Finite Group Databasebeta

← #14416735

Subgroups — #14416735

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#11754414C211yesmaximal, characteristic, complemented
2C2×Dic5×D12C211yesmaximal, characteristic, complemented
3C2×#91304C211yesmaximal, characteristic
4#11751234C211yesmaximal, characteristic, complemented
5C5×#5131C211yesmaximal, characteristic, complemented
6C3×M16×Dic5C211yesmaximal, characteristic, complemented
7#11748460C211yesmaximal, characteristic, complemented
8#11747747C212yesmaximal, complemented
9#11747746C212yesmaximal, complemented
10#11747745C212yesmaximal, complemented
11#11747744C212yesmaximal, complemented
12#10610645—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C22×D3×Dic5—21no—
16C2×C3×C5×M16C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C3×C4×Dic5C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91552—21no—
22#91552—21no—
23C2×(C2×D3)⋊Dic5—21no—
24#91418C2211yescharacteristic, complemented
25#91418C2211yescharacteristic, complemented
26Dic5×D12—21no—
27Dic5×D12—21no—
28Dic5×D12C2212yes—
29Dic5×D12C2212yes—
30C4×#1200—21no—
31#91386—21no—
32#91333C2211yescharacteristic, complemented
33#91333C2211yescharacteristic, complemented
34C2×#6659C2212yes—
35#91304C418yescomplemented
36C2×#6654C2212yes—
37#91105C2212yescomplemented
38#91100C2212yescomplemented
39C5×#821C2212yes—
40C5×#821C2212yes—
41C3×#3947C2212yescomplemented
42C3×C8×Dic5C2212yescomplemented
43#90988C2212yescomplemented
44#90985C2212yescomplemented
45C4×#908—51nomaximal, Hall
46C2×D4×Dic5—31no—
47C2×#4078—31no—
48#65856—31no—
49C5×#418—31no—
50#65422—31no—
51M16×Dic5D311yescharacteristic, complemented
52#65284—31no—
53#65074—32no—
54#65047—32no—
55#65046—32no—
56#65045—32no—
57C23×C5×D3—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C22×Dic15—21no—
61#6817—22no—
62#6817C2×C414yescomplemented
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×Dic30C2311yescharacteristic
66C2×C5×D12—21no—
67C2×C5×D12—22no—
68C2×C5×D12C2×C414yescomplemented
69C2×C5×D12C2312yes—
70C22×C3×Dic5D411yescharacteristic
71C22×C3×Dic5D411yescharacteristic
72C2×#1200—21no—
73C2×#1200—21no—
74C2×D3×Dic5—22no—
75C2×D3×Dic5—22no—
76C2×D3×Dic5—44no—
77C3×C5×M16—22no—
78C2×C3×C5×C8C2312yes—
79C4⋊Dic15—21no—
80C4⋊Dic15C2312yes—
81C5×#217—21no—
82C5×C4⋊Dic3C2311yescharacteristic
83C5×C4⋊Dic3C2311yescharacteristic
84C4×C5×Dic3—21no—
85C3×C4×Dic5D411yescharacteristic
86C3×C4×Dic5D411yescharacteristic
87C3×C4×Dic5C2311yescharacteristic
88C3×C4×Dic5C2311yescharacteristic
89C3×#681C2×C414yescomplemented
90C2×C3×#168C2312yes—
91#6669—21no—
92#6669—21no—
93#6667—21no—
94#6667—21no—
95(C2×D3)⋊Dic5—22no—
96(C2×D3)⋊Dic5—22no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6659C2×C418yescomplemented
100#6654C2×C418yescomplemented
101C2×#908—51no—
102C4×#235—51no—
103C2×C4×D12—51no—
104C3×C4×M16—51no—
105#5133—51no—
106#5131D511yescharacteristic, complemented
107#5121—51no—
108#4711—52no—
109#4710—52no—
110C4×D24—52no—
111C4×#204—52no—
112C22×C5×D4—31no—
113C23×Dic5—61no—
114C2×#709—31no—
115C2×C5×M16C2×D311yescharacteristic
116C5×#117—31no—
117C2×C22⋊Dic5—61no—
118D4×Dic5—32no—
119D4×Dic5—32no—
120D4×Dic5—61no—
121D4×Dic5—61no—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C2×C4⋊Dic5—31no—
126C2×C4×Dic5C2×D311yescharacteristic
127C2×#681C2×D311yescharacteristic
128#4039—31no—
129#4039—31no—
130#4033—31no—
131#4033—31no—
132#4027—61no—
133#4027—61no—
134#4018—61no—
135C42×D5—61no—
136C5×#102—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—32no—
140#3947C2×D312yescomplemented
141C8×Dic5C2×D312yescomplemented
142#3940—32no—
143#3939—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×C5C22×C412yes—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5#4112yes—
154C2×C3×C4×C5C2411yescharacteristic
155#1220—24no—
156C2×Dic15—21no—
157C2×Dic15—22no—
158C2×Dic15—42no—
159D60—21no—
160D60C22×C412yescomplemented
161C4×D15—24no—
162Dic30—21no—
163Dic30C22×C412yescomplemented
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C5×D12—24no—
167C5×D12—22no—
168C5×D12C22×C414yes—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—41no—
171C2×C3×Dic5C2×D411yescharacteristic
172C2×C3×Dic5C2×D411yescharacteristic
173C2×C3×Dic5C2×D411yescharacteristic
174C2×C3×Dic5C2×D411yescharacteristic
175#1200—42no—
176#1200—42no—
177D3×Dic5—44no—
178D3×Dic5—44no—
179C3×C5×C8—22no—
180C3×#168C22×C414yescomplemented
181C2×#235—51no—
182C22×D12C2×D511yescharacteristic
183C22×C4×D3—101no—
184C2×C3×M16—51no—
185C2×C3×M16C2×D511yescharacteristic
186C2×C3×C42—51no—
187C4×#67—101no—
188C4×#67—101no—
189C2×(C2×D3)⋊C4—101no—
190#926C2×D511yescharacteristic
191C2×C4⋊Dic3—51no—
192#908—58no—
193C2×D24—52no—
194C2×#204—52no—
195C4×D12—52no—
196C4×D12—52no—
197C4×D12—51no—
198C4×D12—51no—
199C4×D12—101no—
200C4×D12—101no—
201#872—101no—
202C42×D3—101no—
203C4×Dic6—51no—
204C4×Dic6—51no—
205C3×#97—52no—
206C3×C4×C8—52no—
207#821—52no—
208#821C2×D512yes—
209#821C2×D512yes—
210#818—52no—
211#817—52no—
212#816—52no—
213C24×C5—61no—
214C2×C5×D4—34no—
215C2×C5×D4—32no—
216C2×C5×D4—61no—
217C2×C5×D4—62no—
218C22×C4×C5C22×D311yescharacteristic
219C2×C22⋊D5—61no—
220C22×Dic5—61no—
221C22×Dic5—62no—
222C22×Dic5—62no—
223C22×Dic5—124no—
224C22×Dic5D1211yescharacteristic
225C22×Dic5D1211yescharacteristic
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×M16—22no—
234C2×C5×C8C22×D312yes—
235C5×C4⋊C4—31no—
236C5×C4⋊C4—31no—
237C5×C22⋊C4—61no—
238C42×C5—61no—
239C22⋊Dic5—62no—
240C22⋊Dic5—62no—
241#687—38no—
242#686—38no—
243#685—61no—
244#685—61no—
245C4⋊Dic5—32no—
246C4⋊Dic5—61no—
247#683—61no—
248#683—61no—
249C4×Dic5—61no—
250C4×Dic5—61no—
251C4×Dic5D1211yescharacteristic
252C4×Dic5D1211yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254C4×Dic5C22×D311yescharacteristic
255#681C4×D314yescomplemented
256C2×#168C22×D312yes—
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—151no—
265#418—31no—
266#417—151no—
267C4×M16—51no—
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×C5C4×D412yes—
280C3×C4×C5C23×C411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—22no—
283Dic15—42no—
284C3×Dic5—21no—
285C3×Dic5—21no—
286C3×Dic5—21no—
287C3×Dic5AGL(1,ℤ/8)12yescomplemented
288C5×Dic3—41no—
289C5×Dic3—41no—
290C23×D3—21no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4C22×D511yescharacteristic
294C2×#67—101no—
295C22×Dic3—101no—
296#235—54no—
297#235—102no—
298C2×D12—21no—
299C2×D12—22no—
300C2×D12—51no—
301C2×D12C4×D514yescomplemented
302C2×D12C22×D512yes—
303C2×C4×D3—101no—
304C2×C4×D3—101no—
305C2×C4×D3—101no—
306C2×C4×D3—102no—
307C2×C4×D3—102no—
308C2×C4×D3—204no—
309C2×Dic6—51no—
310C3×M16—22no—
311C3×M16—54no—
312C2×C3×C8—52no—
313C2×C3×C8C22×D512yes—
314C3×C42—51no—
315C3×C42—51no—
316C3×C42—51no—
317C3×C42—51no—
318#217—21no—
319(C2×D3)⋊C4—101no—
320(C2×D3)⋊C4—101no—
321(C2×D3)⋊C4—102no—
322(C2×D3)⋊C4—102no—
323C4⋊Dic3—52no—
324C4⋊Dic3—101no—
325C4⋊Dic3C22×D511yescharacteristic
326C4⋊Dic3C22×D511yescharacteristic
327Dic3⋊C4—101no—
328Dic3⋊C4—101no—
329C4×Dic3—21no—
330C4×Dic3—101no—
331C4×Dic3—101no—
332D24—58no—
333#204—58no—
334C23×C5—64no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—122no—
338C23×C5C2×D1211yescharacteristic
339C22×D5—61no—
340C5×D4—34no—
341C5×D4—64no—
342C5×D4—62no—
343C2×C4×C5—61no—
344C2×C4×C5—61no—
345C2×C4×C5C2×C4×D312yes—
346C2×C4×C5C2×D1211yescharacteristic
347C2×C4×C5#23512yes—
348C2×C4×C5C23×D311yescharacteristic
349C22⋊D5—64no—
350C2×Dic5—22no—
351C2×Dic5—41no—
352C2×Dic5—61no—
353C2×Dic5—62no—
354C2×Dic5—124no—
355C2×Dic5—122no—
356C2×Dic5—124no—
357C2×Dic5C2×D1211yescharacteristic
358C2×Dic5C2×D1211yescharacteristic
359C2×Dic5C2×D1211yescharacteristic
360C2×Dic5C2×D1211yescharacteristic
361D20—32no—
362D20—61no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368C5×C8—22no—
369#168C2×C4×D314yescomplemented
370C2×#41—151no—
371C22×D4—31no—
372C23×C4—301no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—51no—
377C2×M16D3×D511yescharacteristic
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—151no—
381C4×D4—151no—
382C4×D4—152no—
383C4×D4—152no—
384C4×D4—301no—
385C4×D4—301no—
386C4×D4—301no—
387C4×D4—301no—
388#117—31no—
389#117—301no—
390C2×C4⋊C4—151no—
391C2×C22⋊C4—301no—
392C2×C42—51no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—32no—
398#102—32no—
399#102—152no—
400#97—52no—
401C4×C8—52no—
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×C3D4×D511yescharacteristic
409C22×D3—22no—
410C22×D3—24no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—101no—
414C2×C3×C4—51no—
415C2×C3×C4—51no—
416C2×C3×C4—51no—
417C2×C3×C4—51no—
418C2×C3×C4—102no—
419C2×C3×C4—201no—
420C2×C3×C4C2×C4×D512yes—
421C2×C3×C4D4×D511yescharacteristic
422C2×C3×C4#71112yes—
423C2×C3×C4C23×D511yescharacteristic
424#67—104no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—101no—
428C2×Dic3—102no—
429C2×Dic3—202no—
430D12—22no—
431D12—24no—
432D12—52no—
433D12—101no—
434D12C2×C4×D514yes—
435C4×D3—104no—
436C4×D3—202no—
437C4×D3—202no—
438C4×D3—204no—
439C4×D3—204no—
440Dic6—52no—
441Dic6—101no—
442C3×C8—22no—
443C3×C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5C4×D1212yes—
451C22×C5C22×D1211yescharacteristic
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—121no—
456C4×C5—121no—
457C4×C5C4×D1212yes—
458C4×C5C22×C4×D311yescharacteristic
459C4×C5C2×#23511yescharacteristic
460Dic5—21no—
461Dic5—21no—
462Dic5—21no—
463Dic5—62no—
464Dic5—122no—
465Dic5#90812yescomplemented
466C24—61no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4—61no—
473C2×D4—62no—
474C2×D4—151no—
475C2×D4—301no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—301no—
479C22×C4—301no—
480C22×C4—302no—
481C22×C4—302no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—22no—
489M16—54no—
490C2×C8—52no—
491C2×C8C2×D3×D512yes—
492C4⋊C4—31no—
493C4⋊C4—31no—
494C4⋊C4—152no—
495C4⋊C4—301no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—61no—
499C22⋊C4—301no—
500C22⋊C4—301no—
501C22⋊C4—302no—
502C22⋊C4—302no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—61no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3#402712yes—
514C22×C3C2×D4×D511yescharacteristic
515C2×D3—24no—
516C2×D3—48no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—52no—
523C3×C4—101no—
524C3×C4—101no—
525C3×C4—101no—
526C3×C4#402712yes—
527C3×C4C22×C4×D511yescharacteristic
528C3×C4C2×#71111yescharacteristic
529Dic3—41no—
530Dic3—41no—
531Dic3—102no—
532Dic3—202no—
533C2×C5—22no—
534C2×C5—124no—
535C2×C5C2×C4×D1211yescharacteristic
536C2×C5C2×#90811yescharacteristic
537C2×C5#574811yescharacteristic
538D5—122no—
539C23—64no—
540C23—62no—
541C23—122no—
542C23—122no—
543C23—301no—
544C23D5×D1211yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—34no—
548D4—64no—
549D4—62no—
550D4—152no—
551D4—304no—
552D4—301no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—102no—
560C2×C4—201no—
561C2×C4—301no—
562C2×C4—304no—
563C2×C4—302no—
564C2×C4—602no—
565C2×C4—604no—
566C2×C4—602no—
567C2×C4—604no—
568C2×C4—602no—
569C2×C4C4×D3×D512yes—
570C2×C4D5×D1211yescharacteristic
571C2×C4#678212yes—
572C2×C4C22×D3×D511yescharacteristic
573C8—22no—
574C8—54no—
575C2×C3—22no—
576C2×C3C2×#402711yescharacteristic
577C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
578C2×C3#6610711yescharacteristic
579D3—44no—
580D3—202no—
581C5C4×#90811yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—64no—
585C22—128no—
586C22—122no—
587C22—122no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9140512yes—
592C22C2×D5×D1211yescharacteristic
593C4—52no—
594C4—101no—
595C4—101no—
596C4—101no—
597C4—121no—
598C4—121no—
599C4—302no—
600C4—602no—
601C4#9140512yes—
602C4C2×C4×D3×D511yescharacteristic
603C4C2×#678211yescharacteristic
604C3#1061064511yescharacteristic, complemented, Sylow
605C2—22no—
606C2—124no—
607C2—602no—
608C2D5×#90811yescharacteristic
609C2#1175402211yescharacteristic
610C2C2×#9140511yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91304C2
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11754414C2semidirect
2. C2×Dic5×D12C2semidirect
4. #11751234C2semidirect
5. C5×#5131C2semidirect
6. C3×M16×Dic5C2semidirect
7. #11748460C2semidirect
8. #11747747C2semidirect
9. #11747746C2semidirect
10. #11747745C2semidirect
11. #11747744C2semidirect
24. #91418C22semidirect
25. #91418C22semidirect
32. #91333C22semidirect
33. #91333C22semidirect
35. #91304C4semidirect
37. #91105C22semidirect
38. #91100C22semidirect
41. C3×#3947C22semidirect
42. C3×C8×Dic5C22semidirect
43. #90988C22semidirect
44. #90985C22semidirect
51. M16×Dic5D3semidirect
62. #6817C2×C4semidirect
68. C2×C5×D12C2×C4semidirect
89. C3×#681C2×C4semidirect
99. #6659C2×C4semidirect
100. #6654C2×C4semidirect
106. #5131D5semidirect
140. #3947C2×D3semidirect
141. C8×Dic5C2×D3semidirect
160. D60C22×C4semidirect
163. Dic30C22×C4semidirect
180. C3×#168C22×C4semidirect
255. #681C4×D3semidirect
287. C3×Dic5AGL(1,ℤ/8)semidirect
301. C2×D12C4×D5semidirect
369. #168C2×C4×D3semidirect
465. Dic5#908semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5C4×#908semidirect
604. C3#10610645semidirect

Maximal subgroups

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

subgroupindex
#117544142
C2×Dic5×D122
C2×#913042
#117512342
C5×#51312
C3×M16×Dic52
#117484602
#117477472
#117477462
#117477452
#117477442
#106106453
C4×#9085