Finite Group Databasebeta

← #14435432

Subgroups — #14435432

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#11756339C211yesmaximal, characteristic
2C4×Q8×D15C211yesmaximal, characteristic, complemented
3C3×C5×#441C211yesmaximal, characteristic, complemented
4#11751287C211yesmaximal, characteristic, complemented
5#11751286C211yesmaximal, characteristic, complemented
6#11751131C211yesmaximal, characteristic, complemented
7#11751127C211yesmaximal, characteristic, complemented
8#11750964C211yesmaximal, characteristic
9#11750958C211yesmaximal, characteristic, complemented
10#11750912C211yesmaximal, characteristic, complemented
11#11750907C211yesmaximal, characteristic
12#11750899C211yesmaximal, characteristic, complemented
13#11750897C211yesmaximal, characteristic, complemented
14#11750811C211yesmaximal, characteristic, complemented
15#11750806C211yesmaximal, characteristic, complemented
16#10611565—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C3×C5×Q16C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21#91836C2211yescharacteristic
22#91835C2211yescharacteristic
23Q8×Dic15C2211yescharacteristic
24C2×#6718C2211yescharacteristic
25C2×#6717C2211yescharacteristic
26C2×#6706C2211yescharacteristic
27#91787—21no—
28#91784C2211yescharacteristic
29#91783—21no—
30C4⋊C4×D15—21no—
31C4⋊C4×D15C2211yescharacteristic
32#91779C2211yescharacteristic
33#91776—21no—
34#91776C2211yescharacteristic
35C4×D60—21no—
36C4×D60C2211yescharacteristic
37#91761—21no—
38C42×D15—21no—
39C42×D15C2211yescharacteristic
40C4×Dic30—21no—
41C4×Dic30C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×C5×#97C2211yescharacteristic
46#91119C2211yescharacteristic
47#91119C2211yescharacteristic
48#91105C2211yescharacteristic
49#91104C2211yescharacteristic
50#91104C2211yescharacteristic
51#91102C2211yescharacteristic
52#91100C2211yescharacteristic
53#91098C2211yescharacteristic
54#91098C2211yescharacteristic
55#91094C2211yescharacteristic
56#91093C2211yescharacteristic
57#91092C2211yescharacteristic
58#91091C2211yescharacteristic
59#91087C2211yescharacteristic
60#79834—51nomaximal, Hall
61#65914—31no—
62C4×Q8×D5—31no—
63C5×#441D311yescharacteristic, complemented
64#65475—31no—
65#65474—31no—
66#65319—31no—
67#65315—31no—
68#65152—31no—
69#65146—31no—
70#65098—31no—
71#65095—31no—
72#65087—31no—
73#65085—31no—
74#64999—31no—
75#64994—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78Q8×D15—22no—
79Q8×D15—22no—
80C2×D60—21no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×C4×D15D411yescharacteristic
86C2×C4×D15D411yescharacteristic
87C2×C4×D15C2311yescharacteristic
88C2×Dic30—21no—
89C2×Dic30C2311yescharacteristic
90C3×C5×Q16—22no—
91C2×C3×C5×C8C2311yescharacteristic
92C2×C3×C5×C8C2311yescharacteristic
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C42×C5—21no—
98C3×C42×C5—21no—
99C3×C42×C5C2311yescharacteristic
100#6718—22no—
101#6717—22no—
102#6714—21no—
103#6714—21no—
104#6714—21no—
105#6714—21no—
106#6714—21no—
107C4⋊Dic15—21no—
108C4⋊Dic15—21no—
109C4⋊Dic15C2311yescharacteristic
110C4⋊Dic15C2311yescharacteristic
111#6712—21no—
112#6712—21no—
113#6712—21no—
114#6712—21no—
115#6712—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15—21no—
119C4×Dic15D411yescharacteristic
120C4×Dic15D411yescharacteristic
121C4×Dic15C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123C2×C3⋊#168C2311yescharacteristic
124#6706—22no—
125#5580—51no—
126C4×D3×Q8—51no—
127C3×#441D511yescharacteristic, complemented
128#5186—51no—
129#5185—51no—
130#5030—51no—
131#5026—51no—
132#4863—51no—
133#4857—51no—
134#4811—51no—
135#4806—51no—
136#4798—51no—
137#4796—51no—
138#4710—51no—
139#4705—51no—
140C2×Q8×D5—31no—
141C2×C5×Q16C2×D311yescharacteristic
142C4×C5×Q8C2×D311yescharacteristic
143C4×C5×Q8C2×D311yescharacteristic
144#4093—31no—
145#4092—31no—
146Q8×Dic5—31no—
147C2×#689—31no—
148C2×#688—31no—
149C2×#677—31no—
150#4044—61no—
151#4041—31no—
152#4040—61no—
153D5×C4⋊C4—31no—
154D5×C4⋊C4—61no—
155#4036—31no—
156#4033—31no—
157#4033—61no—
158C4×D20—31no—
159C4×D20—61no—
160#4018—61no—
161C42×D5—31no—
162C42×D5—61no—
163C4×Dic10—31no—
164C4×Dic10—61no—
165C5×#106C2×D311yescharacteristic
166C5×#103C2×D311yescharacteristic
167C5×#103C2×D311yescharacteristic
168C5×#97C2×D311yescharacteristic
169#3967—31no—
170#3967—31no—
171#3953—31no—
172#3952—31no—
173#3952—31no—
174#3950—31no—
175#3948—31no—
176#3946—31no—
177#3946—31no—
178#3942—31no—
179#3941—31no—
180#3940—31no—
181#3939—31no—
182#3935—31no—
183#3117—151noSylow
184C22×D15—21no—
185C22×D15C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C2×D411yescharacteristic
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2411yescharacteristic
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15C2×D411yescharacteristic
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203D60—21no—
204D60—21no—
205D60—42no—
206C4×D15—24no—
207C4×D15—22no—
208C4×D15—21no—
209C4×D15—21no—
210C4×D15—41no—
211C4×D15—42no—
212C4×D15—42no—
213Dic30—24no—
214Dic30—21no—
215Dic30#4112yes—
216C3×C5×C8—21no—
217C3×C5×C8—21no—
218C3⋊#168—21no—
219C3⋊#168—21no—
220C2×D3×Q8—51no—
221C2×C3×Q16C2×D511yescharacteristic
222C3×C4×Q8C2×D511yescharacteristic
223C3×C4×Q8C2×D511yescharacteristic
224#947—51no—
225#946—51no—
226Q8×Dic3—51no—
227C2×#216—51no—
228C2×#215—51no—
229C2×#204—51no—
230#898—101no—
231#895—51no—
232#894—101no—
233D3×C4⋊C4—51no—
234D3×C4⋊C4—101no—
235#890—51no—
236#887—51no—
237#887—101no—
238C4×D12—51no—
239C4×D12—101no—
240#872—101no—
241C42×D3—51no—
242C42×D3—101no—
243C4×Dic6—51no—
244C4×Dic6—101no—
245C3×#106C2×D511yescharacteristic
246C3×#103C2×D511yescharacteristic
247C3×#103C2×D511yescharacteristic
248C3×#97C2×D511yescharacteristic
249#835—51no—
250#835—51no—
251#821—51no—
252(C2×D3)⋊C8—51no—
253(C2×D3)⋊C8—51no—
254#818—51no—
255#816—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258#810—51no—
259#809—51no—
260#808—51no—
261#807—51no—
262#803—51no—
263C2×C5×Q8C22×D311yescharacteristic
264C2×C5×Q8C22×D311yescharacteristic
265Q8×D5—62no—
266Q8×D5—62no—
267C2×D20—31no—
268C2×D20—61no—
269C2×C4×D5—31no—
270C2×C4×D5—31no—
271C2×C4×D5—31no—
272C2×C4×D5—61no—
273C2×C4×D5—61no—
274C2×C4×D5—61no—
275C2×Dic10—31no—
276C2×Dic10—61no—
277C5×Q16—22no—
278C2×C5×C8C22×D311yescharacteristic
279C2×C5×C8C22×D311yescharacteristic
280C5×C4⋊C4—21no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4C22×D311yescharacteristic
283C5×C4⋊C4C22×D311yescharacteristic
284C42×C5—21no—
285C42×C5—21no—
286C42×C5C22×D311yescharacteristic
287#689—62no—
288#688—62no—
289#685—61no—
290#685—61no—
291#685—61no—
292#685—61no—
293#685—61no—
294C4⋊Dic5—31no—
295C4⋊Dic5—31no—
296C4⋊Dic5—61no—
297C4⋊Dic5—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303C4×Dic5—31no—
304C4×Dic5—31no—
305C4×Dic5—31no—
306C4×Dic5—61no—
307C4×Dic5—61no—
308C4×Dic5—61no—
309C2×#168—31no—
310C2×#168—31no—
311#677—62no—
312#529—151no—
313C2×C4×Q8—151no—
314#484—151no—
315#481—151no—
316#479—151no—
317#479—151no—
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441D1511yescharacteristic, complemented
324#440—151no—
325#440—151no—
326#432—151no—
327C22×C3×C5C22×D411yescharacteristic
328C2×D15—21no—
329C2×D15—21no—
330C2×D15—41no—
331C2×D15—41no—
332C2×D15—41no—
333C2×D15#13712yes—
334C3×C4×C5—22no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5C2×#4111yescharacteristic
341C3×C4×C5C2×#4111yescharacteristic
342Dic15—21no—
343Dic15—22no—
344Dic15—21no—
345Dic15—21no—
346Dic15—41no—
347Dic15—41no—
348C2×C3×Q8C22×D511yescharacteristic
349C2×C3×Q8C22×D511yescharacteristic
350D3×Q8—102no—
351D3×Q8—102no—
352C2×D12—51no—
353C2×D12—101no—
354C2×C4×D3—51no—
355C2×C4×D3—51no—
356C2×C4×D3—51no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×C4×D3—101no—
360C2×Dic6—51no—
361C2×Dic6—101no—
362C3×Q16—22no—
363C2×C3×C8C22×D511yescharacteristic
364C2×C3×C8C22×D511yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C42—21no—
370C3×C42—21no—
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—51no—
381C4⋊Dic3—101no—
382C4⋊Dic3—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388C4×Dic3—51no—
389C4×Dic3—51no—
390C4×Dic3—51no—
391C4×Dic3—101no—
392C4×Dic3—101no—
393C4×Dic3—101no—
394C2×C3⋊C8—51no—
395C2×C3⋊C8—51no—
396#204—102no—
397C22×D5—31no—
398C22×D5—61no—
399C5×Q8—21no—
400C5×Q8—21no—
401C5×Q8—21no—
402C5×Q8#23512yes—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5D3×D411yescharacteristic
408C2×C4×C5D3×D411yescharacteristic
409C2×C4×C5C23×D311yescharacteristic
410C2×Dic5—31no—
411C2×Dic5—31no—
412C2×Dic5—31no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416D20—61no—
417D20—61no—
418D20—122no—
419C4×D5—62no—
420C4×D5—64no—
421C4×D5—61no—
422C4×D5—61no—
423C4×D5—121no—
424C4×D5—122no—
425C4×D5—122no—
426Dic10—32no—
427Dic10—64no—
428Dic10—61no—
429C5×C8—21no—
430C5×C8—21no—
431#168—61no—
432#168—61no—
433C22×Q8—151no—
434C2×Q16—151no—
435C2×Q16C2×D1511yescharacteristic
436C2×SD16—151no—
437C2×SD16—151no—
438#126—301no—
439#125—151no—
440#124—151no—
441#123—301no—
442C22⋊Q8—151no—
443#121—151no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×Q8—151no—
447C4×Q8—301no—
448C4×Q8—301no—
449C4×Q8C2×D1511yescharacteristic
450C4×Q8C2×D1511yescharacteristic
451C4×D4—151no—
452C4×D4—301no—
453#117—301no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—301no—
456C2×C42—151no—
457C2×C42—301no—
458#107—151no—
459#107—151no—
460#106—151no—
461#106C2×D1511yescharacteristic
462C4⋊C8—151no—
463C4⋊C8—151no—
464#103—151no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103C2×D1511yescharacteristic
469#103C2×D1511yescharacteristic
470#102—151no—
471#102—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474#97—151no—
475#97C2×D1511yescharacteristic
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479D15—22no—
480D15—81no—
481C22×D3—51no—
482C22×D3—101no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8#70912yes—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4D4×D511yescharacteristic
492C2×C3×C4D4×D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494C2×Dic3—51no—
495C2×Dic3—51no—
496C2×Dic3—51no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—101no—
500D12—101no—
501D12—101no—
502D12—202no—
503C4×D3—102no—
504C4×D3—104no—
505C4×D3—101no—
506C4×D3—101no—
507C4×D3—201no—
508C4×D3—202no—
509C4×D3—202no—
510Dic6—52no—
511Dic6—104no—
512Dic6—101no—
513C3×C8—21no—
514C3×C8—21no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5C2×D3×D411yescharacteristic
518C2×D5—32no—
519C2×D5—61no—
520C2×D5—61no—
521C2×D5—121no—
522C2×D5—121no—
523C2×D5—121no—
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—22no—
527C4×C5—41no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5C2×#23511yescharacteristic
531C4×C5D3×#4111yescharacteristic
532Dic5—61no—
533Dic5—61no—
534Dic5—62no—
535Dic5—61no—
536Dic5—121no—
537Dic5—121no—
538C2×Q8—151no—
539C2×Q8—301no—
540C2×Q8—302no—
541C2×Q8—302no—
542C2×Q8C22×D1511yescharacteristic
543C2×Q8C22×D1511yescharacteristic
544C2×D4—151no—
545C2×D4—301no—
546C22×C4—151no—
547C22×C4—151no—
548C22×C4—151no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—301no—
552Q16—22no—
553Q16—302no—
554SD16—302no—
555SD16—302no—
556C2×C8—151no—
557C2×C8—151no—
558C2×C8C22×D1511yescharacteristic
559C2×C8C22×D1511yescharacteristic
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—151no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4C22×D1511yescharacteristic
572C4⋊C4C22×D1511yescharacteristic
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C22⋊C4—301no—
577C22⋊C4—301no—
578C42—21no—
579C42—21no—
580C42—151no—
581C42—151no—
582C42—151no—
583C42—301no—
584C42—301no—
585C42—301no—
586C42C22×D1511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3C2×D4×D511yescharacteristic
589C2×D3—52no—
590C2×D3—101no—
591C2×D3—101no—
592C2×D3—201no—
593C2×D3—201no—
594C2×D3—201no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4C2×#70911yescharacteristic
602C3×C4D5×#4111yescharacteristic
603Dic3—101no—
604Dic3—101no—
605Dic3—102no—
606Dic3—101no—
607Dic3—201no—
608Dic3—201no—
609C2×C5#554711yescharacteristic
610C2×C5D3×#13711yescharacteristic
611C2×C5#577711yescharacteristic
612D5—62no—
613D5—241no—
614C23—151no—
615C23—301no—
616Q8—21no—
617Q8—21no—
618Q8—21no—
619Q8—152no—
620Q8—304no—
621Q8—301no—
622Q8#681712yes—
623D4—301no—
624D4—301no—
625D4—602no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—151no—
631C2×C4—151no—
632C2×C4—151no—
633C2×C4—302no—
634C2×C4—304no—
635C2×C4—301no—
636C2×C4—301no—
637C2×C4—301no—
638C2×C4—301no—
639C2×C4—301no—
640C2×C4—601no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D4×D1511yescharacteristic
644C2×C4D4×D1511yescharacteristic
645C2×C4C23×D1511yescharacteristic
646C8—21no—
647C8—21no—
648C8—301no—
649C8—301no—
650C2×C3#6588111yescharacteristic
651C2×C3D5×#13711yescharacteristic
652C2×C3#6611111yescharacteristic
653D3—102no—
654D3—401no—
655C5#7983411yescharacteristic, complemented, Sylow
656C22—152no—
657C22—301no—
658C22—301no—
659C22—601no—
660C22—601no—
661C22—601no—
662C22C2×D4×D1511yescharacteristic
663C4—22no—
664C4—21no—
665C4—21no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—301no—
670C4—302no—
671C4—301no—
672C4—301no—
673C4—601no—
674C4—601no—
675C4C2×#681711yescharacteristic
676C4#41×D1511yescharacteristic
677C3#1061156511yescharacteristic, complemented, Sylow
678C2—302no—
679C2—1201no—
680C2#1175630611yescharacteristic
681C2D15×#13711yescharacteristic
682C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#441C2
socleC22×C3×C5C22×D4
prime radical#91784C22
hypercenter#441D15
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D15C2semidirect
3. C3×C5×#441C2semidirect
4. #11751287C2semidirect
5. #11751286C2semidirect
6. #11751131C2semidirect
7. #11751127C2semidirect
9. #11750958C2semidirect
10. #11750912C2semidirect
12. #11750899C2semidirect
13. #11750897C2semidirect
14. #11750811C2semidirect
15. #11750806C2semidirect
63. C5×#441D3semidirect
127. C3×#441D5semidirect
323. #441D15semidirect
587. C3×C5#3117semidirect
655. C5#79834semidirect
677. C3#10611565semidirect

Maximal subgroups

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

subgroupindex
#117563392
C4×Q8×D152
C3×C5×#4412
#117512872
#117512862
#117511312
#117511272
#117509642
#117509582
#117509122
#117509072
#117508992
#117508972
#117508112
#117508062
#106115653
#798345