Finite Group Databasebeta

← #11754952

Subgroups — #11754952

Order 960.

692 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×D4C211yesmaximal, characteristic, complemented
2C22×#1203C211yesmaximal, characteristic, complemented
3#91826C211yesmaximal, characteristic, complemented
4C3×#4081C211yesmaximal, characteristic, complemented
5#91573C211yesmaximal, characteristic, complemented
6#91570C212yesmaximal, complemented
7#91558C212yesmaximal, complemented
8D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#91539C211yesmaximal, characteristic, complemented
10#91416C212yesmaximal, complemented
11#91351C212yesmaximal, complemented
12#66138—31nomaximal, Hall
13C23×D15C2211yescharacteristic, complemented
14C23×C5×D3C2211yescharacteristic
15C23×C5×D3C2211yescharacteristic, complemented
16C2×C3×C5×D4C2211yescharacteristic
17C2×#1220C2212yescomplemented
18C2×C5×#67C2211yescharacteristic
19C2×C5×#67C2211yescharacteristic, complemented
20C5×D3×D4—24no—
21C2×C5×D12C2211yescharacteristic, complemented
22C2×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×Dic5C2211yescharacteristic, complemented
24C2×#1203—24no—
25C2×#1203C2212yes—
26C2×#1203C2212yescomplemented
27C2×#1203C2212yescomplemented
28C2×D3×Dic5C2212yescomplemented
29#6719C2211yescharacteristic, complemented
30#6714C2212yescomplemented
31C3×C22⋊Dic5C2211yescharacteristic, complemented
32C3×C22⋊Dic5C2212yescomplemented
33C3×#683C2212yescomplemented
34#6669C2212yescomplemented
35#6667C2212yescomplemented
36(C2×D3)⋊Dic5C2212yescomplemented
37(C2×D3)⋊Dic5C2212yescomplemented
38#5653—51nomaximal, Hall
39C22×C5×D4—31no—
40C22×C22⋊D5—31no—
41#4099—32no—
42C2×C22⋊Dic5—31no—
43#4085—32no—
44#4085—32no—
45#4083—31no—
46#4083—31no—
47#4081—31no—
48#4081D311yescharacteristic, complemented
49#4075—32no—
50C23×C3×C5C2311yescharacteristic
51C23×C3×C5C2311yescharacteristic
52C22×D15—22no—
53C22×D15—42no—
54C22×D15C2312yes—
55C22×C5×D3—22no—
56C22×C5×D3—42no—
57C22×C5×D3—42no—
58C22×C5×D3D414yescomplemented
59C22×C5×D3C2311yescharacteristic
60C22×C5×D3C2311yescharacteristic
61C22×C5×D3C2311yescharacteristic
62C3×C5×D4—22no—
63C2×C3×C4×C5C2311yescharacteristic
64#1220—42no—
65C2×Dic15C2312yes—
66C5×#67—22no—
67C5×#67—22no—
68C2×C5×Dic3C2311yescharacteristic
69C5×D12—22no—
70C4×C5×D3—22no—
71C2×C3×Dic5—22no—
72C2×C3×Dic5C2312yes—
73C2×C3×Dic5C2312yes—
74#1203—24no—
75#1203—24no—
76#1203—42no—
77D3×Dic5—42no—
78C2×D3×D4D511yescharacteristic, complemented
79C22×D12—51no—
80C3×#123—51no—
81#937—51no—
82#929—51no—
83#895—52no—
84#894—52no—
85#884—52no—
86#882—52no—
87#882—51no—
88D3×C22⋊C4—51no—
89C24×C5—31no—
90C24×C5—31no—
91C23×D5—31no—
92C2×C5×D4—31no—
93C2×C5×D4—31no—
94C2×C5×D4—31no—
95C2×C5×D4—64no—
96C2×C5×D4C2×D311yescharacteristic
97C22×C4×C5—31no—
98C2×C22⋊D5—32no—
99C2×C22⋊D5—32no—
100C2×C22⋊D5—32no—
101C2×C22⋊D5—32no—
102C2×C22⋊D5—64no—
103C22×Dic5—32no—
104C22×Dic5C2×D311yescharacteristic, complemented
105C22⋊Dic5—31no—
106C22⋊Dic5—32no—
107C22⋊Dic5—32no—
108C22⋊Dic5C2×D311yescharacteristic, complemented
109C22⋊Dic5C2×D312yescomplemented
110#685—32no—
111#685—32no—
112#683—32no—
113#683C2×D312yescomplemented
114#534—151noSylow
115C22×C3×C5—22no—
116C22×C3×C5—21no—
117C22×C3×C5—22no—
118C22×C3×C5C2×D412yes—
119C22×C3×C5C2411yescharacteristic
120C2×D15—22no—
121C2×D15—22no—
122C2×D15—22no—
123C2×D15—44no—
124C2×C5×D3—22no—
125C2×C5×D3—22no—
126C2×C5×D3—21no—
127C2×C5×D3—22no—
128C2×C5×D3—44no—
129C2×C5×D3—44no—
130C2×C5×D3C2×D412yes—
131C2×C5×D3C2×D412yes—
132C3×C4×C5—21no—
133Dic15—22no—
134C3×Dic5—22no—
135C3×Dic5—22no—
136C5×Dic3—21no—
137C23×D3—51no—
138C23×D3C2×D511yescharacteristic
139C23×D3C2×D511yescharacteristic, complemented
140C2×C3×D4C2×D511yescharacteristic
141C22×C3×C4—51no—
142C2×#67—52no—
143C2×#67C2×D511yescharacteristic
144C2×#67C2×D511yescharacteristic, complemented
145D3×D4—24no—
146C2×D12—52no—
147C2×D12—52no—
148C2×D12—52no—
149C2×D12—104no—
150C2×D12C2×D511yescharacteristic, complemented
151C2×C4×D3—52no—
152C2×C4×D3C2×D511yescharacteristic, complemented
153C3×C4⋊C4—52no—
154C3×C22⋊C4—51no—
155C3×C22⋊C4—52no—
156#217—51no—
157(C2×D3)⋊C4—52no—
158(C2×D3)⋊C4—52no—
159(C2×D3)⋊C4—52no—
160(C2×D3)⋊C4—52no—
161Dic3⋊C4—52no—
162C23×C5—31no—
163C23×C5—31no—
164C23×C5—34no—
165C23×C5—31no—
166C23×C5—62no—
167C23×C5—122no—
168C23×C5—122no—
169C23×C5C22×D311yescharacteristic
170C23×C5C22×D311yescharacteristic
171C22×D5—32no—
172C22×D5—62no—
173C22×D5—122no—
174C5×D4—22no—
175C5×D4—62no—
176C5×D4—62no—
177C5×D4—62no—
178C2×C4×C5—31no—
179C2×C4×C5—62no—
180C2×C4×C5C22×D311yescharacteristic
181C22⋊D5—64no—
182C22⋊D5—64no—
183C22⋊D5—122no—
184C22⋊D5—122no—
185C2×Dic5—22no—
186C2×Dic5—32no—
187C2×Dic5—122no—
188C2×Dic5C22×D312yes—
189C2×Dic5C22×D312yes—
190C22×D4—31no—
191C22×D4—151no—
192#123—51no—
193#123—152no—
194#123—151no—
195#121—152no—
196#121—152no—
197#120—151no—
198#120—152no—
199#120—151no—
200C2×C22⋊C4—151no—
201C2×C3×C5—22no—
202C2×C3×C5—41no—
203C2×C3×C5C22×D411yescharacteristic
204C2×C3×C5H(5,𝔽2)12yes—
205D15—42no—
206C5×D3—22no—
207C5×D3—22no—
208C5×D3—41no—
209C23×C3C22×D511yescharacteristic
210C23×C3C22×D511yescharacteristic
211C22×D3—22no—
212C22×D3—42no—
213C22×D3—42no—
214C22×D3—52no—
215C22×D3—102no—
216C22×D3—202no—
217C22×D3C22⋊D514yescomplemented
218C22×D3C22×D511yescharacteristic
219C22×D3C22×D511yescharacteristic
220C22×D3C22×D511yescharacteristic
221C3×D4—22no—
222C2×C3×C4—52no—
223C2×C3×C4—52no—
224C2×C3×C4—102no—
225C2×C3×C4C22×D511yescharacteristic
226#67—22no—
227#67—22no—
228#67—202no—
229C2×Dic3—52no—
230C2×Dic3C22×D511yescharacteristic
231D12—22no—
232D12—104no—
233D12—104no—
234D12—202no—
235C4×D3—22no—
236C4×D3—202no—
237C22×C5—22no—
238C22×C5—21no—
239C22×C5—22no—
240C22×C5—32no—
241C22×C5—32no—
242C22×C5—62no—
243C22×C5—62no—
244C22×C5—61no—
245C22×C5—62no—
246C22×C5—124no—
247C22×C5—124no—
248C22×C5D3×D412yes—
249C22×C5C23×D311yescharacteristic
250C2×D5—62no—
251C2×D5—62no—
252C2×D5—62no—
253C2×D5—124no—
254C4×C5—21no—
255C4×C5—61no—
256Dic5—22no—
257Dic5—22no—
258Dic5—62no—
259C24—31no—
260C24—31no—
261C24—151no—
262C2×D4—31no—
263C2×D4—31no—
264C2×D4—31no—
265C2×D4—64no—
266C2×D4—152no—
267C2×D4—152no—
268C2×D4—152no—
269C2×D4—152no—
270C2×D4—304no—
271C2×D4D3×D511yescharacteristic
272C22×C4—31no—
273C22×C4—51no—
274C22×C4—152no—
275C4⋊C4—52no—
276C4⋊C4—152no—
277C22⋊C4—51no—
278C22⋊C4—52no—
279C22⋊C4—152no—
280C22⋊C4—152no—
281C22⋊C4—152no—
282C22⋊C4—151no—
283C22⋊C4—152no—
284C3×C5#53411yescharacteristic, complemented, Hall
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3C2×C22⋊D512yes—
289C22×C3C23×D511yescharacteristic
290C2×D3—22no—
291C2×D3—22no—
292C2×D3—22no—
293C2×D3—21no—
294C2×D3—44no—
295C2×D3—44no—
296C2×D3—102no—
297C2×D3—102no—
298C2×D3—102no—
299C2×D3—204no—
300C2×D3C2×C22⋊D512yes—
301C2×D3C2×C22⋊D512yes—
302C3×C4—21no—
303C3×C4—102no—
304C3×C4—102no—
305Dic3—21no—
306Dic3—102no—
307C2×C5—22no—
308C2×C5—41no—
309C2×C5—62no—
310C2×C5—62no—
311C2×C5—121no—
312C2×C5C2×D3×D411yescharacteristic
313C2×C5#100912yes—
314D5—122no—
315C23—31no—
316C23—31no—
317C23—34no—
318C23—31no—
319C23—62no—
320C23—122no—
321C23—122no—
322C23—152no—
323C23—302no—
324C23—602no—
325C23C2×D3×D511yescharacteristic
326C23C2×D3×D511yescharacteristic
327D4—22no—
328D4—62no—
329D4—62no—
330D4—62no—
331D4—304no—
332D4—304no—
333D4—602no—
334D4—602no—
335C2×C4—31no—
336C2×C4—52no—
337C2×C4—52no—
338C2×C4—62no—
339C2×C4—102no—
340C2×C4—152no—
341C2×C4—602no—
342C2×C4C2×D3×D511yescharacteristic
343C2×C3—22no—
344C2×C3—41no—
345C2×C3#414412yes—
346C2×C3C22×C22⋊D511yescharacteristic
347D3—22no—
348D3—22no—
349D3—41no—
350D3—202no—
351C5#565311yescharacteristic, complemented, Sylow
352C22—22no—
353C22—22no—
354C22—21no—
355C22—32no—
356C22—32no—
357C22—62no—
358C22—62no—
359C22—62no—
360C22—61no—
361C22—124no—
362C22—124no—
363C22—302no—
364C22—302no—
365C22—302no—
366C22—604no—
367C22D3×C22⋊D512yes—
368C22C22×D3×D511yescharacteristic
369C4—21no—
370C4—61no—
371C4—102no—
372C4—102no—
373C4—302no—
374C3#6613811yescharacteristic, complemented, Sylow
375C2—22no—
376C2—41no—
377C2—62no—
378C2—62no—
379C2—121no—
380C2—602no—
381C2#9202712yes—
382C2C2×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×D4C2semidirect
2. C22×#1203C2semidirect
3. #91826C2semidirect
4. C3×#4081C2semidirect
5. #91573C2semidirect
6. #91570C2semidirect
7. #91558C2semidirect
8. D3×C22⋊Dic5C2semidirect
9. #91539C2semidirect
10. #91416C2semidirect
11. #91351C2semidirect
13. C23×D15C22semidirect
15. C23×C5×D3C22semidirect
17. C2×#1220C22semidirect
19. C2×C5×#67C22semidirect
21. C2×C5×D12C22semidirect
22. C2×C4×C5×D3C22semidirect
23. C22×C3×Dic5C22semidirect
26. C2×#1203C22semidirect
27. C2×#1203C22semidirect
28. C2×D3×Dic5C22semidirect
29. #6719C22semidirect
30. #6714C22semidirect
31. C3×C22⋊Dic5C22semidirect
32. C3×C22⋊Dic5C22semidirect
33. C3×#683C22semidirect
34. #6669C22semidirect
35. #6667C22semidirect
36. (C2×D3)⋊Dic5C22semidirect
37. (C2×D3)⋊Dic5C22semidirect
48. #4081D3semidirect
58. C22×C5×D3D4semidirect
78. C2×D3×D4D5semidirect
104. C22×Dic5C2×D3semidirect
108. C22⋊Dic5C2×D3semidirect
109. C22⋊Dic5C2×D3semidirect
113. #683C2×D3semidirect
139. C23×D3C2×D5semidirect
144. C2×#67C2×D5semidirect
150. C2×D12C2×D5semidirect
152. C2×C4×D3C2×D5semidirect
217. C22×D3C22⋊D5semidirect
284. C3×C5#534semidirect
351. C5#5653semidirect
374. C3#66138semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×D42
C22×#12032
#918262
C3×#40812
#915732
#915702
#915582
D3×C22⋊Dic52
#915392
#914162
#913512
#661383
#56535