Finite Group Databasebeta

← #14330652

Subgroups — #14330652

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4083C211yesmaximal, characteristic
2#11751321C211yesmaximal, characteristic, complemented
3C5×#5221C211yesmaximal, characteristic, complemented
4#11749500C212yesmaximal, complemented
5#11749489C212yesmaximal, complemented
6#11749488C212yesmaximal, complemented
7#11749485C212yesmaximal, complemented
8#11748771C212yesmaximal, complemented
9#11748770C212yesmaximal, complemented
10#10608165—31nomaximal, Hall
11C24×C3×D5C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic
13C23×Dic15C2211yescharacteristic, complemented
14C22×C3×C22⋊D5C2212yes—
15C2×#6719C2212yes—
16C2×#6719C2211yescharacteristic, complemented
17C2×C5×#217C2212yes—
18C2×C5×#217C2212yescomplemented
19C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
20C2×C4×C5×Dic3C2211yescharacteristic, complemented
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C3×#4083C418yescomplemented
23C2×C3×#685C2212yes—
24C2×#6668C2212yescomplemented
25C2×#6665C2212yes—
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×#6665C2212yes—
29C2×Dic3×Dic5C2212yescomplemented
30#91115C2212yescomplemented
31#90994C2212yescomplemented
32#90994C2212yescomplemented
33#82580—51nomaximal, Hall
34C2×#4083D311yescharacteristic
35C5×#390—31no—
36#65509—31no—
37#65279—32no—
38#65247—32no—
39#65246—32no—
40#65244—32no—
41#65233—32no—
42#65229—32no—
43C24×C3×C5C2311yescharacteristic
44C24×C3×C5C2311yescharacteristic
45C23×C3×D5—41no—
46C23×C3×D5—41no—
47C23×C3×D5—42no—
48C23×C3×D5—42no—
49C23×C3×D5C2×C414yescomplemented
50C23×C3×D5C2312yes—
51C2×C3×C5×D4—41no—
52C2×C3×C5×D4—41no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—41no—
56C22×Dic15—42no—
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2312yes—
61C2×C3×C22⋊D5—42no—
62C2×C3×C22⋊D5—42no—
63C2×C3×C22⋊D5C2×C418yes—
64C22×C3×Dic5C2312yes—
65#6719—42no—
66#6719—41no—
67C5×#217—42no—
68C5×#217—42no—
69C5×C4⋊Dic3—41no—
70C4×C5×Dic3—41no—
71C3×C22⋊Dic5C2×C414yescomplemented
72C3×#685C2×C418yescomplemented
73#6668—42no—
74#6665—42no—
75#6665—42no—
76#6665—42no—
77#6665—42no—
78Dic3×Dic5—42no—
79C2×C3×#120—51no—
80#5247—52no—
81#5221—52no—
82#5221D511yescharacteristic, complemented
83#5220—51no—
84#5220—52no—
85#4951—52no—
86#4951—52no—
87#4951—52no—
88C24×D5C2×D311yescharacteristic
89C22×C5×D4C2×D311yescharacteristic
90C22×C22⋊D5C2×D312yes—
91C23×Dic5—31no—
92C2×C5×C4⋊C4—31no—
93C2×C5×C22⋊C4—32no—
94C2×C5×C22⋊C4—32no—
95C2×C42×C5—31no—
96C2×C22⋊Dic5—32no—
97C2×C22⋊Dic5—31no—
98C2×C22⋊Dic5C2×D311yescharacteristic
99#4083Dic318yescomplemented
100C2×#685—32no—
101C2×#685—32no—
102C2×#685—32no—
103C2×#685—32no—
104C2×#685C2×D312yes—
105C2×#683—32no—
106C2×C4×Dic5—32no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#2375—151noSylow
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—21no—
114C23×C3×C5—22no—
115C23×C3×C5—22no—
116C23×C3×C5—21no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—48no—
129C22×C3×D5—44no—
130C22×C3×D5—44no—
131C22×C3×D5—48no—
132C22×C3×D5—44no—
133C22×C3×D5C22×C414yes—
134C3×C5×D4—44no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—44no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C3×C22⋊D5—48no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22×C414yes—
155C25×C3—51no—
156C22×C3×D4—52no—
157C22×C3×D4C2×D511yescharacteristic
158C23×Dic3—51no—
159C3×#120—58no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C22⋊C4—52no—
162C2×#217—52no—
163C2×#217—51no—
164C2×#217—52no—
165C2×#217—52no—
166C2×#217—52no—
167C2×#217—52no—
168C2×#217C2×D512yes—
169C2×#217C2×D512yescomplemented
170C2×C4⋊Dic3—52no—
171C2×C4⋊Dic3C2×D511yescharacteristic, complemented
172C2×C4×Dic3—52no—
173C2×C4×Dic3C2×D511yescharacteristic, complemented
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C24×C5C22×D311yescharacteristic
178C24×C5C22×D311yescharacteristic
179C23×D5—41no—
180C23×D5—41no—
181C23×D5—42no—
182C23×D5—42no—
183C23×D5C2×Dic314yescomplemented
184C23×D5C22×D312yes—
185C2×C5×D4—41no—
186C2×C5×D4—41no—
187C2×C5×D4C2×Dic314yes—
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—42no—
192C2×C22⋊D5—42no—
193C2×C22⋊D5C2×Dic318yes—
194C22×Dic5—32no—
195C22×Dic5—32no—
196C22×Dic5—121no—
197C22×Dic5—122no—
198C22×Dic5C22×D312yes—
199C5×C4⋊C4—121no—
200C5×C22⋊C4—122no—
201C5×C22⋊C4—122no—
202C42×C5—121no—
203C22⋊Dic5—122no—
204C22⋊Dic5—121no—
205C22⋊Dic5C2×Dic314yescomplemented
206#685—122no—
207#685—122no—
208#685—122no—
209#685—122no—
210#685C2×Dic318yescomplemented
211#683—122no—
212C4×Dic5—122no—
213C2×#120—51no—
214#390—31no—
215#390—152no—
216#388—152no—
217#388—152no—
218#388—152no—
219#386—152no—
220#386—151no—
221#379—152no—
222C22×C3×C5—24no—
223C22×C3×C5—22no—
224C22×C3×C5—22no—
225C22×C3×C5—24no—
226C22×C3×C5—41no—
227C22×C3×C5—42no—
228C22×C3×C5—41no—
229C22×C3×C5—42no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5C23×C411yescharacteristic
233C22×C3×C5H(5,𝔽2)12yes—
234C22×C3×C5H(5,𝔽2)11yescharacteristic
235C22×C3×C5H(5,𝔽2)11yescharacteristic
236C22×C3×C5H(5,𝔽2)12yes—
237C2×C3×D5—24no—
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—416no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C3×C4×C5—22no—
246Dic15—42no—
247Dic15—42no—
248C3×Dic5—24no—
249C5×Dic3—42no—
250C5×Dic3—42no—
251C24×C3—52no—
252C24×C3—54no—
253C24×C3—202no—
254C24×C3—201no—
255C24×C3—201no—
256C24×C3—202no—
257C24×C3C22×D511yescharacteristic
258C24×C3C22×D511yescharacteristic
259C2×C3×D4—41no—
260C2×C3×D4—41no—
261C2×C3×D4—58no—
262C2×C3×D4—202no—
263C2×C3×D4—202no—
264C2×C3×D4C4×D514yes—
265C22×C3×C4—52no—
266C22×C3×C4C22×D511yescharacteristic
267C22×Dic3—52no—
268C22×Dic3—52no—
269C22×Dic3—201no—
270C22×Dic3—202no—
271C22×Dic3C22×D512yes—
272C22×Dic3C22×D512yes—
273C3×C22⋊C4—54no—
274C3×C22⋊C4—58no—
275#217—42no—
276#217—42no—
277#217—202no—
278#217—202no—
279#217—202no—
280#217—202no—
281#217—201no—
282#217—202no—
283C4⋊Dic3—41no—
284C4⋊Dic3—202no—
285C4×Dic3—41no—
286C4×Dic3—202no—
287C23×C5—21no—
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—22no—
291C23×C5—22no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—21no—
295C23×C5C22×Dic312yes—
296C23×C5C22×Dic312yes—
297C23×C5C23×D311yescharacteristic
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—48no—
305C22×D5—44no—
306C22×D5—44no—
307C22×D5—48no—
308C22×D5—44no—
309C22×D5C22×Dic314yes—
310C5×D4—44no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5C22×Dic312yes—
320C22⋊D5—48no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—124no—
330C2×Dic5C22×Dic314yes—
331C25—51no—
332C22×D4—52no—
333C22×D4D3×D511yescharacteristic
334C23×C4—151no—
335#120—58no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—152no—
338C2×C22⋊C4—32no—
339C2×C22⋊C4—32no—
340C2×C22⋊C4—51no—
341C2×C22⋊C4—52no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C22⋊C4—152no—
347C2×C22⋊C4—151no—
348C2×C42—31no—
349C2×C42—152no—
350#95—152no—
351#95—152no—
352#95—152no—
353C2×C3×C5—42no—
354C2×C3×C5—42no—
355C2×C3×C5#51811yescharacteristic
356C2×C3×C5#51812yes—
357C2×C3×C5#56011yescharacteristic
358C2×C3×C5#56012yes—
359C2×C3×C5H(3,𝔽4)11yescharacteristic
360C3×D5—44no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—54no—
370C23×C3—102no—
371C23×C3—102no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—102no—
375C23×C3—102no—
376C23×C3—204no—
377C23×C3—208no—
378C23×C3—204no—
379C23×C3—208no—
380C23×C3—204no—
381C23×C3C2×C4×D512yes—
382C23×C3C2×C4×D512yes—
383C23×C3C23×D511yescharacteristic
384C3×D4—44no—
385C3×D4—208no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—54no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4C2×C4×D512yes—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—204no—
405C22×C5—24no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—24no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—42no—
412C22×C5—41no—
413C22×C5—42no—
414C22×C5—41no—
415C22×C5#100412yes—
416C22×C5#100412yes—
417C22×C5#100411yescharacteristic
418C22×C5#100411yescharacteristic
419C22×C5C23×Dic311yescharacteristic
420C2×D5—24no—
421C2×D5—24no—
422C2×D5—24no—
423C2×D5—416no—
424C2×D5—42no—
425C2×D5—42no—
426C2×D5—42no—
427C2×D5—42no—
428C4×C5—22no—
429C4×C5—122no—
430C4×C5—122no—
431Dic5—24no—
432Dic5—122no—
433Dic5—122no—
434C24—52no—
435C24—54no—
436C24—202no—
437C24—202no—
438C24—201no—
439C24—201no—
440C24C2×D3×D511yescharacteristic
441C24C2×D3×D511yescharacteristic
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—58no—
445C2×D4—202no—
446C2×D4—202no—
447C2×D4D5×Dic314yes—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—52no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—602no—
454C22×C4—601no—
455C22×C4C2×D3×D511yescharacteristic
456C4⋊C4—121no—
457C4⋊C4—602no—
458C22⋊C4—54no—
459C22⋊C4—58no—
460C22⋊C4—122no—
461C22⋊C4—122no—
462C22⋊C4—602no—
463C22⋊C4—602no—
464C22⋊C4—602no—
465C22⋊C4—602no—
466C22⋊C4—602no—
467C22⋊C4—601no—
468C42—121no—
469C42—602no—
470C3×C5#237511yescharacteristic, complemented, Hall
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—104no—
482C22×C3—104no—
483C22×C3—104no—
484C22×C3—2016no—
485C22×C3—202no—
486C22×C3—202no—
487C22×C3—202no—
488C22×C3—202no—
489C22×C3C22×C4×D511yescharacteristic
490C22×C3#414412yes—
491C22×C3#414411yescharacteristic
492C22×C3#414411yescharacteristic
493C22×C3#414912yes—
494C3×C4—22no—
495C3×C4—104no—
496Dic3—42no—
497Dic3—42no—
498Dic3—202no—
499Dic3—202no—
500C2×C5—42no—
501C2×C5—42no—
502C2×C5#559411yescharacteristic
503C2×C5#559512yes—
504C2×C5#559511yescharacteristic
505C2×C5#579811yescharacteristic
506C2×C5#579812yes—
507D5—44no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—54no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—102no—
521C23—102no—
522C23—102no—
523C23—204no—
524C23—208no—
525C23—208no—
526C23—204no—
527C23—204no—
528C23C2×D5×Dic312yes—
529C23C2×D5×Dic312yes—
530C23C22×D3×D511yescharacteristic
531D4—44no—
532D4—208no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—54no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—604no—
551C2×C4C2×D5×Dic312yes—
552C2×C3—42no—
553C2×C3—42no—
554C2×C3—204no—
555C2×C3#6582011yescharacteristic
556C2×C3#6587912yes—
557C2×C3#6595412yes—
558C2×C3#6601711yescharacteristic
559C2×C3#6605411yescharacteristic
560C5#8258011yescharacteristic, complemented, Sylow
561C22—22no—
562C22—22no—
563C22—24no—
564C22—24no—
565C22—42no—
566C22—42no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—104no—
572C22—104no—
573C22—104no—
574C22—2016no—
575C22—202no—
576C22—202no—
577C22—202no—
578C22—202no—
579C22#9202512yes—
580C22#9202612yes—
581C22C22×D5×Dic311yescharacteristic
582C22#9204911yescharacteristic
583C22#9204911yescharacteristic
584C4—22no—
585C4—104no—
586C4—122no—
587C4—122no—
588C4—602no—
589C4—602no—
590C3#1060816511yescharacteristic, complemented, Sylow
591C2—42no—
592C2—42no—
593C2—204no—
594C2#1175491012yes—
595C2#1175498412yes—
596C2#1175498611yescharacteristic
597C2#1175499311yescharacteristic
598C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4083C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11751321C2semidirect
3. C5×#5221C2semidirect
4. #11749500C2semidirect
5. #11749489C2semidirect
6. #11749488C2semidirect
7. #11749485C2semidirect
8. #11748771C2semidirect
9. #11748770C2semidirect
13. C23×Dic15C22semidirect
16. C2×#6719C22semidirect
18. C2×C5×#217C22semidirect
19. C2×C5×C4⋊Dic3C22semidirect
20. C2×C4×C5×Dic3C22semidirect
22. C3×#4083C4semidirect
24. C2×#6668C22semidirect
29. C2×Dic3×Dic5C22semidirect
30. #91115C22semidirect
31. #90994C22semidirect
32. #90994C22semidirect
49. C23×C3×D5C2×C4semidirect
71. C3×C22⋊Dic5C2×C4semidirect
72. C3×#685C2×C4semidirect
82. #5221D5semidirect
99. #4083Dic3semidirect
169. C2×#217C2×D5semidirect
171. C2×C4⋊Dic3C2×D5semidirect
173. C2×C4×Dic3C2×D5semidirect
183. C23×D5C2×Dic3semidirect
205. C22⋊Dic5C2×Dic3semidirect
210. #685C2×Dic3semidirect
470. C3×C5#2375semidirect
560. C5#82580semidirect
590. C3#10608165semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40832
#117513212
C5×#52212
#117495002
#117494892
#117494882
#117494852
#117487712
#117487702
#106081653
#825805