Finite Group Databasebeta

← #11752877

Subgroups — #11752877

Order 960.

668 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C22×#1202C211yesmaximal, characteristic, complemented
2C2×#6779C211yesmaximal, characteristic, complemented
3#91771C211yesmaximal, characteristic, complemented
4C5×#877C211yesmaximal, characteristic, complemented
5C3×#4028C211yesmaximal, characteristic, complemented
6#91572C211yesmaximal, characteristic, complemented
7#91564C211yesmaximal, characteristic, complemented
8#91459C212yesmaximal, complemented
9#91458C212yesmaximal, complemented
10#91409C212yesmaximal, complemented
11#91353C212yesmaximal, complemented
12#65859—31nomaximal, Hall
13C23×D15C2211yescharacteristic
14C23×C3×D5C2211yescharacteristic
15C2×#1220C2211yescharacteristic
16C2×D60C2212yescomplemented
17C22×C5×Dic3C2211yescharacteristic
18C2×C3×C22⋊D5C2211yescharacteristic
19C2×C3×D20C2212yescomplemented
20C2×#1204C2211yescharacteristic, complemented
21C2×#1202—24no—
22C2×#1202C2212yes—
23C2×#1202C2212yes—
24C2×#1202C2211yescharacteristic, complemented
25C2×#1202C2212yescomplemented
26C2×#1202C2212yescomplemented
27C2×#1200C2211yescharacteristic, complemented
28#6779—24no—
29C2×D5×Dic3C2211yescharacteristic, complemented
30C3×C5×C22⋊C4C2211yescharacteristic
31#6714C2212yescomplemented
32C5×#217C2211yescharacteristic
33C5×Dic3⋊C4C2212yescomplemented
34C4×C5×Dic3C2212yescomplemented
35C3×#685C2212yescomplemented
36#6667C2212yescomplemented
37#6665C2212yescomplemented
38#5592—51nomaximal, Hall
39C2×#709—31no—
40C22×D20—31no—
41C5×#117—31no—
42#4041—32no—
43#4041—32no—
44#4028—31no—
45#4028—31no—
46#4028—31no—
47#4028D311yescharacteristic, complemented
48#4021—32no—
49#4020—32no—
50C23×C3×C5C2311yescharacteristic
51C22×D15—22no—
52C22×D15—42no—
53C22×D15C2312yes—
54C22×D15C2311yescharacteristic
55C22×C3×D5—22no—
56C22×C3×D5—42no—
57C22×C3×D5C2312yes—
58C22×C3×D5C2311yescharacteristic
59C2×C3×C4×C5C2312yes—
60#1220—22no—
61C2×Dic15C2311yescharacteristic
62D60—42no—
63C2×C5×Dic3D414yescomplemented
64C2×C5×Dic3C2312yes—
65C2×C5×Dic3C2311yescharacteristic
66C2×C5×Dic3C2311yescharacteristic
67C3×C22⋊D5—22no—
68C2×C3×Dic5C2311yescharacteristic
69C3×D20—42no—
70#1204—22no—
71#1202—22no—
72#1202—24no—
73#1202—24no—
74#1202—42no—
75#1202—42no—
76#1200—22no—
77D5×Dic3—22no—
78C22×#67—51no—
79C2×#237—51no—
80C3×#120—51no—
81#953—51no—
82#940—52no—
83#939—52no—
84#937—51no—
85#885—52no—
86#884—52no—
87#882—51no—
88#877D511yescharacteristic, complemented
89C23×D5—31no—
90C23×D5C2×D311yescharacteristic
91C22×C4×C5—31no—
92C2×C22⋊D5—31no—
93C2×C22⋊D5C2×D311yescharacteristic
94#709—64no—
95C2×D20—32no—
96C2×D20—32no—
97C2×D20—31no—
98C2×D20—32no—
99C2×D20—32no—
100C2×D20—32no—
101C2×D20—64no—
102C2×D20C2×D312yescomplemented
103C2×C4×D5—31no—
104C2×C4×D5—31no—
105C2×Dic10—31no—
106C5×C4⋊C4—32no—
107C5×C22⋊C4—31no—
108C5×C22⋊C4C2×D311yescharacteristic
109C42×C5—32no—
110#685—32no—
111#685—32no—
112#685—32no—
113#685C2×D312yescomplemented
114#535—151noSylow
115C22×C3×C5—22no—
116C22×C3×C5C2×D412yes—
117C22×C3×C5C2411yescharacteristic
118C2×D15—21no—
119C2×D15—22no—
120C2×D15—22no—
121C2×D15—22no—
122C2×D15—22no—
123C2×D15—44no—
124C2×C3×D5—21no—
125C2×C3×D5—22no—
126C2×C3×D5—22no—
127C2×C3×D5—22no—
128C2×C3×D5—22no—
129C2×C3×D5—44no—
130C3×C4×C5—22no—
131Dic15—21no—
132C3×Dic5—21no—
133C5×Dic3—22no—
134C5×Dic3C2×D412yes—
135C5×Dic3C2×D412yes—
136C24×C3—51no—
137C23×D3—51no—
138C2×C3×D4—51no—
139C2×C3×D4—52no—
140C2×#67—51no—
141C2×#67—52no—
142C2×#67—52no—
143C2×#67—51no—
144C2×#67—52no—
145C2×#67—52no—
146C2×#67—104no—
147C22×Dic3—51no—
148C22×Dic3C2×D511yescharacteristic
149#237—104no—
150C2×D12—52no—
151C2×C4×D3—51no—
152C2×Dic6—51no—
153C3×C22⋊C4—52no—
154C3×C22⋊C4C2×D511yescharacteristic
155#217—52no—
156#217C2×D511yescharacteristic
157(C2×D3)⋊C4—52no—
158(C2×D3)⋊C4—52no—
159Dic3⋊C4C2×D512yescomplemented
160C4×Dic3C2×D512yescomplemented
161C23×C5C22×D311yescharacteristic
162C22×D5—22no—
163C22×D5—32no—
164C22×D5—31no—
165C22×D5—42no—
166C22×D5—62no—
167C22×D5—122no—
168C22×D5C22×D312yes—
169C22×D5C22×D311yescharacteristic
170C2×C4×C5—34no—
171C2×C4×C5—31no—
172C2×C4×C5—31no—
173C2×C4×C5—32no—
174C2×C4×C5C22×D312yes—
175C22⋊D5—22no—
176C22⋊D5—62no—
177C2×Dic5—31no—
178C2×Dic5C22×D311yescharacteristic
179D20—42no—
180D20—64no—
181D20—64no—
182D20—62no—
183D20—122no—
184D20—122no—
185D20—122no—
186C4×D5—62no—
187C4×D5—62no—
188Dic10—62no—
189C2×#41—151no—
190C22×D4—151no—
191#127—152no—
192#124—152no—
193#121—152no—
194#121—152no—
195#120—51no—
196#120—151no—
197#120—151no—
198#120—151no—
199#117—31no—
200C2×C3×C5—22no—
201C2×C3×C5C22×D411yescharacteristic
202C2×C3×C5H(5,𝔽2)12yes—
203D15—41no—
204D15—42no—
205C3×D5—41no—
206C3×D5—42no—
207C23×C3—52no—
208C23×C3—51no—
209C23×C3—102no—
210C23×C3—202no—
211C23×C3C22×D511yescharacteristic
212C22×D3—52no—
213C22×D3—51no—
214C22×D3—102no—
215C22×D3—202no—
216C3×D4—102no—
217C3×D4—202no—
218C2×C3×C4—51no—
219C2×C3×C4C22×D512yes—
220#67—102no—
221#67—102no—
222#67—104no—
223#67—104no—
224#67—202no—
225#67—202no—
226C2×Dic3—51no—
227C2×Dic3—102no—
228C2×Dic3D2014yescomplemented
229C2×Dic3C22×D512yes—
230C2×Dic3C22×D511yescharacteristic
231C2×Dic3C22×D511yescharacteristic
232D12—202no—
233C4×D3—102no—
234Dic6—102no—
235C22×C5—22no—
236C22×C5D3×D412yes—
237C22×C5C23×D311yescharacteristic
238C2×D5—21no—
239C2×D5—22no—
240C2×D5—22no—
241C2×D5—22no—
242C2×D5—22no—
243C2×D5—44no—
244C2×D5—61no—
245C2×D5—62no—
246C2×D5—62no—
247C2×D5—62no—
248C2×D5—62no—
249C2×D5—124no—
250C4×C5—22no—
251C4×C5—32no—
252C4×C5—32no—
253C4×C5—62no—
254Dic5—21no—
255Dic5—61no—
256C24—51no—
257C24—151no—
258#41—304no—
259C2×Q8—151no—
260C2×D4—51no—
261C2×D4—52no—
262C2×D4—152no—
263C2×D4—152no—
264C2×D4—151no—
265C2×D4—152no—
266C2×D4—152no—
267C2×D4—151no—
268C2×D4—152no—
269C2×D4—304no—
270C22×C4—31no—
271C22×C4—151no—
272C22×C4—151no—
273C4⋊C4—32no—
274C22⋊C4—31no—
275C22⋊C4—52no—
276C22⋊C4—152no—
277C22⋊C4—152no—
278C22⋊C4—152no—
279C22⋊C4D3×D511yescharacteristic
280C42—32no—
281C3×C5#53511yescharacteristic, complemented, Hall
282C22×C3—22no—
283C22×C3—101no—
284C22×C3—102no—
285C22×C3—102no—
286C22×C3—102no—
287C22×C3—102no—
288C22×C3—204no—
289C22×C3C2×D2012yes—
290C22×C3C23×D511yescharacteristic
291C2×D3—101no—
292C2×D3—102no—
293C2×D3—102no—
294C2×D3—102no—
295C2×D3—102no—
296C2×D3—204no—
297C3×C4—22no—
298C3×C4—101no—
299Dic3—22no—
300Dic3—101no—
301Dic3C2×D2012yes—
302Dic3C2×D2012yes—
303C2×C5—22no—
304C2×C5C2×D3×D411yescharacteristic
305C2×C5#100412yes—
306D5—42no—
307D5—41no—
308D5—122no—
309D5—121no—
310C23—52no—
311C23—51no—
312C23—102no—
313C23—152no—
314C23—151no—
315C23—202no—
316C23—302no—
317C23—602no—
318C23C2×D3×D511yescharacteristic
319Q8—302no—
320D4—102no—
321D4—202no—
322D4—304no—
323D4—304no—
324D4—302no—
325D4—302no—
326D4—602no—
327D4—602no—
328D4—602no—
329C2×C4—34no—
330C2×C4—31no—
331C2×C4—31no—
332C2×C4—32no—
333C2×C4—51no—
334C2×C4—151no—
335C2×C4—302no—
336C2×C4—302no—
337C2×C4C2×D3×D512yes—
338C2×C3—22no—
339C2×C3—202no—
340C2×C3—201no—
341C2×C3C22×D2011yescharacteristic
342C2×C3#414912yes—
343D3—202no—
344D3—201no—
345C5#559211yescharacteristic, complemented, Sylow
346C22—22no—
347C22—101no—
348C22—102no—
349C22—102no—
350C22—102no—
351C22—102no—
352C22—204no—
353C22—301no—
354C22—302no—
355C22—302no—
356C22—302no—
357C22—302no—
358C22—604no—
359C22D3×D2012yes—
360C22C22×D3×D511yescharacteristic
361C4—22no—
362C4—32no—
363C4—32no—
364C4—62no—
365C4—101no—
366C4—301no—
367C3#6585911yescharacteristic, complemented, Sylow
368C2—22no—
369C2—202no—
370C2—201no—
371C2—602no—
372C2—601no—
373C2C2×D3×D2011yescharacteristic
374C2#9202612yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#535
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#1202C2semidirect
2. C2×#6779C2semidirect
3. #91771C2semidirect
4. C5×#877C2semidirect
5. C3×#4028C2semidirect
6. #91572C2semidirect
7. #91564C2semidirect
8. #91459C2semidirect
9. #91458C2semidirect
10. #91409C2semidirect
11. #91353C2semidirect
16. C2×D60C22semidirect
19. C2×C3×D20C22semidirect
20. C2×#1204C22semidirect
24. C2×#1202C22semidirect
25. C2×#1202C22semidirect
26. C2×#1202C22semidirect
27. C2×#1200C22semidirect
29. C2×D5×Dic3C22semidirect
31. #6714C22semidirect
33. C5×Dic3⋊C4C22semidirect
34. C4×C5×Dic3C22semidirect
35. C3×#685C22semidirect
36. #6667C22semidirect
37. #6665C22semidirect
47. #4028D3semidirect
63. C2×C5×Dic3D4semidirect
88. #877D5semidirect
102. C2×D20C2×D3semidirect
113. #685C2×D3semidirect
159. Dic3⋊C4C2×D5semidirect
160. C4×Dic3C2×D5semidirect
228. C2×Dic3D20semidirect
281. C3×C5#535semidirect
345. C5#5592semidirect
367. C3#65859semidirect

Maximal subgroups

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

subgroupindex
C22×#12022
C2×#67792
#917712
C5×#8772
C3×#40282
#915722
#915642
#914592
#914582
#914092
#913532
#658593
#55925