Finite Group Databasebeta

← #14430218

Subgroups — #14430218

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756447C211yesmaximal, characteristic, complemented
2C4×#6819C211yesmaximal, characteristic
3C3×C5×#478C211yesmaximal, characteristic, complemented
4#11751164C211yesmaximal, characteristic, complemented
5#11751110C211yesmaximal, characteristic, complemented
6#11750981C211yesmaximal, characteristic, complemented
7#11750976C211yesmaximal, characteristic, complemented
8#11750961C211yesmaximal, characteristic, complemented
9#11750955C211yesmaximal, characteristic, complemented
10D15×C4⋊C8C211yesmaximal, characteristic, complemented
11#11750930C211yesmaximal, characteristic, complemented
12#11750873C211yesmaximal, characteristic
13#11750873C211yesmaximal, characteristic
14#11750862C211yesmaximal, characteristic, complemented
15#11750860C211yesmaximal, characteristic, complemented
16#10612896—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20D4×Dic15C2211yescharacteristic
21C4×#1220—21no—
22C2×C4×Dic15—21no—
23C2×C8×D15C2211yescharacteristic
24C2×C8×D15C2211yescharacteristic
25#91785—21no—
26#91785—21no—
27#91781C2211yescharacteristic
28#91781C2211yescharacteristic
29#91781C2211yescharacteristic
30#91777C2211yescharacteristic
31#91777C2211yescharacteristic
32#91776—21no—
33#91776—21no—
34#91776C2211yescharacteristic
35#91770—21no—
36#91766—21no—
37C42×D15C2211yescharacteristic
38#91759C2211yescharacteristic
39C4×Dic30C2211yescharacteristic
40C3×C5×#107C2211yescharacteristic
41C3×C5×#106C2211yescharacteristic
42C3×C5×C4⋊C8C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45#91116C2211yescharacteristic
46#91116C2211yescharacteristic
47#91102C2211yescharacteristic
48#91101C2211yescharacteristic
49#91100C2211yescharacteristic
50#91100C2211yescharacteristic
51#91098C2211yescharacteristic
52#91098C2211yescharacteristic
53#91094C2211yescharacteristic
54#91094C2211yescharacteristic
55#91092C2211yescharacteristic
56#91092C2211yescharacteristic
57#91091C2211yescharacteristic
58#91091C2211yescharacteristic
59C4⋊(C3⋊#168)C2211yescharacteristic
60#81165—51nomaximal, Hall
61#66022—31no—
62C4×#711—31no—
63C5×#478D311yescharacteristic, complemented
64#65352—31no—
65#65298—31no—
66#65169—31no—
67#65164—31no—
68#65149—31no—
69#65143—31no—
70D5×C4⋊C8—31no—
71#65118—31no—
72#65061—31no—
73#65061—31no—
74#65050—31no—
75#65048—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×#1220—21no—
79C22×Dic15—21no—
80C22×Dic15—21no—
81#6819—22no—
82#6819Q814yescomplemented
83C2×C4×D15D411yescharacteristic
84C2×C4×D15D411yescharacteristic
85C2×C4×D15C2311yescharacteristic
86C2×Dic30—21no—
87C2×Dic30—21no—
88C2×Dic30C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C22⋊C4—21no—
97C3×C42×C5C2311yescharacteristic
98#6719—21no—
99#6714—21no—
100#6714—21no—
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104C4⋊Dic15C2311yescharacteristic
105#6712—21no—
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110#6712—21no—
111C4×Dic15—21no—
112C4×Dic15—21no—
113C4×Dic15—21no—
114C4×Dic15—21no—
115C4×Dic15—21no—
116C4×Dic15D411yescharacteristic
117C4×Dic15D411yescharacteristic
118C4×Dic15C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120C2×C3⋊#168C2311yescharacteristic
121C8×D15—22no—
122C8×D15—22no—
123#5688—51no—
124C4×#237—51no—
125C3×#478D511yescharacteristic, complemented
126#5063—51no—
127#5009—51no—
128#4880—51no—
129#4875—51no—
130#4860—51no—
131#4854—51no—
132D3×C4⋊C8—51no—
133#4829—51no—
134#4772—51no—
135#4772—51no—
136#4761—51no—
137#4759—51no—
138C2×#711—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×D4C2×D311yescharacteristic
141D4×Dic5—31no—
142C4×C22⋊D5—61no—
143C2×C4×Dic5—61no—
144C2×C8×D5—31no—
145C2×C8×D5—31no—
146#4042—61no—
147#4042—61no—
148#4038—31no—
149#4038—31no—
150#4038—31no—
151#4034—31no—
152#4034—31no—
153#4033—31no—
154#4033—61no—
155#4033—61no—
156#4027—61no—
157#4023—61no—
158C42×D5—31no—
159#4016—31no—
160C4×Dic10—31no—
161C5×#107C2×D311yescharacteristic
162C5×#106C2×D311yescharacteristic
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#102C2×D311yescharacteristic
165C5×#102C2×D311yescharacteristic
166#3964—31no—
167#3964—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942—31no—
175#3942—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3076—151noSylow
182C23×C3×C5—21no—
183C22×D15C2×D411yescharacteristic
184C3×C5×D4—21no—
185C3×C5×D4C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—42no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193#1220—24no—
194C2×Dic15—21no—
195C2×Dic15—24no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—42no—
200C2×Dic15C2×D411yescharacteristic
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203C4×D15—22no—
204C4×D15—41no—
205C4×D15C2×Q812yes—
206C4×D15#4112yes—
207Dic30—21no—
208Dic30—42no—
209Dic30—42no—
210Dic30C2×Q812yes—
211C3×C5×C8—21no—
212C3×C5×C8—21no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C2×#237—51no—
216C3×#125C2×D511yescharacteristic
217C3×C4×D4C2×D511yescharacteristic
218D4×Dic3—51no—
219C4×#67—101no—
220C2×C4×Dic3—101no—
221C2×D3×C8—51no—
222C2×D3×C8—51no—
223#896—101no—
224#896—101no—
225#892—51no—
226#892—51no—
227#892—51no—
228#888—51no—
229#888—51no—
230#887—51no—
231#887—101no—
232#887—101no—
233#67⋊C4—101no—
234#877—101no—
235C42×D3—51no—
236#870—51no—
237C4×Dic6—51no—
238C3×#107C2×D511yescharacteristic
239C3×#106C2×D511yescharacteristic
240C3×C4⋊C8C2×D511yescharacteristic
241C3×#102C2×D511yescharacteristic
242C3×#102C2×D511yescharacteristic
243#832—51no—
244#832—51no—
245#818—51no—
246#817—51no—
247#816—51no—
248#816—51no—
249Dic3⋊C8—51no—
250Dic3⋊C8—51no—
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C2×C5×D4C22×D311yescharacteristic
259C22×C4×C5—21no—
260C2×C22⋊D5—61no—
261C22×Dic5—61no—
262C22×Dic5—61no—
263#711—34no—
264#711—62no—
265C2×C4×D5—31no—
266C2×C4×D5—31no—
267C2×C4×D5—31no—
268C2×Dic10—31no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×C5×C8C22×D311yescharacteristic
272C2×C5×C8C22×D311yescharacteristic
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C4⋊C4C22×D311yescharacteristic
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C22⋊C4—21no—
279C42×C5C22×D311yescharacteristic
280C22⋊Dic5—61no—
281#685—61no—
282#685—61no—
283#685—61no—
284C4⋊Dic5—31no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293C4×Dic5—31no—
294C4×Dic5—31no—
295C4×Dic5—31no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C4×Dic5—61no—
301C2×#168—31no—
302C2×#168—31no—
303C8×D5—62no—
304C8×D5—62no—
305#533—151no—
306C4×#41—151no—
307#479—151no—
308#479—151no—
309#478—151no—
310#478D1511yescharacteristic, complemented
311#477—151no—
312#476—151no—
313#475—151no—
314#474—151no—
315#427—151no—
316#427—151no—
317C2×C4⋊C8—151no—
318#416—151no—
319#416—151no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5C22×D411yescharacteristic
324C2×D15—21no—
325C2×D15—21no—
326C2×D15C22⋊Q812yes—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5—41no—
330C3×C4×C5—41no—
331C3×C4×C5—41no—
332C3×C4×C5C22×Q811yescharacteristic
333C3×C4×C5C2×#4111yescharacteristic
334Dic15—22no—
335Dic15—21no—
336Dic15—41no—
337Dic15—41no—
338Dic15—41no—
339Dic15C22⋊Q812yes—
340Dic15#13512yes—
341C2×C3×D4C22×D511yescharacteristic
342C22×C3×C4—21no—
343C2×#67—101no—
344C22×Dic3—101no—
345C22×Dic3—101no—
346#237—54no—
347#237—102no—
348C2×C4×D3—51no—
349C2×C4×D3—51no—
350C2×C4×D3—51no—
351C2×Dic6—51no—
352C2×Dic6—101no—
353C2×Dic6—101no—
354C2×C3×C8C22×D511yescharacteristic
355C2×C3×C8C22×D511yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4C22×D511yescharacteristic
359C3×C4⋊C4C22×D511yescharacteristic
360C3×C4⋊C4C22×D511yescharacteristic
361C3×C22⋊C4—21no—
362C3×C42C22×D511yescharacteristic
363#217—101no—
364(C2×D3)⋊C4—101no—
365(C2×D3)⋊C4—101no—
366(C2×D3)⋊C4—101no—
367C4⋊Dic3—51no—
368C4⋊Dic3—51no—
369C4⋊Dic3—51no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376C4×Dic3—51no—
377C4×Dic3—51no—
378C4×Dic3—51no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3—101no—
382C4×Dic3—101no—
383C4×Dic3—101no—
384C2×C3⋊C8—51no—
385C2×C3⋊C8—51no—
386D3×C8—102no—
387D3×C8—102no—
388C23×C5—21no—
389C22×D5—31no—
390C5×D4—21no—
391C5×D4D3×Q812yes—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—42no—
396C2×C4×C5D3×D411yescharacteristic
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C22⋊D5—64no—
400C2×Dic5—31no—
401C2×Dic5—31no—
402C2×Dic5—31no—
403C2×Dic5—64no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—61no—
408C2×Dic5—122no—
409C4×D5—32no—
410C4×D5—32no—
411C4×D5—62no—
412C4×D5—121no—
413Dic10—32no—
414Dic10—61no—
415Dic10—122no—
416Dic10—122no—
417C5×C8—21no—
418C5×C8—21no—
419#168—61no—
420#168—61no—
421C2×#41—151no—
422C22×C8—151no—
423C22×C8—151no—
424C4⋊Q8—151no—
425C4⋊Q8—151no—
426#125—151no—
427#125C2×D1511yescharacteristic
428C22⋊Q8—301no—
429C22⋊Q8—301no—
430C4×Q8—151no—
431C4×Q8—151no—
432C4×Q8—301no—
433C4×Q8—301no—
434C4×D4—151no—
435C4×D4—301no—
436C4×D4—301no—
437C4×D4C2×D1511yescharacteristic
438#117—151no—
439#117—151no—
440#117—151no—
441#117—301no—
442C2×C42—151no—
443C2×C42—301no—
444#107—151no—
445#107—151no—
446#107—151no—
447#107C2×D1511yescharacteristic
448#106—151no—
449#106—151no—
450#106—151no—
451#106C2×D1511yescharacteristic
452C4⋊C8—151no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8C2×D1511yescharacteristic
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460#102—151no—
461#102—151no—
462#102C2×D1511yescharacteristic
463#102C2×D1511yescharacteristic
464C2×C3×C5—42no—
465C2×C3×C5C2×C22⋊Q811yescharacteristic
466C2×C3×C5C2×#13511yescharacteristic
467C2×C3×C5#57511yescharacteristic
468D15—22no—
469C23×C3—21no—
470C22×D3—51no—
471C3×D4—21no—
472C3×D4Q8×D512yes—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—42no—
477C2×C3×C4D4×D511yescharacteristic
478C2×C3×C4D4×D511yescharacteristic
479C2×C3×C4C23×D511yescharacteristic
480#67—104no—
481C2×Dic3—51no—
482C2×Dic3—51no—
483C2×Dic3—51no—
484C2×Dic3—104no—
485C2×Dic3—101no—
486C2×Dic3—101no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C2×Dic3—202no—
490C4×D3—52no—
491C4×D3—52no—
492C4×D3—102no—
493C4×D3—201no—
494Dic6—52no—
495Dic6—101no—
496Dic6—202no—
497Dic6—202no—
498C3×C8—21no—
499C3×C8—21no—
500C3⋊C8—101no—
501C3⋊C8—101no—
502C22×C5—22no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5C2×D3×D411yescharacteristic
506C2×D5—32no—
507C2×D5—61no—
508C2×D5—61no—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—41no—
512C4×C5—41no—
513C4×C5—41no—
514C4×C5C2×D3×Q811yescharacteristic
515C4×C5D3×#4111yescharacteristic
516Dic5—32no—
517Dic5—32no—
518Dic5—61no—
519Dic5—62no—
520Dic5—121no—
521Dic5—121no—
522Dic5—121no—
523#41—154no—
524#41—302no—
525C2×Q8—151no—
526C2×Q8—301no—
527C2×Q8—301no—
528C2×D4—301no—
529C2×D4C22×D1511yescharacteristic
530C22×C4—21no—
531C22×C4—151no—
532C22×C4—151no—
533C22×C4—151no—
534C22×C4—301no—
535C22×C4—301no—
536C2×C8—151no—
537C2×C8—151no—
538C2×C8—302no—
539C2×C8—302no—
540C2×C8C22×D1511yescharacteristic
541C2×C8C22×D1511yescharacteristic
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—151no—
545C4⋊C4—151no—
546C4⋊C4—151no—
547C4⋊C4—301no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4—301no—
553C4⋊C4C22×D1511yescharacteristic
554C4⋊C4C22×D1511yescharacteristic
555C4⋊C4C22×D1511yescharacteristic
556C22⋊C4—21no—
557C22⋊C4—301no—
558C22⋊C4—301no—
559C22⋊C4—301no—
560C22⋊C4—301no—
561C42—151no—
562C42—151no—
563C42—151no—
564C42—301no—
565C42—301no—
566C42—301no—
567C42—301no—
568C42—301no—
569C42C22×D1511yescharacteristic
570C3×C5#307611yescharacteristic, complemented, Hall
571C22×C3—22no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3C2×D4×D511yescharacteristic
575C2×D3—52no—
576C2×D3—101no—
577C2×D3—101no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4C2×Q8×D511yescharacteristic
584C3×C4D5×#4111yescharacteristic
585Dic3—52no—
586Dic3—52no—
587Dic3—101no—
588Dic3—102no—
589Dic3—201no—
590Dic3—201no—
591Dic3—201no—
592C2×C5—42no—
593C2×C5D3×C22⋊Q811yescharacteristic
594C2×C5D3×#13511yescharacteristic
595C2×C5#577311yescharacteristic
596D5—62no—
597C23—21no—
598C23—151no—
599Q8—152no—
600Q8—301no—
601Q8—602no—
602Q8—602no—
603D4—21no—
604D4—304no—
605D4Q8×D1512yes—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—42no—
610C2×C4—151no—
611C2×C4—151no—
612C2×C4—152no—
613C2×C4—152no—
614C2×C4—151no—
615C2×C4—302no—
616C2×C4—304no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—601no—
622C2×C4—602no—
623C2×C4D4×D1511yescharacteristic
624C2×C4D4×D1511yescharacteristic
625C2×C4C23×D1511yescharacteristic
626C8—21no—
627C8—21no—
628C8—301no—
629C8—301no—
630C2×C3—42no—
631C2×C3D5×C22⋊Q811yescharacteristic
632C2×C3D5×#13511yescharacteristic
633C2×C3#6610711yescharacteristic
634D3—102no—
635C5#8116511yescharacteristic, complemented, Sylow
636C22—22no—
637C22—41no—
638C22—41no—
639C22—152no—
640C22—301no—
641C22—301no—
642C22C2×D4×D1511yescharacteristic
643C4—21no—
644C4—21no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—152no—
649C4—152no—
650C4—302no—
651C4—301no—
652C4—601no—
653C4—601no—
654C4—601no—
655C4C2×Q8×D1511yescharacteristic
656C4#41×D1511yescharacteristic
657C3#1061289611yescharacteristic, complemented, Sylow
658C2—42no—
659C2—302no—
660C2D15×C22⋊Q811yescharacteristic
661C2D15×#13511yescharacteristic
662C2#1175653211yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#478C2
socleC22×C3×C5C22×D4
prime radicalC2×#6819C22
hypercenter#478D15
hypocenterC3×C5#3076
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #11756447C2semidirect
3. C3×C5×#478C2semidirect
4. #11751164C2semidirect
5. #11751110C2semidirect
6. #11750981C2semidirect
7. #11750976C2semidirect
8. #11750961C2semidirect
9. #11750955C2semidirect
10. D15×C4⋊C8C2semidirect
11. #11750930C2semidirect
14. #11750862C2semidirect
15. #11750860C2semidirect
63. C5×#478D3semidirect
82. #6819Q8semidirect
125. C3×#478D5semidirect
310. #478D15semidirect
570. C3×C5#3076semidirect
635. C5#81165semidirect
657. C3#10612896semidirect

Maximal subgroups

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

subgroupindex
#117564472
C4×#68192
C3×C5×#4782
#117511642
#117511102
#117509812
#117509762
#117509612
#117509552
D15×C4⋊C82
#117509302
#117508732
#117508622
#117508602
#106128963
#811655