Finite Group Databasebeta

← #14435526

Subgroups — #14435526

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752701C211yesmaximal, characteristic
2C4×D3×Dic10C211yesmaximal, characteristic, complemented
3#11750946C211yesmaximal, characteristic, complemented
4C5×#4835C211yesmaximal, characteristic, complemented
5C3×#65118C211yesmaximal, characteristic, complemented
6#11748133C211yesmaximal, characteristic, complemented
7#11748132C211yesmaximal, characteristic
8#11747876C211yesmaximal, characteristic, complemented
9#11747832C211yesmaximal, characteristic, complemented
10#11747800C211yesmaximal, characteristic, complemented
11#11747743C211yesmaximal, characteristic, complemented
12#11747631C211yesmaximal, characteristic, complemented
13#11747625C211yesmaximal, characteristic
14#11747065C211yesmaximal, characteristic, complemented
15#11746934C211yesmaximal, characteristic, complemented
16#10611088—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18C2×Dic60C2211yescharacteristic
19C2×#6706C2211yescharacteristic
20#91764C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C42×C5×D3C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25C4×#1204—21no—
26#91460C2211yescharacteristic
27#91446—21no—
28#91428C2211yescharacteristic
29D3×C4⋊Dic5C2211yescharacteristic
30#91403—21no—
31D3×#683—21no—
32C4×D3×Dic5—21no—
33#91380—21no—
34#91365C2211yescharacteristic
35#91351—21no—
36#91340C2211yescharacteristic
37#91340C2211yescharacteristic
38Dic3×Dic10C2211yescharacteristic
39#91324—21no—
40C2×#6662C2211yescharacteristic
41C2×#6658C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43#91105C2211yescharacteristic
44#91100C2211yescharacteristic
45C5×(C2×D3)⋊C8C2211yescharacteristic
46C5×(C2×D3)⋊C8C2211yescharacteristic
47C5×#815C2211yescharacteristic
48C5×#815C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×#3950C2211yescharacteristic
51C3×#3949C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54#90990C2211yescharacteristic
55#90987C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90974C2211yescharacteristic
59#90968C2211yescharacteristic
60#81207—51nomaximal, Hall
61#65813—31no—
62C2×C4×Dic10—31no—
63C5×#432—31no—
64#65134—31no—
65#65134—31no—
66#65118—31no—
67#65118D311yescharacteristic, complemented
68#65028—31no—
69#65027—31no—
70#65024—31no—
71#65011—31no—
72#65005—31no—
73#65005—31no—
74#64999—31no—
75#64999—31no—
76C2×D60C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C4×C5×D3D411yescharacteristic
80C2×C4×C5×D3D411yescharacteristic
81C2×C4×C5×D3C2311yescharacteristic
82C2×C3×Dic10C2311yescharacteristic
83C2×#1204—21no—
84C2×#1203—21no—
85C2×#1200—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88D3×Dic10—22no—
89D3×Dic10—22no—
90C2×C3×C5×C8C2311yescharacteristic
91C2×C3×C5×C8C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93#6714—21no—
94#6714—21no—
95C4⋊Dic15C2311yescharacteristic
96#6712—21no—
97C4×Dic15—21no—
98Dic60—22no—
99#6706—22no—
100C4×C5×Dic3D411yescharacteristic
101C4×C5×Dic3D411yescharacteristic
102C4×C5×Dic3C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×C4×Dic5—21no—
112Dic3⋊Dic5—21no—
113#6669—21no—
114#6669—21no—
115#6668—21no—
116#6668—21no—
117#6667—21no—
118#6667—21no—
119(C2×D3)⋊Dic5—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6662—22no—
124#6658—22no—
125#5691—51no—
126C4×D3×Q8—51no—
127C3×#479—51no—
128#5063—51no—
129#5028—51no—
130#4889—51no—
131#4884—51no—
132#4863—51no—
133#4853—51no—
134#4845—51no—
135#4835D511yescharacteristic, complemented
136#4817—51no—
137#4809—51no—
138#4806—51no—
139#4789—51no—
140C22×Dic10—31no—
141C2×C42×C5—31no—
142#4076—31no—
143#4075—61no—
144C4×C22⋊D5—61no—
145C2×C4⋊Dic5—31no—
146#4070—31no—
147C2×#683—61no—
148C2×C4×Dic5—61no—
149C2×Dic20—31no—
150C2×Dic20—31no—
151C2×#677—31no—
152C2×#677—31no—
153#4022—61no—
154#4021—31no—
155C4×D20—31no—
156#4018—61no—
157#4016C2×D311yescharacteristic
158C4×Dic10—31no—
159C4×Dic10—31no—
160C4×Dic10—31no—
161C4×Dic10—31no—
162C4×Dic10—61no—
163C4×Dic10—61no—
164C4×Dic10C2×D311yescharacteristic
165C5×C4⋊C8—31no—
166C5×C4⋊C8C2×D311yescharacteristic
167C5×C22⋊C8—31no—
168C5×C22⋊C8—31no—
169C5×#97—31no—
170C5×#97—31no—
171#3953—31no—
172#3953—31no—
173#3950—31no—
174#3950C2×D311yescharacteristic
175#3949—31no—
176#3949C2×D311yescharacteristic
177#3948—31no—
178#3948—31no—
179#3948—31no—
180#3948—31no—
181#3948C2×D311yescharacteristic
182#3948C2×D311yescharacteristic
183#3117—151noSylow
184C22×D15—21no—
185C22×C5×D3C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15—21no—
192D60—21no—
193D60—21no—
194Dic30—21no—
195Dic30—21no—
196Dic30—21no—
197Dic30#4112yes—
198C2×C5×Dic3C2×D411yescharacteristic
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C4×C5×D3—22no—
202C4×C5×D3—21no—
203C4×C5×D3—21no—
204C4×C5×D3—41no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C3×Dic10—21no—
210C3×Dic10#4112yes—
211#1204—24no—
212#1203—42no—
213#1200—42no—
214D3×Dic5—24no—
215D3×Dic5—42no—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C5×C3⋊C8—21no—
219C5×C3⋊C8—21no—
220C2×D3×Q8—51no—
221C3×#125—51no—
222C3×C4×Q8—51no—
223Q8×Dic3—51no—
224C2×#216—51no—
225C2×#215—51no—
226C2×Dic12—51no—
227C2×#204—51no—
228#898—101no—
229#897—51no—
230#895—51no—
231#894—101no—
232#893—51no—
233#893—101no—
234#892—101no—
235D3×C4⋊C4—51no—
236D3×C4⋊C4—101no—
237#887—51no—
238#887—51no—
239#887—101no—
240#875—51no—
241C42×D3—101no—
242C42×D3C2×D511yescharacteristic
243C4×Dic6—51no—
244C4×Dic6—101no—
245C3×#107—51no—
246C3×#106—51no—
247C3×C4⋊C8C2×D511yescharacteristic
248C3×#103—51no—
249C3×#103—51no—
250#821—51no—
251(C2×D3)⋊C8C2×D511yescharacteristic
252(C2×D3)⋊C8C2×D511yescharacteristic
253#816—51no—
254#815C2×D511yescharacteristic
255#815C2×D511yescharacteristic
256#810—51no—
257#810—51no—
258#810—51no—
259#809—51no—
260#808—51no—
261#807—51no—
262C4⋊(C3⋊C8)C2×D511yescharacteristic
263C22×C4×C5—31no—
264C22×C4×C5—31no—
265C22×C4×C5—31no—
266C2×C22⋊D5—61no—
267C22×Dic5—61no—
268C22×Dic5—61no—
269C2×D20—31no—
270C2×C4×D5—61no—
271C2×Dic10—31no—
272C2×Dic10—31no—
273C2×Dic10—62no—
274C2×Dic10—61no—
275C2×Dic10—62no—
276C2×Dic10C22×D311yescharacteristic
277C2×C5×C8—31no—
278C2×C5×C8—31no—
279C2×C5×C8C22×D311yescharacteristic
280C2×C5×C8C22×D311yescharacteristic
281C42×C5—31no—
282C42×C5—31no—
283C42×C5—31no—
284C42×C5C22×D311yescharacteristic
285C22⋊Dic5—61no—
286#685—61no—
287#685—61no—
288#685—61no—
289#685—61no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294C4⋊Dic5C22×D311yescharacteristic
295#683—21no—
296#683—21no—
297#683—21no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5—61no—
308Dic20—62no—
309Dic20—62no—
310#677—62no—
311#677—62no—
312#529—151no—
313C2×C4×Q8—151no—
314#484—151no—
315#481—151no—
316#479—51no—
317#479—151no—
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441—151no—
324#440—151no—
325#440—151no—
326#432—31no—
327C22×C3×C5C22×D411yescharacteristic
328C2×D15—41no—
329C2×D15—41no—
330C2×D15—41no—
331C2×C5×D3—21no—
332C2×C5×D3—21no—
333C2×C5×D3#13712yes—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5C2×#4111yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—22no—
339Dic15—41no—
340Dic15—41no—
341C3×Dic5—22no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C5×Dic3—21no—
346C5×Dic3—21no—
347C5×Dic3—21no—
348C2×C3×Q8—51no—
349D3×Q8—102no—
350D3×Q8—102no—
351C2×D12—51no—
352C2×D12—101no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×C4×D3D2011yescharacteristic
357C2×C4×D3D2011yescharacteristic
358C2×C4×D3C22×D511yescharacteristic
359C2×Dic6—51no—
360C2×Dic6—51no—
361C2×Dic6—101no—
362C2×C3×C8C22×D511yescharacteristic
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—51no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4—101no—
370C3×C42—101no—
371C3×C42C22×D511yescharacteristic
372#216—102no—
373#215—102no—
374(C2×D3)⋊C4—101no—
375(C2×D3)⋊C4—101no—
376(C2×D3)⋊C4—101no—
377(C2×D3)⋊C4—101no—
378(C2×D3)⋊C4—101no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386C4×Dic3—101no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C4×Dic3D2011yescharacteristic
391C4×Dic3D2011yescharacteristic
392C4×Dic3C22×D511yescharacteristic
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395Dic12—102no—
396#204—102no—
397C23×C5—31no—
398C22×D5—61no—
399C2×C4×C5—31no—
400C2×C4×C5—31no—
401C2×C4×C5—31no—
402C2×C4×C5—62no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5—121no—
406C2×C4×C5D3×D411yescharacteristic
407C2×C4×C5D3×D411yescharacteristic
408C2×C4×C5C23×D311yescharacteristic
409C22⋊D5—122no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—64no—
415C2×Dic5—61no—
416C2×Dic5—61no—
417C2×Dic5—61no—
418C2×Dic5—122no—
419D20—61no—
420D20—61no—
421C4×D5—122no—
422Dic10—21no—
423Dic10—32no—
424Dic10—64no—
425Dic10—61no—
426Dic10—61no—
427Dic10—61no—
428Dic10#23912yes—
429C5×C8—21no—
430C5×C8—21no—
431C5×C8—61no—
432C5×C8—61no—
433C22×Q8—151no—
434C2×Q16—151no—
435C2×Q16—151no—
436C2×SD16—151no—
437C2×SD16—151no—
438#126—301no—
439#125—51no—
440#124—151no—
441#123—301no—
442C22⋊Q8—151no—
443#121—151no—
444C4×Q8—51no—
445C4×Q8—151no—
446C4×Q8—151no—
447C4×Q8—151no—
448C4×Q8—151no—
449C4×Q8—301no—
450C4×Q8—301no—
451C4×D4—151no—
452C4×D4—301no—
453#117—301no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—301no—
456C2×C42—31no—
457C2×C42—301no—
458#107—51no—
459#107—151no—
460#106—51no—
461#106—151no—
462C4⋊C8—31no—
463C4⋊C8D3×D511yescharacteristic
464#103—51no—
465#103—51no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#102—151no—
471#102—151no—
472C22⋊C8—31no—
473C22⋊C8—31no—
474#97—31no—
475#97—31no—
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479D15—81no—
480C5×D3—22no—
481C22×D3—101no—
482C22×D3C2×D2011yescharacteristic
483C3×Q8—52no—
484C3×Q8—101no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4C2×D2011yescharacteristic
490C2×C3×C4C2×D2011yescharacteristic
491C2×C3×C4C23×D511yescharacteristic
492C2×Dic3—101no—
493C2×Dic3—101no—
494C2×Dic3—101no—
495C2×Dic3C2×D2011yescharacteristic
496C2×Dic3C2×D2011yescharacteristic
497C2×Dic3C2×D2011yescharacteristic
498D12—101no—
499D12—101no—
500D12—202no—
501C4×D3—22no—
502C4×D3—21no—
503C4×D3—21no—
504C4×D3—41no—
505C4×D3—104no—
506C4×D3—202no—
507C4×D3—202no—
508Dic6—52no—
509Dic6—104no—
510Dic6—101no—
511Dic6—101no—
512Dic6—101no—
513C3×C8—21no—
514C3×C8—21no—
515C3⋊C8—21no—
516C3⋊C8—21no—
517C22×C5—32no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5C2×D3×D411yescharacteristic
521C2×D5—121no—
522C2×D5—121no—
523C2×D5—121no—
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—61no—
527C4×C5—61no—
528C4×C5—61no—
529C4×C5C2×#23911yescharacteristic
530C4×C5D3×#4111yescharacteristic
531Dic5—22no—
532Dic5—41no—
533Dic5—41no—
534Dic5—41no—
535Dic5—62no—
536Dic5—121no—
537Dic5—121no—
538C2×Q8—51no—
539C2×Q8—151no—
540C2×Q8—151no—
541C2×Q8—301no—
542C2×Q8—302no—
543C2×Q8—302no—
544C2×D4—151no—
545C2×D4—301no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—301no—
552Q16—302no—
553Q16—302no—
554SD16—302no—
555SD16—302no—
556C2×C8—31no—
557C2×C8—31no—
558C2×C8C2×D3×D511yescharacteristic
559C2×C8C2×D3×D511yescharacteristic
560C4⋊C4—51no—
561C4⋊C4—51no—
562C4⋊C4—51no—
563C4⋊C4—101no—
564C4⋊C4—101no—
565C4⋊C4—101no—
566C4⋊C4—151no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C22⋊C4—301no—
577C22⋊C4—301no—
578C42—31no—
579C42—31no—
580C42—31no—
581C42—101no—
582C42—301no—
583C42—301no—
584C42—301no—
585C42—301no—
586C42C2×D3×D511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3C22×D2011yescharacteristic
589C2×D3—21no—
590C2×D3—21no—
591C2×D3—201no—
592C2×D3—201no—
593C2×D3—201no—
594C2×D3#405512yes—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—102no—
598C3×C4—201no—
599C3×C4—201no—
600C3×C4—201no—
601C3×C4D5×#4111yescharacteristic
602C3×C4D5×#4111yescharacteristic
603Dic3—21no—
604Dic3—21no—
605Dic3—21no—
606Dic3—102no—
607Dic3—201no—
608Dic3—201no—
609C2×C5—62no—
610C2×C5#562711yescharacteristic
611C2×C5#576811yescharacteristic
612C2×C5D3×#13711yescharacteristic
613D5—241no—
614C23—31no—
615C23—301no—
616Q8—52no—
617Q8—101no—
618Q8—152no—
619Q8—304no—
620Q8—301no—
621Q8—301no—
622Q8—301no—
623D4—301no—
624D4—301no—
625D4—602no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—62no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—101no—
635C2×C4—101no—
636C2×C4—121no—
637C2×C4—304no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D3×D2011yescharacteristic
644C2×C4D3×D2011yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—21no—
647C8—21no—
648C8—61no—
649C8—61no—
650C2×C3#6585811yescharacteristic
651C2×C3C2×#405511yescharacteristic
652C2×C3#6608211yescharacteristic
653D3—22no—
654D3—401no—
655C5#8120711yescharacteristic, complemented, Sylow
656C22—32no—
657C22—61no—
658C22—61no—
659C22—601no—
660C22—601no—
661C22—601no—
662C22C2×D3×D2011yescharacteristic
663C4—21no—
664C4—21no—
665C4—61no—
666C4—61no—
667C4—61no—
668C4—102no—
669C4—201no—
670C4—201no—
671C4—201no—
672C4—302no—
673C4—601no—
674C4—601no—
675C4#9202411yescharacteristic
676C4D5×#23911yescharacteristic
677C3#1061108811yescharacteristic, complemented, Sylow
678C2—62no—
679C2—1201no—
680C2#1175388011yescharacteristic
681C2#1175396911yescharacteristic
682C2D3×#405511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#91460C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×D3×Dic10C2semidirect
3. #11750946C2semidirect
4. C5×#4835C2semidirect
5. C3×#65118C2semidirect
6. #11748133C2semidirect
8. #11747876C2semidirect
9. #11747832C2semidirect
10. #11747800C2semidirect
11. #11747743C2semidirect
12. #11747631C2semidirect
14. #11747065C2semidirect
15. #11746934C2semidirect
67. #65118D3semidirect
135. #4835D5semidirect
587. C3×C5#3117semidirect
655. C5#81207semidirect
677. C3#10611088semidirect

Maximal subgroups

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

subgroupindex
#117527012
C4×D3×Dic102
#117509462
C5×#48352
C3×#651182
#117481332
#117481322
#117478762
#117478322
#117478002
#117477432
#117476312
#117476252
#117470652
#117469342
#106110883
#812075