Finite Group Databasebeta

← #14416816

Subgroups — #14416816

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic15C211yesmaximal, characteristic, complemented
2C2×#91831C211yesmaximal, characteristic
3#11756281C211yesmaximal, characteristic
4C3×C5×#419C211yesmaximal, characteristic, complemented
5#11751234C211yesmaximal, characteristic
6M16×Dic15C211yesmaximal, characteristic, complemented
7#11751096C211yesmaximal, characteristic, complemented
8#11750918C212yesmaximal, complemented
9#11750891C212yesmaximal, complemented
10#11750890C212yesmaximal, complemented
11#11750889C212yesmaximal, complemented
12#10610677—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17Q8×Dic15—21no—
18Q8×Dic15—21no—
19Q8×Dic15C2212yes—
20Q8×Dic15C2212yes—
21C2×#6718C2212yes—
22#91831C418yescomplemented
23C2×#6717C2212yes—
24C2×C4⋊Dic15—21no—
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4×Dic15—21no—
27C2×C4×Dic15C2211yescharacteristic
28C2×#6710C2211yescharacteristic
29#91782C2211yescharacteristic
30#91782C2211yescharacteristic
31#91776C2211yescharacteristic
32#91776C2211yescharacteristic
33#91770—21no—
34#91770—21no—
35#91761—21no—
36C42×D15—21no—
37C3×C5×#103C2212yes—
38C3×C5×#103C2212yes—
39#91105C2212yes—
40#91100C2212yes—
41#91099C2212yes—
42C8×Dic15C2212yes—
43#91092C2212yes—
44#91091C2212yes—
45#78946—51nomaximal, Hall
46C2×Q8×Dic5—31no—
47C2×#4088—31no—
48#65856—31no—
49C5×#419D311yescharacteristic, complemented
50#65422—31no—
51M16×Dic5—31no—
52#65284—31no—
53#65106—32no—
54#65079—32no—
55#65078—32no—
56#65077—32no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2×C414yescomplemented
60C2×C3×C5×Q8C2312yes—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C22×Dic15—21no—
65C22×Dic15D411yescharacteristic
66C22×Dic15D411yescharacteristic
67#6817—22no—
68#6817C2×C414yes—
69C2×D60C2311yescharacteristic
70C2×C4×D15—21no—
71C2×C4×D15—21no—
72C2×C4×D15—21no—
73C2×Dic30C2311yescharacteristic
74C3×C5×M16—22no—
75C2×C3×C5×C8C2312yes—
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C22⋊C4—21no—
79C3×C42×C5—21no—
80#6718C2×C418yescomplemented
81#6717C2×C418yescomplemented
82#6714—21no—
83#6714—21no—
84C4⋊Dic15—21no—
85C4⋊Dic15—22no—
86C4⋊Dic15—22no—
87C4⋊Dic15C2312yes—
88#6712—21no—
89#6712—21no—
90C4×Dic15—21no—
91C4×Dic15—21no—
92C4×Dic15—22no—
93C4×Dic15—22no—
94C4×Dic15D411yescharacteristic
95C4×Dic15D411yescharacteristic
96C4×Dic15C2311yescharacteristic
97C4×Dic15C2311yescharacteristic
98#6710C2×C414yescomplemented
99C2×C3⋊#168C2312yes—
100C2×Q8×Dic3—51no—
101C2×#942—51no—
102#5522—51no—
103C3×#419D511yescharacteristic, complemented
104#5133—51no—
105Dic3×M16—51no—
106#4995—51no—
107#4817—52no—
108#4790—52no—
109#4789—52no—
110#4788—52no—
111C22×C5×Q8C2×D311yescharacteristic
112C2×#709—31no—
113C2×C5×M16C2×D311yescharacteristic
114C5×#117C2×D311yescharacteristic
115Q8×Dic5—32no—
116Q8×Dic5—32no—
117Q8×Dic5—61no—
118Q8×Dic5—61no—
119C2×#689—32no—
120#4088—38no—
121C2×#688—32no—
122C2×C4⋊Dic5—31no—
123C2×C4⋊Dic5—61no—
124C2×C4×Dic5—31no—
125C2×C4×Dic5—61no—
126C2×#681—31no—
127#4039—31no—
128#4039—31no—
129#4033—31no—
130#4033—31no—
131#4027—61no—
132#4027—61no—
133#4018—61no—
134C42×D5—61no—
135C5×#103C2×D312yes—
136C5×#103C2×D312yes—
137#3953—32no—
138#3948—32no—
139#3947—32no—
140C8×Dic5—32no—
141#3940—32no—
142#3939—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C3×C5×Q8—24no—
147C3×C5×Q8—22no—
148C3×C5×Q8C22×C414yes—
149C2×C3×C4×C5—24no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5#4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157#1220—24no—
158C2×Dic15—21no—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15—41no—
162C2×Dic15—42no—
163C2×Dic15C2×D411yescharacteristic
164C2×Dic15C2×D411yescharacteristic
165C2×Dic15C2×D411yescharacteristic
166C2×Dic15C2×D411yescharacteristic
167D60—21no—
168D60C22×C412yes—
169C4×D15—24no—
170C4×D15—42no—
171C4×D15—42no—
172Dic30—21no—
173Dic30C22×C412yes—
174C3×C5×C8—22no—
175C3⋊#168C22×C414yes—
176C22×C3×Q8C2×D511yescharacteristic
177C2×#235—51no—
178C2×C3×M16C2×D511yescharacteristic
179C3×#117C2×D511yescharacteristic
180Q8×Dic3—52no—
181Q8×Dic3—52no—
182Q8×Dic3—101no—
183Q8×Dic3—101no—
184C2×#216—52no—
185#942—58no—
186C2×#215—52no—
187C2×C4⋊Dic3—51no—
188C2×C4⋊Dic3—101no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—101no—
191C2×#208—51no—
192#893—51no—
193#893—51no—
194#887—51no—
195#887—51no—
196#67⋊C4—101no—
197#67⋊C4—101no—
198#872—101no—
199C42×D3—101no—
200C3×#103C2×D512yes—
201C3×#103C2×D512yes—
202#821—52no—
203#816—52no—
204#815—52no—
205C8×Dic3—52no—
206#808—52no—
207#807—52no—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8C4×D314yescomplemented
211C2×C5×Q8C22×D312yes—
212C22×C4×C5—21no—
213C22×C4×C5C22×D311yescharacteristic
214C2×C22⋊D5—61no—
215C22×Dic5—31no—
216C22×Dic5—31no—
217C22×Dic5—61no—
218#709—34no—
219#709—62no—
220C2×D20—31no—
221C2×C4×D5—61no—
222C2×C4×D5—61no—
223C2×C4×D5—61no—
224C2×Dic10—31no—
225C5×M16—22no—
226C2×C5×C8C22×D312yes—
227C5×C4⋊C4C22×D311yescharacteristic
228C5×C4⋊C4C22×D311yescharacteristic
229C5×C22⋊C4—21no—
230C42×C5—21no—
231#689—38no—
232#688—38no—
233#685—61no—
234#685—61no—
235C4⋊Dic5—32no—
236C4⋊Dic5—62no—
237C4⋊Dic5—62no—
238C4⋊Dic5—61no—
239#683—61no—
240#683—61no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—31no—
244C4×Dic5—31no—
245C4×Dic5—61no—
246C4×Dic5—61no—
247C4×Dic5—62no—
248C4×Dic5—62no—
249#681—34no—
250C2×#168—32no—
251C2×#137—151no—
252C4×#41—151no—
253C2×C4×Q8—151no—
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428—151no—
259#419D1511yescharacteristic, complemented
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—22no—
267C2×D15—41no—
268C2×D15—41no—
269C3×C4×C5—24no—
270C3×C4×C5—41no—
271C3×C4×C5—41no—
272C3×C4×C5C4×D412yes—
273C3×C4×C5C23×C411yescharacteristic
274C3×C4×C5C2×#4111yescharacteristic
275Dic15—22no—
276Dic15—21no—
277Dic15—21no—
278Dic15—21no—
279Dic15—42no—
280Dic15#13712yescomplemented
281C2×C3×Q8—21no—
282C2×C3×Q8—22no—
283C2×C3×Q8C4×D514yescomplemented
284C2×C3×Q8C22×D512yes—
285C22×C3×C4—21no—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—101no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3—101no—
291#235—54no—
292#235—102no—
293C2×D12—51no—
294C2×C4×D3—101no—
295C2×C4×D3—101no—
296C2×C4×D3—101no—
297C2×Dic6—51no—
298C3×M16—22no—
299C2×C3×C8C22×D512yes—
300C3×C4⋊C4C22×D511yescharacteristic
301C3×C4⋊C4C22×D511yescharacteristic
302C3×C22⋊C4—21no—
303C3×C42—21no—
304#216—58no—
305#215—58no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308C4⋊Dic3—52no—
309C4⋊Dic3—102no—
310C4⋊Dic3—102no—
311C4⋊Dic3—101no—
312Dic3⋊C4—101no—
313Dic3⋊C4—101no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—51no—
317C4×Dic3—51no—
318C4×Dic3—101no—
319C4×Dic3—101no—
320C4×Dic3—102no—
321C4×Dic3—102no—
322#208—54no—
323C2×C3⋊C8—52no—
324C23×C5D3×D411yescharacteristic
325C22×D5—61no—
326C5×Q8—24no—
327C5×Q8—22no—
328C5×Q8C2×C4×D314yes—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5C2×C4×D312yes—
334C2×C4×C5D3×D411yescharacteristic
335C2×C4×C5#23712yes—
336C2×C4×C5C23×D311yescharacteristic
337C22⋊D5—64no—
338C2×Dic5—31no—
339C2×Dic5—31no—
340C2×Dic5—31no—
341C2×Dic5—31no—
342C2×Dic5—62no—
343C2×Dic5—61no—
344C2×Dic5—62no—
345C2×Dic5—121no—
346C2×Dic5—122no—
347D20—32no—
348D20—61no—
349C4×D5—64no—
350C4×D5—122no—
351C4×D5—122no—
352Dic10—32no—
353Dic10—61no—
354C5×C8—22no—
355#168—34no—
356C2×#41—151no—
357C22×Q8C2×D1511yescharacteristic
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—151no—
362C2×M16C2×D1511yescharacteristic
363C4×Q8—152no—
364C4×Q8—152no—
365C4×Q8—151no—
366C4×Q8—151no—
367C4×Q8—301no—
368C4×Q8—301no—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—301no—
374#117C2×D1511yescharacteristic
375C2×C4⋊C4—151no—
376C2×C4⋊C4—301no—
377C2×C42—151no—
378C2×C42—301no—
379C2×C42—301no—
380#107—152no—
381#106—152no—
382#103—152no—
383#103C2×D1512yes—
384#103C2×D1512yes—
385#102—152no—
386#97—152no—
387C4×C8—152no—
388C2×C3×C5—22no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×#13711yescharacteristic
391C2×C3×C5#57511yescharacteristic
392D15—42no—
393C23×C3D4×D511yescharacteristic
394C22×D3—101no—
395C3×Q8—22no—
396C3×Q8—24no—
397C3×Q8C2×C4×D514yes—
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4C2×C4×D512yes—
403C2×C3×C4D4×D511yescharacteristic
404C2×C3×C4#71112yes—
405C2×C3×C4C23×D511yescharacteristic
406#67—104no—
407C2×Dic3—51no—
408C2×Dic3—51no—
409C2×Dic3—51no—
410C2×Dic3—51no—
411C2×Dic3—102no—
412C2×Dic3—101no—
413C2×Dic3—102no—
414C2×Dic3—201no—
415C2×Dic3—202no—
416D12—52no—
417D12—101no—
418C4×D3—104no—
419C4×D3—202no—
420C4×D3—202no—
421Dic6—52no—
422Dic6—101no—
423C3×C8—22no—
424C3⋊C8—54no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5#67⋊C412yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—62no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—24no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5#67⋊C412yes—
436C4×C5C22×C4×D311yescharacteristic
437C4×C5C2×#23711yescharacteristic
438Dic5—32no—
439Dic5—62no—
440Dic5—61no—
441Dic5—61no—
442Dic5—61no—
443Dic5—122no—
444#41—154no—
445#41—302no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—151no—
449C2×Q8C4×D1514yescomplemented
450C2×Q8C22×D1512yes—
451C2×D4—151no—
452C2×D4—301no—
453C22×C4—21no—
454C22×C4—151no—
455C22×C4—151no—
456C22×C4—301no—
457C22×C4—301no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C22×D1511yescharacteristic
461Q16—158no—
462SD16—158no—
463M16—22no—
464M16—154no—
465C2×C8—152no—
466C2×C8C22×D1512yes—
467C4⋊C4—152no—
468C4⋊C4—302no—
469C4⋊C4—302no—
470C4⋊C4—301no—
471C4⋊C4—301no—
472C4⋊C4—301no—
473C4⋊C4C22×D1511yescharacteristic
474C4⋊C4C22×D1511yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—21no—
479C42—151no—
480C42—151no—
481C42—151no—
482C42—151no—
483C42—301no—
484C42—301no—
485C42—302no—
486C42—302no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3#402712yes—
491C22×C3C2×D4×D511yescharacteristic
492C2×D3—102no—
493C2×D3—201no—
494C2×D3—201no—
495C3×C4—24no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4#402712yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×#71111yescharacteristic
501Dic3—52no—
502Dic3—102no—
503Dic3—101no—
504Dic3—101no—
505Dic3—101no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5C2×#67⋊C411yescharacteristic
509C2×C5D3×#13711yescharacteristic
510C2×C5#577711yescharacteristic
511D5—122no—
512C23—301no—
513C23D4×D1511yescharacteristic
514Q8—24no—
515Q8—22no—
516Q8—152no—
517Q8—301no—
518Q8C2×C4×D1514yes—
519D4—152no—
520D4—304no—
521D4—301no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—151no—
527C2×C4—151no—
528C2×C4—151no—
529C2×C4—151no—
530C2×C4—302no—
531C2×C4—301no—
532C2×C4—304no—
533C2×C4—302no—
534C2×C4—602no—
535C2×C4—602no—
536C2×C4—601no—
537C2×C4—602no—
538C2×C4C2×C4×D1512yes—
539C2×C4D4×D1511yescharacteristic
540C2×C4#681912yes—
541C2×C4C23×D1511yescharacteristic
542C8—22no—
543C8—154no—
544C2×C3—22no—
545C2×C3C2×#402711yescharacteristic
546C2×C3D5×#13711yescharacteristic
547C2×C3#6611111yescharacteristic
548D3—202no—
549C5#7894611yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—302no—
553C22—601no—
554C22—601no—
555C22#9177012yes—
556C22C2×D4×D1511yescharacteristic
557C4—24no—
558C4—41no—
559C4—41no—
560C4—152no—
561C4—302no—
562C4—301no—
563C4—301no—
564C4—301no—
565C4—602no—
566C4#9177012yes—
567C4C22×C4×D1511yescharacteristic
568C4C2×#681911yescharacteristic
569C3#1061067711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—602no—
572C2C2×#9177011yescharacteristic
573C2D15×#13711yescharacteristic
574C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#419C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#419D15
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic15C2semidirect
4. C3×C5×#419C2semidirect
6. M16×Dic15C2semidirect
7. #11751096C2semidirect
8. #11750918C2semidirect
9. #11750891C2semidirect
10. #11750890C2semidirect
11. #11750889C2semidirect
22. #91831C4semidirect
49. C5×#419D3semidirect
59. C2×C3×C5×Q8C2×C4semidirect
80. #6718C2×C4semidirect
81. #6717C2×C4semidirect
98. #6710C2×C4semidirect
103. C3×#419D5semidirect
210. C2×C5×Q8C4×D3semidirect
259. #419D15semidirect
280. Dic15#137semidirect
283. C2×C3×Q8C4×D5semidirect
449. C2×Q8C4×D15semidirect
487. C3×C5C4×#137semidirect
549. C5#78946semidirect
569. C3#10610677semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
C2×#918312
#117562812
C3×C5×#4192
#117512342
M16×Dic152
#117510962
#117509182
#117508912
#117508902
#117508892
#106106773
#789465