—
227C2×C3×C4C22×D511yescharacteristic
228#67—52no—
229#67—102no—
230#67—102no—
231#67—102no—
232#67—101no—
233C2×Dic3—102no—
234D12—21no—
235D12—51no—
236D12—51no—
237D12—102no—
238D12C22×D512yes—
239C4×D3—52no—
240C4×D3—102no—
241C4×D3—101no—
242Dic6—51no—
243Dic6—51no—
244C3×C8—52no—
245C3⋊C8C22×D511yescharacteristic
246C3⋊C8C22×D511yescharacteristic
247C22×C5—22no—
248C22×C5—62no—
249C22×C5—81no—
250C22×C5—241no—
251C22×C5D3×D411yescharacteristic
252C2×D5—21no—
253C2×D5—32no—
254C2×D5—61no—
255C2×D5—242no—
256C2×D5—242no—
257C4×C5D3×D411yescharacteristic
258C4×C5C23×D311yescharacteristic
259Dic5—21no—
260Dic5—32no—
261Dic5—61no—
262#41—51no—
263#41—151no—
264#41—152no—
265#41—152no—
266#41—151no—
267#41—301no—
268#41—301no—
269C2×D4—31no—
270C2×D4—152no—
271C2×D4—152no—
272C2×D4—301no—
273C2×D4—301no—
274C2×D4—302no—
275C2×D4—302no—
276C2×D4D3×D511yescharacteristic, complemented
277Q16—151no—
278SD16—52no—
279SD16—151no—
280SD16—151no—
281SD16—152no—
282D8—32no—
283D8—32no—
284D8—52no—
285D8—151no—
286D8—152no—
287M16—51no—
288M16—152no—
289C2×C8—31no—
290C2×C8—152no—
291C3×C5#57611yescharacteristic, complemented, Hall
292C22×C3—22no—
293C22×C3—81no—
294C22×C3—101no—
295C22×C3D4×D511yescharacteristic
296C2×D3—22no—
297C2×D3—52no—
298C2×D3—81no—
299C2×D3—101no—
300C2×D3—402no—
301C2×D3—402no—
302C3×C4—101no—
303C3×C4D4×D511yescharacteristic
304C3×C4C23×D511yescharacteristic
305Dic3—52no—
306Dic3—101no—
307C2×C5—21no—
308C2×C5—42no—
309C2×C5—122no—
310C2×C5C2×D3×D411yescharacteristic
311D5—41no—
312D5—62no—
313D5—121no—
314C23—21no—
315C23—61no—
316C23—302no—
317C23—302no—
318Q8—51no—
319Q8—151no—
320Q8—151no—
321D4—21no—
322D4—32no—
323D4—51no—
324D4—61no—
325D4—101no—
326D4—152no—
327D4—151no—
328D4—151no—
329D4—302no—
330D4—302no—
331D4—302no—
332D4—302no—
333D4—301no—
334D4C2×D3×D512yes—
335C2×C4—101no—
336C2×C4—152no—
337C2×C4—302no—
338C2×C4—302no—
339C2×C4—301no—
340C2×C4C2×D3×D511yescharacteristic
341C8—31no—
342C8—31no—
343C8—52no—
344C2×C3—21no—
345C2×C3—42no—
346C2×C3—201no—
347C2×C3C2×D4×D511yescharacteristic
348D3—42no—
349D3—102no—
350D3—201no—
351C5#577411yescharacteristic, complemented, Sylow
352C22—22no—
353C22—62no—
354C22—81no—
355C22—101no—
356C22—152no—
357C22—241no—
358C22—301no—
359C22—1202no—
360C22—1202no—
361C22#679011yescharacteristic
362C4—101no—
363C4—152no—
364C4—301no—
365C4#679011yescharacteristic
366C4C22×D3×D511yescharacteristic
367C3#6609111yescharacteristic, complemented, Sylow
368C2—21no—
369C2—42no—
370C2—122no—
371C2—201no—
372C2—302no—
373C2—601no—
374C2C2×#679011yescharacteristic
subgroupG/H
centerC2C2×#6790
commutator, cosocleC3×C4×C5C24
FrattiniC4C22×D3×D5
FittingC2×C3×C5×D4C22
socleC2×C3×C5C22×D4
hypercenterC2×D4D3×D5
hypocenterC3×C5#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #92095C2semidirect
2. #92018C2semidirect
3. C2×C5×#213C2semidirect
4. C3×#4078C2semidirect
5. #91500C2semidirect
6. #91499C2semidirect
7. #91482C2semidirect
8. #91481C2semidirect
9. #91311C2semidirect
10. #91304C2semidirect
11. #91291C2semidirect
13. C2×C3×C5×D4C22semidirect
16. #6819C22semidirect
18. D4×D15C22semidirect
20. #6817C22semidirect
21. C2×C5×D12C22semidirect
22. C3×#709C22semidirect
24. #6777C22semidirect
27. #6768C22semidirect
28. C5×#213C22semidirect
29. C5×#213C22semidirect
30. C2×C5×C3⋊C8C22semidirect
31. C3×#687C22semidirect
32. C3×#686C22semidirect
33. C3×#681C22semidirect
34. #6662C22semidirect
35. #6659C22semidirect
36. #6658C22semidirect
37. #6657C22semidirect
38. #6654C22semidirect
39. #6653C22semidirect
40. #6651C22semidirect
41. #6648C22semidirect
47. #4078D3semidirect
88. C2×#213D5semidirect
96. C2×C5×D4C2×D3semidirect
109. #709C2×D3semidirect
114. #687C2×D3semidirect
116. #686C2×D3semidirect
117. #681C2×D3semidirect
141. C2×C3×D4C2×D5semidirect
154. C2×D12C2×D5semidirect
162. #213C2×D5semidirect
163. #213C2×D5semidirect
164. C2×C3⋊C8C2×D5semidirect
276. C2×D4D3×D5semidirect
291. C3×C5#576semidirect
351. C5#5774semidirect
367. C3#66091semidirect

Maximal subgroups

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

subgroupindex
#920952
#920182
C2×C5×#2132
C3×#40782
#915002
#914992
#914822
#914812
#913112
#913042
#912912
#660913
#57745