Finite Group Databasebeta

← #14472090

Subgroups — #14472090

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic
2#11756480C211yesmaximal, characteristic, complemented
3C3×C5×#487C211yesmaximal, characteristic, complemented
4#11751191C211yesmaximal, characteristic, complemented
5#11751188C211yesmaximal, characteristic
6#11750901C212yesmaximal
7#11750900C212yesmaximal, complemented
8#11750899C212yesmaximal
9#11750891C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10613356—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91836C2212yes—
16Q8×Dic15—21no—
17Q8×Dic15C2212yes—
18#91833—21no—
19C2×#6718C2212yes—
20C2×#6706C2211yescharacteristic
21#91787—22no—
22#91786—21no—
23#91781—21no—
24#91779C2212yes—
25#91778—22no—
26#91776C2212yes—
27C4×D60C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#103C2212yes—
31C3×C5×#103C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91119C2212yes—
34#91105C2211yescharacteristic
35#91101C2211yescharacteristic
36#91100C2211yescharacteristic
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2212yes—
40#91091C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81625—51nomaximal, Hall
43#66066—31no—
44#66055—31no—
45C5×#487D311yescharacteristic, complemented
46#65379—31no—
47#65376—31no—
48#65089—32no—
49#65088—32no—
50#65087—32no—
51#65079—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8C2312yes—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×Dic30D411yescharacteristic
59C2×Dic30C2311yescharacteristic
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C5×C4⋊C4—21no—
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C3×C42×C5C2311yescharacteristic
67#6718—24no—
68#6714—21no—
69#6714—22no—
70#6714—22no—
71C4⋊Dic15—22no—
72C4⋊Dic15—22no—
73C4⋊Dic15D411yescharacteristic
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76#6712—21no—
77#6712—22no—
78#6712—22no—
79#6712D412yes—
80C4×Dic15—21no—
81C4×Dic15—22no—
82C4×Dic15—22no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2312yes—
85#6706—22no—
86#5732—51no—
87#5721—51no—
88C3×#487D511yescharacteristic, complemented
89#5090—51no—
90#5087—51no—
91#4800—52no—
92#4799—52no—
93#4798—52no—
94#4790—52no—
95C4×#204—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×C4⋊Q8C2×D311yescharacteristic
99#4093—32no—
100Q8×Dic5—32no—
101Q8×Dic5—61no—
102#4090—61no—
103C2×#689—32no—
104C2×#677—31no—
105#4044—62no—
106#4043—61no—
107#4038—61no—
108#4036—32no—
109#4035—62no—
110#4033—32no—
111C4×D20—31no—
112C4×Dic10—31no—
113C4×Dic10—31no—
114C5×#103C2×D312yes—
115C5×#103C2×D312yes—
116C4×C5×C8C2×D311yescharacteristic
117#3967—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3364—151noSylow
127C22×D15—21no—
128C3×C5×Q8—22no—
129C3×C5×Q8—22no—
130C3×C5×Q8—42no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141D60—21no—
142D60—21no—
143C4×D15—42no—
144Dic30—22no—
145Dic30—21no—
146Dic30#4112yes—
147C3×C5×C8—21no—
148C3×C5×C8—21no—
149C3⋊#168—22no—
150C3×C4⋊Q8C2×D511yescharacteristic
151C3×C4⋊Q8C2×D511yescharacteristic
152#947—52no—
153Q8×Dic3—52no—
154Q8×Dic3—101no—
155#944—101no—
156C2×#216—52no—
157C2×#204—51no—
158#898—102no—
159#897—101no—
160#892—101no—
161#890—52no—
162#889—102no—
163#887—52no—
164C4×D12—51no—
165C4×Dic6—51no—
166C4×Dic6—51no—
167C3×#103C2×D512yes—
168C3×#103C2×D512yes—
169C3×C4×C8C2×D511yescharacteristic
170#835—52no—
171#821—51no—
172#817—51no—
173#816—51no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#809—52no—
177#807—52no—
178C4⋊(C3⋊C8)—51no—
179C2×C5×Q8—21no—
180C2×C5×Q8C22×D312yes—
181C2×D20—31no—
182C2×C4×D5—61no—
183C2×Dic10—31no—
184C2×Dic10—31no—
185C2×C5×C8C22×D311yescharacteristic
186C2×C5×C8C22×D311yescharacteristic
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—21no—
190C5×C4⋊C4C22×D312yes—
191C42×C5C22×D311yescharacteristic
192#689—64no—
193#685—62no—
194#685—62no—
195#685—61no—
196C4⋊Dic5—31no—
197C4⋊Dic5—31no—
198C4⋊Dic5—31no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201#683—32no—
202#683—62no—
203#683—62no—
204#683—61no—
205C4×Dic5—32no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5—61no—
209C2×#168—32no—
210#677—62no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487D1511yescharacteristic, complemented
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—41no—
224C2×D15—41no—
225C2×D15—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5—42no—
229C3×C4×C5#13512yes—
230C3×C4×C5C2×#4111yescharacteristic
231C3×C4×C52−1+411yescharacteristic
232Dic15—22no—
233Dic15—22no—
234Dic15—22no—
235Dic15—41no—
236Dic15—41no—
237C2×C3×Q8—21no—
238C2×C3×Q8C22×D512yes—
239C2×D12—51no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6—51no—
243C2×C3×C8C22×D511yescharacteristic
244C2×C3×C8C22×D511yescharacteristic
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4C22×D512yes—
249C3×C42C22×D511yescharacteristic
250#216—104no—
251(C2×D3)⋊C4—102no—
252(C2×D3)⋊C4—102no—
253(C2×D3)⋊C4—101no—
254C4⋊Dic3—51no—
255C4⋊Dic3—51no—
256C4⋊Dic3—51no—
257C4⋊Dic3—102no—
258C4⋊Dic3—102no—
259Dic3⋊C4—52no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—101no—
263C4×Dic3—52no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C4×Dic3—101no—
267C2×C3⋊C8—52no—
268#204—102no—
269C22×D5—61no—
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—42no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5C23×D311yescharacteristic
278C2×Dic5—32no—
279C2×Dic5—32no—
280C2×Dic5—61no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283D20—61no—
284D20—61no—
285C4×D5—122no—
286Dic10—32no—
287Dic10—62no—
288Dic10—61no—
289C5×C8—21no—
290C5×C8—21no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—301no—
295C4⋊Q8C2×D1511yescharacteristic
296C4⋊Q8C2×D1511yescharacteristic
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—151no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—152no—
314#103—151no—
315#103C2×D1512yes—
316#103C2×D1512yes—
317#102—151no—
318#102—152no—
319C4×C8—152no—
320C4×C8C2×D1511yescharacteristic
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—42no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4D4×D511yescharacteristic
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4C23×D511yescharacteristic
334C2×Dic3—52no—
335C2×Dic3—52no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3—101no—
339D12—101no—
340D12—101no—
341C4×D3—202no—
342Dic6—52no—
343Dic6—101no—
344Dic6—102no—
345C3×C8—21no—
346C3×C8—21no—
347C3⋊C8—102no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—42no—
355C4×C5#91612yes—
356C4×C5D3×#4111yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—62no—
359Dic5—62no—
360Dic5—62no—
361Dic5—121no—
362Dic5—121no—
363C2×Q8—21no—
364C2×Q8—151no—
365C2×Q8—151no—
366C2×Q8C22×D1512yes—
367C2×D4—151no—
368C22×C4—301no—
369Q16—304no—
370SD16—302no—
371C2×C8—152no—
372C2×C8C22×D1511yescharacteristic
373C2×C8C22×D1511yescharacteristic
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—151no—
378C4⋊C4—152no—
379C4⋊C4—151no—
380C4⋊C4—151no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C22×D1512yes—
387C22⋊C4—302no—
388C22⋊C4—302no—
389C22⋊C4—301no—
390C42—152no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C22×D1511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C2×D4×D511yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4#406212yes—
404C3×C4D5×#4111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—102no—
407Dic3—102no—
408Dic3—102no—
409Dic3—201no—
410Dic3—201no—
411C2×C5#567711yescharacteristic
412C2×C5C2×#91611yescharacteristic
413C2×C5#576611yescharacteristic
414D5—241no—
415C23—301no—
416Q8—22no—
417Q8—22no—
418Q8—42no—
419Q8—152no—
420Q8—302no—
421Q8—301no—
422D4—301no—
423D4—301no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—152no—
427C2×C4—152no—
428C2×C4—301no—
429C2×C4—301no—
430C2×C4—301no—
431C2×C4—602no—
432C2×C4D4×D1511yescharacteristic
433C2×C4D4×D1511yescharacteristic
434C2×C4C23×D1511yescharacteristic
435C8—21no—
436C8—21no—
437C8—302no—
438C2×C3#6601111yescharacteristic
439C2×C3C2×#406211yescharacteristic
440C2×C3#6610011yescharacteristic
441D3—401no—
442C5#8162511yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C2×D4×D1511yescharacteristic
447C4—21no—
448C4—42no—
449C4—42no—
450C4—302no—
451C4—302no—
452C4—302no—
453C4—601no—
454C4—601no—
455C4#9180512yes—
456C4#41×D1511yescharacteristic
457C4#9210111yescharacteristic
458C3#1061335611yescharacteristic, complemented, Sylow
459C2—1201no—
460C2#1175643611yescharacteristic
461C2C2×#9180511yescharacteristic
462C2#1175652511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#487C2
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenter#487D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #11756480C2semidirect
3. C3×C5×#487C2semidirect
4. #11751191C2semidirect
7. #11750900C2semidirect
9. #11750891C2semidirect
11. C8×Dic30C2semidirect
45. C5×#487D3semidirect
88. C3×#487D5semidirect
214. #487D15semidirect
395. C3×C5#3364semidirect
442. C5#81625semidirect
458. C3#10613356semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117564802
C3×C5×#4872
#117511912
#117511882
#117509012
#117509002
#117508992
#117508912
C4×#67062
C8×Dic302
#106133563
#816255