Finite Group Databasebeta

← #14471966

Subgroups — #14471966

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66056C211yesmaximal, characteristic, complemented
2#11752536C211yesmaximal, characteristic
3#11751185C211yesmaximal, characteristic, complemented
4C5×#5088C211yesmaximal, characteristic, complemented
5#11747400C212yesmaximal, complemented
6#11747239C212yesmaximal, complemented
7#11747218C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11747060C211yesmaximal, characteristic, complemented
10C4×#6658C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10613319—31nomaximal, Hall
13C2×#6768—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C4×D60C2211yescharacteristic
16C5×#874C2211yescharacteristic
17C3×#4090—22no—
18C3×#4034—21no—
19C3×#4034C2212yes—
20C3×#4033—21no—
21C3×#4033C2212yes—
22C3×C4×Dic10C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91466—21no—
25#91451C2212yes—
26#91416—22no—
27Dic5×D12C2212yes—
28C2×#6658C2211yescharacteristic
29C2×#6656C2212yes—
30#91093C2212yes—
31#91092C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#809C2212yes—
34C5×#809C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36#90987C2211yescharacteristic
37#90982C2212yes—
38#90971C2211yescharacteristic
39#90968C2211yescharacteristic
40#90966C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83703—51nomaximal, Hall
43#66056D311yescharacteristic, complemented
44#66052—31no—
45C5×#486—31no—
46#65373—31no—
47#65364—31no—
48#65051—32no—
49#65050—32no—
50#65049—32no—
51#65047—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C3×Dic10—22no—
61C2×C3×Dic10D411yescharacteristic
62C2×C3×Dic10C2311yescharacteristic
63C2×#1203—22no—
64C2×#1203—22no—
65C2×D3×Dic5—22no—
66#6768—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2312yes—
69C3×C42×C5C2311yescharacteristic
70#6714—21no—
71C4⋊Dic15C2311yescharacteristic
72C2×C3⋊#168C2312yes—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×C4⋊Dic5D411yescharacteristic
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×#683—22no—
79C3×#683—22no—
80C3×#683D412yes—
81C3×C4×Dic5—21no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5C2312yes—
84(C2×D3)⋊Dic5—22no—
85#6658—22no—
86#6656—24no—
87C3×Q82—51no—
88#5577—51no—
89#5088—52no—
90#5088D511yescharacteristic, complemented
91#5084—51no—
92#5084—52no—
93#5027—51no—
94#5027—52no—
95C4×#215—52no—
96C4×#215—51no—
97Q8×C3⋊C8—51no—
98C2×#711—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C5×#127—31no—
101#4090—22no—
102#4086—32no—
103#4085—62no—
104#4084—61no—
105D4×Dic5—32no—
106C2×#687—32no—
107C2×#677—31no—
108#4034—21no—
109#4034C2×D312yes—
110#4033—21no—
111#4033C2×D312yes—
112C4×D20—31no—
113C4×Dic10C2×D311yescharacteristic
114C4×Dic10C2×D311yescharacteristic
115C5×#102—32no—
116C5×#102—32no—
117C4×C5×C8—31no—
118#3964—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C22×D15—21no—
129C22×C5×D3—22no—
130C3×C5×Q8—81no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139C5×D12—22no—
140C5×D12—22no—
141C5×D12—42no—
142C5×D12—81no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—21no—
148C3×Dic10—82no—
149C3×Dic10SD1614yescomplemented
150C3×Dic10#4112yescomplemented
151#1203—44no—
152#1203—82no—
153D3×Dic5—44no—
154C3⋊#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#239—101no—
158C3×C4⋊Q8—52no—
159C3×C4⋊Q8—101no—
160C3×C4⋊Q8—102no—
161C3×C4⋊Q8C2×D511yescharacteristic
162C3×C4×Q8—51no—
163C3×C4×Q8—52no—
164C3×C4×Q8—51no—
165C3×C4×Q8—101no—
166C2×#215—52no—
167C2×#215—51no—
168#895—102no—
169#895—101no—
170#874—52no—
171#874C2×D511yescharacteristic
172C4×D12—52no—
173C4×D12—51no—
174#835—51no—
175#809—52no—
176#809—52no—
177#809—51no—
178#809C2×D512yes—
179#809C2×D512yes—
180#808—52no—
181#808—51no—
182C4⋊(C3⋊C8)—51no—
183C4⋊(C3⋊C8)—52no—
184C4×C3⋊C8—52no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—21no—
187C2×C5×D4—32no—
188C2×C5×D4—61no—
189C2×C5×D4—61no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20—31no—
195C2×C4×D5—61no—
196C2×Dic10—22no—
197C2×Dic10#6711yescharacteristic
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—31no—
200C2×C5×C8—31no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D312yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205#687—64no—
206#685—61no—
207C4⋊Dic5—31no—
208C4⋊Dic5#6711yescharacteristic
209C4⋊Dic5C22×D311yescharacteristic
210#683—21no—
211#683—22no—
212#683—22no—
213#683#6712yes—
214C4×Dic5—21no—
215C4×Dic5—22no—
216C4×Dic5C22×D312yes—
217C2×#168—32no—
218#677—62no—
219Q82—51no—
220#550—151no—
221#486—31no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—41no—
232C2×D15—41no—
233C2×D15—41no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—42no—
237C3×C4×C5—21no—
238C3×C4×C5—42no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—41no—
243C3×Dic5—22no—
244C3×Dic5—22no—
245C3×Dic5—41no—
246C3×Dic5C2×SD1614yes—
247C2×C3×Q8—21no—
248C2×C3×Q8—51no—
249C2×C3×Q8—51no—
250C2×C3×Q8—102no—
251#239—204no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—51no—
255C2×D12—102no—
256C2×D12—102no—
257C2×D12C22×D512yes—
258C2×C4×D3—102no—
259C2×C4×D3—101no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—51no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D512yes—
268C3×C42—52no—
269C3×C42—102no—
270C3×C42—101no—
271C3×C42C22×D511yescharacteristic
272#215—102no—
273#215—104no—
274(C2×D3)⋊C4—102no—
275(C2×D3)⋊C4—101no—
276C4⋊Dic3—51no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D511yescharacteristic
280C23×C5—62no—
281C22×D5—61no—
282C5×Q8—81no—
283C5×D4—62no—
284C5×D4—62no—
285C5×D4—122no—
286C5×D4—241no—
287C2×C4×C5—22no—
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—61no—
296C2×Dic5—124no—
297C2×Dic5C2×#6712yes—
298C2×Dic5C2×#6712yes—
299D20—61no—
300D20—61no—
301C4×D5—122no—
302Dic10—21no—
303Dic10—82no—
304Dic10#21514yescomplemented
305Dic10#23912yescomplemented
306C5×C8—61no—
307C5×C8—61no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16—152no—
312C4⋊Q8—52no—
313C4⋊Q8—101no—
314C4⋊Q8—102no—
315C4⋊Q8D3×D511yescharacteristic
316#127—31no—
317#127—152no—
318#121—301no—
319#121—302no—
320C4×Q8—51no—
321C4×Q8—52no—
322C4×Q8—51no—
323C4×Q8—101no—
324C4×D4—152no—
325C4×D4—151no—
326#106—151no—
327#106—152no—
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103—151no—
331#102—32no—
332#102—32no—
333#102—151no—
334#102—152no—
335#102—152no—
336C4×C8—31no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—81no—
342C5×D3—82no—
343C22×D3—22no—
344C22×D3—101no—
345C3×Q8—54no—
346C3×Q8—52no—
347C3×Q8—81no—
348C3×Q8—101no—
349C3×Q8—402no—
350C2×C3×C4—22no—
351C2×C3×C4—52no—
352C2×C3×C4—52no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358C2×Dic3—101no—
359D12—22no—
360D12—22no—
361D12—42no—
362D12—81no—
363D12—101no—
364D12—101no—
365D12—204no—
366D12—402no—
367C4×D3—204no—
368C4×D3—202no—
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—102no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5C2×#21512yes—
382C4×C5C2×#23911yescharacteristic
383C4×C5#100711yescharacteristic
384Dic5—22no—
385Dic5—22no—
386Dic5—41no—
387Dic5—121no—
388Dic5C2×#21514yes—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—51no—
392C2×Q8—51no—
393C2×Q8—102no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—302no—
401C22×C4—301no—
402SD16—302no—
403SD16—304no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—152no—
407C4⋊C4—21no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—51no—
411C4⋊C4—102no—
412C4⋊C4—102no—
413C4⋊C4—101no—
414C4⋊C4—151no—
415C4⋊C4C2×D3×D512yes—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—52no—
419C42—102no—
420C42—101no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—54no—
433C3×C4—102no—
434C3×C4—102no—
435C3×C4—201no—
436C3×C4D5×SD1612yes—
437C3×C4D5×#4111yescharacteristic
438C3×C4#415011yescharacteristic
439Dic3—201no—
440C2×C5—242no—
441C2×C5C22×#21511yescharacteristic
442C2×C5#581711yescharacteristic
443C2×C5#583511yescharacteristic
444D5—241no—
445C23—62no—
446C23—301no—
447Q8—54no—
448Q8—52no—
449Q8—81no—
450Q8—101no—
451Q8—402no—
452D4—62no—
453D4—62no—
454D4—122no—
455D4—241no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—52no—
462C2×C4—52no—
463C2×C4—101no—
464C2×C4—101no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—302no—
474C2×C3#6601111yescharacteristic
475C2×C3#6609111yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477D3—82no—
478D3—401no—
479C5#8370311yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—42no—
489C4—54no—
490C4—102no—
491C4—102no—
492C4—201no—
493C4—601no—
494C4D5×#21512yes—
495C4#9203011yescharacteristic
496C4D5×#23911yescharacteristic
497C3#1061331911yescharacteristic, complemented, Sylow
498C2—242no—
499C2—1201no—
500C2#1175469111yescharacteristic
501C2C2×D5×#21511yescharacteristic
502C2#1175522611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752536C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66056C2semidirect
3. #11751185C2semidirect
4. C5×#5088C2semidirect
5. #11747400C2semidirect
6. #11747239C2semidirect
7. #11747218C2semidirect
8. #11747138C2semidirect
9. #11747060C2semidirect
10. C4×#6658C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. #66056D3semidirect
90. #5088D5semidirect
149. C3×Dic10SD16semidirect
150. C3×Dic10#41semidirect
304. Dic10#215semidirect
305. Dic10#239semidirect
422. C3×C5#3362semidirect
479. C5#83703semidirect
497. C3#10613319semidirect

Maximal subgroups

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

subgroupindex
C3×#660562
#117525362
#117511852
C5×#50882
#117474002
#117472392
#117472182
#117471382
#117470602
C4×#66582
C3⋊C8×Dic102
#106133193
#837035