Finite Group Databasebeta

← #14416750

Subgroups — #14416750

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
2Dic3×#709C211yesmaximal, characteristic, complemented
3C2×#91299C211yesmaximal, characteristic
4#11751065C211yesmaximal, characteristic, complemented
5C3×#65255C211yesmaximal, characteristic, complemented
6#11748389C211yesmaximal, characteristic, complemented
7Dic3×#681C211yesmaximal, characteristic, complemented
8#11747265C212yesmaximal, complemented
9#11747264C212yesmaximal, complemented
10#11747220C212yesmaximal, complemented
11#11747219C212yesmaximal, complemented
12C4×#4078—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3—21no—
15C2×C3×#709C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91815C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4—21no—
20C2×C4×C5×Dic3C2211yescharacteristic
21C5×#893—21no—
22C5×#893—21no—
23C5×#893C2212yes—
24C5×#893C2212yes—
25C2×C3×#681C2211yescharacteristic
26Dic3×C22⋊D5—21no—
27Dic3×C22⋊D5—21no—
28Dic3×D20C2211yescharacteristic, complemented
29Dic3×D20C2211yescharacteristic, complemented
30C4×D5×Dic3—21no—
31#91357—21no—
32Dic3×Dic10C2211yescharacteristic, complemented
33Dic3×Dic10C2211yescharacteristic, complemented
34C2×#6656C2212yes—
35#91299C418yescomplemented
36C2×#6652C2212yes—
37#91092C2212yescomplemented
38#91091C2212yescomplemented
39C3×#3942C2212yescomplemented
40C3×#3941C2212yescomplemented
41#90967C2212yes—
42#90967C2212yes—
43#90953C2212yescomplemented
44Dic3×#168C2212yescomplemented
45#78866—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#65255D311yescharacteristic, complemented
55#65253—31no—
56C4×#681—31no—
57C23×C5×D3—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×C5×Dic3D411yescharacteristic
61C22×C5×Dic3D411yescharacteristic
62C2×C5×D12—21no—
63C2×C5×D12—22no—
64C2×C5×D12C2×C414yescomplemented
65C2×C5×D12C2312yes—
66C2×C4×C5×D3—22no—
67C2×C4×C5×D3—22no—
68C2×C4×C5×D3—44no—
69C2×C3×C22⋊D5—21no—
70C3×#709—22no—
71C3×#709C2×C414yescomplemented
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10C2311yescharacteristic
75C2×D5×Dic3—21no—
76C2×D5×Dic3—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6719—21no—
80C4⋊Dic15C2311yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82C4×Dic15—21no—
83#6710C2×C414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×(C2×D3)⋊C4—22no—
86C5×(C2×D3)⋊C4—22no—
87C4×C5×Dic3D411yescharacteristic
88C4×C5×Dic3D411yescharacteristic
89C4×C5×Dic3C2311yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C3×#681—22no—
92C2×C3×#168C2312yes—
93#6668—21no—
94#6668—21no—
95#6665—21no—
96#6665—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6656C2×C418yescomplemented
100#6652C2×C418yescomplemented
101Dic3×#41—51no—
102C2×#949—51no—
103C2×#893D511yescharacteristic, complemented
104C3×#417—51no—
105#5131—51no—
106Dic3×M16—51no—
107#4964—51no—
108#4817—52no—
109#4788—52no—
110#4785—52no—
111#4756—52no—
112C22×C5×D4—31no—
113C23×C4×C5—61no—
114C2×#709C2×D311yescharacteristic
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#4072—31no—
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#3942C2×D312yescomplemented
139#3941C2×D312yescomplemented
140#3940—32no—
141#3939—32no—
142#3935—32no—
143C4×#168—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—24no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—42no—
150C22×C3×D5—21no—
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
157C2×Dic15—21no—
158C2×Dic15—21no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—41no—
161C2×C5×Dic3C2×D411yescharacteristic
162C2×C5×Dic3C2×D411yescharacteristic
163C2×C5×Dic3C2×D411yescharacteristic
164C2×C5×Dic3C2×D411yescharacteristic
165C5×D12—24no—
166C5×D12—22no—
167C5×D12C22×C414yes—
168C4×C5×D3—44no—
169C4×C5×D3—44no—
170C3×C22⋊D5—24no—
171C2×C3×Dic5—21no—
172C3×D20—21no—
173C3×D20C22×C412yescomplemented
174C3×C4×D5—24no—
175C3×Dic10—21no—
176C3×Dic10C22×C412yescomplemented
177D5×Dic3—42no—
178D5×Dic3—42no—
179C3⋊#168C22×C414yescomplemented
180C3×#168—22no—
181C2×C3×#41—51no—
182C22×D12C2×D511yescharacteristic
183C22×C4×D3—21no—
184C2×C3×M16—51no—
185C2×C3×C4⋊C4C2×D511yescharacteristic
186#949—58no—
187Q8×Dic3—51no—
188Q8×Dic3—51no—
189C2×#215—52no—
190D4×Dic3—51no—
191D4×Dic3—51no—
192D4×Dic3—101no—
193D4×Dic3—101no—
194C2×#213—52no—
195C2×(C2×D3)⋊C4—21no—
196#926—51no—
197#926—101no—
198C2×C4×Dic3—101no—
199C2×C4×Dic3C2×D511yescharacteristic
200C2×#208—51no—
201#893—21no—
202#893—21no—
203#893C2×D512yes—
204#893C2×D512yes—
205C3×#103—52no—
206C3×#102—52no—
207#821—52no—
208#821—52no—
209#815—52no—
210C8×Dic3—52no—
211#808—52no—
212#807—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—21no—
226#709—22no—
227#709C4×D314yescomplemented
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×C4×D5—61no—
231C2×C4×D5—61no—
232C2×Dic10C22×D311yescharacteristic
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—61no—
242#687—38no—
243#686—38no—
244#685—61no—
245#685—61no—
246C4⋊Dic5—31no—
247C4⋊Dic5—31no—
248#683—61no—
249#683—61no—
250C4×Dic5—61no—
251C4×Dic5—61no—
252C4×Dic5—61no—
253#681—22no—
254#681—34no—
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—151no—
265#418—151no—
266#417—51no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—24no—
273C2×C5×D3—48no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C3×D5—22no—
277C2×C3×D5—41no—
278C2×C3×D5—41no—
279C3×C4×C5—42no—
280C3×C4×C5C4×D412yes—
281C3×C4×C5C23×C411yescharacteristic
282C3×C4×C5C2×#4111yescharacteristic
283Dic15—41no—
284Dic15—41no—
285C3×Dic5—22no—
286C5×Dic3—21no—
287C5×Dic3—21no—
288C5×Dic3—21no—
289C5×Dic3AGL(1,ℤ/8)12yescomplemented
290C23×D3—21no—
291C3×#41—54no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—51no—
295C2×C3×D4—101no—
296C22×C3×C4—21no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C22×Dic3—101no—
300C22×Dic3—101no—
301C22×Dic3C22⋊D511yescharacteristic
302C22×Dic3C22⋊D511yescharacteristic
303C2×D12—22no—
304C2×D12—21no—
305C2×D12C4×D514yescomplemented
306C2×D12C22×D512yes—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—44no—
310C3×M16—102no—
311C2×C3×C8—52no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4C22×D512yes—
314#217—101no—
315#217—101no—
316#217—101no—
317#215—58no—
318#213—58no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—22no—
321C4⋊Dic3—51no—
322C4⋊Dic3—51no—
323C4⋊Dic3—101no—
324C4⋊Dic3—101no—
325C4×Dic3—101no—
326C4×Dic3—101no—
327C4×Dic3—101no—
328C4×Dic3C22⋊D511yescharacteristic
329C4×Dic3C22⋊D511yescharacteristic
330C4×Dic3C22×D511yescharacteristic
331C4×Dic3C22×D511yescharacteristic
332#208—54no—
333C2×C3⋊C8—52no—
334C23×C5—64no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—122no—
338C23×C5D3×D411yescharacteristic
339C22×D5—21no—
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#23712yes—
356C2×C4×C5C23×D311yescharacteristic
357C22⋊D5—24no—
358C2×Dic5—21no—
359C2×Dic5—61no—
360C2×Dic5—61no—
361D20—21no—
362D20C2×C4×D312yescomplemented
363C4×D5—24no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—21no—
367Dic10C2×C4×D312yescomplemented
368#168—22no—
369#168—34no—
370C2×#41—51no—
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—151no—
389#117—301no—
390C2×C4⋊C4D3×D511yescharacteristic
391C2×C22⋊C4—61no—
392C2×C42—31no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—52no—
397#102—52no—
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
406C3×D5—42no—
407C5×D3—44no—
408C23×C3—101no—
409C23×C3C2×C22⋊D511yescharacteristic
410C22×D3—22no—
411C22×D3—24no—
412C22×D3—42no—
413C22×D3—42no—
414C3×Q8—52no—
415C3×Q8—101no—
416C3×D4—52no—
417C3×D4—104no—
418C3×D4—101no—
419C2×C3×C4—22no—
420C2×C3×C4—42no—
421C2×C3×C4—101no—
422C2×C3×C4—104no—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4#70912yes—
425C2×C3×C4C2×C22⋊D511yescharacteristic
426C2×C3×C4C23×D511yescharacteristic
427C2×Dic3—22no—
428C2×Dic3—41no—
429C2×Dic3—101no—
430C2×Dic3—101no—
431C2×Dic3—202no—
432C2×Dic3—202no—
433C2×Dic3C2×C22⋊D511yescharacteristic
434C2×Dic3C2×C22⋊D511yescharacteristic
435C2×Dic3C2×C22⋊D511yescharacteristic
436C2×Dic3C2×C22⋊D511yescharacteristic
437D12—22no—
438D12—24no—
439D12C2×C4×D514yes—
440C4×D3—44no—
441C4×D3—44no—
442C3×C8—102no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5#67⋊C412yes—
451C22×C5C2×D3×D411yescharacteristic
452C2×D5—22no—
453C2×D5—41no—
454C2×D5—41no—
455C4×C5—32no—
456C4×C5—42no—
457C4×C5—61no—
458C4×C5—61no—
459C4×C5—61no—
460C4×C5#67⋊C412yes—
461C4×C5C22×C4×D311yescharacteristic
462C4×C5C2×#23711yescharacteristic
463Dic5—22no—
464Dic5—121no—
465Dic5—121no—
466C24—61no—
467#41—54no—
468#41—102no—
469C2×Q8—51no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4—51no—
473C2×D4—62no—
474C2×D4—61no—
475C2×D4—101no—
476C22×C4—21no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—101no—
482C22×C4—124no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—102no—
489M16—154no—
490C2×C8—52no—
491C2×C8—152no—
492C4⋊C4—21no—
493C4⋊C4—151no—
494C4⋊C4—151no—
495C4⋊C4—301no—
496C4⋊C4—301no—
497C4⋊C4C2×D3×D512yes—
498C22⋊C4—62no—
499C22⋊C4—62no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—31no—
504C42—31no—
505C42—31no—
506C42—31no—
507C42—301no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—102no—
514C22×C3—201no—
515C22×C3—201no—
516C22×C3C4×C22⋊D512yes—
517C22×C3C22×C22⋊D511yescharacteristic
518C2×D3—24no—
519C2×D3—48no—
520C2×D3—42no—
521C2×D3—42no—
522C3×C4—42no—
523C3×C4—102no—
524C3×C4C4×C22⋊D512yes—
525C3×C4C22×C4×D511yescharacteristic
526C3×C4C2×#70911yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—21no—
530Dic3—201no—
531Dic3—201no—
532Dic3#407812yescomplemented
533C2×C5—22no—
534C2×C5—124no—
535C2×C5C2×#67⋊C411yescharacteristic
536C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
537C2×C5#577711yescharacteristic
538D5—42no—
539C23—64no—
540C23—62no—
541C23—101no—
542C23—122no—
543C23—122no—
544C23D3×C22⋊D511yescharacteristic
545Q8—52no—
546Q8—101no—
547D4—34no—
548D4—52no—
549D4—64no—
550D4—62no—
551D4—104no—
552D4—101no—
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—104no—
562C2×C4—124no—
563C2×C4—124no—
564C2×C4—121no—
565C2×C4—301no—
566C2×C4—301no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4#676512yes—
570C2×C4C4×D3×D512yes—
571C2×C4D3×C22⋊D511yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—102no—
574C8—154no—
575C2×C3—22no—
576C2×C3—202no—
577C2×C3C2×C4×C22⋊D511yescharacteristic
578C2×C3C2×#407811yescharacteristic
579C2×C3#6615611yescharacteristic
580D3—44no—
581C5#7886611yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—64no—
585C22—102no—
586C22—128no—
587C22—122no—
588C22—122no—
589C22—201no—
590C22—201no—
591C22#9144112yes—
592C22C2×D3×C22⋊D511yescharacteristic
593C4—32no—
594C4—42no—
595C4—61no—
596C4—61no—
597C4—61no—
598C4—102no—
599C4—601no—
600C4—601no—
601C4#9144112yes—
602C4C2×#676511yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3C4×#407811yescharacteristic, complemented, Sylow
605C2—22no—
606C2—124no—
607C2—202no—
608C2C2×#9144111yescharacteristic
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×#91299C2
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. Dic3×#709C2semidirect
4. #11751065C2semidirect
5. C3×#65255C2semidirect
6. #11748389C2semidirect
7. Dic3×#681C2semidirect
8. #11747265C2semidirect
9. #11747264C2semidirect
10. #11747220C2semidirect
11. #11747219C2semidirect
28. Dic3×D20C22semidirect
29. Dic3×D20C22semidirect
32. Dic3×Dic10C22semidirect
33. Dic3×Dic10C22semidirect
35. #91299C4semidirect
37. #91092C22semidirect
38. #91091C22semidirect
39. C3×#3942C22semidirect
40. C3×#3941C22semidirect
43. #90953C22semidirect
44. Dic3×#168C22semidirect
54. #65255D3semidirect
64. C2×C5×D12C2×C4semidirect
71. C3×#709C2×C4semidirect
83. #6710C2×C4semidirect
99. #6656C2×C4semidirect
100. #6652C2×C4semidirect
103. C2×#893D5semidirect
138. #3942C2×D3semidirect
139. #3941C2×D3semidirect
173. C3×D20C22×C4semidirect
176. C3×Dic10C22×C4semidirect
179. C3⋊#168C22×C4semidirect
227. #709C4×D3semidirect
289. C5×Dic3AGL(1,ℤ/8)semidirect
305. C2×D12C4×D5semidirect
362. D20C2×C4×D3semidirect
367. Dic10C2×C4×D3semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
532. Dic3#4078semidirect
581. C5#78866semidirect
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
Dic3×#7092
C2×#912992
#117510652
C3×#652552
#117483892
Dic3×#6812
#117472652
#117472642
#117472202
#117472192
C4×#40783
#788665