Finite Group Databasebeta

← #14416721

Subgroups — #14416721

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#11756281C211yesmaximal, characteristic, complemented
2C2×#91434C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic
4C5×#4995C211yesmaximal, characteristic, complemented
5C3×#65290C211yesmaximal, characteristic, complemented
6#11748394C211yesmaximal, characteristic, complemented
7#11748328C211yesmaximal, characteristic, complemented
8#11747229C212yesmaximal, complemented
9#11747228C212yesmaximal, complemented
10#11747227C212yesmaximal, complemented
11#11747226C212yesmaximal, complemented
12#10610930—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×D5×Dic3—21no—
16C3×C5×#117C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18#91782C2211yescharacteristic, complemented
19#91782C2211yescharacteristic, complemented
20#91776C2211yescharacteristic, complemented
21#91776C2211yescharacteristic, complemented
22#91770—21no—
23#91770—21no—
24#91761—21no—
25C42×D15—21no—
26C2×C5×C4⋊Dic3C2211yescharacteristic
27C2×C5×#208C2211yescharacteristic
28C2×C3×#681C2211yescharacteristic
29C2×#6665—21no—
30#91434—21no—
31#91434—21no—
32#91434C2212yes—
33#91434C2212yes—
34#91312C418yescomplemented
35C2×#6657C2212yes—
36C2×#6653C2212yes—
37C5×#808C2212yescomplemented
38C5×#807C2212yescomplemented
39C3×#3941C2212yes—
40C3×#3941C2212yes—
41#90975C2212yescomplemented
42#90969C2212yescomplemented
43#90954C2212yescomplemented
44#90951C2212yescomplemented
45#78914—51nomaximal, Hall
46C2×#4054—31no—
47#65856—31no—
48C2×#4039—31no—
49C5×#428—31no—
50M16×Dic5—31no—
51#65290D311yescharacteristic, complemented
52#65255—31no—
53#65178—32no—
54#65161—32no—
55#65158—32no—
56#65141—32no—
57C23×C3×D5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C22×Dic15D411yescharacteristic
61C22×Dic15D411yescharacteristic
62#6817—22no—
63#6817C2×C414yescomplemented
64C2×D60C2311yescharacteristic
65C2×C4×D15—21no—
66C2×C4×D15—21no—
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
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—
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C4⋊C4C2311yescharacteristic
79C3×C5×C22⋊C4—21no—
80C3×C42×C5—21no—
81#6714—21no—
82#6714—21no—
83#6712—21no—
84#6712—21no—
85C4×Dic15—21no—
86C4×Dic15—21no—
87C4×Dic15D411yescharacteristic
88C4×Dic15D411yescharacteristic
89C4×Dic15C2311yescharacteristic
90C4×Dic15C2311yescharacteristic
91C5×C4⋊Dic3—21no—
92C5×C4⋊Dic3C2312yes—
93C5×#208C2×C414yescomplemented
94C2×C5×C3⋊C8C2312yes—
95C3×#681—22no—
96C2×C3×#168C2312yes—
97#6665—22no—
98#6665—22no—
99#6657C2×C418yescomplemented
100#6653C2×C418yescomplemented
101C2×D4×Dic3—51no—
102C2×#932—51no—
103#5522—51no—
104C3×#418—51no—
105#5133—51no—
106Dic3×M16—51no—
107#4995D511yescharacteristic, complemented
108#4785—52no—
109#4758—52no—
110#4757—52no—
111#4756—52no—
112C2×#709—31no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—61no—
115C2×C5×M16—31no—
116C5×#117C2×D311yescharacteristic
117C2×C5×C4⋊C4—31no—
118C2×#685—61no—
119C2×C4×Dic5—31no—
120C2×#681C2×D311yescharacteristic
121#4054—38no—
122C2×D40—32no—
123C2×#677—32no—
124#4039—32no—
125#4039—32no—
126#4039—31no—
127#4039—31no—
128#4039—61no—
129#4039—61no—
130#4033—31no—
131#4033—31no—
132#4027—61no—
133#4027—61no—
134#4018—61no—
135C42×D5—61no—
136C5×#107—32no—
137C5×#106—32no—
138#3947—32no—
139C8×Dic5—32no—
140#3942—32no—
141#3941—32no—
142#3941C2×D312yes—
143#3941C2×D312yes—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
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—41no—
161C2×Dic15C2×D411yescharacteristic
162C2×Dic15C2×D411yescharacteristic
163C2×Dic15C2×D411yescharacteristic
164C2×Dic15C2×D411yescharacteristic
165D60—21no—
166D60C22×C412yescomplemented
167C4×D15—24no—
168C4×D15—42no—
169C4×D15—42no—
170Dic30—21no—
171Dic30C22×C412yescomplemented
172C2×C5×Dic3—22no—
173C2×C5×Dic3—42no—
174C3×D20—24no—
175C3×D20—22no—
176C3×D20C22×C414yes—
177D5×Dic3—44no—
178D5×Dic3—44no—
179C3×#168—22no—
180C5×C3⋊C8C22×C414yescomplemented
181C22×C3×D4—51no—
182C23×Dic3—101no—
183C2×#235—51no—
184C2×C3×M16—51no—
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⋊Dic3C2×D511yescharacteristic
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#808C2×D512yescomplemented
212#807C2×D512yescomplemented
213C23×D5—21no—
214C22×C4×C5—61no—
215C22×C4×C5C22×D311yescharacteristic
216C2×C22⋊D5—61no—
217C22×Dic5—31no—
218C22×Dic5—31no—
219#709—34no—
220#709—62no—
221C2×D20—21no—
222C2×D20—22no—
223C2×D20—31no—
224C2×D20C4×D314yescomplemented
225C2×D20C22×D312yes—
226C2×C4×D5—61no—
227C2×C4×D5—61no—
228C2×C4×D5—61no—
229C2×C4×D5—62no—
230C2×C4×D5—62no—
231C2×C4×D5—124no—
232C2×Dic10—31no—
233C5×M16—34no—
234C2×C5×C8—32no—
235C5×C4⋊C4—32no—
236C5×C4⋊C4—61no—
237C5×C4⋊C4C22×D311yescharacteristic
238C5×C4⋊C4C22×D311yescharacteristic
239C5×C22⋊C4—21no—
240C42×C5—21no—
241#685—61no—
242#685—61no—
243#685—62no—
244#685—62no—
245#683—61no—
246#683—61no—
247C4×Dic5—31no—
248C4×Dic5—31no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—61no—
252C4×Dic5—61no—
253#681—22no—
254C2×#168C22×D312yes—
255D40—38no—
256#677—38no—
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—31no—
265#418—51no—
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—22no—
273C2×D15—41no—
274C2×D15—41no—
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
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—
288Dic15AGL(1,ℤ/8)12yescomplemented
289C5×Dic3—42no—
290C24×C3—101no—
291C2×C3×D4—54no—
292C2×C3×D4—52no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C22×C3×C4C22×D511yescharacteristic
296C2×#67—101no—
297C22×Dic3—21no—
298C22×Dic3—51no—
299C22×Dic3—51no—
300C22×Dic3—102no—
301C22×Dic3—102no—
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—102no—
311C2×C3×C8—52no—
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—21no—
323C4⋊Dic3C22×D512yes—
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#208C4×D514yescomplemented
333C2×C3⋊C8C22×D512yes—
334C23×C5D3×D411yescharacteristic
335C22×D5—24no—
336C22×D5—22no—
337C22×D5—42no—
338C22×D5—42no—
339C22×D5—61no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—62no—
343C2×C4×C5—122no—
344C2×C4×C5C2×C4×D312yes—
345C2×C4×C5D3×D411yescharacteristic
346C2×C4×C5#23712yes—
347C2×C4×C5C23×D311yescharacteristic
348C22⋊D5—64no—
349C2×Dic5—31no—
350C2×Dic5—31no—
351C2×Dic5—31no—
352C2×Dic5—31no—
353C2×Dic5—62no—
354C2×Dic5—61no—
355C2×Dic5—121no—
356D20—24no—
357D20—22no—
358D20—32no—
359D20—61no—
360D20C2×C4×D314yes—
361C4×D5—64no—
362C4×D5—122no—
363C4×D5—124no—
364C4×D5—122no—
365C4×D5—124no—
366Dic10—32no—
367Dic10—61no—
368C5×C8—34no—
369#168—22no—
370C2×#41—151no—
371C22×D4—51no—
372C23×C4—301no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
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—301no—
389#117D3×D511yescharacteristic
390C2×C4⋊C4—31no—
391C2×C22⋊C4—301no—
392C2×C42—151no—
393C2×C42—301no—
394#107—32no—
395#106—32no—
396#103—152no—
397#102—52no—
398#102—52no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C3×C5#57511yescharacteristic
406D15—42no—
407C3×D5—44no—
408C23×C3—102no—
409C23×C3—104no—
410C23×C3—202no—
411C23×C3—202no—
412C23×C3D4×D511yescharacteristic
413C22×D3—101no—
414C3×D4—54no—
415C3×D4—102no—
416C3×D4—104no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4D4×D511yescharacteristic
421C2×C3×C4#71312yes—
422C2×C3×C4C23×D511yescharacteristic
423#67—104no—
424C2×Dic3—22no—
425C2×Dic3—42no—
426C2×Dic3—51no—
427C2×Dic3—51no—
428C2×Dic3—51no—
429C2×Dic3—51no—
430C2×Dic3—102no—
431C2×Dic3—101no—
432C2×Dic3—204no—
433C2×Dic3—204no—
434C2×Dic3—201no—
435D12—52no—
436D12—101no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3×C8—102no—
443C3⋊C8C2×C4×D514yescomplemented
444C22×C5—21no—
445C22×C5—21no—
446C22×C5#67⋊C412yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—24no—
449C2×D5—48no—
450C2×D5—42no—
451C2×D5—42no—
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5—122no—
458C4×C5#67⋊C412yes—
459C4×C5C22×C4×D311yescharacteristic
460C4×C5C2×#23711yescharacteristic
461Dic5—32no—
462Dic5—62no—
463Dic5—61no—
464Dic5—61no—
465Dic5—61no—
466C24—101no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—54no—
471C2×D4—52no—
472C2×D4—102no—
473C2×D4—101no—
474C2×D4—151no—
475C2×D4—301no—
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—158no—
487D8—158no—
488M16—34no—
489M16—102no—
490C2×C8—32no—
491C2×C8—52no—
492C4⋊C4—32no—
493C4⋊C4—61no—
494C4⋊C4—301no—
495C4⋊C4—301no—
496C4⋊C4C2×D3×D511yescharacteristic
497C4⋊C4C2×D3×D511yescharacteristic
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—104no—
514C22×C3—208no—
515C22×C3—202no—
516C22×C3—202no—
517C22×C3#403912yes—
518C22×C3C2×D4×D511yescharacteristic
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4#403912yes—
525C3×C4C22×C4×D511yescharacteristic
526C3×C4C2×#71311yescharacteristic
527Dic3—42no—
528Dic3—52no—
529Dic3—102no—
530Dic3—101no—
531Dic3—101no—
532Dic3—101no—
533C2×C5—22no—
534C2×C5C2×#67⋊C411yescharacteristic
535C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
536C2×C5#577311yescharacteristic
537D5—44no—
538D5—122no—
539C23—104no—
540C23—102no—
541C23—202no—
542C23—202no—
543C23—301no—
544C23#679011yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—54no—
548D4—104no—
549D4—102no—
550D4—152no—
551D4—304no—
552D4—301no—
553C2×C4—21no—
554C2×C4—21no—
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—304no—
564C2×C4—602no—
565C2×C4—602no—
566C2×C4—604no—
567C2×C4—604no—
568C2×C4—601no—
569C2×C4#676612yes—
570C2×C4C4×D3×D512yes—
571C2×C4#679011yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—34no—
574C8—102no—
575C2×C3—22no—
576C2×C3—204no—
577C2×C3C2×#403911yescharacteristic
578C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#6611111yescharacteristic
580D3—202no—
581C5#7891411yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—104no—
585C22—208no—
586C22—202no—
587C22—202no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9139612yes—
592C22C2×#679011yescharacteristic
593C4—41no—
594C4—41no—
595C4—122no—
596C4—152no—
597C4—302no—
598C4—301no—
599C4—301no—
600C4—301no—
601C4#9139612yes—
602C4C2×#676611yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3#1061093011yescharacteristic, complemented, Sylow
605C2—22no—
606C2—204no—
607C2—602no—
608C2C2×#9139611yescharacteristic
609C2#1175532711yescharacteristic
610C2#1175534911yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91312C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756281C2semidirect
2. C2×#91434C2semidirect
4. C5×#4995C2semidirect
5. C3×#65290C2semidirect
6. #11748394C2semidirect
7. #11748328C2semidirect
8. #11747229C2semidirect
9. #11747228C2semidirect
10. #11747227C2semidirect
11. #11747226C2semidirect
18. #91782C22semidirect
19. #91782C22semidirect
20. #91776C22semidirect
21. #91776C22semidirect
34. #91312C4semidirect
37. C5×#808C22semidirect
38. C5×#807C22semidirect
41. #90975C22semidirect
42. #90969C22semidirect
43. #90954C22semidirect
44. #90951C22semidirect
51. #65290D3semidirect
63. #6817C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
93. C5×#208C2×C4semidirect
99. #6657C2×C4semidirect
100. #6653C2×C4semidirect
107. #4995D5semidirect
166. D60C22×C4semidirect
171. Dic30C22×C4semidirect
180. C5×C3⋊C8C22×C4semidirect
211. #808C2×D5semidirect
212. #807C2×D5semidirect
224. C2×D20C4×D3semidirect
288. Dic15AGL(1,ℤ/8)semidirect
332. #208C4×D5semidirect
443. C3⋊C8C2×C4×D5semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5#78914semidirect
604. C3#10610930semidirect

Maximal subgroups

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

subgroupindex
#117562812
C2×#914342
C2×#913122
C5×#49952
C3×#652902
#117483942
#117483282
#117472292
#117472282
#117472272
#117472262
#106109303
#789145