Finite Group Databasebeta

← Dic5×#932 #14416728

Subgroups — Dic5×#932 #14416728

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×C5×#932C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3Dic5×#235C211yesmaximal, characteristic, complemented
4#11751316C211yesmaximal, characteristic, complemented
5#11749001C212yesmaximal, complemented
6Dic5×#214C212yesmaximal, complemented
7#11748977C212yesmaximal, complemented
8Dic5×#213C212yesmaximal, complemented
9#11748453C211yesmaximal, characteristic, complemented
10#11748384C211yesmaximal, characteristic, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12Dic5×AGL(1,ℤ/8)—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C23×C3×Dic5—21no—
16#91815C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C5×#214C2212yes—
19C5×#932C418yescomplemented
20C2×C5×#213C2212yes—
21C2×C5×#208C2211yescharacteristic
22C2×C3×C22⋊Dic5—21no—
23C3×D4×Dic5—21no—
24C3×D4×Dic5—21no—
25C3×D4×Dic5C2212yes—
26C3×D4×Dic5C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29Dic5×#67—21no—
30Dic5×#67—21no—
31Dic5×D12C2211yescharacteristic, complemented
32Dic5×D12C2211yescharacteristic, complemented
33C4×D3×Dic5—21no—
34#91371—21no—
35Dic5×Dic6C2211yescharacteristic, complemented
36Dic5×Dic6C2211yescharacteristic, complemented
37#91116C2212yes—
38#91116C2212yes—
39#90990C2212yescomplemented
40#90987C2212yescomplemented
41#90972C2212yescomplemented
42#90966C2212yescomplemented
43#90952C2212yescomplemented
44Dic5×C3⋊C8C2212yescomplemented
45C4×#932—51nomaximal, Hall
46C2×C5×AGL(1,ℤ/8)—31no—
47#41×Dic5—31no—
48C2×D4×Dic5D311yescharacteristic, complemented
49#65521—31no—
50#65504—31no—
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
63C2×C5×#67—21no—
64C5×#235—22no—
65C5×#235C2×C414yescomplemented
66C2×C5×D12C2311yescharacteristic
67C2×C4×C5×D3—21no—
68C2×C5×Dic6C2311yescharacteristic
69C22×C3×Dic5—21no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—44no—
73C22×C3×Dic5D411yescharacteristic
74C22×C3×Dic5D411yescharacteristic
75C2×D3×Dic5—21no—
76C2×D3×Dic5—21no—
77#6719—21no—
78C4⋊Dic15C2311yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80C4×Dic15—21no—
81#6710—22no—
82C2×C3⋊#168C2312yes—
83C5×#214C2×C418yescomplemented
84C5×#213C2×C418yescomplemented
85C5×#208C2×C414yescomplemented
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—22no—
88C3×C22⋊Dic5—22no—
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91C3×C4×Dic5D411yescharacteristic
92C3×C4×Dic5D411yescharacteristic
93C3×C4×Dic5C2311yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95Dic3⋊Dic5—21no—
96Dic3⋊Dic5—21no—
97(C2×D3)⋊Dic5—21no—
98(C2×D3)⋊Dic5—21no—
99Dic3×Dic5—21no—
100Dic3×Dic5—21no—
101C2×C3×C4×D4—51no—
102C2×#932D511yescharacteristic
103C4×#235—51no—
104#5215—51no—
105#5018—52no—
106C4×#214—52no—
107#5014—52no—
108C4×#213—52no—
109#4966—51no—
110#4964—51no—
111C4×#208—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C23×Dic5—21no—
115C5×AGL(1,ℤ/8)—38no—
116C2×C5×SD16—32no—
117C2×C5×D8—32no—
118C2×C5×M16—31no—
119C2×C22⋊Dic5—21no—
120Q8×Dic5—31no—
121Q8×Dic5—31no—
122D4×Dic5—21no—
123D4×Dic5—21no—
124D4×Dic5—31no—
125D4×Dic5—31no—
126D4×Dic5—61no—
127D4×Dic5—61no—
128D4×Dic5C2×D312yes—
129D4×Dic5C2×D312yes—
130#4072—31no—
131#4072—61no—
132C2×C4⋊Dic5C2×D311yescharacteristic
133C2×C4×Dic5—61no—
134C2×C4×Dic5C2×D311yescharacteristic
135C2×#681—31no—
136#3967—32no—
137#3964—32no—
138#3964—32no—
139#3964—32no—
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—21no—
159C2×Dic15—21no—
160C5×#67—24no—
161C2×C5×Dic3—21no—
162C5×D12—21no—
163C5×D12C22×C412yescomplemented
164C4×C5×D3—24no—
165C5×Dic6—21no—
166C5×Dic6C22×C412yescomplemented
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—41no—
170C2×C3×Dic5—44no—
171C2×C3×Dic5—42no—
172C2×C3×Dic5—44no—
173C2×C3×Dic5C2×D411yescharacteristic
174C2×C3×Dic5C2×D411yescharacteristic
175C2×C3×Dic5C2×D411yescharacteristic
176C2×C3×Dic5C2×D411yescharacteristic
177D3×Dic5—42no—
178D3×Dic5—42no—
179C3⋊#168—22no—
180C5×C3⋊C8C22×C414yescomplemented
181C22×C3×D4C2×D511yescharacteristic
182C23×C3×C4—101no—
183C2×#235C2×D511yescharacteristic
184C3×C4×D4—52no—
185C3×C4×D4—52no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—101no—
190C2×C3×C42—51no—
191C2×#214C2×D512yes—
192#932Dic518yesdirect product factor
193C2×#213C2×D512yes—
194C4×#67—101no—
195C4×#67—101no—
196#926—51no—
197C2×#208—51no—
198C2×#208C2×D511yescharacteristic
199C4×D12—51no—
200C4×D12—51no—
201#872—101no—
202C42×D3—101no—
203C4×Dic6—51no—
204C4×Dic6—51no—
205#832—52no—
206#832—52no—
207#810—52no—
208#809—52no—
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C24×C5—21no—
214C5×#41—34no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—22no—
218C2×C5×D4—21no—
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—21no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—44no—
229C22×Dic5—61no—
230C22×Dic5—61no—
231C22×Dic5#6711yescharacteristic
232C22×Dic5#6711yescharacteristic
233C5×SD16—38no—
234C5×D8—38no—
235C5×M16—34no—
236C2×C5×C8—32no—
237C22⋊Dic5—22no—
238C22⋊Dic5—22no—
239C22⋊Dic5—61no—
240C22⋊Dic5—61no—
241C22⋊Dic5—61no—
242C4⋊Dic5—21no—
243C4⋊Dic5—31no—
244C4⋊Dic5—31no—
245C4⋊Dic5—61no—
246C4⋊Dic5—61no—
247C4⋊Dic5C22×D312yes—
248C4×Dic5—61no—
249C4×Dic5—61no—
250C4×Dic5—61no—
251C4×Dic5#6711yescharacteristic
252C4×Dic5#6711yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254C4×Dic5C22×D311yescharacteristic
255#681—62no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—31no—
258C4×#41—151no—
259C2×C4×D4—51no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
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—41no—
283Dic15—41no—
284C3×Dic5—21no—
285C3×Dic5—21no—
286C3×Dic5—21no—
287C3×Dic5—42no—
288C3×Dic5AGL(1,ℤ/8)12yescomplemented
289C5×Dic3—22no—
290C24×C3—21no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C2×Dic514yescomplemented
294C2×C3×D4C22×D512yes—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—102no—
298C22×C3×C4—102no—
299C22×C3×C4—101no—
300C22×C3×C4—204no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
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×C4⋊C4—52no—
311C3×C4⋊C4—101no—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C42—51no—
315C3×C42—51no—
316C3×C42—51no—
317C3×C42—51no—
318#217—101no—
319#214C2×Dic518yescomplemented
320#213C2×Dic518yescomplemented
321(C2×D3)⋊C4—101no—
322(C2×D3)⋊C4—101no—
323C4⋊Dic3—51no—
324C4⋊Dic3—51no—
325Dic3⋊C4—101no—
326Dic3⋊C4—101no—
327C4×Dic3—101no—
328C4×Dic3—101no—
329C4×Dic3—101no—
330#208—102no—
331#208C2×Dic514yescomplemented
332C2×C3⋊C8—52no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—24no—
335C23×C5—22no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5—61no—
339C23×C5C2×#6711yescharacteristic
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×C5#23512yes—
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C23×D311yescharacteristic
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—41no—
357C2×Dic5—44no—
358C2×Dic5—42no—
359C2×Dic5—44no—
360C2×Dic5—61no—
361C2×Dic5—61no—
362C2×Dic5—122no—
363C2×Dic5—122no—
364C2×Dic5C2×#6711yescharacteristic
365C2×Dic5C2×#6711yescharacteristic
366C2×Dic5C2×#6711yescharacteristic
367C2×Dic5C2×#6711yescharacteristic
368C5×C8—34no—
369#168—62no—
370C2×#41—31no—
371C22×D4D3×D511yescharacteristic
372C23×C4—101no—
373AGL(1,ℤ/8)—38no—
374C2×SD16—32no—
375C2×D8—32no—
376C2×M16—31no—
377C2×M16—151no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—52no—
381C4×D4—52no—
382C4×D4—101no—
383C4×D4—101no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—101no—
392C2×C42—51no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—152no—
398#102—152no—
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—51no—
418C2×C3×C4—51no—
419C2×C3×C4—51no—
420C2×C3×C4—51no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—204no—
424C2×C3×C4—201no—
425C2×C3×C4—204no—
426C2×C3×C4—202no—
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4#71112yes—
429C2×C3×C4C22×Dic512yes—
430C2×C3×C4C23×D511yescharacteristic
431#67—24no—
432C2×Dic3—21no—
433C2×Dic3—101no—
434C2×Dic3—101no—
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×C5C4×#6712yes—
454C22×C5C22×#6711yescharacteristic
455C4×C5—62no—
456C4×C5C4×#6712yes—
457C4×C5C22×C4×D311yescharacteristic
458C4×C5C2×#23511yescharacteristic
459Dic5—21no—
460Dic5—21no—
461Dic5—21no—
462Dic5—42no—
463Dic5—121no—
464Dic5—121no—
465Dic5#93212yesdirect product factor
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—51no—
477C22×C4—51no—
478C22×C4—61no—
479C22×C4—102no—
480C22×C4—102no—
481C22×C4—101no—
482C22×C4—204no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—38no—
487D8—38no—
488M16—34no—
489M16—302no—
490C2×C8—32no—
491C2×C8—152no—
492C4⋊C4—52no—
493C4⋊C4—101no—
494C4⋊C4—151no—
495C4⋊C4—151no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—102no—
499C22⋊C4—102no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—301no—
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—52no—
523C3×C4—101no—
524C3×C4—101no—
525C3×C4—101no—
526C3×C4—202no—
527C3×C4D4×Dic512yes—
528C3×C4C2×#71111yescharacteristic
529C3×C4C23×Dic511yescharacteristic
530Dic3—22no—
531Dic3—201no—
532Dic3—201no—
533C2×C5—22no—
534C2×C5—44no—
535C2×C5—122no—
536C2×C5C2×C4×#6711yescharacteristic
537C2×C5C2×#93211yescharacteristic
538C2×C5#582211yescharacteristic
539C23—22no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—61no—
544C23D5×#6711yescharacteristic
545Q8—32no—
546Q8—61no—
547D4—22no—
548D4—24no—
549D4—32no—
550D4—64no—
551D4—61no—
552D4C2×D3×Dic514yes—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—61no—
558C2×C4—64no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—204no—
562C2×C4—201no—
563C2×C4—204no—
564C2×C4—202no—
565C2×C4—301no—
566C2×C4—301no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4C2×D3×Dic512yes—
570C2×C4#678212yes—
571C2×C4D5×#6711yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—34no—
574C8—302no—
575C2×C3—22no—
576C2×C3—44no—
577C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
578C2×C3#6610711yescharacteristic
579C2×C3C2×D4×Dic511yescharacteristic
580D3—42no—
581C5C4×#93211yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—24no—
585C22—48no—
586C22—42no—
587C22—42no—
588C22—62no—
589C22—121no—
590C22—121no—
591C22Dic5×#6712yes—
592C22C2×D5×#6711yescharacteristic
593C4—52no—
594C4—62no—
595C4—101no—
596C4—101no—
597C4—101no—
598C4—202no—
599C4—601no—
600C4—601no—
601C4Dic5×#6712yes—
602C4C22×D3×Dic511yescharacteristic
603C4C2×#678211yescharacteristic
604C3Dic5×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
605C2—22no—
606C2—44no—
607C2—122no—
608C2D5×#93211yescharacteristic
609C2#1175469011yescharacteristic
610C2C2×Dic5×#6711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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
2. C2×C3×D4×Dic5C2semidirect
3. Dic5×#235C2semidirect
4. #11751316C2semidirect
5. #11749001C2semidirect
6. Dic5×#214C2semidirect
7. #11748977C2semidirect
8. Dic5×#213C2semidirect
9. #11748453C2semidirect
10. #11748384C2semidirect
11. Dic5×#208C2semidirect
19. C5×#932C4semidirect
31. Dic5×D12C22semidirect
32. Dic5×D12C22semidirect
35. Dic5×Dic6C22semidirect
36. Dic5×Dic6C22semidirect
39. #90990C22semidirect
40. #90987C22semidirect
41. #90972C22semidirect
42. #90966C22semidirect
43. #90952C22semidirect
44. Dic5×C3⋊C8C22semidirect
48. C2×D4×Dic5D3semidirect
60. C2×C3×C5×D4C2×C4semidirect
65. C5×#235C2×C4semidirect
83. C5×#214C2×C4semidirect
84. C5×#213C2×C4semidirect
85. C5×#208C2×C4semidirect
163. C5×D12C22×C4semidirect
166. C5×Dic6C22×C4semidirect
180. C5×C3⋊C8C22×C4semidirect
192. #932Dic5direct (N × H)
221. C2×C5×D4C4×D3semidirect
288. C3×Dic5AGL(1,ℤ/8)semidirect
293. C2×C3×D4C2×Dic5semidirect
304. #235C2×Dic5semidirect
319. #214C2×Dic5semidirect
320. #213C2×Dic5semidirect
331. #208C2×Dic5semidirect
436. D12C22×Dic5semidirect
441. Dic6C22×Dic5semidirect
443. C3⋊C8C22×Dic5semidirect
465. Dic5#932direct (N × H)
474. C2×D4D3×Dic5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5C4×#932semidirect
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×C5×#9322
C2×C3×D4×Dic52
Dic5×#2352
#117513162
#117490012
Dic5×#2142
#117489772
Dic5×#2132
#117484532
#117483842
Dic5×#2082
Dic5×AGL(1,ℤ/8)3
C4×#9325