Finite Group Databasebeta

← #14417290

Subgroups — #14417290

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91260C211yesmaximal, characteristic
2#11753671C211yesmaximal, characteristic
3#11753397C211yesmaximal, characteristic, complemented
4#11750954C211yesmaximal, characteristic, complemented
5C5×#4852C211yesmaximal, characteristic, complemented
6C3×#65150C211yesmaximal, characteristic, complemented
7#11748050C211yesmaximal, characteristic, complemented
8#11747873C211yesmaximal, characteristic, complemented
9#11747816C211yesmaximal, characteristic, complemented
10#11747499C211yesmaximal, characteristic
11D5×#810C211yesmaximal, characteristic, complemented
12#11747473C211yesmaximal, characteristic, complemented
13#11747278C211yesmaximal, characteristic, complemented
14#11747276C211yesmaximal, characteristic, complemented
15#11747234C211yesmaximal, characteristic, complemented
16#10611379—31nomaximal, Hall
17C2×#6772C2211yescharacteristic
18C2×D5×Dic6C2211yescharacteristic
19C2×Dic60C2211yescharacteristic
20#91776C2211yescharacteristic
21#91776C2211yescharacteristic
22C2×C5×#204C2211yescharacteristic
23C5×#893C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C2×C3×#676C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27C3×D5×C4⋊C4C2211yescharacteristic
28C4×#1204—21no—
29#91440—21no—
30C4×#1201—21no—
31#91435C2211yescharacteristic
32#91400—21no—
33D3×#683—21no—
34#91394—21no—
35#91393—21no—
36#91357C2211yescharacteristic
37#91344C2211yescharacteristic
38#91340C2211yescharacteristic
39#91340C2211yescharacteristic
40#91323—21no—
41C2×#6663C2211yescharacteristic
42C2×#6659C2211yescharacteristic
43C2×D5×C3⋊C8C2211yescharacteristic
44#91260C418yescomplemented
45C3×C5×#106C2211yescharacteristic
46#91099C2211yescharacteristic
47#91094C2211yescharacteristic
48#91094C2211yescharacteristic
49C5×C8×Dic3C2211yescharacteristic
50C5×#810C2211yescharacteristic
51C5×#809C2211yescharacteristic
52C3×#3950C2211yescharacteristic
53C3×#3940C2211yescharacteristic
54C3×#3939C2211yescharacteristic
55#90974C2211yescharacteristic
56#90974C2211yescharacteristic
57#90972C2211yescharacteristic
58#90966C2211yescharacteristic
59#90953C2211yescharacteristic
60#90951C2211yescharacteristic
61#79202—51nomaximal, Hall
62C2×#4061—31no—
63#65906—31no—
64#65880—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67#65319—31no—
68#65307—31no—
69#65150D311yescharacteristic, complemented
70#65142—31no—
71D5×#103—31no—
72#65079—31no—
73#65061—31no—
74#65047—31no—
75C4×Dic20—31no—
76#64978—31no—
77C2×Dic30C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×D12C2311yescharacteristic
80C2×C4×C5×D3—21no—
81C2×C5×Dic6C2311yescharacteristic
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5C2311yescharacteristic
84C2×#1204—21no—
85C2×#1201—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88C2×D5×Dic3—21no—
89#6772—22no—
90#6772C2×C414yes—
91D5×Dic6—22no—
92D5×Dic6C2×C414yescomplemented
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96#6712—21no—
97#6712—21no—
98C4×Dic15—21no—
99C4×Dic15—21no—
100C4×Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102Dic60C2×C414yescomplemented
103C5×(C2×D3)⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3C2311yescharacteristic
107C2×C5×C3⋊C8C2311yescharacteristic
108C5×#204C2×C414yescomplemented
109C3×#685—21no—
110C3×C4⋊Dic5C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C2×C3×#168C2311yescharacteristic
115C3×#676C2×C414yescomplemented
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6669—21no—
119#6668D411yescharacteristic
120#6668D411yescharacteristic
121(C2×D3)⋊Dic5—21no—
122#6665D411yescharacteristic
123#6665D411yescharacteristic
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6663C2×C414yescomplemented
128#6659C2×C414yescomplemented
129D5×C3⋊C8—22no—
130C2×#909—51no—
131#5516—51no—
132#5504—51no—
133C3×#428—51no—
134#5122—51no—
135#5002—51no—
136C2×#810—51no—
137#4889—51no—
138#4889—51no—
139#4873—51no—
140#4873—51no—
141#4853—51no—
142#4853—51no—
143#4852—51no—
144#4852D511yescharacteristic, complemented
145C2×Q8×D5—31no—
146C2×#711—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#689—31no—
152D4×Dic5—31no—
153C2×#687—31no—
154C4×C22⋊D5—61no—
155C2×#683—61no—
156#4061—38no—
157C2×Dic20—31no—
158C2×#676C2×D311yescharacteristic
159C2×C8×D5—31no—
160#4038—61no—
161#4038C2×D311yescharacteristic
162D5×C4⋊C4C2×D311yescharacteristic
163#4033—31no—
164#4033—31no—
165#4033—61no—
166#4027—61no—
167#4023—61no—
168#4018—31no—
169#4018—61no—
170C4×Dic10—31no—
171C4×Dic10—31no—
172C4×Dic10—61no—
173C5×#106C2×D311yescharacteristic
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8—31no—
177#3967—31no—
178#3964—31no—
179#3950C2×D311yescharacteristic
180#3948—31no—
181#3948—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3942—31no—
186#3940C2×D311yescharacteristic
187#3939C2×D311yescharacteristic
188#3935—31no—
189#2947—151noSylow
190C22×C5×D3—21no—
191C22×C3×D5C2×D411yescharacteristic
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5C2411yescharacteristic
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15C2×D411yescharacteristic
198C2×Dic15C2×D411yescharacteristic
199Dic30—21no—
200Dic30—21no—
201Dic30C22×C412yes—
202Dic30C22×C412yes—
203C2×C5×Dic3—21no—
204C2×C5×Dic3C2×D411yescharacteristic
205C2×C5×Dic3C2×D411yescharacteristic
206C5×D12—21no—
207C5×D12C22×C412yes—
208C4×C5×D3—81no—
209C5×Dic6—21no—
210C5×Dic6C22×C412yes—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5C2×D411yescharacteristic
214C3×C4×D5—81no—
215C3×C4×D5C22×C412yes—
216C3×C4×D5#4112yes—
217#1204—24no—
218#1201—24no—
219D3×Dic5—24no—
220D3×Dic5—81no—
221D5×Dic3—24no—
222C3×C5×C8C22×C412yes—
223C3⋊#168—21no—
224C3×#168C22×C412yes—
225C5×C3⋊C8—21no—
226C2×#235—51no—
227C22×Dic6—51no—
228C2×C3×M16—51no—
229C3×#117—51no—
230C2×C3×C4⋊C4—51no—
231C4×#67—101no—
232C4×#67—101no—
233#926—51no—
234C22×C3⋊C8—51no—
235#909—58no—
236C2×Dic12—51no—
237C2×Dic12—51no—
238C2×#204—51no—
239C2×#204C2×D511yescharacteristic
240#893—51no—
241#893C2×D511yescharacteristic
242#892—101no—
243D3×C4⋊C4—101no—
244#887—51no—
245#887—51no—
246#887—51no—
247#887—51no—
248#887—51no—
249#887C2×D511yescharacteristic
250#877—101no—
251#877—101no—
252C4×Dic6—101no—
253C4×Dic6—101no—
254C3×#107—51no—
255C3×#107—51no—
256C3×#106—51no—
257C3×#106C2×D511yescharacteristic
258#815—51no—
259#815—51no—
260C8×Dic3—51no—
261C8×Dic3C2×D511yescharacteristic
262#810—51no—
263#810—51no—
264#810—51no—
265#810—51no—
266#810—51no—
267#810C2×D511yescharacteristic
268#809—51no—
269#809C2×D511yescharacteristic
270C2×C5×Q8—31no—
271C2×C5×D4—31no—
272C22×C4×C5—61no—
273C2×C22⋊D5—61no—
274C22×Dic5—61no—
275C22×Dic5—61no—
276Q8×D5—34no—
277Q8×D5—62no—
278#711—34no—
279#711—62no—
280C2×C4×D5—21no—
281C2×C4×D5—61no—
282C2×C4×D5C22×D311yescharacteristic
283C2×Dic10—31no—
284C2×Dic10—31no—
285C2×Dic10—61no—
286C5×SD16—34no—
287C2×C5×C8—31no—
288C2×C5×C8C22×D311yescharacteristic
289C5×C4⋊C4—61no—
290C5×C4⋊C4C22×D311yescharacteristic
291C5×C4⋊C4C22×D311yescharacteristic
292C5×C22⋊C4—61no—
293C42×C5—31no—
294C42×C5—61no—
295C22⋊Dic5—61no—
296#689—34no—
297#687—34no—
298#685—21no—
299#685—31no—
300#685—31no—
301C4⋊Dic5—61no—
302C4⋊Dic5C22×D311yescharacteristic
303C4⋊Dic5C22×D311yescharacteristic
304#683—21no—
305#683—31no—
306#683—31no—
307#683—61no—
308#683—61no—
309#683—61no—
310#683—61no—
311C4×Dic5—21no—
312C4×Dic5—31no—
313C4×Dic5—61no—
314C4×Dic5—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C2×#168—31no—
319C2×#168C22×D311yescharacteristic
320Dic20—34no—
321#676C4×D314yescomplemented
322C8×D5—62no—
323C2×#137—151no—
324#520—151no—
325#519—151no—
326#441—151no—
327#441—151no—
328#440—151no—
329#440—151no—
330C4×Q16—151no—
331C4×Q16—151no—
332C4×SD16—31no—
333C4×SD16—151no—
334#428—51no—
335#416—151no—
336C2×#103—151no—
337#405—151no—
338C22×C3×C5C22×D411yescharacteristic
339C2×C5×D3—22no—
340C2×C5×D3—41no—
341C2×C5×D3—41no—
342C2×C3×D5—21no—
343C2×C3×D5—21no—
344C2×C3×D5C4×D412yes—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347C3×C4×C5C23×C411yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349Dic15—22no—
350Dic15—22no—
351Dic15—21no—
352Dic15—21no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C3×Dic5C4×D412yes—
356C5×Dic3—22no—
357C5×Dic3—21no—
358C5×Dic3—21no—
359C22×C3×C4—51no—
360C22×C3×C4—101no—
361C2×#67—101no—
362C22×Dic3—101no—
363#235—54no—
364#235—102no—
365C2×D12C22×D511yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—101no—
368C2×C4×D3—101no—
369C2×Dic6—51no—
370C2×Dic6—51no—
371C2×Dic6—54no—
372C2×Dic6—102no—
373C2×Dic6—101no—
374C2×Dic6C22×D511yescharacteristic
375C3×M16—54no—
376C2×C3×C8—51no—
377C2×C3×C8C22×D511yescharacteristic
378C3×C4⋊C4—51no—
379C3×C4⋊C4—51no—
380C3×C4⋊C4—101no—
381C3×C4⋊C4C22×D511yescharacteristic
382C3×C4⋊C4C22×D511yescharacteristic
383C3×C22⋊C4—101no—
384C3×C42—101no—
385#217—51no—
386#217—51no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—101no—
389C4⋊Dic3—51no—
390C4⋊Dic3—51no—
391Dic3⋊C4—21no—
392Dic3⋊C4—101no—
393Dic3⋊C4—101no—
394Dic3⋊C4—101no—
395Dic3⋊C4—101no—
396Dic3⋊C4—101no—
397C4×Dic3—21no—
398C4×Dic3—51no—
399C4×Dic3—101no—
400C4×Dic3—101no—
401C4×Dic3—101no—
402C4×Dic3—101no—
403C4×Dic3—101no—
404C4×Dic3C22×D511yescharacteristic
405C2×C3⋊C8—51no—
406C2×C3⋊C8—102no—
407C2×C3⋊C8C22×D511yescharacteristic
408Dic12—54no—
409Dic12—54no—
410#204—54no—
411#204C4×D514yescomplemented
412C23×C5—61no—
413C22×D5D3×D411yescharacteristic
414C5×Q8—32no—
415C5×Q8—61no—
416C5×D4—32no—
417C5×D4—61no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—31no—
421C2×C4×C5—31no—
422C2×C4×C5—61no—
423C2×C4×C5—241no—
424C2×C4×C5C23×D311yescharacteristic
425C22⋊D5—64no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—31no—
429C2×Dic5—31no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—64no—
433C2×Dic5—241no—
434C2×Dic5D3×D411yescharacteristic
435C4×D5—64no—
436C4×D5—81no—
437C4×D5C2×C4×D312yes—
438C4×D5#23912yes—
439Dic10—32no—
440Dic10—32no—
441Dic10—61no—
442Dic10—61no—
443Dic10—64no—
444C5×C8—61no—
445C5×C8C2×C4×D312yes—
446#168—61no—
447#168C2×C4×D312yes—
448C2×#41—151no—
449C22×Q8—151no—
450#137—158no—
451C2×Q16—151no—
452C2×Q16—151no—
453C2×SD16—31no—
454C2×SD16—151no—
455C2×M16—51no—
456C22×C8—151no—
457C4×Q8—31no—
458C4×Q8—151no—
459C4×Q8—151no—
460C4×Q8—151no—
461C4×Q8—151no—
462C4×Q8—151no—
463C4×Q8—301no—
464C4×Q8—301no—
465C4×D4—31no—
466C4×D4—151no—
467C4×D4—301no—
468C4×D4—301no—
469#117—51no—
470#117—151no—
471#117—301no—
472#117—301no—
473#117—301no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—301no—
476#107—51no—
477#107—51no—
478#106—51no—
479#106D3×D511yescharacteristic
480#103—31no—
481#103—151no—
482#103—151no—
483#103—151no—
484#103—151no—
485#103—151no—
486#102—31no—
487#102—151no—
488#97—151no—
489#97—151no—
490C4×C8—31no—
491C4×C8—151no—
492C2×C3×C5C2×C4×D411yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C2×C3×C5#57811yescharacteristic
495C3×D5—22no—
496C5×D3—42no—
497C23×C3—51no—
498C22×D3—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—51no—
502C2×C3×C4—52no—
503C2×C3×C4—52no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—401no—
507C2×C3×C4C23×D511yescharacteristic
508#67—104no—
509C2×Dic3—21no—
510C2×Dic3—51no—
511C2×Dic3—51no—
512C2×Dic3—104no—
513C2×Dic3—101no—
514C2×Dic3—101no—
515C2×Dic3D4×D511yescharacteristic
516C2×Dic3D4×D511yescharacteristic
517D12—21no—
518D12C2×C4×D512yes—
519C4×D3—81no—
520C4×D3—104no—
521C4×D3—401no—
522Dic6—21no—
523Dic6—52no—
524Dic6—52no—
525Dic6—104no—
526Dic6—101no—
527Dic6—101no—
528Dic6C2×C4×D512yes—
529C3×C8—52no—
530C3×C8C2×C4×D512yes—
531C3⋊C8—21no—
532C3⋊C8—101no—
533C22×C5—62no—
534C22×C5—121no—
535C22×C5—121no—
536C22×C5C2×D3×D411yescharacteristic
537C2×D5—21no—
538C2×D5—21no—
539C2×D5#89312yes—
540C4×C5—41no—
541C4×C5—41no—
542C4×C5—62no—
543C4×C5—61no—
544C4×C5—61no—
545C4×C5C22×C4×D311yescharacteristic
546C4×C5C2×#23911yescharacteristic
547Dic5—41no—
548Dic5—41no—
549Dic5—62no—
550Dic5—62no—
551Dic5—61no—
552Dic5—61no—
553Dic5#89312yes—
554#41—154no—
555#41—302no—
556C2×Q8—31no—
557C2×Q8—154no—
558C2×Q8—151no—
559C2×Q8—151no—
560C2×Q8—301no—
561C2×Q8—302no—
562C2×D4—31no—
563C2×D4—301no—
564C22×C4—51no—
565C22×C4—61no—
566C22×C4—101no—
567C22×C4—301no—
568C22×C4—301no—
569C22×C4—301no—
570Q16—154no—
571Q16—154no—
572SD16—34no—
573SD16—154no—
574M16—54no—
575C2×C8—31no—
576C2×C8—51no—
577C2×C8—151no—
578C2×C8—302no—
579C2×C8C2×D3×D511yescharacteristic
580C4⋊C4—51no—
581C4⋊C4—51no—
582C4⋊C4—61no—
583C4⋊C4—101no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—301no—
587C4⋊C4—301no—
588C4⋊C4—301no—
589C4⋊C4—301no—
590C4⋊C4—301no—
591C4⋊C4C2×D3×D511yescharacteristic
592C4⋊C4C2×D3×D511yescharacteristic
593C22⋊C4—61no—
594C22⋊C4—101no—
595C22⋊C4—151no—
596C22⋊C4—151no—
597C22⋊C4—301no—
598C42—31no—
599C42—61no—
600C42—101no—
601C42—151no—
602C42—301no—
603C42—301no—
604C42—301no—
605C42—301no—
606C42—301no—
607C3×C5#294711yescharacteristic, complemented, Hall
608C22×C3—52no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3C2×D4×D511yescharacteristic
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—52no—
618C3×C4—201no—
619C3×C4—201no—
620C3×C4C22×C4×D511yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—22no—
625Dic3—101no—
626Dic3—101no—
627Dic3—102no—
628Dic3—102no—
629C2×C5—122no—
630C2×C5C2×#89311yescharacteristic
631C2×C5#577511yescharacteristic
632C2×C5#577911yescharacteristic
633D5—22no—
634C23—51no—
635C23—61no—
636Q8—32no—
637Q8—61no—
638Q8—152no—
639Q8—152no—
640Q8—304no—
641Q8—301no—
642Q8—301no—
643D4—32no—
644D4—61no—
645D4—304no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—51no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—61no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—151no—
657C2×C4—151no—
658C2×C4—241no—
659C2×C4—304no—
660C2×C4—304no—
661C2×C4—301no—
662C2×C4—301no—
663C2×C4—401no—
664C2×C4—1201no—
665C2×C4C22×D3×D511yescharacteristic
666C8—52no—
667C8—61no—
668C8—301no—
669C8C4×D3×D512yes—
670C2×C3—102no—
671C2×C3C4×D4×D511yescharacteristic
672C2×C3#6609611yescharacteristic
673C2×C3#6610511yescharacteristic
674D3—42no—
675C5#7920211yescharacteristic, complemented, Sylow
676C22—52no—
677C22—62no—
678C22—101no—
679C22—101no—
680C22—121no—
681C22—121no—
682C22D3×D4×D511yescharacteristic
683C4—41no—
684C4—41no—
685C4—52no—
686C4—61no—
687C4—61no—
688C4—62no—
689C4—201no—
690C4—201no—
691C4—301no—
692C4—301no—
693C4—302no—
694C4—302no—
695C4C2×C4×D3×D511yescharacteristic
696C4D5×#23911yescharacteristic
697C3#1061137911yescharacteristic, complemented, Sylow
698C2—102no—
699C2—122no—
700C2D5×#89311yescharacteristic
701C2#1175408211yescharacteristic
702C2#1175409111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#6772C22
cosocleC2×C3×C4×C5C24
hypercenter#106D3×D5
hypocenterC3×C5#2947
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #11753397C2semidirect
4. #11750954C2semidirect
5. C5×#4852C2semidirect
6. C3×#65150C2semidirect
7. #11748050C2semidirect
8. #11747873C2semidirect
9. #11747816C2semidirect
11. D5×#810C2semidirect
12. #11747473C2semidirect
13. #11747278C2semidirect
14. #11747276C2semidirect
15. #11747234C2semidirect
44. #91260C4semidirect
69. #65150D3semidirect
92. D5×Dic6C2×C4semidirect
102. Dic60C2×C4semidirect
108. C5×#204C2×C4semidirect
115. C3×#676C2×C4semidirect
127. #6663C2×C4semidirect
128. #6659C2×C4semidirect
144. #4852D5semidirect
321. #676C4×D3semidirect
411. #204C4×D5semidirect
607. C3×C5#2947semidirect
675. C5#79202semidirect
697. C3#10611379semidirect

Maximal subgroups

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

subgroupindex
C2×#912602
#117536712
#117533972
#117509542
C5×#48522
C3×#651502
#117480502
#117478732
#117478162
#117474992
D5×#8102
#117474732
#117472782
#117472762
#117472342
#106113793
#792025