Finite Group Databasebeta

← #14302034

Subgroups — #14302034

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×#91826C211yesmaximal, characteristic
2C2×C22⋊C4×D15C211yesmaximal, characteristic, complemented
3C2×C3×C5×#99C211yesmaximal, characteristic, complemented
4C2×#91118C211yesmaximal, characteristic, complemented
5#11751056C211yesmaximal, characteristic, complemented
6#11746348C211yesmaximal, characteristic, complemented
7#11746348C211yesmaximal, characteristic, complemented
8#10600829—31nomaximal, Hall
9C24×D15C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C22×#1220C412yescomplemented
12C22×C4×D15—21no—
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×C3×C5×C22⋊C4C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16C2×#6719C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18#91826—21no—
19#91826—22no—
20#91826—21no—
21C2×#6714—21no—
22C2×#6714—22no—
23C2×#6714C412yescomplemented
24C22⋊C4×D15—22no—
25C22⋊C4×D15—22no—
26C3×C5×#99—22no—
27#91118—22no—
28#70036—51nomaximal, Hall
29C2×#4083—31no—
30C2×D5×C22⋊C4—31no—
31C2×C5×#99D311yescharacteristic, complemented
32C2×#3966—31no—
33#65244—31no—
34#64747—31no—
35#64747—31no—
36C24×C3×C5C2×C411yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×D15—21no—
39C23×D15—21no—
40C23×D15—21no—
41C23×D15—21no—
42C23×D15—44no—
43C23×D15C2×C412yes—
44C23×D15D411yescharacteristic
45C23×D15D412yes—
46C23×D15D411yescharacteristic
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×C5—21no—
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2×C411yescharacteristic, complemented
56C2×#1220—22no—
57C2×#1220—22no—
58C2×#1220—44no—
59C22×Dic15—21no—
60C22×Dic15—21no—
61C22×Dic15C2×C412yescomplemented
62C2×C4×D15—24no—
63C2×C4×D15—44no—
64C3×C5×C22⋊C4—21no—
65C3×C5×C22⋊C4—21no—
66C3×C5×C22⋊C4—21no—
67C3×C5×C22⋊C4D412yescomplemented
68#6719—21no—
69#6719—21no—
70#6719—21no—
71#6719—21no—
72#6719—21no—
73#6719D412yescomplemented
74#6714—24no—
75#6714—22no—
76#6714—22no—
77#6714—44no—
78C2×#937—51no—
79C2×D3×C22⋊C4—51no—
80C2×C3×#99D511yescharacteristic, complemented
81C2×#834—51no—
82#4955—51no—
83#4527—51no—
84#4527—51no—
85C24×D5—31no—
86C22×C5×D4C2×D311yescharacteristic
87C22×C22⋊D5—32no—
88C22×C4×D5—61no—
89C2×C5×C22⋊C4C2×D311yescharacteristic
90C2×C5×C22⋊C4C2×D311yescharacteristic
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5—31no—
94#4083—61no—
95#4083—62no—
96#4083—61no—
97C2×#685—32no—
98C2×#685—61no—
99C2×#685—62no—
100D5×C22⋊C4—62no—
101D5×C22⋊C4—62no—
102C5×#99—22no—
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×D15—21no—
118C22×D15—21no—
119C22×D15—24no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—21no—
123C22×D15—22no—
124C22×D15—22no—
125C22×D15—21no—
126C22×D15—24no—
127C22×D15—24no—
128C22×D15—42no—
129C22×D15—42no—
130C22×D15—42no—
131C22×D15—44no—
132C22×D15—44no—
133C22×D15—44no—
134C22×D15—44no—
135C22×D15C22⋊C412yes—
136C22×D15C22⋊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×C3×C4×C5—22no—
145C2×C3×C4×C5—42no—
146C2×C3×C4×C5—42no—
147C2×C3×C4×C5—41no—
148#1220—44no—
149#1220—44no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—42no—
153C2×Dic15—42no—
154C2×Dic15—42no—
155C2×Dic15—41no—
156C4×D15—48no—
157C24×D3—51no—
158C22×C3×D4C2×D511yescharacteristic
159C22×#67—52no—
160C22×C4×D3—101no—
161C2×C3×C22⋊C4C2×D511yescharacteristic
162C2×C3×C22⋊C4C2×D511yescharacteristic
163C2×#217—51no—
164C2×#217—51no—
165C2×#217—51no—
166#937—101no—
167#937—102no—
168#937—101no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—101no—
171C2×(C2×D3)⋊C4—102no—
172D3×C22⋊C4—102no—
173D3×C22⋊C4—102no—
174C3×#99—22no—
175#834—102no—
176C24×C5C4×D311yescharacteristic, complemented
177C24×C5C22×D311yescharacteristic
178C23×D5—31no—
179C23×D5—32no—
180C23×D5—32no—
181C23×D5—31no—
182C23×D5—61no—
183C23×D5—61no—
184C23×D5—61no—
185C23×D5—61no—
186C23×D5—124no—
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—21no—
194C22×C4×C5—21no—
195C22×C4×C5C4×D311yescharacteristic, complemented
196C2×C22⋊D5—62no—
197C2×C22⋊D5—62no—
198C2×C22⋊D5—124no—
199C22×Dic5—32no—
200C22×Dic5—61no—
201C22×Dic5—61no—
202C2×C4×D5—64no—
203C2×C4×D5—124no—
204C5×C22⋊C4—21no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—21no—
207C5×C22⋊C4#6712yescomplemented
208C22⋊Dic5—32no—
209C22⋊Dic5—61no—
210C22⋊Dic5—61no—
211C22⋊Dic5—61no—
212C22⋊Dic5—61no—
213C22⋊Dic5—61no—
214#685—62no—
215#685—62no—
216#685—64no—
217#685—124no—
218C2×#120—151no—
219C22×C22⋊C4—151no—
220C2×#99—151no—
221C2×#99D1511yescharacteristic, complemented
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×D15—24no—
244C2×D15—24no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15—22no—
248C2×D15—22no—
249C2×D15—22no—
250C2×D15—44no—
251C2×D15—44no—
252C2×D15—44no—
253C2×D15—44no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15#9914yescomplemented
257C3×C4×C5—42no—
258C3×C4×C5—41no—
259C3×C4×C5—81no—
260Dic15—42no—
261Dic15—42no—
262Dic15—81no—
263C24×C3C4×D511yescharacteristic, complemented
264C24×C3C22×D511yescharacteristic
265C23×D3—51no—
266C23×D3—52no—
267C23×D3—52no—
268C23×D3—51no—
269C23×D3—101no—
270C23×D3—101no—
271C23×D3—101no—
272C23×D3—101no—
273C23×D3—204no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4C4×D511yescharacteristic, complemented
283C2×#67—102no—
284C2×#67—102no—
285C2×#67—204no—
286C22×Dic3—52no—
287C22×Dic3—101no—
288C22×Dic3—101no—
289C2×C4×D3—104no—
290C2×C4×D3—204no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4C22⋊D512yescomplemented
295#217—52no—
296#217—101no—
297#217—101no—
298#217—101no—
299#217—101no—
300#217—101no—
301(C2×D3)⋊C4—102no—
302(C2×D3)⋊C4—102no—
303(C2×D3)⋊C4—104no—
304(C2×D3)⋊C4—204no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—42no—
309C23×C5—42no—
310C23×C5C2×C4×D311yescharacteristic
311C23×C5#23511yescharacteristic
312C23×C5D3×D411yescharacteristic
313C23×C5D3×D411yescharacteristic
314C23×C5D3×D411yescharacteristic
315C23×C5#23711yescharacteristic
316C23×C5C2×#6711yescharacteristic
317C22×D5—32no—
318C22×D5—32no—
319C22×D5—64no—
320C22×D5—64no—
321C22×D5—64no—
322C22×D5—61no—
323C22×D5—61no—
324C22×D5—62no—
325C22×D5—61no—
326C22×D5—62no—
327C22×D5—62no—
328C22×D5—61no—
329C22×D5—62no—
330C22×D5—122no—
331C22×D5—122no—
332C22×D5—122no—
333C22×D5—124no—
334C22×D5—124no—
335C22×D5—124no—
336C22×D5—124no—
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—22no—
345C2×C4×C5—42no—
346C2×C4×C5—42no—
347C2×C4×C5—41no—
348C22⋊D5—124no—
349C22⋊D5—124no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5—122no—
353C2×Dic5—122no—
354C2×Dic5—122no—
355C2×Dic5—121no—
356C4×D5—128no—
357C25—151no—
358C22×D4—152no—
359C22×D4C2×D1511yescharacteristic
360C23×C4—301no—
361#120—301no—
362#120—302no—
363#120—301no—
364C2×C22⋊C4—151no—
365C2×C22⋊C4—151no—
366C2×C22⋊C4—152no—
367C2×C22⋊C4—151no—
368C2×C22⋊C4—302no—
369C2×C22⋊C4—301no—
370C2×C22⋊C4—302no—
371C2×C22⋊C4—302no—
372C2×C22⋊C4C2×D1511yescharacteristic
373C2×C22⋊C4C2×D1511yescharacteristic
374#99—22no—
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—
385D15—24no—
386D15—42no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—42no—
391C23×C3—42no—
392C23×C3C2×C4×D511yescharacteristic
393C23×C3#70911yescharacteristic
394C23×C3D4×D511yescharacteristic
395C23×C3D4×D511yescharacteristic
396C23×C3D4×D511yescharacteristic
397C23×C3#71111yescharacteristic
398C23×C3C2×C22⋊D511yescharacteristic
399C22×D3—52no—
400C22×D3—52no—
401C22×D3—104no—
402C22×D3—104no—
403C22×D3—104no—
404C22×D3—101no—
405C22×D3—101no—
406C22×D3—102no—
407C22×D3—101no—
408C22×D3—102no—
409C22×D3—102no—
410C22×D3—101no—
411C22×D3—102no—
412C22×D3—202no—
413C22×D3—202no—
414C22×D3—202no—
415C22×D3—204no—
416C22×D3—204no—
417C22×D3—204no—
418C22×D3—204no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—41no—
422C3×D4—41no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430#67—204no—
431#67—204no—
432C2×Dic3—102no—
433C2×Dic3—102no—
434C2×Dic3—202no—
435C2×Dic3—202no—
436C2×Dic3—202no—
437C2×Dic3—201no—
438C4×D3—208no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—42no—
448C22×C5—81no—
449C22×C5—81no—
450C22×C5D3×C22⋊C411yescharacteristic
451C22×C5#67⋊C411yescharacteristic
452C22×C5#88311yescharacteristic
453C22×C5#88411yescharacteristic
454C22×C5C4×#6711yescharacteristic
455C22×C5#93711yescharacteristic
456C22×C5#93811yescharacteristic
457C2×D5—34no—
458C2×D5—64no—
459C2×D5—64no—
460C2×D5—62no—
461C2×D5—62no—
462C2×D5—62no—
463C2×D5—62no—
464C2×D5—62no—
465C2×D5—124no—
466C2×D5—124no—
467C2×D5—124no—
468C2×D5—124no—
469C2×D5—122no—
470C2×D5—122no—
471C4×C5—42no—
472C4×C5—41no—
473C4×C5—81no—
474Dic5—122no—
475Dic5—122no—
476Dic5—241no—
477C24—151no—
478C24—152no—
479C24—152no—
480C24—151no—
481C24—301no—
482C24—301no—
483C24—301no—
484C24—301no—
485C24—604no—
486C24C4×D1511yescharacteristic, complemented
487C24C22×D1511yescharacteristic
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—302no—
495C2×D4—302no—
496C2×D4—604no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—152no—
500C22×C4—304no—
501C22×C4—301no—
502C22×C4—301no—
503C22×C4—604no—
504C22×C4C4×D1511yescharacteristic, complemented
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—152no—
509C22⋊C4—302no—
510C22⋊C4—302no—
511C22⋊C4—304no—
512C22⋊C4—301no—
513C22⋊C4—301no—
514C22⋊C4—301no—
515C22⋊C4—301no—
516C22⋊C4—301no—
517C22⋊C4—604no—
518C22⋊C4#122012yescomplemented
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—81no—
530C22×C3—81no—
531C22×C3D5×C22⋊C411yescharacteristic
532C22×C3#402711yescharacteristic
533C22×C3#402911yescharacteristic
534C22×C3#403011yescharacteristic
535C22×C3C4×C22⋊D511yescharacteristic
536C22×C3#408311yescharacteristic
537C22×C3#408411yescharacteristic
538C2×D3—54no—
539C2×D3—104no—
540C2×D3—104no—
541C2×D3—102no—
542C2×D3—102no—
543C2×D3—102no—
544C2×D3—102no—
545C2×D3—102no—
546C2×D3—204no—
547C2×D3—204no—
548C2×D3—204no—
549C2×D3—204no—
550C2×D3—202no—
551C2×D3—202no—
552C3×C4—42no—
553C3×C4—41no—
554C3×C4—81no—
555Dic3—202no—
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×C5D3×#9912yes—
566C2×C5#495611yescharacteristic
567D5—64no—
568D5—122no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—42no—
573C23—42no—
574C23—152no—
575C23—152no—
576C23—304no—
577C23—304no—
578C23—304no—
579C23—301no—
580C23—301no—
581C23—302no—
582C23—301no—
583C23—302no—
584C23—302no—
585C23—301no—
586C23—302no—
587C23—602no—
588C23—602no—
589C23—602no—
590C23—604no—
591C23—604no—
592C23—604no—
593C23—604no—
594C23C2×C4×D1511yescharacteristic
595C23#681711yescharacteristic
596C23D4×D1511yescharacteristic
597C23D4×D1511yescharacteristic
598C23D4×D1511yescharacteristic
599C23#681911yescharacteristic
600C23C2×#122011yescharacteristic
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—604no—
606D4—604no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—302no—
615C2×C4—302no—
616C2×C4—608no—
617C2×C4—602no—
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×C3D5×#9912yes—
629C2×C3#6524511yescharacteristic
630D3—104no—
631D3—202no—
632C5#7003611yescharacteristic, complemented, Sylow
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—154no—
645C22—304no—
646C22—304no—
647C22—302no—
648C22—302no—
649C22—302no—
650C22—302no—
651C22—302no—
652C22—604no—
653C22—604no—
654C22—604no—
655C22—604no—
656C22—602no—
657C22—602no—
658C22C22⋊C4×D1511yescharacteristic
659C22#9177011yescharacteristic
660C22#9177211yescharacteristic
661C22#9177311yescharacteristic
662C22C4×#122011yescharacteristic
663C22#9182611yescharacteristic
664C22#9182711yescharacteristic
665C4—42no—
666C4—41no—
667C4—81no—
668C4—602no—
669C4—602no—
670C4—1201no—
671C3#1060082911yescharacteristic, complemented, Sylow
672C2—21no—
673C2—21no—
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—81no—
679C2—304no—
680C2—602no—
681C2D15×#9912yes—
682C2#1175105711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC2×C3×C5×#99C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91826C2
cosocleC24×C3×C5C23
hypercenterC2×#99D15
hypocenterC3×C5#1898
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D15C2semidirect
3. C2×C3×C5×#99C2semidirect
4. C2×#91118C2semidirect
5. #11751056C2semidirect
6. #11746348C2semidirect
7. #11746348C2semidirect
11. C22×#1220C4semidirect
23. C2×#6714C4semidirect
31. C2×C5×#99D3semidirect
36. C24×C3×C5C2×C4semidirect
55. C22×C3×C4×C5C2×C4semidirect
61. C22×Dic15C2×C4semidirect
67. C3×C5×C22⋊C4D4semidirect
73. #6719D4semidirect
80. C2×C3×#99D5semidirect
176. C24×C5C4×D3semidirect
195. C22×C4×C5C4×D3semidirect
207. C5×C22⋊C4#67semidirect
221. C2×#99D15semidirect
256. C2×D15#99semidirect
263. C24×C3C4×D5semidirect
282. C22×C3×C4C4×D5semidirect
294. C3×C22⋊C4C22⋊D5semidirect
486. C24C4×D15semidirect
504. C22×C4C4×D15semidirect
518. C22⋊C4#1220semidirect
519. C3×C5#1898semidirect
632. C5#70036semidirect
671. C3#10600829semidirect

Maximal subgroups

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

subgroupindex
C2×#918262
C2×C22⋊C4×D152
C2×C3×C5×#992
C2×#911182
#117510562
#117463482
#106008293
#700365