Finite Group Databasebeta

← #14425660

Subgroups — #14425660

Order 1920.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic, complemented
2C3×C5×#525C211yesmaximal, characteristic, complemented
3#11756550C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11751154C214yesmaximal, complemented
6#11751133C214yesmaximal, complemented
7#11751107C212yesmaximal, complemented
8#10614667—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic, complemented
11#92101—22no—
12#92100—22no—
13#41×D15—24no—
14#92098—21no—
15#92095—21no—
16#92095C2214yes—
17C2×#6817—22no—
18C2×#6817C2212yes—
19C3×C5×#123C2212yescomplemented
20C3×C5×C22⋊Q8—21no—
21C3×C5×#121—21no—
22C3×C5×#120C2212yescomplemented
23C3×C4×C5×D4—22no—
24C3×C5×#117C2211yescharacteristic, complemented
25#91842C2214yescomplemented
26#91819—22no—
27#91818C2214yescomplemented
28C4×#1220—24no—
29#91815C2212yescomplemented
30#91813—22no—
31#91118C2214yescomplemented
32#91090C2218yescomplemented
33#82936—51nomaximal, Hall
34#66283—31no—
35C5×#525D311yescharacteristic, complemented
36#66125—32no—
37#65529—31no—
38#65342—34no—
39#65321—34no—
40#65295—32no—
41C24×C3×C5C2311yescharacteristic
42C3×C5×#41—22no—
43C3×C5×#41—22no—
44C2×C3×C5×Q8D411yescharacteristic, complemented
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4D411yescharacteristic, complemented
47C2×C3×C5×D4C2312yes—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5D412yescomplemented
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—24no—
56C2×#1220—24no—
57C2×#1220C2314yes—
58#6821—24no—
59Q8×D15—24no—
60#6819—24no—
61#6819—28no—
62D4×D15—24no—
63D4×D15—28no—
64#6817—24no—
65#6817—24no—
66#6817—22no—
67#6817—24no—
68#6817—22no—
69#6817—22no—
70#6817—22no—
71C2×D60—22no—
72C2×D60D412yescomplemented
73C2×C4×D15—24no—
74C2×C4×D15D414yescomplemented
75C2×Dic30—22no—
76C2×Dic30D412yescomplemented
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4—22no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4C2312yes—
82C3×C42×C5—21no—
83#6719—24no—
84#6719C2314yes—
85#6714—24no—
86C4⋊Dic15—22no—
87#6712—24no—
88C4×Dic15—22no—
89#5964—51no—
90C3×#525D511yescharacteristic, complemented
91#5791—52no—
92#5240—51no—
93#5053—54no—
94#5032—54no—
95#5006—52no—
96C2×C5×#41C2×D311yescharacteristic
97C23×C4×C5C2×D311yescharacteristic, complemented
98#4150—62no—
99#4149—62no—
100D5×#41—64no—
101#4147—61no—
102#4144—34no—
103#4144—61no—
104C2×#709—32no—
105C2×#709—62no—
106C5×#123C2×D312yescomplemented
107C5×C22⋊Q8—21no—
108C5×#121—21no—
109C5×#120C2×D312yescomplemented
110C4×C5×D4—22no—
111C5×#117C2×D311yescharacteristic, complemented
112#4099—34no—
113#4076—62no—
114#4075—34no—
115C4×C22⋊D5—64no—
116#4072—32no—
117#4070—62no—
118#3966—34no—
119#3938—38no—
120#3025—151noSylow
121C23×C3×C5—22no—
122C23×C3×C5—21no—
123C23×C3×C5—42no—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2411yescharacteristic
126C22×D15—24no—
127C22×D15C2×D414yes—
128C3×C5×Q8—22no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C3×C5×D4—44no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—42no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145#1220—28no—
146#1220—24no—
147#1220—24no—
148#1220—48no—
149C2×Dic15—24no—
150C2×Dic15—24no—
151C2×Dic15C2×D414yes—
152D60—24no—
153D60—22no—
154D60—22no—
155C4×D15—28no—
156C4×D15—24no—
157C4×D15—24no—
158Dic30—24no—
159Dic30—22no—
160Dic30—22no—
161C2×C3×#41C2×D511yescharacteristic
162C23×C3×C4C2×D511yescharacteristic, complemented
163#1010—102no—
164#1009—102no—
165D3×#41—104no—
166#1007—101no—
167#1004—54no—
168#1004—101no—
169C2×#235—52no—
170C2×#235—102no—
171C3×#123C2×D512yescomplemented
172C3×C22⋊Q8—21no—
173C3×#121—21no—
174C3×#120C2×D512yescomplemented
175C3×C4×D4—22no—
176C3×#117C2×D511yescharacteristic, complemented
177#953—54no—
178#930—102no—
179#929—54no—
180C4×#67—104no—
181#926—52no—
182#924—102no—
183#834—54no—
184#806—58no—
185C24×C5C22×D311yescharacteristic
186C5×#41—22no—
187C5×#41—22no—
188C2×C5×Q8#6711yescharacteristic, complemented
189C2×C5×D4—22no—
190C2×C5×D4#6711yescharacteristic, complemented
191C2×C5×D4C22×D312yes—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5#6712yescomplemented
197C22×C4×C5C22×D311yescharacteristic
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—34no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5—64no—
202#713—64no—
203Q8×D5—64no—
204#711—68no—
205#711—64no—
206D4×D5—68no—
207D4×D5—64no—
208#709—64no—
209#709—64no—
210#709—62no—
211#709—62no—
212#709—62no—
213#709—62no—
214#709—64no—
215C2×D20—32no—
216C2×D20—62no—
217C2×C4×D5—34no—
218C2×C4×D5—64no—
219C2×Dic10—32no—
220C2×Dic10—62no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4C22×D312yes—
226C42×C5—21no—
227C22⋊Dic5—34no—
228C22⋊Dic5—64no—
229#685—64no—
230C4⋊Dic5—62no—
231#683—64no—
232C4×Dic5—62no—
233#585—151no—
234#525—152no—
235#525D1511yescharacteristic, complemented
236#458—154no—
237B(4,𝔽2)—154no—
238#410—151no—
239#410—152no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—41no—
244C22×C3×C5—42no—
245C22×C3×C5—42no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5C22×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—24no—
251C2×D15—44no—
252C2×D15—84no—
253C3×C4×C5—22no—
254C3×C4×C5—42no—
255C3×C4×C5—41no—
256C3×C4×C5#12011yescharacteristic
257C3×C4×C5#12012yes—
258C3×C4×C5#12011yescharacteristic
259Dic15—24no—
260Dic15—44no—
261C24×C3C22×D511yescharacteristic
262C3×#41—22no—
263C3×#41—22no—
264C2×C3×Q8C22⋊D511yescharacteristic, complemented
265C2×C3×D4—22no—
266C2×C3×D4C22⋊D511yescharacteristic, complemented
267C2×C3×D4C22×D512yes—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4C22⋊D512yescomplemented
273C22×C3×C4C22×D511yescharacteristic
274C22×C3×C4C22×D511yescharacteristic
275C2×#67—54no—
276C2×#67—104no—
277C2×#67—104no—
278#239—104no—
279D3×Q8—104no—
280#237—108no—
281#237—104no—
282D3×D4—108no—
283D3×D4—104no—
284#235—104no—
285#235—104no—
286#235—102no—
287#235—102no—
288#235—102no—
289#235—102no—
290#235—104no—
291C2×D12—52no—
292C2×D12—102no—
293C2×C4×D3—54no—
294C2×C4×D3—104no—
295C2×Dic6—52no—
296C2×Dic6—102no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4C22×D512yes—
302C3×C42—21no—
303#217—54no—
304#217—104no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—102no—
307Dic3⋊C4—104no—
308C4×Dic3—102no—
309C23×C5—22no—
310C23×C5—21no—
311C23×C5—42no—
312C23×C5C2×#6712yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—34no—
315C22×D5—64no—
316C5×Q8—22no—
317C5×D4—24no—
318C5×D4—22no—
319C5×D4—44no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—41no—
326C2×C4×C5—42no—
327C2×C4×C5—41no—
328C2×C4×C5D3×D412yes—
329C2×C4×C5D3×D412yes—
330C2×C4×C5C2×#6712yes—
331C2×C4×C5C2×#6711yescharacteristic
332C2×C4×C5C2×#6711yescharacteristic
333C22⋊D5—68no—
334C22⋊D5—64no—
335C22⋊D5—64no—
336C22⋊D5—128no—
337C2×Dic5—34no—
338C2×Dic5—64no—
339C2×Dic5—64no—
340D20—64no—
341D20—62no—
342D20—62no—
343C4×D5—68no—
344C4×D5—64no—
345C4×D5—64no—
346Dic10—64no—
347Dic10—62no—
348Dic10—62no—
3492−1+4—302no—
3502−1+4—301no—
351H(5,𝔽2)—154no—
352H(5,𝔽2)—302no—
353H(5,𝔽2)—301no—
354C2×#41—152no—
355C2×#41—304no—
356C2×#41—302no—
357C2×#41C2×D1511yescharacteristic
358C23×C4C2×D1511yescharacteristic, complemented
359#123—154no—
360#123C2×D1512yescomplemented
361C22⋊Q8—21no—
362C22⋊Q8—302no—
363#121—21no—
364#121—302no—
365#120—154no—
366#120C2×D1512yescomplemented
367C4×D4—22no—
368C4×D4—304no—
369#117—152no—
370#117C2×D1511yescharacteristic, complemented
371#99—154no—
372#99—158no—
373C2×C3×C5—22no—
374C2×C3×C5—21no—
375C2×C3×C5—42no—
376C2×C3×C5—42no—
377C2×C3×C5C2×#12011yescharacteristic
378D15—44no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—42no—
382C23×C3C2×C22⋊D512yes—
383C23×C3C23×D511yescharacteristic
384C22×D3—54no—
385C22×D3—104no—
386C3×Q8—22no—
387C3×D4—24no—
388C3×D4—22no—
389C3×D4—44no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4D4×D512yes—
399C2×C3×C4D4×D512yes—
400C2×C3×C4C2×C22⋊D512yes—
401C2×C3×C4C2×C22⋊D511yescharacteristic
402C2×C3×C4C2×C22⋊D511yescharacteristic
403#67—108no—
404#67—104no—
405#67—104no—
406#67—208no—
407C2×Dic3—54no—
408C2×Dic3—104no—
409C2×Dic3—104no—
410D12—104no—
411D12—102no—
412D12—102no—
413C4×D3—108no—
414C4×D3—104no—
415C4×D3—104no—
416Dic6—104no—
417Dic6—102no—
418Dic6—102no—
419C22×C5—24no—
420C22×C5—22no—
421C22×C5—22no—
422C22×C5—41no—
423C22×C5—42no—
424C22×C5—42no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5C2×D3×D412yes—
428C22×C5C22×#6711yescharacteristic
429C2×D5—64no—
430C2×D5—124no—
431C2×D5—244no—
432C4×C5—22no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5#93711yescharacteristic
436C4×C5#93712yes—
437C4×C5#93711yescharacteristic
438Dic5—64no—
439Dic5—124no—
440C24C22×D1511yescharacteristic
441#41—22no—
442#41—22no—
443#41—304no—
444#41—304no—
445#41—308no—
446#41—304no—
447#41—304no—
448#41—302no—
449#41—302no—
450#41—302no—
451#41—302no—
452#41—304no—
453C2×Q8—152no—
454C2×Q8—302no—
455C2×Q8—304no—
456C2×Q8#122011yescharacteristic, complemented
457C2×D4—22no—
458C2×D4—154no—
459C2×D4—152no—
460C2×D4—302no—
461C2×D4—308no—
462C2×D4—304no—
463C2×D4—304no—
464C2×D4—304no—
465C2×D4#122011yescharacteristic, complemented
466C2×D4C22×D1512yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—154no—
472C22×C4—304no—
473C22×C4#122012yescomplemented
474C22×C4C22×D1511yescharacteristic
475C22×C4C22×D1511yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—304no—
479C4⋊C4—302no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—154no—
483C22⋊C4—304no—
484C22⋊C4—304no—
485C22⋊C4C22×D1512yes—
486C42—21no—
487C42—302no—
488C3×C5#302511yescharacteristic, complemented, Hall
489C22×C3—24no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3C2×D4×D512yes—
498C22×C3C22×C22⋊D511yescharacteristic
499C2×D3—104no—
500C2×D3—204no—
501C2×D3—404no—
502C3×C4—22no—
503C3×C4—42no—
504C3×C4—41no—
505C3×C4#408311yescharacteristic
506C3×C4#408312yes—
507C3×C4#408311yescharacteristic
508Dic3—104no—
509Dic3—204no—
510C2×C5—22no—
511C2×C5—21no—
512C2×C5—42no—
513C2×C5—42no—
514C2×C5C2×#93711yescharacteristic
515D5—124no—
516C23—22no—
517C23—21no—
518C23—42no—
519C23—154no—
520C23—304no—
521C23C2×#122012yes—
522C23C23×D1511yescharacteristic
523Q8—22no—
524Q8—304no—
525Q8—302no—
526Q8—302no—
527D4—24no—
528D4—22no—
529D4—44no—
530D4—304no—
531D4—308no—
532D4—304no—
533D4—304no—
534D4—302no—
535D4—302no—
536D4—608no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—154no—
546C2×C4—308no—
547C2×C4—304no—
548C2×C4—304no—
549C2×C4—304no—
550C2×C4—304no—
551C2×C4D4×D1512yes—
552C2×C4D4×D1512yes—
553C2×C4C2×#122012yes—
554C2×C4C2×#122011yescharacteristic
555C2×C4C2×#122011yescharacteristic
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—42no—
559C2×C3—42no—
560C2×C3C2×#408311yescharacteristic
561D3—204no—
562C5#8293611yescharacteristic, complemented, Sylow
563C22—22no—
564C22—24no—
565C22—22no—
566C22—41no—
567C22—42no—
568C22—41no—
569C22—42no—
570C22—41no—
571C22—304no—
572C22—604no—
573C22—1204no—
574C22C2×D4×D1512yes—
575C22C22×#122011yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—304no—
580C4—604no—
581C4#9182611yescharacteristic
582C4#9182612yes—
583C4#9182611yescharacteristic
584C3#1061466711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—42no—
589C2—604no—
590C2C2×#9182611yescharacteristic
subgroupG/H
centerC4#91826
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC3×C5×#525C2
socleC2×C3×C5C2×#120
hypercenter#525D15
hypocenterC3×C5#3025
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #11757146C2semidirect
2. C3×C5×#525C2semidirect
3. #11756550C2semidirect
4. #11751341C2semidirect
5. #11751154C2semidirect
6. #11751133C2semidirect
7. #11751107C2semidirect
10. C23×C3×C4×C5C22semidirect
19. C3×C5×#123C22semidirect
22. C3×C5×#120C22semidirect
24. C3×C5×#117C22semidirect
25. #91842C22semidirect
27. #91818C22semidirect
29. #91815C22semidirect
31. #91118C22semidirect
32. #91090C22semidirect
35. C5×#525D3semidirect
44. C2×C3×C5×Q8D4semidirect
46. C2×C3×C5×D4D4semidirect
52. C22×C3×C4×C5D4semidirect
72. C2×D60D4semidirect
74. C2×C4×D15D4semidirect
76. C2×Dic30D4semidirect
90. C3×#525D5semidirect
97. C23×C4×C5C2×D3semidirect
106. C5×#123C2×D3semidirect
109. C5×#120C2×D3semidirect
111. C5×#117C2×D3semidirect
162. C23×C3×C4C2×D5semidirect
171. C3×#123C2×D5semidirect
174. C3×#120C2×D5semidirect
176. C3×#117C2×D5semidirect
188. C2×C5×Q8#67semidirect
190. C2×C5×D4#67semidirect
196. C22×C4×C5#67semidirect
235. #525D15semidirect
264. C2×C3×Q8C22⋊D5semidirect
266. C2×C3×D4C22⋊D5semidirect
272. C22×C3×C4C22⋊D5semidirect
358. C23×C4C2×D15semidirect
360. #123C2×D15semidirect
366. #120C2×D15semidirect
370. #117C2×D15semidirect
456. C2×Q8#1220semidirect
465. C2×D4#1220semidirect
473. C22×C4#1220semidirect
488. C3×C5#3025semidirect
562. C5#82936semidirect
584. C3#10614667semidirect

Maximal subgroups

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

subgroupindex
#117571462
C3×C5×#5252
#117565502
#117513412
#117511542
#117511332
#117511072
#106146673
#829365