Finite Group Databasebeta

← #14416745

Subgroups — #14416745

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
1#41×Dic15C211yesmaximal, characteristic, complemented
2C2×C3×#4095C211yesmaximal, characteristic
3C2×#91434C211yesmaximal, characteristic, complemented
4C5×#5232C211yesmaximal, characteristic, complemented
5#11749241C212yesmaximal, complemented
6#11749239C212yesmaximal, complemented
7#11748995C212yesmaximal, complemented
8#11748993C212yesmaximal, complemented
9#11748459C211yesmaximal, characteristic, complemented
10#11748367C211yesmaximal, characteristic, complemented
11#11748328C211yesmaximal, characteristic, complemented
12#10610597—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×D5×Dic3—21no—
16Q8×Dic15C2211yescharacteristic, complemented
17Q8×Dic15C2211yescharacteristic, complemented
18D4×Dic15—21no—
19D4×Dic15—21no—
20D4×Dic15C2211yescharacteristic, complemented
21D4×Dic15C2211yescharacteristic, complemented
22#91815—21no—
23#91815C2211yescharacteristic
24C2×C4×Dic15—21no—
25C2×C4×Dic15C2211yescharacteristic
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×#208C2211yescharacteristic
28C3×#4095C418yescomplemented
29C2×C3×#688C2212yes—
30C2×C3×#686C2212yes—
31C2×C3×#681C2211yescharacteristic
32C2×#6665—21no—
33#91434—21no—
34#91434—21no—
35#91434C2212yes—
36#91434C2212yes—
37C5×#835C2212yescomplemented
38C5×#832C2212yescomplemented
39#90988C2212yescomplemented
40#90985C2212yescomplemented
41#90965C2212yes—
42#90965C2212yes—
43#90954C2212yescomplemented
44#90951C2212yescomplemented
45Dic3×AGL(1,ℤ/8)—51nomaximal, Hall
46#41×Dic5—31no—
47C2×#4095D311yescharacteristic
48C2×#4039—31no—
49C5×#417—31no—
50#65420—31no—
51M16×Dic5—31no—
52#65253—31no—
53#65106—32no—
54#65077—32no—
55#65074—32no—
56#65045—32no—
57C23×C3×D5—21no—
58C3×C5×#41—22no—
59C3×C5×#41C2×C414yescomplemented
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15—21no—
66C22×Dic15—21no—
67C22×Dic15D411yescharacteristic
68C22×Dic15D411yescharacteristic
69C22×C5×Dic3—21no—
70C2×C3×D20—21no—
71C2×C3×D20—22no—
72C2×C3×D20C2×C414yescomplemented
73C2×C3×D20C2312yes—
74C2×D5×Dic3—22no—
75C2×D5×Dic3—22no—
76C2×D5×Dic3—44no—
77#6719—21no—
78#6719—21no—
79#6719—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15C2311yescharacteristic
83C4⋊Dic15C2311yescharacteristic
84C4×Dic15—21no—
85C4×Dic15—21no—
86C4×Dic15—21no—
87C4×Dic15D411yescharacteristic
88C4×Dic15D411yescharacteristic
89C4×Dic15C2311yescharacteristic
90C4×Dic15C2311yescharacteristic
91C5×C4⋊Dic3—21no—
92C5×C4⋊Dic3C2312yes—
93C5×#208—22no—
94C2×C5×C3⋊C8C2312yes—
95C3×#688C2×C418yescomplemented
96C3×#686C2×C418yescomplemented
97C3×#681C2×C414yescomplemented
98C2×C3×#168C2312yes—
99#6665—22no—
100#6665—22no—
101C2×C3×AGL(1,ℤ/8)—51no—
102Dic3×#41—51no—
103C2×D4×Dic3—51no—
104#5232D511yescharacteristic, complemented
105#5215—51no—
106#5164—52no—
107Dic3×SD16—52no—
108#5152—52no—
109Dic3×D8—52no—
110#5121—51no—
111Dic3×M16—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—61no—
115C2×C5×M16—31no—
116C2×C5×C4⋊C4—31no—
117#4095Dic318yescomplemented
118Q8×Dic5—31no—
119Q8×Dic5—31no—
120C2×#688C2×D312yes—
121D4×Dic5—31no—
122D4×Dic5—31no—
123D4×Dic5—61no—
124D4×Dic5—61no—
125C2×#686C2×D312yes—
126C2×#685—61no—
127#4072—31no—
128#4072—61no—
129C2×C4×Dic5—31no—
130C2×C4×Dic5—61no—
131C2×#681C2×D311yescharacteristic
132#4039—32no—
133#4039—32no—
134#4039—61no—
135#4039—61no—
136C5×#103—32no—
137C5×#102—32no—
138#3953—32no—
139#3953—32no—
140#3947—32no—
141C8×Dic5—32no—
142#3940—32no—
143#3939—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C3×C5×Q8—21no—
152C3×C5×Q8C22×C412yescomplemented
153C3×C5×D4—24no—
154C3×C5×D4—21no—
155C3×C5×D4C22×C412yescomplemented
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—24no—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5#4112yes—
161C2×C3×C4×C5C2411yescharacteristic
162C2×Dic15—22no—
163C2×Dic15—21no—
164C2×Dic15—21no—
165C2×Dic15—41no—
166C2×Dic15—42no—
167C2×Dic15—42no—
168C2×Dic15C2×D411yescharacteristic
169C2×Dic15C2×D411yescharacteristic
170C2×Dic15C2×D411yescharacteristic
171C2×Dic15C2×D411yescharacteristic
172C2×C5×Dic3—22no—
173C2×C5×Dic3—42no—
174C3×D20—24no—
175C3×D20—22no—
176C3×D20C22×C414yes—
177D5×Dic3—44no—
178D5×Dic3—44no—
179C3×#168C22×C414yescomplemented
180C5×C3⋊C8—22no—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×D4—51no—
183C23×Dic3—101no—
184C3×AGL(1,ℤ/8)—58no—
185C2×C3×SD16—52no—
186C2×C3×D8—52no—
187C2×C3×M16—51no—
188C2×#217—101no—
189Q8×Dic3—51no—
190Q8×Dic3—51no—
191D4×Dic3—51no—
192D4×Dic3—51no—
193D4×Dic3—52no—
194D4×Dic3—52no—
195D4×Dic3—101no—
196D4×Dic3—101no—
197D4×Dic3—101no—
198D4×Dic3—101no—
199#926—51no—
200#926—101no—
201C2×C4⋊Dic3C2×D511yescharacteristic
202C2×C4×Dic3—51no—
203C2×C4×Dic3—101no—
204C2×#208C2×D511yescharacteristic
205#835C2×D512yescomplemented
206#832—52no—
207#832—52no—
208#832C2×D512yescomplemented
209#818—52no—
210#817—52no—
211#815—52no—
212C8×Dic3—52no—
213C23×D5—21no—
214C5×#41—22no—
215C5×#41C2×Dic314yescomplemented
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4C22×D311yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—61no—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—31no—
223C22×Dic5—31no—
224C22×Dic5—61no—
225C22×Dic5—61no—
226C2×D20—21no—
227C2×D20—22no—
228C2×D20C2×Dic314yescomplemented
229C2×D20C22×D312yes—
230C2×C4×D5—62no—
231C2×C4×D5—62no—
232C2×C4×D5—124no—
233C5×M16—62no—
234C2×C5×C8—32no—
235C5×C4⋊C4—32no—
236C5×C4⋊C4—61no—
237C22⋊Dic5—61no—
238C22⋊Dic5—61no—
239C22⋊Dic5—61no—
240#688C2×Dic318yescomplemented
241#686C2×Dic318yescomplemented
242#685—62no—
243#685—62no—
244C4⋊Dic5—31no—
245C4⋊Dic5—31no—
246C4⋊Dic5—61no—
247C4⋊Dic5—61no—
248C4×Dic5—31no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—31no—
252C4×Dic5—61no—
253C4×Dic5—61no—
254C4×Dic5—61no—
255#681C2×Dic314yescomplemented
256C2×#168C22×D312yes—
257C2×AGL(1,ℤ/8)—51no—
258C4×#41—151no—
259C2×C4×D4—151no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
266#417—31no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5—22no—
271C22×C3×C5—41no—
272C22×C3×C5—41no—
273C22×C3×C5C4×D412yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C3×C4×C5—22no—
280C3×C4×C5C4×D412yes—
281C3×C4×C5C23×C411yescharacteristic
282C3×C4×C5C2×#4111yescharacteristic
283Dic15—21no—
284Dic15—21no—
285Dic15—21no—
286Dic15—41no—
287Dic15—41no—
288Dic15AGL(1,ℤ/8)12yescomplemented
289C5×Dic3—42no—
290C24×C3—101no—
291C3×#41—22no—
292C3×#41C4×D514yescomplemented
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—54no—
296C2×C3×D4—52no—
297C2×C3×D4—101no—
298C2×C3×D4—102no—
299C2×C3×D4C22×D511yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—21no—
303C22×Dic3—51no—
304C22×Dic3—51no—
305C22×Dic3—102no—
306C22×Dic3—102no—
307C22×Dic3—101no—
308C22×Dic3—101no—
309C22×Dic3—204no—
310C3×SD16—58no—
311C3×D8—58no—
312C3×M16—54no—
313C2×C3×C8—52no—
314#217—102no—
315#217—102no—
316#217—101no—
317#217—101no—
318#217—101no—
319C4⋊Dic3—21no—
320C4⋊Dic3—51no—
321C4⋊Dic3—51no—
322C4⋊Dic3—101no—
323C4⋊Dic3—101no—
324C4⋊Dic3C22×D512yes—
325C4×Dic3—51no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328C4×Dic3—51no—
329C4×Dic3—101no—
330C4×Dic3—101no—
331C4×Dic3—101no—
332#208—22no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—21no—
335C23×C5D3×D411yescharacteristic
336C22×D5—24no—
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—42no—
340C5×Q8—21no—
341C5×Q8C22×Dic312yescomplemented
342C5×D4—24no—
343C5×D4—21no—
344C5×D4C22×Dic312yescomplemented
345C2×C4×C5—21no—
346C2×C4×C5—24no—
347C2×C4×C5—62no—
348C2×C4×C5—122no—
349C2×C4×C5D3×D411yescharacteristic
350C2×C4×C5#23712yes—
351C2×C4×C5C22×Dic312yes—
352C2×C4×C5C23×D311yescharacteristic
353C2×Dic5—31no—
354C2×Dic5—31no—
355C2×Dic5—31no—
356C2×Dic5—31no—
357C2×Dic5—62no—
358C2×Dic5—61no—
359C2×Dic5—61no—
360C2×Dic5—122no—
361C2×Dic5—121no—
362C2×Dic5—122no—
363D20—24no—
364D20—22no—
365D20C22×Dic314yes—
366C4×D5—124no—
367C4×D5—124no—
368C5×C8—62no—
369#168C22×Dic314yescomplemented
370C2×#41D3×D511yescharacteristic
371C22×D4—51no—
372C23×C4—301no—
373AGL(1,ℤ/8)—58no—
374C2×SD16—52no—
375C2×D8—52no—
376C2×M16—31no—
377C2×M16—51no—
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—151no—
389#117—301no—
390C2×C4⋊C4—31no—
391C2×C22⋊C4—301no—
392C2×C42—151no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—32no—
397#102—32no—
398#102—152no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5—42no—
404C2×C3×C5C2×C4×D411yescharacteristic
405C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C3×C5#57511yescharacteristic
407C3×D5—44no—
408C23×C3—21no—
409C23×C3—102no—
410C23×C3—104no—
411C23×C3—202no—
412C23×C3—202no—
413C23×C3D4×D511yescharacteristic
414C3×Q8—21no—
415C3×Q8C2×C4×D512yescomplemented
416C3×D4—24no—
417C3×D4—21no—
418C3×D4—54no—
419C3×D4—102no—
420C3×D4—104no—
421C3×D4C2×C4×D512yescomplemented
422C2×C3×C4—21no—
423C2×C3×C4—24no—
424C2×C3×C4C2×C4×D512yes—
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4#71112yes—
427C2×C3×C4C23×D511yescharacteristic
428C2×Dic3—22no—
429C2×Dic3—42no—
430C2×Dic3—51no—
431C2×Dic3—51no—
432C2×Dic3—51no—
433C2×Dic3—51no—
434C2×Dic3—102no—
435C2×Dic3—101no—
436C2×Dic3—101no—
437C2×Dic3—204no—
438C2×Dic3—204no—
439C2×Dic3—202no—
440C2×Dic3—201no—
441C2×Dic3—202no—
442C3×C8—54no—
443C3⋊C8—22no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—22no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5D4×Dic312yes—
450C22×C5C2×D3×D411yescharacteristic
451C2×D5—24no—
452C2×D5—48no—
453C2×D5—42no—
454C2×D5—42no—
455C4×C5—22no—
456C4×C5—122no—
457C4×C5D4×Dic312yes—
458C4×C5C2×#23711yescharacteristic
459C4×C5C23×Dic311yescharacteristic
460Dic5—32no—
461Dic5—61no—
462Dic5—61no—
463Dic5—61no—
464Dic5—121no—
465Dic5—121no—
466C24—101no—
467#41—22no—
468#41D5×Dic314yescomplemented
469C2×Q8C2×D3×D511yescharacteristic
470C2×D4—21no—
471C2×D4—54no—
472C2×D4—52no—
473C2×D4—102no—
474C2×D4—101no—
475C2×D4C2×D3×D511yescharacteristic
476C22×C4—21no—
477C22×C4—61no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—302no—
481C22×C4—302no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—58no—
487D8—58no—
488M16—54no—
489M16—62no—
490C2×C8—32no—
491C2×C8—52no—
492C4⋊C4—32no—
493C4⋊C4—61no—
494C4⋊C4—151no—
495C4⋊C4—151no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—302no—
499C22⋊C4—302no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—151no—
504C42—151no—
505C42—151no—
506C42—151no—
507C42—301no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—104no—
517C22×C3—208no—
518C22×C3—202no—
519C22×C3—202no—
520C22×C3#402712yes—
521C22×C3C2×D4×D511yescharacteristic
522C3×C4—22no—
523C3×C4#402712yes—
524C3×C4C22×C4×D511yescharacteristic
525C3×C4C2×#71111yescharacteristic
526Dic3—42no—
527Dic3—52no—
528Dic3—101no—
529Dic3—101no—
530Dic3—101no—
531Dic3—201no—
532Dic3—201no—
533C2×C5—22no—
534C2×C5—42no—
535C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
536C2×C5#577311yescharacteristic
537C2×C5C2×D4×Dic311yescharacteristic
538D5—44no—
539C23—21no—
540C23—102no—
541C23—104no—
542C23—202no—
543C23—202no—
544C23#679011yescharacteristic
545Q8—21no—
546Q8C2×D5×Dic312yescomplemented
547D4—24no—
548D4—21no—
549D4—54no—
550D4—102no—
551D4—104no—
552D4C2×D5×Dic312yescomplemented
553C2×C4—21no—
554C2×C4—24no—
555C2×C4—62no—
556C2×C4—122no—
557C2×C4—151no—
558C2×C4—151no—
559C2×C4—151no—
560C2×C4—151no—
561C2×C4—302no—
562C2×C4—301no—
563C2×C4—301no—
564C2×C4—604no—
565C2×C4—604no—
566C2×C4—602no—
567C2×C4—601no—
568C2×C4—602no—
569C2×C4C2×D5×Dic312yes—
570C2×C4#678012yes—
571C2×C4#679011yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—54no—
574C8—62no—
575C2×C3—22no—
576C2×C3—42no—
577C2×C3—204no—
578C2×C3C2×#402711yescharacteristic
579C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
580C2×C3#6611111yescharacteristic
581C5Dic3×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—104no—
588C22—208no—
589C22—202no—
590C22—202no—
591C22#9155912yes—
592C22C2×#679011yescharacteristic
593C4—22no—
594C4—122no—
595C4—152no—
596C4—301no—
597C4—301no—
598C4—301no—
599C4—601no—
600C4—601no—
601C4#9155912yes—
602C4C22×D5×Dic311yescharacteristic
603C4C2×#678011yescharacteristic
604C3#1061059711yescharacteristic, complemented, Sylow
605C2—22no—
606C2—42no—
607C2—204no—
608C2#1175532711yescharacteristic
609C2#1175534911yescharacteristic
610C2C2×#9155911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4095C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×Dic15C2semidirect
3. C2×#91434C2semidirect
4. C5×#5232C2semidirect
5. #11749241C2semidirect
6. #11749239C2semidirect
7. #11748995C2semidirect
8. #11748993C2semidirect
9. #11748459C2semidirect
10. #11748367C2semidirect
11. #11748328C2semidirect
16. Q8×Dic15C22semidirect
17. Q8×Dic15C22semidirect
20. D4×Dic15C22semidirect
21. D4×Dic15C22semidirect
28. C3×#4095C4semidirect
37. C5×#835C22semidirect
38. C5×#832C22semidirect
39. #90988C22semidirect
40. #90985C22semidirect
43. #90954C22semidirect
44. #90951C22semidirect
59. C3×C5×#41C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
95. C3×#688C2×C4semidirect
96. C3×#686C2×C4semidirect
97. C3×#681C2×C4semidirect
104. #5232D5semidirect
117. #4095Dic3semidirect
152. C3×C5×Q8C22×C4semidirect
155. C3×C5×D4C22×C4semidirect
179. C3×#168C22×C4semidirect
205. #835C2×D5semidirect
208. #832C2×D5semidirect
215. C5×#41C2×Dic3semidirect
228. C2×D20C2×Dic3semidirect
240. #688C2×Dic3semidirect
241. #686C2×Dic3semidirect
255. #681C2×Dic3semidirect
288. Dic15AGL(1,ℤ/8)semidirect
292. C3×#41C4×D5semidirect
341. C5×Q8C22×Dic3semidirect
344. C5×D4C22×Dic3semidirect
369. #168C22×Dic3semidirect
415. C3×Q8C2×C4×D5semidirect
421. C3×D4C2×C4×D5semidirect
468. #41D5×Dic3semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
546. Q8C2×D5×Dic3semidirect
552. D4C2×D5×Dic3semidirect
581. C5Dic3×AGL(1,ℤ/8)semidirect
604. C3#10610597semidirect

Maximal subgroups

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

subgroupindex
#41×Dic152
C2×C3×#40952
C2×#914342
C5×#52322
#117492412
#117492392
#117489952
#117489932
#117484592
#117483672
#117483282
#106105973
Dic3×AGL(1,ℤ/8)5