Finite Group Databasebeta

← #14416749

Subgroups — #14416749

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×#893C211yesmaximal, characteristic, complemented
2#11754436C211yesmaximal, characteristic, complemented
3C2×#91304C211yesmaximal, characteristic
4#11751067C211yesmaximal, characteristic, complemented
5C3×#65253C211yesmaximal, characteristic, complemented
6#11748386C211yesmaximal, characteristic, complemented
7Dic3×#681C211yesmaximal, characteristic, complemented
8#11747473C212yesmaximal, complemented
9#11747470C212yesmaximal, complemented
10#11747277C212yesmaximal, complemented
11#11747230C212yesmaximal, complemented
12C4×#4078—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C22×C4×C5×D3—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×#6710C2211yescharacteristic
18C2×C5×(C2×D3)⋊C4—21no—
19C2×C4×C5×Dic3C2211yescharacteristic
20C5×#893—21no—
21C5×#893—21no—
22C5×#893C2212yes—
23C5×#893C2212yes—
24C3×#4072C2211yescharacteristic
25C2×C3×#681C2211yescharacteristic
26#91556—21no—
27#91556—21no—
28#91428C2211yescharacteristic, complemented
29#91428C2211yescharacteristic, complemented
30C4×#1200—21no—
31#91386—21no—
32#91340C2211yescharacteristic, complemented
33#91340C2211yescharacteristic, complemented
34C2×#6659C2212yes—
35#91304C418yescomplemented
36C2×#6654C2212yes—
37#91094C2212yescomplemented
38#91093C2212yescomplemented
39C3×#3940C2212yescomplemented
40C3×#3939C2212yescomplemented
41#90966C2212yes—
42#90966C2212yes—
43#90953C2212yescomplemented
44Dic3×#168C2212yescomplemented
45#79199—51nomaximal, Hall
46C2×C4×C5×D4—31no—
47C2×#4078—31no—
48C4×#709—31no—
49#65504—31no—
50#65307—32no—
51C4×#687—32no—
52#65303—32no—
53C4×#686—32no—
54#65255—31no—
55#65253D311yescharacteristic, complemented
56C4×#681—31no—
57C23×C5×D3—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—21no—
61#6817—22no—
62#6817C2×C414yescomplemented
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×Dic30C2311yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C22×C5×Dic3D411yescharacteristic
68C2×C5×D12—21no—
69C2×C5×D12—22no—
70C2×C5×D12C2×C414yescomplemented
71C2×C5×D12C2312yes—
72C2×C4×C5×D3—22no—
73C2×C4×C5×D3—22no—
74C2×C4×C5×D3—44no—
75C2×#1200—21no—
76C2×#1200—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6710—22no—
80C2×C3⋊#168C2312yes—
81C5×(C2×D3)⋊C4—22no—
82C5×(C2×D3)⋊C4—22no—
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3D411yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C4×C5×Dic3C2311yescharacteristic
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2311yescharacteristic
89C3×C4⋊Dic5C2311yescharacteristic
90C3×C4×Dic5—21no—
91C3×#681C2×C414yescomplemented
92C2×C3×#168C2312yes—
93#6669—21no—
94#6669—21no—
95#6667—21no—
96#6667—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6659C2×C418yescomplemented
100#6654C2×C418yescomplemented
101C2×#908—51no—
102#5522—51no—
103C2×#893D511yescharacteristic, complemented
104C3×#428—51no—
105Dic3×M16—51no—
106#5001—51no—
107#4966—51no—
108#4889—52no—
109#4872—52no—
110#4869—52no—
111#4852—52no—
112C22×C5×D4—31no—
113C23×C4×C5—61no—
114C2×#709—31no—
115C4×C5×D4—32no—
116C4×C5×D4—32no—
117C4×C5×D4—61no—
118C4×C5×D4—61no—
119C2×C5×C4⋊C4C2×D311yescharacteristic
120C2×C5×C22⋊C4—61no—
121C2×C42×C5—31no—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C4×C22⋊D5—61no—
126C4×C22⋊D5—61no—
127#4072C2×D311yescharacteristic
128C2×#681—31no—
129C2×#681C2×D311yescharacteristic
130C4×D20—31no—
131C4×D20—31no—
132#4018—61no—
133C42×D5—61no—
134C4×Dic10—31no—
135C4×Dic10—31no—
136#3964—32no—
137#3964—32no—
138#3942—32no—
139#3941—32no—
140#3940C2×D312yescomplemented
141#3939C2×D312yescomplemented
142#3935—32no—
143C4×#168—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—21no—
147C22×C5×D3—24no—
148C22×C5×D3—22no—
149C22×C5×D3—42no—
150C22×C5×D3—42no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—42no—
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—
159D60—21no—
160D60C22×C412yescomplemented
161C4×D15—24no—
162Dic30—21no—
163Dic30C22×C412yescomplemented
164C2×C5×Dic3—22no—
165C2×C5×Dic3—41no—
166C2×C5×Dic3C2×D411yescharacteristic
167C2×C5×Dic3C2×D411yescharacteristic
168C2×C5×Dic3C2×D411yescharacteristic
169C2×C5×Dic3C2×D411yescharacteristic
170C5×D12—24no—
171C5×D12—22no—
172C5×D12C22×C414yes—
173C4×C5×D3—44no—
174C4×C5×D3—44no—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177#1200—42no—
178#1200—42no—
179C3⋊#168—22no—
180C3×#168C22×C414yescomplemented
181C2×#235—51no—
182C22×D12C2×D511yescharacteristic
183C22×C4×D3—21no—
184C2×C3×M16—51no—
185C3×#117—51no—
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×(C2×D3)⋊C4—21no—
188C2×C4×Dic3C2×D511yescharacteristic
189C2×#208—51no—
190#908—58no—
191C2×D24—52no—
192C2×#204—52no—
193#893—21no—
194#893—21no—
195#893—51no—
196#893—51no—
197#893C2×D512yes—
198#893C2×D512yes—
199#887—51no—
200#887—51no—
201#67⋊C4—101no—
202#67⋊C4—101no—
203#872—101no—
204C42×D3—101no—
205C3×#107—52no—
206C3×#106—52no—
207#815—52no—
208C8×Dic3—52no—
209#810—52no—
210#809—52no—
211#809—52no—
212#809—52no—
213C24×C5—61no—
214C2×C5×D4—34no—
215C2×C5×D4—32no—
216C2×C5×D4—61no—
217C2×C5×D4—62no—
218C22×C4×C5—21no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5—62no—
222C22×C4×C5—62no—
223C22×C4×C5—124no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
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×C4⋊C4—21no—
234C5×C4⋊C4C22×D312yes—
235C5×C22⋊C4—62no—
236C5×C22⋊C4—62no—
237C42×C5—31no—
238C42×C5—31no—
239C42×C5—31no—
240C42×C5—31no—
241C22⋊Dic5—21no—
242#687—38no—
243#686—38no—
244#685—61no—
245#685—61no—
246C4⋊Dic5C22×D311yescharacteristic
247C4⋊Dic5C22×D311yescharacteristic
248#683—61no—
249#683—61no—
250C4×Dic5—21no—
251C4×Dic5—61no—
252C4×Dic5—61no—
253#681—62no—
254#681C4×D314yescomplemented
255C2×#168—32no—
256C2×#168C22×D312yes—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—31no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—51no—
265#418—151no—
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×C5×D3—24no—
276C2×C5×D3—48no—
277C2×C5×D3—42no—
278C2×C5×D3—42no—
279C3×C4×C5—42no—
280C3×C4×C5C4×D412yes—
281C3×C4×C5C23×C411yescharacteristic
282C3×C4×C5C2×#4111yescharacteristic
283Dic15—22no—
284C3×Dic5—41no—
285C3×Dic5—41no—
286C5×Dic3—21no—
287C5×Dic3—21no—
288C5×Dic3—21no—
289C5×Dic3AGL(1,ℤ/8)12yescomplemented
290C23×D3—21no—
291C22×C3×C4—21no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—101no—
294C22×Dic3C22⋊D511yescharacteristic
295C22×Dic3C22⋊D511yescharacteristic
296#235—54no—
297#235—102no—
298C2×D12—22no—
299C2×D12—21no—
300C2×D12—51no—
301C2×D12C4×D514yescomplemented
302C2×D12C22×D512yes—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—44no—
306C2×C4×D3—101no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6—51no—
310C3×M16—54no—
311C2×C3×C8—52no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—51no—
314C3×C4⋊C4—51no—
315C3×C4⋊C4C22×D512yes—
316C3×C22⋊C4—101no—
317C3×C42—101no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—101no—
321(C2×D3)⋊C4—101no—
322Dic3⋊C4—101no—
323Dic3⋊C4—101no—
324C4×Dic3—101no—
325C4×Dic3—101no—
326C4×Dic3C22⋊D511yescharacteristic
327C4×Dic3C22⋊D511yescharacteristic
328C4×Dic3C22×D511yescharacteristic
329C4×Dic3C22×D511yescharacteristic
330#208—102no—
331C2×C3⋊C8—52no—
332D24—58no—
333#204—58no—
334C23×C5—64no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—122no—
338C23×C5D3×D411yescharacteristic
339C22×D5—61no—
340C5×D4—34no—
341C5×D4—64no—
342C5×D4—62no—
343C2×C4×C5—22no—
344C2×C4×C5—31no—
345C2×C4×C5—31no—
346C2×C4×C5—31no—
347C2×C4×C5—31no—
348C2×C4×C5—42no—
349C2×C4×C5—62no—
350C2×C4×C5—124no—
351C2×C4×C5—124no—
352C2×C4×C5—121no—
353C2×C4×C5C2×C4×D312yes—
354C2×C4×C5D3×D411yescharacteristic
355C2×C4×C5#23912yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—64no—
358C2×Dic5—21no—
359C2×Dic5—21no—
360C2×Dic5—61no—
361D20—32no—
362D20—61no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368#168—62no—
369#168C2×C4×D314yescomplemented
370C2×#41—151no—
371C22×D4—31no—
372C23×C4—61no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—51no—
377C2×M16—151no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—32no—
381C4×D4—32no—
382C4×D4—61no—
383C4×D4—61no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—51no—
389#117—301no—
390C2×C4⋊C4D3×D511yescharacteristic
391C2×C22⋊C4—61no—
392C2×C42—31no—
393C2×C42—301no—
394#107—52no—
395#106—52no—
396#103—152no—
397#102—152no—
398#102—152no—
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—
407C5×D3—44no—
408C23×C3C2×C22⋊D511yescharacteristic
409C22×D3—22no—
410C22×D3—24no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—101no—
414C2×C3×C4—22no—
415C2×C3×C4—42no—
416C2×C3×C4—101no—
417C2×C3×C4—101no—
418C2×C3×C4C2×C4×D512yes—
419C2×C3×C4#70912yes—
420C2×C3×C4C2×C22⋊D511yescharacteristic
421C2×C3×C4C23×D511yescharacteristic
422#67—104no—
423C2×Dic3—22no—
424C2×Dic3—41no—
425C2×Dic3—101no—
426C2×Dic3C2×C22⋊D511yescharacteristic
427C2×Dic3C2×C22⋊D511yescharacteristic
428C2×Dic3C2×C22⋊D511yescharacteristic
429C2×Dic3C2×C22⋊D511yescharacteristic
430D12—22no—
431D12—24no—
432D12—52no—
433D12—101no—
434D12C2×C4×D514yes—
435C4×D3—44no—
436C4×D3—44no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3×C8—54no—
443C3⋊C8—102no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5#89312yes—
451C22×C5C2×D3×D411yescharacteristic
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—32no—
456C4×C5—42no—
457C4×C5—61no—
458C4×C5—61no—
459C4×C5—61no—
460C4×C5#89312yes—
461C4×C5C22×C4×D311yescharacteristic
462C4×C5C2×#23911yescharacteristic
463Dic5—41no—
464Dic5—41no—
465Dic5—62no—
466C24—61no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4—62no—
473C2×D4—61no—
474C2×D4—151no—
475C2×D4—301no—
476C22×C4—21no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—124no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—54no—
489M16—302no—
490C2×C8—52no—
491C2×C8—152no—
492C4⋊C4—21no—
493C4⋊C4—51no—
494C4⋊C4—51no—
495C4⋊C4—301no—
496C4⋊C4—301no—
497C4⋊C4C2×D3×D512yes—
498C22⋊C4—62no—
499C22⋊C4—62no—
500C22⋊C4—101no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—31no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—101no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3C4×C22⋊D512yes—
514C22×C3C22×C22⋊D511yescharacteristic
515C2×D3—24no—
516C2×D3—48no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—42no—
523C3×C4—201no—
524C3×C4—201no—
525C3×C4C4×C22⋊D512yes—
526C3×C4C22×C4×D511yescharacteristic
527C3×C4C2×#70911yescharacteristic
528Dic3—21no—
529Dic3—21no—
530Dic3—21no—
531Dic3—102no—
532Dic3#407812yescomplemented
533C2×C5—22no—
534C2×C5—124no—
535C2×C5C2×#89311yescharacteristic
536C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
537C2×C5#577711yescharacteristic
538D5—122no—
539C23—64no—
540C23—62no—
541C23—122no—
542C23—122no—
543C23—301no—
544C23D3×C22⋊D511yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—34no—
548D4—64no—
549D4—62no—
550D4—152no—
551D4—304no—
552D4—301no—
553C2×C4—22no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—42no—
559C2×C4—62no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—124no—
563C2×C4—124no—
564C2×C4—121no—
565C2×C4—301no—
566C2×C4—304no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4#676912yes—
570C2×C4C4×D3×D512yes—
571C2×C4D3×C22⋊D511yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—54no—
574C8—302no—
575C2×C3—22no—
576C2×C3C2×C4×C22⋊D511yescharacteristic
577C2×C3C2×#407811yescharacteristic
578C2×C3#6615611yescharacteristic
579D3—44no—
580D3—202no—
581C5#7919911yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—64no—
585C22—128no—
586C22—122no—
587C22—122no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9144612yes—
592C22C2×D3×C22⋊D511yescharacteristic
593C4—32no—
594C4—42no—
595C4—61no—
596C4—61no—
597C4—61no—
598C4—201no—
599C4—201no—
600C4—302no—
601C4#9144612yes—
602C4C2×#676911yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3C4×#407811yescharacteristic, complemented, Sylow
605C2—22no—
606C2—124no—
607C2—602no—
608C2C2×#9144611yescharacteristic
609C2D3×#407811yescharacteristic
610C2#1175509011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91304C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#893C2semidirect
2. #11754436C2semidirect
4. #11751067C2semidirect
5. C3×#65253C2semidirect
6. #11748386C2semidirect
7. Dic3×#681C2semidirect
8. #11747473C2semidirect
9. #11747470C2semidirect
10. #11747277C2semidirect
11. #11747230C2semidirect
28. #91428C22semidirect
29. #91428C22semidirect
32. #91340C22semidirect
33. #91340C22semidirect
35. #91304C4semidirect
37. #91094C22semidirect
38. #91093C22semidirect
39. C3×#3940C22semidirect
40. C3×#3939C22semidirect
43. #90953C22semidirect
44. Dic3×#168C22semidirect
55. #65253D3semidirect
62. #6817C2×C4semidirect
70. C2×C5×D12C2×C4semidirect
91. C3×#681C2×C4semidirect
99. #6659C2×C4semidirect
100. #6654C2×C4semidirect
103. C2×#893D5semidirect
140. #3940C2×D3semidirect
141. #3939C2×D3semidirect
160. D60C22×C4semidirect
163. Dic30C22×C4semidirect
180. C3×#168C22×C4semidirect
254. #681C4×D3semidirect
289. C5×Dic3AGL(1,ℤ/8)semidirect
301. C2×D12C4×D5semidirect
369. #168C2×C4×D3semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
532. Dic3#4078semidirect
581. C5#79199semidirect
604. C3C4×#4078semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
#117544362
C2×#913042
#117510672
C3×#652532
#117483862
Dic3×#6812
#117474732
#117474702
#117472772
#117472302
C4×#40783
#791995