Finite Group Databasebeta

← #14416993

Subgroups — #14416993

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#520C211yesmaximal, characteristic, complemented
2C2×#91838C211yesmaximal, characteristic
3#11756280C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic, complemented
5#11751127C212yesmaximal, complemented
6C4×#6717C212yesmaximal, complemented
7#11751115C212yesmaximal, complemented
8C4×#6715C212yesmaximal, complemented
9#11751098C211yesmaximal, characteristic, complemented
10C2×#91093C211yesmaximal, characteristic, complemented
11#11751065C211yesmaximal, characteristic, complemented
12#10614295—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C3×C4×C5×Q8C2212yescomplemented
16C3×C4×C5×D4—22no—
17C3×C4×C5×D4C2212yescomplemented
18C3×C5×#117—21no—
19C3×C5×#117C2211yescharacteristic
20C2×C3×C5×C4⋊C4—21no—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22#91838C418yescomplemented
23C2×#6717C2212yes—
24C2×#6715C2212yes—
25#91815C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28#91782—21no—
29#91782—21no—
30C22⋊C4×D15—22no—
31C4×D60C2212yes—
32C4×D60C2212yes—
33#91119C2211yescharacteristic, complemented
34#91119C2211yescharacteristic, complemented
35#91116C2211yescharacteristic, complemented
36#91116C2211yescharacteristic, complemented
37#91093C2212yes—
38#91093C2212yes—
39#91092C2212yescomplemented
40#91091C2212yescomplemented
41#91087C2212yescomplemented
42C4×C3⋊#168C2212yescomplemented
43#82564—51nomaximal, Hall
44C5×#520D311yescharacteristic, complemented
45C2×#4095—31no—
46#65855—31no—
47#65522—31no—
48#65315—32no—
49C4×#688—32no—
50#65303—32no—
51C4×#686—32no—
52#65286—31no—
53C2×#3941—31no—
54#65253—31no—
55C23×D15—21no—
56C3×C5×#41—22no—
57C3×C5×#41C2×C414yescomplemented
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×D60—21no—
66C2×D60—22no—
67C2×D60C2×C414yescomplemented
68C2×D60C2312yes—
69C2×C4×D15—22no—
70C2×C4×D15—22no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4D411yescharacteristic
74C3×C5×C4⋊C4D411yescharacteristic
75C3×C5×C4⋊C4C2312yes—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4D412yes—
78C3×C42×C5—22no—
79C3×C42×C5C2312yes—
80#6719—21no—
81#6717C2×C418yescomplemented
82#6715C2×C418yescomplemented
83#6714—22no—
84#6714—22no—
85C4⋊Dic15C2311yescharacteristic
86C4⋊Dic15C2311yescharacteristic
87C4×Dic15—21no—
88#6710C2×C414yescomplemented
89C2×C3⋊#168—22no—
90C2×C3⋊#168C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2312yes—
93C3×#520D511yescharacteristic, complemented
94C2×#949—51no—
95#5521—51no—
96#5233—51no—
97#5026—52no—
98C4×#215—52no—
99#5014—52no—
100C4×#213—52no—
101#4997—51no—
102C2×#809—51no—
103#4964—51no—
104C2×C5×#41C2×D311yescharacteristic
105C22×D20—31no—
106C4×C5×Q8C2×D312yescomplemented
107C4×C5×D4—22no—
108C4×C5×D4C2×D312yescomplemented
109C5×#117—21no—
110C5×#117C2×D311yescharacteristic
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4C2×D311yescharacteristic
113#4095—38no—
114C2×#688—32no—
115C2×#686—32no—
116#4072—31no—
117C2×#681—31no—
118C22×#168—31no—
119#4039—61no—
120#4039—61no—
121D5×C22⋊C4—62no—
122C4×D20—32no—
123C4×D20—32no—
124#3967—31no—
125#3967—31no—
126#3964—31no—
127#3964—31no—
128#3941—32no—
129#3941—32no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2946—151noSylow
135C23×C3×C5—21no—
136C23×C3×C5C2×D411yescharacteristic
137C22×D15—22no—
138C22×D15—24no—
139C22×D15—81no—
140C22×D15—81no—
141C3×C5×Q8—21no—
142C3×C5×Q8C22×C412yes—
143C3×C5×D4—24no—
144C3×C5×D4—21no—
145C3×C5×D4C22×C412yes—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—24no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—82no—
150C2×C3×C4×C5—81no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5#4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—21no—
158C2×Dic15—21no—
159D60—24no—
160D60—22no—
161D60C22×C414yes—
162C4×D15—82no—
163C4×D15—82no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3⋊#168C22×C414yes—
167C2×C3×#41C2×D511yescharacteristic
168C22×D12—51no—
169C3×C4×Q8C2×D512yescomplemented
170C3×C4×D4—22no—
171C3×C4×D4C2×D512yescomplemented
172C3×#117—21no—
173C3×#117C2×D511yescharacteristic
174C2×C3×C4⋊C4—21no—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176#949—58no—
177C2×#215—52no—
178C2×#213—52no—
179#926—51no—
180C2×#208—51no—
181C22×C3⋊C8—51no—
182#893—101no—
183#893—101no—
184D3×C22⋊C4—102no—
185C4×D12—52no—
186C4×D12—52no—
187#835—51no—
188#835—51no—
189#832—51no—
190#832—51no—
191#809—52no—
192#809—52no—
193#808—52no—
194#807—52no—
195#803—52no—
196C4×C3⋊C8—52no—
197C23×D5—61no—
198C5×#41—22no—
199C5×#41C4×D314yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4C22×D311yescharacteristic
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—22no—
206C22×C4×C5C22×D311yescharacteristic
207C2×D20—34no—
208C2×D20—32no—
209C2×D20—62no—
210C2×D20—61no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4#6711yescharacteristic
216C5×C4⋊C4#6711yescharacteristic
217C5×C4⋊C4C22×D312yes—
218C5×C22⋊C4—22no—
219C5×C22⋊C4#6712yes—
220C42×C5—22no—
221C42×C5C22×D312yes—
222C22⋊Dic5—61no—
223#688—38no—
224#686—38no—
225#685—62no—
226#685—62no—
227C4⋊Dic5—31no—
228C4⋊Dic5—31no—
229C4×Dic5—61no—
230#681—34no—
231C2×#168—32no—
232C2×#168—31no—
233C2×#168—31no—
234C2×#168—62no—
235C2×AGL(1,ℤ/8)—151no—
236#520D1511yescharacteristic, complemented
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5C4×D412yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×D15—24no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—84no—
257C3×C4×C5—22no—
258C3×C4×C5—22no—
259C3×C4×C5—22no—
260C3×C4×C5—42no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—41no—
265Dic15—41no—
266C23×D3—101no—
267C3×#41—22no—
268C3×#41C4×D514yescomplemented
269C2×C3×Q8C22×D511yescharacteristic
270C2×C3×D4—21no—
271C2×C3×D4C22×D511yescharacteristic
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—22no—
275C22×C3×C4C22×D511yescharacteristic
276C2×D12—54no—
277C2×D12—52no—
278C2×D12—102no—
279C2×D12—101no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4C22⋊D511yescharacteristic
285C3×C4⋊C4C22⋊D511yescharacteristic
286C3×C4⋊C4C22×D512yes—
287C3×C22⋊C4—22no—
288C3×C22⋊C4C22⋊D512yes—
289C3×C42—22no—
290C3×C42C22×D512yes—
291#217—101no—
292#215—58no—
293#213—58no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3—51no—
297C4⋊Dic3—51no—
298C4×Dic3—101no—
299#208—54no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—102no—
304C23×C5—21no—
305C23×C5C2×#6711yescharacteristic
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C5×Q8—21no—
311C5×Q8C2×C4×D312yes—
312C5×D4—24no—
313C5×D4—21no—
314C5×D4C2×C4×D312yes—
315C2×C4×C5—21no—
316C2×C4×C5—24no—
317C2×C4×C5—22no—
318C2×C4×C5—82no—
319C2×C4×C5—81no—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5#23512yes—
322C2×C4×C5C2×#6712yes—
323C2×C4×C5C2×#6712yes—
324C2×C4×C5C2×#6711yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—61no—
327C2×Dic5—61no—
328D20—34no—
329D20—64no—
330D20—62no—
331C4×D5—242no—
332C4×D5—242no—
333#168—34no—
334#168—61no—
335#168—61no—
336C2×#41C2×D1511yescharacteristic
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—151no—
343C4×Q8C2×D1512yescomplemented
344C4×D4—22no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4C2×D1512yescomplemented
350#117—21no—
351#117—151no—
352#117C2×D1511yescharacteristic
353C2×C4⋊C4—21no—
354C2×C4⋊C4C2×D1511yescharacteristic
355C2×C22⋊C4—302no—
356#107—152no—
357#106—152no—
358#103—151no—
359#103—151no—
360#102—151no—
361#102—151no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5—42no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—44no—
372C23×C3—21no—
373C23×C3C2×C22⋊D511yescharacteristic
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C3×Q8—21no—
379C3×Q8C2×C4×D512yes—
380C3×D4—24no—
381C3×D4—21no—
382C3×D4C2×C4×D512yes—
383C2×C3×C4—21no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—82no—
387C2×C3×C4—81no—
388C2×C3×C4C2×C4×D512yes—
389C2×C3×C4#70912yes—
390C2×C3×C4C2×C22⋊D512yes—
391C2×C3×C4C2×C22⋊D512yes—
392C2×C3×C4C2×C22⋊D511yescharacteristic
393C2×C3×C4C23×D511yescharacteristic
394C2×Dic3—101no—
395C2×Dic3—101no—
396D12—54no—
397D12—102no—
398D12—104no—
399C4×D3—402no—
400C4×D3—402no—
401C3⋊C8—54no—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—22no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5C4×#6712yes—
410C22×C5C22×#6711yescharacteristic
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5C4×#6712yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23511yescharacteristic
422Dic5—121no—
423Dic5—121no—
424C24—301no—
425#41—22no—
426#41C4×D1514yescomplemented
427C2×Q8C22×D1511yescharacteristic
428C2×D4—21no—
429C2×D4—154no—
430C2×D4—152no—
431C2×D4—302no—
432C2×D4—301no—
433C2×D4C22×D1511yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C22×D1511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—152no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—151no—
450C4⋊C4—151no—
451C4⋊C4#122011yescharacteristic
452C4⋊C4#122011yescharacteristic
453C4⋊C4C22×D1512yes—
454C22⋊C4—22no—
455C22⋊C4—301no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4#122012yes—
459C42—22no—
460C42—301no—
461C42C22×D1512yes—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3C4×C22⋊D512yes—
469C22×C3C22×C22⋊D511yescharacteristic
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—404no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—42no—
478C3×C4C4×C22⋊D512yes—
479C3×C4C22×C4×D511yescharacteristic
480C3×C4C2×#70911yescharacteristic
481Dic3—201no—
482Dic3—201no—
483C2×C5—22no—
484C2×C5—42no—
485C2×C5C2×C4×#6711yescharacteristic
486C2×C5#583511yescharacteristic
487C2×C5#583711yescharacteristic
488D5—124no—
489C23—21no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23C2×#122011yescharacteristic
495Q8—21no—
496Q8C2×C4×D1512yes—
497D4—24no—
498D4—21no—
499D4—154no—
500D4—304no—
501D4—302no—
502D4C2×C4×D1512yes—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—301no—
509C2×C4—301no—
510C2×C4—1202no—
511C2×C4—1202no—
512C2×C4C2×C4×D1512yes—
513C2×C4#681712yes—
514C2×C4C2×#122012yes—
515C2×C4C2×#122012yes—
516C2×C4C2×#122011yescharacteristic
517C2×C4C23×D1511yescharacteristic
518C8—154no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3—42no—
523C2×C3C2×C4×C22⋊D511yescharacteristic
524C2×C3#6616911yescharacteristic
525C2×C3#6617111yescharacteristic
526D3—204no—
527C5#8256411yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22—304no—
534C22—602no—
535C22—602no—
536C22—1204no—
537C22C4×#122012yes—
538C22C22×#122011yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—42no—
543C4—601no—
544C4—601no—
545C4C4×#122012yes—
546C4C22×C4×D1511yescharacteristic
547C4C2×#681711yescharacteristic
548C3#1061429511yescharacteristic, complemented, Sylow
549C2—22no—
550C2—42no—
551C2—604no—
552C2C2×C4×#122011yescharacteristic
553C2#1175659411yescharacteristic
554C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
prime radicalC2×#91838C2
cosocleC2×C3×C4×C5C24
hypercenter#520D15
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C3×C5×#520C2semidirect
3. #11756280C2semidirect
4. #11751334C2semidirect
5. #11751127C2semidirect
6. C4×#6717C2semidirect
7. #11751115C2semidirect
8. C4×#6715C2semidirect
9. #11751098C2semidirect
10. C2×#91093C2semidirect
11. #11751065C2semidirect
15. C3×C4×C5×Q8C22semidirect
17. C3×C4×C5×D4C22semidirect
22. #91838C4semidirect
33. #91119C22semidirect
34. #91119C22semidirect
35. #91116C22semidirect
36. #91116C22semidirect
39. #91092C22semidirect
40. #91091C22semidirect
41. #91087C22semidirect
42. C4×C3⋊#168C22semidirect
44. C5×#520D3semidirect
57. C3×C5×#41C2×C4semidirect
67. C2×D60C2×C4semidirect
81. #6717C2×C4semidirect
82. #6715C2×C4semidirect
88. #6710C2×C4semidirect
93. C3×#520D5semidirect
106. C4×C5×Q8C2×D3semidirect
108. C4×C5×D4C2×D3semidirect
169. C3×C4×Q8C2×D5semidirect
171. C3×C4×D4C2×D5semidirect
199. C5×#41C4×D3semidirect
236. #520D15semidirect
268. C3×#41C4×D5semidirect
343. C4×Q8C2×D15semidirect
349. C4×D4C2×D15semidirect
426. #41C4×D15semidirect
462. C3×C5#2946semidirect
527. C5#82564semidirect
548. C3#10614295semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5202
C2×#918382
#117562802
#117513342
#117511272
C4×#67172
#117511152
C4×#67152
#117510982
C2×#910932
#117510652
#106142953
#825645