Finite Group Databasebeta

← #14416727

Subgroups — #14416727

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×C5×#932C211yesmaximal, characteristic
3#11754455C211yesmaximal, characteristic, complemented
4C3×#65504C211yesmaximal, characteristic, complemented
5#11749020C212yesmaximal, complemented
6#11749019C212yesmaximal, complemented
7#11748996C212yesmaximal, complemented
8#11748994C212yesmaximal, complemented
9#11748455C211yesmaximal, characteristic, complemented
10#11748390C211yesmaximal, characteristic, complemented
11#11748328C211yesmaximal, characteristic, complemented
12Dic5×AGL(1,ℤ/8)—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×Dic15—21no—
15C2×C5×#235C2211yescharacteristic
16C2×#6719—21no—
17D4×Dic15—21no—
18D4×Dic15—21no—
19D4×Dic15C2212yes—
20D4×Dic15C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×#214C2212yes—
24C5×#932C418yescomplemented
25C2×C5×#213C2212yes—
26C2×C5×#208C2211yescharacteristic
27C3×#4072C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29#67⋊Dic5—21no—
30#67⋊Dic5—21no—
31#91435C2211yescharacteristic, complemented
32#91435C2211yescharacteristic, complemented
33C4×D3×Dic5—21no—
34#91371—21no—
35#91344C2211yescharacteristic, complemented
36#91344C2211yescharacteristic, complemented
37C3×#3964C2212yes—
38C3×#3964C2212yes—
39#90990C2212yescomplemented
40#90987C2212yescomplemented
41#90973C2212yescomplemented
42#90967C2212yescomplemented
43#90954C2212yescomplemented
44#90951C2212yescomplemented
45#78914—51nomaximal, Hall
46C2×C5×AGL(1,ℤ/8)—31no—
47#41×Dic5—31no—
48C2×D4×Dic5—31no—
49#65521—31no—
50#65504D311yescharacteristic, complemented
51#65453—32no—
52SD16×Dic5—32no—
53#65441—32no—
54D8×Dic5—32no—
55#65410—31no—
56M16×Dic5—31no—
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
63C22×Dic15—21no—
64C22×Dic15—22no—
65C22×Dic15—22no—
66C22×Dic15—44no—
67C22×Dic15D411yescharacteristic
68C22×Dic15D411yescharacteristic
69C2×C5×#67—21no—
70C5×#235—22no—
71C5×#235C2×C414yescomplemented
72C2×C5×D12C2311yescharacteristic
73C2×C4×C5×D3—21no—
74C2×C5×Dic6C2311yescharacteristic
75C2×D3×Dic5—21no—
76C2×D3×Dic5—21no—
77#6719—22no—
78#6719—22no—
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C4×Dic15D411yescharacteristic
82C4×Dic15D411yescharacteristic
83C4×Dic15C2311yescharacteristic
84C4×Dic15C2311yescharacteristic
85C5×#214C2×C418yescomplemented
86C5×#213C2×C418yescomplemented
87C5×#208C2×C414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—21no—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2311yescharacteristic
92C3×C4×Dic5—21no—
93C3×#681—22no—
94C2×C3×#168C2312yes—
95Dic3⋊Dic5—21no—
96Dic3⋊Dic5—21no—
97(C2×D3)⋊Dic5—21no—
98(C2×D3)⋊Dic5—21no—
99Dic3×Dic5—21no—
100Dic3×Dic5—21no—
101C2×D4×Dic3—51no—
102C2×#932D511yescharacteristic
103#5522—51no—
104C3×#418—51no—
105#5133—51no—
106Dic3×M16—51no—
107#4995—51no—
108#4785—52no—
109#4758—52no—
110#4757—52no—
111#4756—52no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C23×Dic5—61no—
115C5×AGL(1,ℤ/8)—38no—
116C2×C5×SD16—32no—
117C2×C5×D8—32no—
118C2×C5×M16—31no—
119C2×C22⋊Dic5—61no—
120Q8×Dic5—31no—
121Q8×Dic5—31no—
122D4×Dic5—32no—
123D4×Dic5—32no—
124D4×Dic5—31no—
125D4×Dic5—31no—
126D4×Dic5—61no—
127D4×Dic5—61no—
128D4×Dic5—61no—
129D4×Dic5—61no—
130#4072—61no—
131#4072C2×D311yescharacteristic
132C2×C4⋊Dic5—31no—
133C2×C4×Dic5—31no—
134C2×C4×Dic5—61no—
135C2×#681C2×D311yescharacteristic
136#3967—32no—
137#3964—32no—
138#3964C2×D312yes—
139#3964C2×D312yes—
140#3950—32no—
141#3949—32no—
142#3947—32no—
143C8×Dic5—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×C5×D3—21no—
151C3×C5×D4—24no—
152C3×C5×D4—22no—
153C3×C5×D4C22×C414yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15—41no—
161C2×Dic15—44no—
162C2×Dic15—42no—
163C2×Dic15—44no—
164C2×Dic15C2×D411yescharacteristic
165C2×Dic15C2×D411yescharacteristic
166C2×Dic15C2×D411yescharacteristic
167C2×Dic15C2×D411yescharacteristic
168C5×#67—24no—
169C2×C5×Dic3—21no—
170C5×D12—21no—
171C5×D12C22×C412yescomplemented
172C4×C5×D3—24no—
173C5×Dic6—21no—
174C5×Dic6C22×C412yescomplemented
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177D3×Dic5—42no—
178D3×Dic5—42no—
179C3×#168—22no—
180C5×C3⋊C8C22×C414yescomplemented
181C22×C3×D4C2×D511yescharacteristic
182C23×Dic3—101no—
183C2×#235C2×D511yescharacteristic
184C2×C3×M16—51no—
185C3×#117—51no—
186C2×#217—101no—
187D4×Dic3—52no—
188D4×Dic3—52no—
189D4×Dic3—101no—
190D4×Dic3—101no—
191C2×#214C2×D512yes—
192#932Dic518yescomplemented
193C2×#213C2×D512yes—
194C2×C4⋊Dic3—51no—
195C2×C4×Dic3—51no—
196C2×#208C2×D511yescharacteristic
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×#102—52no—
206C3×#102—52no—
207#821—52no—
208#816—52no—
209#815—52no—
210C8×Dic3—52no—
211#808—52no—
212#807—52no—
213C24×C5—21no—
214C5×#41—34no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—21no—
218C2×C5×D4—22no—
219C2×C5×D4—31no—
220C2×C5×D4—61no—
221C2×C5×D4C4×D314yescomplemented
222C2×C5×D4C22×D312yes—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C22×Dic5—31no—
226C22×Dic5—31no—
227C22×Dic5—61no—
228C22×Dic5—61no—
229C22×Dic5—62no—
230C22×Dic5—62no—
231C22×Dic5—61no—
232C22×Dic5—124no—
233C5×SD16—38no—
234C5×D8—38no—
235C5×M16—34no—
236C2×C5×C8—32no—
237C22⋊Dic5—21no—
238C22⋊Dic5—61no—
239C22⋊Dic5—61no—
240C22⋊Dic5—62no—
241C22⋊Dic5—62no—
242C4⋊Dic5—32no—
243C4⋊Dic5—61no—
244C4⋊Dic5—61no—
245C4⋊Dic5—61no—
246C4⋊Dic5C22×D311yescharacteristic
247C4⋊Dic5C22×D311yescharacteristic
248C4×Dic5—21no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253C4×Dic5—61no—
254C4×Dic5—61no—
255#681—22no—
256C2×#168C22×D312yes—
257C2×AGL(1,ℤ/8)—31no—
258C4×#41—151no—
259C2×C4×D4—151no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—51no—
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×C5×D3—22no—
277C2×C5×D3—41no—
278C2×C5×D3—41no—
279C3×C4×C5C4×D412yes—
280C3×C4×C5C23×C411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—21no—
283Dic15—21no—
284Dic15—21no—
285Dic15—42no—
286Dic15AGL(1,ℤ/8)12yescomplemented
287C3×Dic5—41no—
288C3×Dic5—41no—
289C5×Dic3—22no—
290C24×C3—21no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C2×Dic514yescomplemented
294C2×C3×D4C22×D512yes—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—21no—
297C22×Dic3—51no—
298C22×Dic3—51no—
299C22×Dic3—102no—
300C22×Dic3—102no—
301C22×Dic3—101no—
302C22×Dic3—204no—
303#235—22no—
304#235C2×Dic514yescomplemented
305C2×D12C22×D511yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6C22×D511yescharacteristic
310C3×M16—102no—
311C2×C3×C8—52no—
312C3×C4⋊C4—51no—
313C3×C4⋊C4—51no—
314C3×C22⋊C4—101no—
315C3×C42—101no—
316#217—102no—
317#217—102no—
318#214C2×Dic518yescomplemented
319#213C2×Dic518yescomplemented
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#208C2×Dic514yescomplemented
333C2×C3⋊C8C22×D512yes—
334C23×C5—24no—
335C23×C5—22no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5—61no—
339C23×C5D3×D411yescharacteristic
340C5×Q8—32no—
341C5×Q8—61no—
342C5×D4—24no—
343C5×D4—22no—
344C5×D4—32no—
345C5×D4—64no—
346C5×D4—61no—
347C5×D4C2×C4×D314yes—
348C2×C4×C5—61no—
349C2×C4×C5—64no—
350C2×C4×C5C2×C4×D312yes—
351C2×C4×C5D3×D411yescharacteristic
352C2×C4×C5#23712yes—
353C2×C4×C5C23×D311yescharacteristic
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—31no—
357C2×Dic5—31no—
358C2×Dic5—31no—
359C2×Dic5—31no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5—122no—
363C2×Dic5—124no—
364C2×Dic5—122no—
365C2×Dic5—121no—
366C2×Dic5—124no—
367C2×Dic5—122no—
368C5×C8—34no—
369#168—22no—
370C2×#41—31no—
371C22×D4D3×D511yescharacteristic
372C23×C4—301no—
373AGL(1,ℤ/8)—38no—
374C2×SD16—32no—
375C2×D8—32no—
376C2×M16—31no—
377C2×M16—51no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—151no—
381C4×D4—151no—
382C4×D4—152no—
383C4×D4—152no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—51no—
389#117—301no—
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—52no—
398#102—52no—
399#102—152no—
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
407C5×D3—42no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3D4×D511yescharacteristic
413C22×D3—21no—
414C3×D4—22no—
415C3×D4—24no—
416C3×D4C22×Dic514yes—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4D4×D511yescharacteristic
420C2×C3×C4#71112yes—
421C2×C3×C4C22×Dic512yes—
422C2×C3×C4C23×D511yescharacteristic
423#67—24no—
424C2×Dic3—21no—
425C2×Dic3—51no—
426C2×Dic3—51no—
427C2×Dic3—51no—
428C2×Dic3—51no—
429C2×Dic3—102no—
430C2×Dic3—102no—
431C2×Dic3—204no—
432C2×Dic3—201no—
433C2×Dic3—204no—
434C2×Dic3—202no—
435D12—21no—
436D12C22×Dic512yescomplemented
437C4×D3—24no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—21no—
441Dic6C22×Dic512yescomplemented
442C3×C8—102no—
443C3⋊C8C22×Dic514yescomplemented
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—24no—
447C22×C5—48no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—62no—
451C22×C5—121no—
452C22×C5—121no—
453C22×C5#67⋊C412yes—
454C22×C5C2×D3×D411yescharacteristic
455C4×C5—62no—
456C4×C5#67⋊C412yes—
457C4×C5C22×C4×D311yescharacteristic
458C4×C5C2×#23711yescharacteristic
459Dic5—32no—
460Dic5—41no—
461Dic5—41no—
462Dic5—61no—
463Dic5—61no—
464Dic5—61no—
465Dic5—122no—
466C24—21no—
467#41—34no—
468#41—62no—
469C2×Q8—31no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—31no—
473C2×D4—61no—
474C2×D4D3×Dic514yescomplemented
475C2×D4C2×D3×D512yes—
476C22×C4—61no—
477C22×C4—151no—
478C22×C4—151no—
479C22×C4—301no—
480C22×C4—301no—
481C22×C4—302no—
482C22×C4—302no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—38no—
487D8—38no—
488M16—34no—
489M16—102no—
490C2×C8—32no—
491C2×C8—52no—
492C4⋊C4—51no—
493C4⋊C4—51no—
494C4⋊C4—152no—
495C4⋊C4—301no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—101no—
499C22⋊C4—301no—
500C22⋊C4—301no—
501C22⋊C4—302no—
502C22⋊C4—302no—
503C42—101no—
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×C3D4×Dic512yes—
518C22×C3C2×D4×D511yescharacteristic
519C2×D3—22no—
520C2×D3—41no—
521C2×D3—41no—
522C3×C4—201no—
523C3×C4—201no—
524C3×C4D4×Dic512yes—
525C3×C4C2×#71111yescharacteristic
526C3×C4C23×Dic511yescharacteristic
527Dic3—22no—
528Dic3—52no—
529Dic3—101no—
530Dic3—101no—
531Dic3—101no—
532Dic3—202no—
533C2×C5—22no—
534C2×C5—44no—
535C2×C5—122no—
536C2×C5C2×#67⋊C411yescharacteristic
537C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
538C2×C5#577311yescharacteristic
539C23—22no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—61no—
544C23#679011yescharacteristic
545Q8—32no—
546Q8—61no—
547D4—22no—
548D4—24no—
549D4—32no—
550D4—64no—
551D4—61no—
552D4C2×D3×Dic514yes—
553C2×C4—61no—
554C2×C4—64no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—151no—
558C2×C4—151no—
559C2×C4—151no—
560C2×C4—151no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—602no—
564C2×C4—604no—
565C2×C4—602no—
566C2×C4—601no—
567C2×C4—604no—
568C2×C4—602no—
569C2×C4#678012yes—
570C2×C4C2×D3×Dic512yes—
571C2×C4#679011yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—34no—
574C8—102no—
575C2×C3—22no—
576C2×C3—44no—
577C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
578C2×C3#6610711yescharacteristic
579C2×C3C2×D4×Dic511yescharacteristic
580D3—42no—
581C5#7891411yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—24no—
585C22—48no—
586C22—42no—
587C22—42no—
588C22—62no—
589C22—121no—
590C22—121no—
591C22#67⋊Dic512yes—
592C22C2×#679011yescharacteristic
593C4—62no—
594C4—152no—
595C4—201no—
596C4—201no—
597C4—301no—
598C4—301no—
599C4—301no—
600C4—602no—
601C4#67⋊Dic512yes—
602C4C2×#678011yescharacteristic
603C4C22×D3×Dic511yescharacteristic
604C3Dic5×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
605C2—22no—
606C2—44no—
607C2—122no—
608C2#1175470111yescharacteristic
609C2#1175470211yescharacteristic
610C2C2×#67⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#932C2
cosocleC2×C3×C4×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic15C2semidirect
3. #11754455C2semidirect
4. C3×#65504C2semidirect
5. #11749020C2semidirect
6. #11749019C2semidirect
7. #11748996C2semidirect
8. #11748994C2semidirect
9. #11748455C2semidirect
10. #11748390C2semidirect
11. #11748328C2semidirect
24. C5×#932C4semidirect
31. #91435C22semidirect
32. #91435C22semidirect
35. #91344C22semidirect
36. #91344C22semidirect
39. #90990C22semidirect
40. #90987C22semidirect
41. #90973C22semidirect
42. #90967C22semidirect
43. #90954C22semidirect
44. #90951C22semidirect
50. #65504D3semidirect
60. C2×C3×C5×D4C2×C4semidirect
71. C5×#235C2×C4semidirect
85. C5×#214C2×C4semidirect
86. C5×#213C2×C4semidirect
87. C5×#208C2×C4semidirect
171. C5×D12C22×C4semidirect
174. C5×Dic6C22×C4semidirect
180. C5×C3⋊C8C22×C4semidirect
192. #932Dic5semidirect
221. C2×C5×D4C4×D3semidirect
286. Dic15AGL(1,ℤ/8)semidirect
293. C2×C3×D4C2×Dic5semidirect
304. #235C2×Dic5semidirect
318. #214C2×Dic5semidirect
319. #213C2×Dic5semidirect
332. #208C2×Dic5semidirect
436. D12C22×Dic5semidirect
441. Dic6C22×Dic5semidirect
443. C3⋊C8C22×Dic5semidirect
474. C2×D4D3×Dic5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5#78914semidirect
604. C3Dic5×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C5×#9322
#117544552
C3×#655042
#117490202
#117490192
#117489962
#117489942
#117484552
#117483902
#117483282
Dic5×AGL(1,ℤ/8)3
#789145