Finite Group Databasebeta

← #14416645

Subgroups — #14416645

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic15C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic
3#11756281C211yesmaximal, characteristic, complemented
4C3×C5×#418C211yesmaximal, characteristic, complemented
5#11751234C211yesmaximal, characteristic, complemented
6M16×Dic15C211yesmaximal, characteristic, complemented
7#11751096C211yesmaximal, characteristic, complemented
8#11750886C212yesmaximal, complemented
9#11750859C212yesmaximal, complemented
10#11750858C212yesmaximal, complemented
11#11750857C212yesmaximal, complemented
12#10610645—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×Dic15—21no—
15C2×#6817C2211yescharacteristic
16C2×C3×C5×M16C2211yescharacteristic
17C3×C5×#117C2211yescharacteristic
18C2×#6719—21no—
19D4×Dic15—21no—
20D4×Dic15—21no—
21D4×Dic15C2212yes—
22D4×Dic15C2212yes—
23C2×#6716C2212yes—
24#91821C418yescomplemented
25C2×#6715C2212yes—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28C2×#6710C2211yescharacteristic
29#91782C2211yescharacteristic, complemented
30#91782C2211yescharacteristic, complemented
31#91776C2211yescharacteristic, complemented
32#91776C2211yescharacteristic, complemented
33#91770—21no—
34#91770—21no—
35#91761—21no—
36C42×D15—21no—
37C3×C5×#102C2212yes—
38C3×C5×#102C2212yes—
39#91105C2212yescomplemented
40#91100C2212yescomplemented
41#91099C2212yescomplemented
42C8×Dic15C2212yescomplemented
43#91092C2212yescomplemented
44#91091C2212yescomplemented
45#78914—51nomaximal, Hall
46C2×D4×Dic5—31no—
47C2×#4078—31no—
48#65856—31no—
49C5×#418D311yescharacteristic, complemented
50#65422—31no—
51M16×Dic5—31no—
52#65284—31no—
53#65074—32no—
54#65047—32no—
55#65046—32no—
56#65045—32no—
57C24×C3×C5—21no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4C2×C414yescomplemented
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C22×Dic15—21no—
65C22×Dic15—22no—
66C22×Dic15—22no—
67C22×Dic15—44no—
68C22×Dic15D411yescharacteristic
69C22×Dic15D411yescharacteristic
70#6817—22no—
71#6817C2×C414yescomplemented
72C2×D60C2311yescharacteristic
73C2×C4×D15—21no—
74C2×C4×D15—21no—
75C2×C4×D15—21no—
76C2×Dic30C2311yescharacteristic
77C3×C5×M16—22no—
78C2×C3×C5×C8C2312yes—
79C3×C5×C4⋊C4C2311yescharacteristic
80C3×C5×C4⋊C4C2311yescharacteristic
81C3×C5×C22⋊C4—21no—
82C3×C42×C5—21no—
83#6719—22no—
84#6719—22no—
85#6716C2×C418yescomplemented
86#6715C2×C418yescomplemented
87#6714—21no—
88#6714—21no—
89C4⋊Dic15—21no—
90C4⋊Dic15C2312yes—
91#6712—21no—
92#6712—21no—
93C4×Dic15—21no—
94C4×Dic15—21no—
95C4×Dic15D411yescharacteristic
96C4×Dic15D411yescharacteristic
97C4×Dic15C2311yescharacteristic
98C4×Dic15C2311yescharacteristic
99#6710C2×C414yescomplemented
100C2×C3⋊#168C2312yes—
101C2×D4×Dic3—51no—
102C2×#932—51no—
103#5522—51no—
104C3×#418D511yescharacteristic, complemented
105#5133—51no—
106Dic3×M16—51no—
107#4995—51no—
108#4785—52no—
109#4758—52no—
110#4757—52no—
111#4756—52no—
112C22×C5×D4C2×D311yescharacteristic
113C23×Dic5—61no—
114C2×#709—31no—
115C2×C5×M16C2×D311yescharacteristic
116C5×#117C2×D311yescharacteristic
117C2×C22⋊Dic5—61no—
118D4×Dic5—32no—
119D4×Dic5—32no—
120D4×Dic5—61no—
121D4×Dic5—61no—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C2×C4⋊Dic5—31no—
126C2×C4×Dic5—31no—
127C2×#681—31no—
128#4039—31no—
129#4039—31no—
130#4033—31no—
131#4033—31no—
132#4027—61no—
133#4027—61no—
134#4018—61no—
135C42×D5—61no—
136C5×#102C2×D312yes—
137C5×#102C2×D312yes—
138#3953—32no—
139#3948—32no—
140#3947—32no—
141C8×Dic5—32no—
142#3940—32no—
143#3939—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5—24no—
146C23×C3×C5—22no—
147C23×C3×C5—42no—
148C23×C3×C5—42no—
149C23×C3×C5C2×D411yescharacteristic
150C22×D15—21no—
151C3×C5×D4—24no—
152C3×C5×D4—22no—
153C3×C5×D4C22×C414yes—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5#4112yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220—24no—
161C2×Dic15—21no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—41no—
165C2×Dic15—44no—
166C2×Dic15—42no—
167C2×Dic15—44no—
168C2×Dic15C2×D411yescharacteristic
169C2×Dic15C2×D411yescharacteristic
170C2×Dic15C2×D411yescharacteristic
171C2×Dic15C2×D411yescharacteristic
172D60—21no—
173D60C22×C412yescomplemented
174C4×D15—24no—
175C4×D15—42no—
176C4×D15—42no—
177Dic30—21no—
178Dic30C22×C412yescomplemented
179C3×C5×C8—22no—
180C3⋊#168C22×C414yescomplemented
181C22×C3×D4C2×D511yescharacteristic
182C23×Dic3—101no—
183C2×#235—51no—
184C2×C3×M16C2×D511yescharacteristic
185C3×#117C2×D511yescharacteristic
186C2×#217—101no—
187D4×Dic3—52no—
188D4×Dic3—52no—
189D4×Dic3—101no—
190D4×Dic3—101no—
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C2×C4⋊Dic3—51no—
195C2×C4×Dic3—51no—
196C2×#208—51no—
197#893—51no—
198#893—51no—
199#887—51no—
200#887—51no—
201#67⋊C4—101no—
202#67⋊C4—101no—
203#872—101no—
204C42×D3—101no—
205C3×#102C2×D512yes—
206C3×#102C2×D512yes—
207#821—52no—
208#816—52no—
209#815—52no—
210C8×Dic3—52no—
211#808—52no—
212#807—52no—
213C24×C5—21no—
214C2×C5×D4—21no—
215C2×C5×D4—22no—
216C2×C5×D4C4×D314yescomplemented
217C2×C5×D4C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C2×C22⋊D5—61no—
220C22×Dic5—31no—
221C22×Dic5—31no—
222C22×Dic5—62no—
223C22×Dic5—62no—
224C22×Dic5—61no—
225C22×Dic5—124no—
226#709—34no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×C4×D5—61no—
231C2×C4×D5—61no—
232C2×Dic10—31no—
233C5×M16—22no—
234C2×C5×C8C22×D312yes—
235C5×C4⋊C4C22×D311yescharacteristic
236C5×C4⋊C4C22×D311yescharacteristic
237C5×C22⋊C4—21no—
238C42×C5—21no—
239C22⋊Dic5—62no—
240C22⋊Dic5—62no—
241#687—38no—
242#686—38no—
243#685—61no—
244#685—61no—
245C4⋊Dic5—32no—
246C4⋊Dic5—61no—
247#683—61no—
248#683—61no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253C4×Dic5—61no—
254C4×Dic5—61no—
255#681—34no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—151no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418D1511yescharacteristic, complemented
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5—24no—
271C22×C3×C5—48no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5C4×D412yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—22no—
277C2×D15—41no—
278C2×D15—41no—
279C3×C4×C5—41no—
280C3×C4×C5—41no—
281C3×C4×C5C4×D412yes—
282C3×C4×C5C23×C411yescharacteristic
283C3×C4×C5C2×#4111yescharacteristic
284Dic15—22no—
285Dic15—21no—
286Dic15—21no—
287Dic15—21no—
288Dic15—42no—
289Dic15AGL(1,ℤ/8)12yescomplemented
290C24×C3—21no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C4×D514yescomplemented
294C2×C3×D4C22×D512yes—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—101no—
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3—102no—
300C22×Dic3—102no—
301C22×Dic3—101no—
302C22×Dic3—204no—
303#235—54no—
304#235—102no—
305C2×D12—51no—
306C2×C4×D3—101no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6—51no—
310C3×M16—22no—
311C2×C3×C8C22×D512yes—
312C3×C4⋊C4C22×D511yescharacteristic
313C3×C4⋊C4C22×D511yescharacteristic
314C3×C22⋊C4—21no—
315C3×C42—21no—
316#217—102no—
317#217—102no—
318#214—58no—
319#213—58no—
320(C2×D3)⋊C4—101no—
321(C2×D3)⋊C4—101no—
322C4⋊Dic3—52no—
323C4⋊Dic3—101no—
324Dic3⋊C4—101no—
325Dic3⋊C4—101no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328C4×Dic3—51no—
329C4×Dic3—51no—
330C4×Dic3—101no—
331C4×Dic3—101no—
332#208—54no—
333C2×C3⋊C8—52no—
334C23×C5—24no—
335C23×C5—22no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5D3×D411yescharacteristic
339C22×D5—61no—
340C5×D4—24no—
341C5×D4—22no—
342C5×D4C2×C4×D314yes—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5C2×C4×D312yes—
346C2×C4×C5D3×D411yescharacteristic
347C2×C4×C5#23712yes—
348C2×C4×C5C23×D311yescharacteristic
349C22⋊D5—64no—
350C2×Dic5—31no—
351C2×Dic5—31no—
352C2×Dic5—31no—
353C2×Dic5—31no—
354C2×Dic5—62no—
355C2×Dic5—61no—
356C2×Dic5—62no—
357C2×Dic5—124no—
358C2×Dic5—121no—
359C2×Dic5—124no—
360C2×Dic5—122no—
361D20—32no—
362D20—61no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368C5×C8—22no—
369#168—34no—
370C2×#41—151no—
371C22×D4C2×D1511yescharacteristic
372C23×C4—301no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—151no—
377C2×M16C2×D1511yescharacteristic
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—152no—
381C4×D4—152no—
382C4×D4—151no—
383C4×D4—151no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—301no—
389#117C2×D1511yescharacteristic
390C2×C4⋊C4—151no—
391C2×C22⋊C4—301no—
392C2×C42—151no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—152no—
398#102C2×D1512yes—
399#102C2×D1512yes—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5—44no—
404C2×C3×C5C2×C4×D411yescharacteristic
405C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C3×C5#57511yescharacteristic
407D15—42no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3D4×D511yescharacteristic
413C22×D3—101no—
414C3×D4—22no—
415C3×D4—24no—
416C3×D4C2×C4×D514yes—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4#71112yes—
422C2×C3×C4C23×D511yescharacteristic
423#67—104no—
424C2×Dic3—51no—
425C2×Dic3—51no—
426C2×Dic3—51no—
427C2×Dic3—51no—
428C2×Dic3—102no—
429C2×Dic3—101no—
430C2×Dic3—102no—
431C2×Dic3—204no—
432C2×Dic3—201no—
433C2×Dic3—204no—
434C2×Dic3—202no—
435D12—52no—
436D12—101no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3×C8—22no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—24no—
447C22×C5—48no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5#67⋊C412yes—
451C22×C5C2×D3×D411yescharacteristic
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5#67⋊C412yes—
458C4×C5C22×C4×D311yescharacteristic
459C4×C5C2×#23711yescharacteristic
460Dic5—32no—
461Dic5—62no—
462Dic5—61no—
463Dic5—61no—
464Dic5—61no—
465Dic5—122no—
466C24—21no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—151no—
473C2×D4—301no—
474C2×D4C4×D1514yescomplemented
475C2×D4C22×D1512yes—
476C22×C4—151no—
477C22×C4—151no—
478C22×C4—301no—
479C22×C4—301no—
480C22×C4—302no—
481C22×C4—302no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C22×D1511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—22no—
489M16—154no—
490C2×C8—152no—
491C2×C8C22×D1512yes—
492C4⋊C4—152no—
493C4⋊C4—301no—
494C4⋊C4—301no—
495C4⋊C4—301no—
496C4⋊C4C22×D1511yescharacteristic
497C4⋊C4C22×D1511yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—301no—
500C22⋊C4—301no—
501C22⋊C4—302no—
502C22⋊C4—302no—
503C42—21no—
504C42—151no—
505C42—151no—
506C42—151no—
507C42—151no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—24no—
514C22×C3—48no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3#402712yes—
518C22×C3C2×D4×D511yescharacteristic
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4#402712yes—
525C3×C4C22×C4×D511yescharacteristic
526C3×C4C2×#71111yescharacteristic
527Dic3—52no—
528Dic3—102no—
529Dic3—101no—
530Dic3—101no—
531Dic3—101no—
532Dic3—202no—
533C2×C5—22no—
534C2×C5—44no—
535C2×C5C2×#67⋊C411yescharacteristic
536C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
537C2×C5#577311yescharacteristic
538D5—122no—
539C23—24no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—301no—
544C23D4×D1511yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—24no—
548D4—22no—
549D4—152no—
550D4—304no—
551D4—301no—
552D4C2×C4×D1514yes—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—151no—
556C2×C4—151no—
557C2×C4—151no—
558C2×C4—151no—
559C2×C4—302no—
560C2×C4—301no—
561C2×C4—304no—
562C2×C4—302no—
563C2×C4—602no—
564C2×C4—602no—
565C2×C4—604no—
566C2×C4—601no—
567C2×C4—604no—
568C2×C4—602no—
569C2×C4C2×C4×D1512yes—
570C2×C4D4×D1511yescharacteristic
571C2×C4#681912yes—
572C2×C4C23×D1511yescharacteristic
573C8—22no—
574C8—154no—
575C2×C3—22no—
576C2×C3—44no—
577C2×C3C2×#402711yescharacteristic
578C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#6610711yescharacteristic
580D3—202no—
581C5#7891411yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—24no—
585C22—48no—
586C22—42no—
587C22—42no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9177012yes—
592C22C2×D4×D1511yescharacteristic
593C4—41no—
594C4—41no—
595C4—152no—
596C4—302no—
597C4—301no—
598C4—301no—
599C4—301no—
600C4—602no—
601C4#9177012yes—
602C4C22×C4×D1511yescharacteristic
603C4C2×#681911yescharacteristic
604C3#1061064511yescharacteristic, complemented, Sylow
605C2—22no—
606C2—44no—
607C2—602no—
608C2C2×#9177011yescharacteristic
609C2D15×AGL(1,ℤ/8)11yescharacteristic
610C2#1175653211yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#418C2
socleC22×C3×C5C22×D4
prime radicalC2×#91821C2
cosocleC2×C3×C4×C5C24
hypercenter#418D15
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic15C2semidirect
3. #11756281C2semidirect
4. C3×C5×#418C2semidirect
5. #11751234C2semidirect
6. M16×Dic15C2semidirect
7. #11751096C2semidirect
8. #11750886C2semidirect
9. #11750859C2semidirect
10. #11750858C2semidirect
11. #11750857C2semidirect
24. #91821C4semidirect
29. #91782C22semidirect
30. #91782C22semidirect
31. #91776C22semidirect
32. #91776C22semidirect
39. #91105C22semidirect
40. #91100C22semidirect
41. #91099C22semidirect
42. C8×Dic15C22semidirect
43. #91092C22semidirect
44. #91091C22semidirect
49. C5×#418D3semidirect
60. C2×C3×C5×D4C2×C4semidirect
71. #6817C2×C4semidirect
85. #6716C2×C4semidirect
86. #6715C2×C4semidirect
99. #6710C2×C4semidirect
104. C3×#418D5semidirect
173. D60C22×C4semidirect
178. Dic30C22×C4semidirect
180. C3⋊#168C22×C4semidirect
216. C2×C5×D4C4×D3semidirect
265. #418D15semidirect
289. Dic15AGL(1,ℤ/8)semidirect
293. C2×C3×D4C4×D5semidirect
474. C2×D4C4×D15semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5#78914semidirect
604. C3#10610645semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×#918212
#117562812
C3×C5×#4182
#117512342
M16×Dic152
#117510962
#117508862
#117508592
#117508582
#117508572
#106106453
#789145