Finite Group Databasebeta

← #14302069

Subgroups — #14302069

Order 1920.

1196 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
1C2×C3×#4083C211yesmaximal, characteristic
2C2×D5×#217C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5#11749488C211yesmaximal, characteristic, complemented
6#11746019C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10600829—31nomaximal, Hall
9C24×C3×D5C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C22×C3×C22⋊D5C412yescomplemented
12C22×D5×Dic3—21no—
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×#217C2211yescharacteristic
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C3×#4083—21no—
19C3×#4083—22no—
20C3×#4083—21no—
21C2×C3×#685C412yescomplemented
22D5×#217—22no—
23D5×#217—22no—
24C2×#6665—21no—
25C2×#6665—22no—
26#91118—22no—
27C5×#834—22no—
28#71670—51nomaximal, Hall
29C2×#4083D311yescharacteristic
30C2×D5×C22⋊C4—31no—
31C2×C5×#99—31no—
32C2×#3966—31no—
33#65244—31no—
34#64747—31no—
35#64747—31no—
36C24×C3×C5C2×C411yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5—21no—
39C23×C3×D5—21no—
40C23×C3×D5—21no—
41C23×C3×D5—21no—
42C23×C3×D5—44no—
43C23×C3×D5C2×C412yes—
44C23×C3×D5D411yescharacteristic
45C23×C3×D5D412yes—
46C23×C3×D5D411yescharacteristic
47C2×C3×C5×D4—21no—
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4—21no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4—21no—
53C22×C3×C4×C5C2×C411yescharacteristic, complemented
54C22×Dic15—21no—
55C22×Dic15—21no—
56C22×C5×Dic3—21no—
57C22×C5×Dic3—21no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—44no—
61C22×C3×Dic5C2×C412yescomplemented
62C2×D5×Dic3—24no—
63C2×D5×Dic3—44no—
64#6719—21no—
65#6719—21no—
66#6719—21no—
67#6719D412yescomplemented
68C5×#217—21no—
69C5×#217—21no—
70C5×#217—21no—
71C5×#217D412yescomplemented
72C3×C22⋊Dic5—21no—
73C3×C22⋊Dic5—21no—
74C3×#685—22no—
75C3×#685—22no—
76#6665—24no—
77#6665—44no—
78C2×C3×#120—51no—
79C22×#217—51no—
80#5247—51no—
81C2×#834—51no—
82C2×#834D511yescharacteristic, complemented
83#4526—51no—
84#4526—51no—
85C24×D5C2×D311yescharacteristic
86C22×C5×D4C2×D311yescharacteristic
87C22×C22⋊D5Dic312yescomplemented
88C22×C4×D5—61no—
89C2×C5×C22⋊C4—31no—
90C2×C5×C22⋊C4—31no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5C2×D311yescharacteristic
94#4083—21no—
95#4083—22no—
96#4083—21no—
97C2×#685—61no—
98C2×#685—62no—
99C2×#685Dic312yescomplemented
100D5×C22⋊C4—62no—
101D5×C22⋊C4—62no—
102C5×#99—62no—
103#3966—62no—
104#1898—151noSylow
105C23×C3×C5—21no—
106C23×C3×C5—21no—
107C23×C3×C5—21no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5C22×C411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5C2×D411yescharacteristic
114C23×C3×C5C2×D411yescharacteristic
115C23×C3×C5#4111yescharacteristic
116C23×C3×C5#4111yescharacteristic
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—24no—
120C22×C3×D5—22no—
121C22×C3×D5—22no—
122C22×C3×D5—21no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—21no—
126C22×C3×D5—24no—
127C22×C3×D5—24no—
128C22×C3×D5—42no—
129C22×C3×D5—42no—
130C22×C3×D5—42no—
131C22×C3×D5—44no—
132C22×C3×D5—44no—
133C22×C3×D5—44no—
134C22×C3×D5—44no—
135C22×C3×D5C22⋊C412yes—
136C22×C3×D5C22⋊C412yes—
137C3×C5×D4—41no—
138C3×C5×D4—41no—
139C3×C5×D4—41no—
140C3×C5×D4—41no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×Dic15—22no—
145C2×Dic15—42no—
146C2×Dic15—42no—
147C2×Dic15—41no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—42no—
150C2×C5×Dic3—42no—
151C2×C5×Dic3—41no—
152C3×C22⋊D5—44no—
153C3×C22⋊D5—44no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—42no—
156D5×Dic3—48no—
157C25×C3—51no—
158C22×C3×D4—52no—
159C22×C3×D4C2×D511yescharacteristic
160C23×Dic3—101no—
161C3×#120—101no—
162C3×#120—102no—
163C3×#120—101no—
164C2×C3×C22⋊C4—51no—
165C2×C3×C22⋊C4—52no—
166C2×#217—51no—
167C2×#217—51no—
168C2×#217—102no—
169C2×#217—101no—
170C2×#217—102no—
171C2×#217—102no—
172C2×#217C2×D511yescharacteristic
173C2×#217C2×D511yescharacteristic
174#834—22no—
175#834—102no—
176C24×C5C2×Dic311yescharacteristic, complemented
177C24×C5C22×D311yescharacteristic
178C23×D5—21no—
179C23×D5—21no—
180C23×D5—21no—
181C23×D5—21no—
182C23×D5—44no—
183C23×D5C2×Dic312yes—
184C23×D5#6711yescharacteristic
185C23×D5#6712yes—
186C23×D5#6711yescharacteristic
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C22×C4×C5—61no—
194C22×C4×C5—61no—
195C22×C4×C5C2×Dic311yescharacteristic, complemented
196C2×C22⋊D5—22no—
197C2×C22⋊D5—22no—
198C2×C22⋊D5—44no—
199C22×Dic5—61no—
200C22×Dic5—61no—
201C22×Dic5C2×Dic312yescomplemented
202C2×C4×D5—64no—
203C2×C4×D5—124no—
204C5×C22⋊C4—32no—
205C5×C22⋊C4—61no—
206C5×C22⋊C4—61no—
207C5×C22⋊C4—61no—
208C22⋊Dic5—21no—
209C22⋊Dic5—21no—
210C22⋊Dic5—32no—
211C22⋊Dic5—61no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214#685—22no—
215#685—22no—
216#685—64no—
217#685—124no—
218C2×#120—51no—
219C22×C22⋊C4—151no—
220C2×#99—31no—
221C2×#99—151no—
222#379—151no—
223#342—151no—
224#342—151no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5—41no—
233C22×C3×C5—42no—
234C22×C3×C5—81no—
235C22×C3×C5—81no—
236C22×C3×C5C2×C22⋊C411yescharacteristic
237C22×C3×C5C4×D411yescharacteristic
238C22×C3×C5C4×D411yescharacteristic
239C22×C3×C5#12011yescharacteristic
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5#12311yescharacteristic
243C2×C3×D5—24no—
244C2×C3×D5—24no—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—44no—
251C2×C3×D5—44no—
252C2×C3×D5—44no—
253C2×C3×D5—44no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5#9914yescomplemented
257C3×C4×C5—41no—
258Dic15—42no—
259Dic15—81no—
260C3×Dic5—42no—
261C5×Dic3—42no—
262C5×Dic3—81no—
263C24×C3—51no—
264C24×C3—52no—
265C24×C3—52no—
266C24×C3—51no—
267C24×C3—101no—
268C24×C3—101no—
269C24×C3—101no—
270C24×C3—101no—
271C24×C3—204no—
272C24×C3C4×D511yescharacteristic, complemented
273C24×C3C22×D511yescharacteristic
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—102no—
281C2×C3×D4—102no—
282C2×C3×D4—204no—
283C22×C3×C4—52no—
284C22×C3×C4C4×D511yescharacteristic, complemented
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—104no—
288C22×Dic3—101no—
289C22×Dic3—101no—
290C22×Dic3—204no—
291C3×C22⋊C4—102no—
292C3×C22⋊C4—102no—
293C3×C22⋊C4—101no—
294C3×C22⋊C4—101no—
295#217—21no—
296#217—21no—
297#217—21no—
298#217—52no—
299#217—104no—
300#217—101no—
301#217—101no—
302#217—101no—
303#217—204no—
304#217C22⋊D512yescomplemented
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5D3×D411yescharacteristic
311C23×C5D3×D411yescharacteristic
312C23×C5#23711yescharacteristic
313C23×C5#23711yescharacteristic
314C23×C5C22×Dic311yescharacteristic
315C23×C5C2×#6711yescharacteristic
316C23×C5C2×#6711yescharacteristic
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—24no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—24no—
327C22×D5—24no—
328C22×D5—42no—
329C22×D5—42no—
330C22×D5—42no—
331C22×D5—44no—
332C22×D5—44no—
333C22×D5—44no—
334C22×D5—44no—
335C22×D5#21712yes—
336C22×D5#21712yes—
337C5×D4—41no—
338C5×D4—41no—
339C5×D4—41no—
340C5×D4—41no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—62no—
345C2×C4×C5—122no—
346C2×C4×C5—122no—
347C2×C4×C5—121no—
348C22⋊D5—44no—
349C22⋊D5—44no—
350C2×Dic5—22no—
351C2×Dic5—42no—
352C2×Dic5—62no—
353C2×Dic5—122no—
354C2×Dic5—122no—
355C2×Dic5—121no—
356C4×D5—128no—
357C25—51no—
358C22×D4—52no—
359C22×D4D3×D511yescharacteristic
360C23×C4—301no—
361#120—101no—
362#120—102no—
363#120—101no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—51no—
367C2×C22⋊C4—52no—
368C2×C22⋊C4—151no—
369C2×C22⋊C4—151no—
370C2×C22⋊C4—302no—
371C2×C22⋊C4—302no—
372C2×C22⋊C4—301no—
373C2×C22⋊C4—302no—
374#99—62no—
375#99—302no—
376C2×C3×C5—21no—
377C2×C3×C5—21no—
378C2×C3×C5—21no—
379C2×C3×C5—21no—
380C2×C3×C5—21no—
381C2×C3×C5—21no—
382C2×C3×C5—81no—
383C2×C3×C5#38611yescharacteristic
384C2×C3×C5C2×#9912yes—
385C3×D5—24no—
386C3×D5—42no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3—52no—
393C23×C3—52no—
394C23×C3—104no—
395C23×C3—104no—
396C23×C3—104no—
397C23×C3—101no—
398C23×C3—101no—
399C23×C3—102no—
400C23×C3—101no—
401C23×C3—102no—
402C23×C3—102no—
403C23×C3—101no—
404C23×C3—102no—
405C23×C3—202no—
406C23×C3—202no—
407C23×C3—202no—
408C23×C3—204no—
409C23×C3—204no—
410C23×C3—204no—
411C23×C3—204no—
412C23×C3C2×C4×D511yescharacteristic
413C23×C3#70911yescharacteristic
414C23×C3D4×D511yescharacteristic
415C23×C3D4×D511yescharacteristic
416C23×C3D4×D511yescharacteristic
417C23×C3#71111yescharacteristic
418C23×C3C2×C22⋊D511yescharacteristic
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—41no—
423C3×D4—204no—
424C3×D4—204no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—102no—
429C2×C3×C4—202no—
430C2×Dic3—22no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—41no—
434C2×Dic3—102no—
435C2×Dic3—208no—
436C2×Dic3—202no—
437C2×Dic3—202no—
438C2×Dic3—201no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—42no—
447C22×C5—41no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5D4×Dic311yescharacteristic
451C22×C5D4×Dic311yescharacteristic
452C22×C5#93511yescharacteristic
453C22×C5#93711yescharacteristic
454C22×C5#93911yescharacteristic
455C22×C5#93911yescharacteristic
456C22×C5C2×#21711yescharacteristic
457C2×D5—24no—
458C2×D5—24no—
459C2×D5—22no—
460C2×D5—22no—
461C2×D5—22no—
462C2×D5—22no—
463C2×D5—22no—
464C2×D5—44no—
465C2×D5—44no—
466C2×D5—44no—
467C2×D5—44no—
468C2×D5—42no—
469C2×D5—42no—
470C2×D5#83414yescomplemented
471C4×C5—41no—
472C4×C5—122no—
473C4×C5—241no—
474Dic5—42no—
475Dic5—122no—
476Dic5—241no—
477C24—51no—
478C24—52no—
479C24—52no—
480C24—51no—
481C24—101no—
482C24—101no—
483C24—101no—
484C24—101no—
485C24—204no—
486C24D5×Dic311yescharacteristic, complemented
487C24C2×D3×D511yescharacteristic
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—102no—
495C2×D4—102no—
496C2×D4—204no—
497C22×C4—52no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—304no—
501C22×C4—301no—
502C22×C4—301no—
503C22×C4—604no—
504C22×C4D5×Dic311yescharacteristic, complemented
505C22⋊C4—32no—
506C22⋊C4—61no—
507C22⋊C4—61no—
508C22⋊C4—61no—
509C22⋊C4—102no—
510C22⋊C4—102no—
511C22⋊C4—101no—
512C22⋊C4—101no—
513C22⋊C4—152no—
514C22⋊C4—304no—
515C22⋊C4—301no—
516C22⋊C4—301no—
517C22⋊C4—301no—
518C22⋊C4—604no—
519C3×C5#189811yescharacteristic, complemented, Hall
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—54no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3—104no—
533C22×C3—104no—
534C22×C3—102no—
535C22×C3—102no—
536C22×C3—102no—
537C22×C3—102no—
538C22×C3—102no—
539C22×C3—204no—
540C22×C3—204no—
541C22×C3—204no—
542C22×C3—204no—
543C22×C3—202no—
544C22×C3—202no—
545C22×C3D5×C22⋊C411yescharacteristic
546C22×C3#402711yescharacteristic
547C22×C3#402911yescharacteristic
548C22×C3#403011yescharacteristic
549C22×C3C4×C22⋊D511yescharacteristic
550C22×C3#408311yescharacteristic
551C22×C3#408411yescharacteristic
552C3×C4—41no—
553C3×C4—202no—
554Dic3—42no—
555Dic3—81no—
556Dic3—202no—
557Dic3—401no—
558C2×C5—21no—
559C2×C5—21no—
560C2×C5—21no—
561C2×C5—21no—
562C2×C5—21no—
563C2×C5—21no—
564C2×C5—81no—
565C2×C5C2×#83412yes—
566C2×C5#522011yescharacteristic
567D5—24no—
568D5—42no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—42no—
573C23—42no—
574C23—52no—
575C23—52no—
576C23—104no—
577C23—104no—
578C23—104no—
579C23—101no—
580C23—101no—
581C23—101no—
582C23—102no—
583C23—102no—
584C23—102no—
585C23—102no—
586C23—101no—
587C23—202no—
588C23—202no—
589C23—202no—
590C23—204no—
591C23—204no—
592C23—204no—
593C23—204no—
594C23C2×D5×Dic311yescharacteristic
595C23#677911yescharacteristic
596C23#678011yescharacteristic
597C23D5×#6711yescharacteristic
598C23D5×#6711yescharacteristic
599C23D3×C22⋊D511yescharacteristic
600C23#679011yescharacteristic
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—204no—
606D4—204no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—62no—
611C2×C4—102no—
612C2×C4—122no—
613C2×C4—122no—
614C2×C4—121no—
615C2×C4—202no—
616C2×C4—302no—
617C2×C4—608no—
618C2×C4—602no—
619C2×C4—602no—
620C2×C4—601no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—81no—
628C2×C3—104no—
629C2×C3—202no—
630C2×C3D5×#9912yes—
631C2×C3#6524511yescharacteristic
632C5#7167011yescharacteristic, complemented, Sylow
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—42no—
641C22—41no—
642C22—54no—
643C22—81no—
644C22—81no—
645C22—104no—
646C22—104no—
647C22—102no—
648C22—102no—
649C22—102no—
650C22—102no—
651C22—102no—
652C22—204no—
653C22—204no—
654C22—204no—
655C22—204no—
656C22—202no—
657C22—202no—
658C22D5×#21711yescharacteristic
659C22#9154811yescharacteristic
660C22#9154911yescharacteristic
661C22#9155011yescharacteristic
662C22Dic3×C22⋊D511yescharacteristic
663C22#9155911yescharacteristic
664C22#9157711yescharacteristic
665C4—41no—
666C4—122no—
667C4—202no—
668C4—241no—
669C4—602no—
670C4—1201no—
671C3#1060082911yescharacteristic, complemented, Sylow
672C2—21no—
673C2—21no—
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—81no—
679C2—104no—
680C2—202no—
681C2D5×#83412yes—
682C2#1174951811yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4083C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1898
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D5×#217C2semidirect
3. C2×#91118C2semidirect
4. C2×C5×#834C2semidirect
5. #11749488C2semidirect
6. #11746019C2semidirect
7. #11746019C2semidirect
11. C22×C3×C22⋊D5C4semidirect
21. C2×C3×#685C4semidirect
36. C24×C3×C5C2×C4semidirect
53. C22×C3×C4×C5C2×C4semidirect
61. C22×C3×Dic5C2×C4semidirect
67. #6719D4semidirect
71. C5×#217D4semidirect
82. C2×#834D5semidirect
87. C22×C22⋊D5Dic3semidirect
99. C2×#685Dic3semidirect
176. C24×C5C2×Dic3semidirect
195. C22×C4×C5C2×Dic3semidirect
201. C22×Dic5C2×Dic3semidirect
256. C2×C3×D5#99semidirect
272. C24×C3C4×D5semidirect
284. C22×C3×C4C4×D5semidirect
304. #217C22⋊D5semidirect
470. C2×D5#834semidirect
486. C24D5×Dic3semidirect
504. C22×C4D5×Dic3semidirect
519. C3×C5#1898semidirect
632. C5#71670semidirect
671. C3#10600829semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40832
C2×D5×#2172
C2×#911182
C2×C5×#8342
#117494882
#117460192
#106008293
#716705