Finite Group Databasebeta

← D5×#935 #11754786

Subgroups — D5×#935 #11754786

Order 960.

684 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D5C211yesmaximal, characteristic
2C22×D5×Dic3C211yesmaximal, characteristic, complemented
3#91824C211yesmaximal, characteristic, complemented
4C5×#935C211yesmaximal, characteristic, complemented
5#91548C212yesmaximal, complemented
6D5×#217C212yesmaximal, complemented
7D5×#217C211yesmaximal, characteristic, complemented
8#91537C211yesmaximal, characteristic, complemented
9#91536C211yesmaximal, characteristic, complemented
10#91407C212yesmaximal, complemented
11D5×Dic3⋊C4C212yesmaximal, complemented
12D5×#123—31nomaximal, Hall
13C23×C3×D5C2211yescharacteristic
14C23×C3×D5C2211yescharacteristic
15C2×C3×C5×D4C2211yescharacteristic
16C22×Dic15C2211yescharacteristic, complemented
17C22×C5×Dic3C2211yescharacteristic, complemented
18C2×C3×C22⋊D5C2211yescharacteristic
19C2×C3×C22⋊D5C2211yescharacteristic
20C3×D4×D5—24no—
21C2×C3×D20C2211yescharacteristic
22C2×C3×C4×D5C2211yescharacteristic
23C2×D5×Dic3—24no—
24C2×D5×Dic3C2212yes—
25C2×D5×Dic3C2212yes—
26C2×D5×Dic3C2212yescomplemented
27#6719C2211yescharacteristic, complemented
28#6719C2212yescomplemented
29#6712C2212yescomplemented
30C5×#217C2211yescharacteristic, complemented
31C5×#217C2212yescomplemented
32C5×Dic3⋊C4C2212yescomplemented
33Dic3⋊Dic5C2212yescomplemented
34#6669C2212yescomplemented
35#6665C2212yescomplemented
36#6665C2212yescomplemented
37#6665C2212yescomplemented
38C2×#935—51nomaximal, Hall
39C2×D4×D5D311yescharacteristic
40C22×C4×D5—31no—
41C5×#123—31no—
42#4081—31no—
43#4075—31no—
44#4040—32no—
45D5×C4⋊C4—32no—
46#4032—31no—
47#4029—32no—
48D5×C22⋊C4—31no—
49D5×C22⋊C4—32no—
50C23×C3×C5C2311yescharacteristic
51C23×C3×C5C2311yescharacteristic
52C22×C3×D5—24no—
53C22×C3×D5—22no—
54C22×C3×D5—24no—
55C22×C3×D5D414yes—
56C22×C3×D5C2311yescharacteristic
57C22×C3×D5C2311yescharacteristic
58C22×C3×D5C2311yescharacteristic
59C3×C5×D4—22no—
60C2×C3×C4×C5C2311yescharacteristic
61C2×Dic15—22no—
62C2×Dic15C2312yes—
63C2×Dic15C2312yes—
64C2×C5×Dic3—22no—
65C2×C5×Dic3C2312yes—
66C2×C5×Dic3C2312yes—
67C3×C22⋊D5—22no—
68C3×C22⋊D5—22no—
69C2×C3×Dic5C2311yescharacteristic
70C3×D20—22no—
71C3×C4×D5—22no—
72D5×Dic3—24no—
73D5×Dic3—24no—
74D5×Dic3—24no—
75C22×C3×D4—51no—
76C23×Dic3—51no—
77C2×#217—51no—
78C2×#217—52no—
79#935—51no—
80#935—51no—
81#935—51no—
82#935—52no—
83#935—52no—
84#935D511yescharacteristic, direct product factor
85C2×Dic3⋊C4—52no—
86C23×D5C2×D311yescharacteristic
87C23×D5C2×D311yescharacteristic
88C2×C5×D4C2×D311yescharacteristic
89C22×C4×C5—31no—
90C2×C22⋊D5C2×D311yescharacteristic
91C2×C22⋊D5C2×D311yescharacteristic
92C22×Dic5—31no—
93D4×D5—24no—
94C2×D20C2×D311yescharacteristic
95C2×C4×D5—32no—
96C2×C4×D5—32no—
97C2×C4×D5—32no—
98C2×C4×D5—64no—
99C2×C4×D5C2×D311yescharacteristic
100C5×C4⋊C4—32no—
101C5×C22⋊C4—32no—
102C5×C22⋊C4—31no—
103C22⋊Dic5—32no—
104C22⋊Dic5—31no—
105#685—32no—
106#685—32no—
107#685—32no—
108C4⋊Dic5—32no—
109#683—32no—
110#683—32no—
111C2×#123—151noSylow
112C22×C3×C5—22no—
113C22×C3×C5—21no—
114C22×C3×C5—22no—
115C22×C3×C5C2×D412yes—
116C22×C3×C5C2411yescharacteristic
117C2×C3×D5—22no—
118C2×C3×D5—28no—
119C2×C3×D5—21no—
120C2×C3×D5—22no—
121C2×C3×D5—44no—
122C2×C3×D5C2×D412yes—
123C2×C3×D5C2×D412yes—
124C2×C3×D5#4114yes—
125C3×C4×C5—21no—
126Dic15—22no—
127Dic15—22no—
128C3×Dic5—21no—
129C5×Dic3—22no—
130C5×Dic3—22no—
131C24×C3—51no—
132C24×C3—51no—
133C2×C3×D4—51no—
134C2×C3×D4—51no—
135C2×C3×D4—51no—
136C2×C3×D4—104no—
137C2×C3×D4C2×D511yescharacteristic
138C22×C3×C4—51no—
139C22×Dic3—51no—
140C22×Dic3—52no—
141C22×Dic3—52no—
142C22×Dic3—52no—
143C22×Dic3—104no—
144C22×Dic3C2×D511yescharacteristic, complemented
145#217—51no—
146#217—52no—
147#217—52no—
148#217—52no—
149#217—52no—
150#217C2×D511yescharacteristic, complemented
151#217C2×D512yescomplemented
152Dic3⋊C4—52no—
153Dic3⋊C4—52no—
154Dic3⋊C4—52no—
155Dic3⋊C4C2×D512yescomplemented
156C23×C5C22×D311yescharacteristic
157C23×C5C22×D311yescharacteristic
158C22×D5—24no—
159C22×D5—24no—
160C22×D5—22no—
161C22×D5#6714yes—
162C22×D5C22×D311yescharacteristic
163C22×D5C22×D311yescharacteristic
164C22×D5C22×D311yescharacteristic
165C5×D4—22no—
166C2×C4×C5—32no—
167C2×C4×C5—32no—
168C2×C4×C5—62no—
169C2×C4×C5C22×D311yescharacteristic
170C22⋊D5—22no—
171C22⋊D5—22no—
172C2×Dic5—32no—
173C2×Dic5—32no—
174C2×Dic5—62no—
175C2×Dic5C22×D311yescharacteristic
176D20—22no—
177C4×D5—22no—
178C4×D5—64no—
179C4×D5—64no—
180C4×D5—64no—
181C22×D4—51no—
182C23×C4—151no—
183#123—31no—
184#123—152no—
185#123—151no—
186#123—152no—
187#123—151no—
188#123—151no—
189C2×C4⋊C4—152no—
190C2×C22⋊C4—151no—
191C2×C22⋊C4—152no—
192C2×C3×C5—22no—
193C2×C3×C5—41no—
194C2×C3×C5C22×D411yescharacteristic
195C2×C3×C5C2×#4112yes—
196C3×D5—22no—
197C3×D5—41no—
198C3×D5#12314yescomplemented
199C23×C3—51no—
200C23×C3—54no—
201C23×C3—51no—
202C23×C3—51no—
203C23×C3—104no—
204C23×C3—102no—
205C23×C3—104no—
206C23×C3C22×D511yescharacteristic
207C23×C3C22×D511yescharacteristic
208C3×D4—22no—
209C3×D4—102no—
210C3×D4—102no—
211C3×D4—102no—
212C2×C3×C4—51no—
213C2×C3×C4—102no—
214C2×C3×C4C22×D511yescharacteristic
215C2×Dic3—22no—
216C2×Dic3—52no—
217C2×Dic3—52no—
218C2×Dic3—104no—
219C2×Dic3—104no—
220C2×Dic3—104no—
221C2×Dic3—102no—
222C2×Dic3C22×D512yes—
223C2×Dic3C22×D512yes—
224C22×C5—22no—
225C22×C5—22no—
226C22×C5—21no—
227C22×C5C2×#6712yes—
228C22×C5C23×D311yescharacteristic
229C2×D5—22no—
230C2×D5—28no—
231C2×D5—22no—
232C2×D5—21no—
233C2×D5—44no—
234C2×D5#23714yes—
235C2×D5C2×#6712yes—
236C2×D5C2×#6712yes—
237C4×C5—21no—
238C4×C5—62no—
239C4×C5—62no—
240Dic5—21no—
241Dic5—62no—
242Dic5—62no—
243C24—51no—
244C24—51no—
245C2×D4—51no—
246C2×D4—51no—
247C2×D4—51no—
248C2×D4—104no—
249C2×D4D3×D511yescharacteristic
250C22×C4—31no—
251C22×C4—51no—
252C22×C4—152no—
253C22×C4—152no—
254C22×C4—152no—
255C22×C4—151no—
256C22×C4—304no—
257C4⋊C4—32no—
258C4⋊C4—152no—
259C4⋊C4—152no—
260C4⋊C4—152no—
261C22⋊C4—31no—
262C22⋊C4—32no—
263C22⋊C4—152no—
264C22⋊C4—152no—
265C22⋊C4—152no—
266C22⋊C4—151no—
267C22⋊C4—152no—
268C3×C5C2×#12311yescharacteristic, complemented, Hall
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—22no—
272C22×C3—52no—
273C22×C3—54no—
274C22×C3—52no—
275C22×C3—108no—
276C22×C3—102no—
277C22×C3—101no—
278C22×C3—102no—
279C22×C3—204no—
280C22×C3D4×D512yes—
281C22×C3C23×D511yescharacteristic
282C3×C4—21no—
283C3×C4—101no—
284Dic3—22no—
285Dic3—22no—
286Dic3—102no—
287Dic3—102no—
288C2×C5—22no—
289C2×C5—41no—
290C2×C5C2×#23712yes—
291C2×C5C22×#6711yescharacteristic
292D5—22no—
293D5—41no—
294D5#93514yesdirect product factor
295C23—51no—
296C23—54no—
297C23—51no—
298C23—51no—
299C23—104no—
300C23—102no—
301C23—104no—
302C23C2×D3×D511yescharacteristic
303C23C2×D3×D511yescharacteristic
304D4—22no—
305D4—102no—
306D4—102no—
307D4—102no—
308C2×C4—32no—
309C2×C4—32no—
310C2×C4—51no—
311C2×C4—62no—
312C2×C4—102no—
313C2×C4—152no—
314C2×C4—152no—
315C2×C4—304no—
316C2×C4—304no—
317C2×C4—304no—
318C2×C4—302no—
319C2×C4C2×D3×D511yescharacteristic
320C2×C3—22no—
321C2×C3—41no—
322C2×C3—54no—
323C2×C3—102no—
324C2×C3—201no—
325C2×C3C2×D4×D511yescharacteristic
326C2×C3D5×#4112yes—
327C5C2×#93511yescharacteristic, complemented, Sylow
328C22—22no—
329C22—22no—
330C22—21no—
331C22—54no—
332C22—52no—
333C22—52no—
334C22—108no—
335C22—102no—
336C22—102no—
337C22—101no—
338C22—204no—
339C22D5×#6712yes—
340C22C22×D3×D511yescharacteristic
341C4—21no—
342C4—62no—
343C4—62no—
344C4—101no—
345C4—302no—
346C4—302no—
347C3D5×#12311yescharacteristic, complemented, Sylow
348C2—22no—
349C2—41no—
350C2—54no—
351C2—102no—
352C2—201no—
353C2D5×#23712yes—
354C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC2×C3×D4×D5C2
hypercenterC2×D4D3×D5
hypocenterC3×C5C2×#123
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×D5×Dic3C2semidirect
3. #91824C2semidirect
4. C5×#935C2semidirect
5. #91548C2semidirect
6. D5×#217C2semidirect
7. D5×#217C2semidirect
8. #91537C2semidirect
9. #91536C2semidirect
10. #91407C2semidirect
11. D5×Dic3⋊C4C2semidirect
16. C22×Dic15C22semidirect
17. C22×C5×Dic3C22semidirect
26. C2×D5×Dic3C22semidirect
27. #6719C22semidirect
28. #6719C22semidirect
29. #6712C22semidirect
30. C5×#217C22semidirect
31. C5×#217C22semidirect
32. C5×Dic3⋊C4C22semidirect
33. Dic3⋊Dic5C22semidirect
34. #6669C22semidirect
35. #6665C22semidirect
36. #6665C22semidirect
37. #6665C22semidirect
84. #935D5direct (N × H)
144. C22×Dic3C2×D5semidirect
150. #217C2×D5semidirect
151. #217C2×D5semidirect
155. Dic3⋊C4C2×D5semidirect
198. C3×D5#123semidirect
268. C3×C5C2×#123semidirect
294. D5#935direct (N × H)
327. C5C2×#935semidirect
347. C3D5×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D52
C22×D5×Dic32
#918242
C5×#9352
#915482
D5×#2172
#915372
#915362
#914072
D5×Dic3⋊C42
D5×#1233
C2×#9355