Finite Group Databasebeta

← #14301632

Subgroups — #14301632

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65820C211yesmaximal, characteristic, complemented
2C2×#91568C211yesmaximal, characteristic
3C5×#4955C211yesmaximal, characteristic, complemented
4#11749496C211yesmaximal, characteristic, complemented
5C2×#90995C211yesmaximal, characteristic, complemented
6#11746347C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10600292—31nomaximal, Hall
9C24×C5×D3C2211yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C22×#1201—21no—
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×(C2×D3)⋊C4—22no—
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C3×C4×C22⋊D5—22no—
19C3×#4027—22no—
20C3×D5×C22⋊C4—21no—
21C3×#4023—21no—
22#91568—22no—
23#91568C414yescomplemented
24C2×(C2×D3)⋊Dic5—21no—
25C2×(C2×D3)⋊Dic5—22no—
26#90995—22no—
27#71654—51nomaximal, Hall
28C2×#4099—31no—
29#65820D311yescharacteristic, complemented
30C5×#379—31no—
31#65536—31no—
32C2×#3938—31no—
33#64747—31no—
34#64746—31no—
35C24×C3×C5C2311yescharacteristic
36C23×C5×D3—21no—
37C23×C5×D3—21no—
38C23×C5×D3—21no—
39C23×C5×D3—21no—
40C23×C5×D3—21no—
41C23×C5×D3—21no—
42C23×C5×D3—44no—
43C23×C5×D3C2×C412yescomplemented
44C23×C3×D5D411yescharacteristic
45C22×C3×C4×C5D412yescomplemented
46C22×Dic15—21no—
47C22×Dic15—21no—
48C22×C5×Dic3—21no—
49C2×C3×C22⋊D5—21no—
50C2×C3×C22⋊D5—21no—
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5C2×C412yes—
54C2×C3×C22⋊D5D412yes—
55C22×C3×Dic5D411yescharacteristic
56C22×C3×Dic5D412yescomplemented
57C2×C3×C4×D5—22no—
58C2×#1201—24no—
59C2×#1201—44no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62#6719—21no—
63#6719—21no—
64#6719—21no—
65#6719C2×C412yescomplemented
66C5×#217—21no—
67C5×#217—21no—
68C5×(C2×D3)⋊C4—44no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×#685—22no—
72C3×#683—22no—
73C3×C4×Dic5—22no—
74(C2×D3)⋊Dic5—24no—
75(C2×D3)⋊Dic5—44no—
76C3×#518—51no—
77C2×#937—51no—
78C2×#834—51no—
79#4955—51no—
80#4955D511yescharacteristic, complemented
81#4526—51no—
82#4526—51no—
83C25×C5—31no—
84C22×C22⋊D5—61no—
85C22×C22⋊D5C2×D311yescharacteristic
86C2×C5×C22⋊C4—31no—
87C2×C5×C22⋊C4—62no—
88C2×C5×C22⋊C4C2×D311yescharacteristic
89#4099—34no—
90#4099—62no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5—61no—
94C2×C22⋊Dic5—62no—
95C2×C22⋊Dic5C2×D311yescharacteristic
96C4×C22⋊D5—22no—
97#4027—22no—
98D5×C22⋊C4—21no—
99#4023—21no—
100#3938—62no—
101#1889—151noSylow
102C23×C3×C5—42no—
103C23×C3×C5C22×C411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5#4111yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C22×C5×D3—24no—
111C22×C5×D3—24no—
112C22×C5×D3—24no—
113C22×C5×D3—22no—
114C22×C5×D3—22no—
115C22×C5×D3—22no—
116C22×C5×D3—44no—
117C22×C5×D3—44no—
118C22×C5×D3—44no—
119C22×C5×D3—44no—
120C22×C5×D3—42no—
121C22×C5×D3—42no—
122C22×C5×D3—42no—
123C22×C5×D3—41no—
124C22×C5×D3—41no—
125C22×C5×D3—41no—
126C22×C5×D3—41no—
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C22×C3×D5—42no—
130C22×C3×D5C22⋊C412yescomplemented
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—42no—
133C2×Dic15—22no—
134C2×Dic15—42no—
135C2×Dic15—42no—
136C2×Dic15—41no—
137C2×C5×Dic3—42no—
138C2×C5×Dic3—41no—
139C3×C22⋊D5—22no—
140C3×C22⋊D5—22no—
141C3×C22⋊D5—22no—
142C3×C22⋊D5—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—42no—
147C2×C3×Dic5C22⋊C412yescomplemented
148C3×C4×D5—82no—
149#1201—48no—
150C24×D3C2×D511yescharacteristic
151C22×C3×D4—51no—
152C22×#67—101no—
153C3×C4×D4—102no—
154C3×C4×D4—102no—
155C3×#117—101no—
156C2×C3×C22⋊C4—51no—
157C2×C3×C22⋊C4—101no—
158C2×C3×C22⋊C4C2×D511yescharacteristic
159C2×#217—51no—
160C2×#217—51no—
161C2×#217C2×D511yescharacteristic
162#937—54no—
163#937—102no—
164C2×(C2×D3)⋊C4—22no—
165C2×(C2×D3)⋊C4—101no—
166C2×(C2×D3)⋊C4—102no—
167#834—102no—
168C24×C5—32no—
169C24×C5—61no—
170C24×C5—61no—
171C24×C5—61no—
172C24×C5—61no—
173C24×C5—61no—
174C24×C5—61no—
175C24×C5—124no—
176C24×C5C22×D311yescharacteristic
177C23×D5#6711yescharacteristic
178C22×C4×C5—61no—
179C22×C4×C5#6712yescomplemented
180C2×C22⋊D5—21no—
181C2×C22⋊D5—21no—
182C2×C22⋊D5—21no—
183C2×C22⋊D5—21no—
184C2×C22⋊D5—64no—
185C2×C22⋊D5—124no—
186C2×C22⋊D5C4×D312yes—
187C2×C22⋊D5D1212yes—
188C22×Dic5—61no—
189C22×Dic5—61no—
190C22×Dic5#6711yescharacteristic
191C22×Dic5#6712yescomplemented
192C2×C4×D5—22no—
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—61no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—124no—
198C22⋊Dic5—21no—
199C22⋊Dic5—21no—
200C22⋊Dic5—32no—
201C22⋊Dic5—61no—
202C22⋊Dic5—64no—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205C22⋊Dic5—124no—
206#685—22no—
207#683—22no—
208C4×Dic5—22no—
209C2×#120—151no—
210#518—51no—
211C2×#99—151no—
212#379—31no—
213#379—151no—
214#342—151no—
215#342—151no—
216C22×C3×C5—22no—
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—41no—
220C22×C3×C5—41no—
221C22×C3×C5—41no—
222C22×C3×C5—41no—
223C22×C3×C5C2×C22⋊C411yescharacteristic
224C22×C3×C5C4×D411yescharacteristic
225C22×C3×C5C4×D411yescharacteristic
226C22×C3×C5#12011yescharacteristic
227C22×C3×C5#12111yescharacteristic
228C22×C3×C5#12111yescharacteristic
229C22×C3×C5#12311yescharacteristic
230C2×C5×D3—24no—
231C2×C5×D3—24no—
232C2×C5×D3—24no—
233C2×C5×D3—44no—
234C2×C5×D3—42no—
235C2×C5×D3—44no—
236C2×C5×D3—44no—
237C2×C5×D3—42no—
238C2×C5×D3—42no—
239C2×C5×D3—42no—
240C2×C5×D3—44no—
241C2×C3×D5—22no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—81no—
245C3×C4×C5—42no—
246Dic15—42no—
247Dic15—81no—
248C3×Dic5—22no—
249C3×Dic5—42no—
250C5×Dic3—81no—
251C24×C3—51no—
252C24×C3C22×D511yescharacteristic
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—21no—
259C23×D3—44no—
260C23×D3C4×D512yescomplemented
261C2×C3×D4—52no—
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4—101no—
267C22×C3×C4—51no—
268C22×C3×C4—52no—
269C22×C3×C4—102no—
270C22×C3×C4C22⋊D512yescomplemented
271C2×#67—104no—
272C2×#67—204no—
273C22×Dic3—21no—
274C22×Dic3—101no—
275C22×Dic3—101no—
276C3×C4⋊C4—102no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—21no—
279C3×C22⋊C4—102no—
280C3×C22⋊C4—101no—
281C3×C22⋊C4—101no—
282C3×C42—102no—
283#217—21no—
284#217—21no—
285#217—52no—
286#217—101no—
287#217—101no—
288#217—101no—
289(C2×D3)⋊C4—44no—
290(C2×D3)⋊C4—104no—
291(C2×D3)⋊C4—204no—
292C23×C5—42no—
293C23×C5—64no—
294C23×C5—64no—
295C23×C5—64no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5—122no—
300C23×C5—122no—
301C23×C5—122no—
302C23×C5—124no—
303C23×C5—124no—
304C23×C5—124no—
305C23×C5—124no—
306C23×C5—121no—
307C23×C5—121no—
308C23×C5—121no—
309C23×C5—121no—
310C23×C5C2×C4×D311yescharacteristic
311C23×C5C2×D1211yescharacteristic
312C23×C5#23511yescharacteristic
313C23×C5#23511yescharacteristic
314C23×C5C2×#6711yescharacteristic
315C23×C5C2×#6711yescharacteristic
316C23×C5C2×#6711yescharacteristic
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—42no—
320C22×D5(C2×D3)⋊C412yescomplemented
321C2×C4×C5—22no—
322C2×C4×C5—42no—
323C2×C4×C5—122no—
324C2×C4×C5—121no—
325C22⋊D5—22no—
326C22⋊D5—22no—
327C22⋊D5—22no—
328C22⋊D5—22no—
329C22⋊D5—128no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—22no—
333C2×Dic5—42no—
334C2×Dic5—62no—
335C2×Dic5—122no—
336C2×Dic5—122no—
337C2×Dic5—121no—
338C2×Dic5(C2×D3)⋊C412yescomplemented
339C4×D5—82no—
340C25—31no—
341C22×D4—51no—
342C22×D4—301no—
343#120—154no—
344#120—302no—
345C4×D4—102no—
346C4×D4—102no—
347#117—101no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—62no—
351C2×C22⋊C4—101no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—301no—
355C2×C22⋊C4—302no—
356C2×C22⋊C4D3×D511yescharacteristic
357#99—302no—
358C2×C3×C5—21no—
359C2×C3×C5—21no—
360C2×C3×C5—21no—
361C2×C3×C5—21no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#38611yescharacteristic
365C2×C3×C5B(4,𝔽2)12yes—
366C3×D5—42no—
367C5×D3—44no—
368C23×C3—42no—
369C23×C3—52no—
370C23×C3—101no—
371C23×C3—101no—
372C23×C3—202no—
373C23×C3C2×C4×D511yescharacteristic
374C23×C3#70911yescharacteristic
375C23×C3D4×D511yescharacteristic
376C23×C3D4×D511yescharacteristic
377C23×C3D4×D511yescharacteristic
378C23×C3#71111yescharacteristic
379C23×C3C2×C22⋊D511yescharacteristic
380C22×D3—24no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—22no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—44no—
387C22×D3—44no—
388C22×D3—44no—
389C22×D3—44no—
390C22×D3—42no—
391C22×D3—42no—
392C22×D3—42no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C3×D4—102no—
398C3×D4—102no—
399C3×D4—102no—
400C3×D4—102no—
401C2×C3×C4—22no—
402C2×C3×C4—42no—
403C2×C3×C4—52no—
404C2×C3×C4—101no—
405C2×C3×C4—101no—
406C2×C3×C4—102no—
407C2×C3×C4—202no—
408C2×C3×C4—402no—
409#67—208no—
410C2×Dic3—42no—
411C2×Dic3—41no—
412C2×Dic3—102no—
413C2×Dic3—202no—
414C2×Dic3—202no—
415C2×Dic3—201no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—64no—
424C22×C5—64no—
425C22×C5—64no—
426C22×C5—122no—
427C22×C5—124no—
428C22×C5—124no—
429C22×C5—124no—
430C22×C5—122no—
431C22×C5—122no—
432C22×C5—122no—
433C22×C5—124no—
434C22×C5C2×(C2×D3)⋊C411yescharacteristic
435C22×C5C4×#6711yescharacteristic
436C22×C5C4×#6711yescharacteristic
437C22×C5#92911yescharacteristic
438C22×C5#93011yescharacteristic
439C22×C5#93011yescharacteristic
440C22×C5#95311yescharacteristic
441C2×D5—22no—
442C2×D5—42no—
443C2×D5—42no—
444C2×D5—81no—
445C4×C5—42no—
446C4×C5—241no—
447Dic5—22no—
448Dic5—42no—
449Dic5—122no—
450Dic5—241no—
451C24—32no—
452C24—51no—
453C24—61no—
454C24—61no—
455C24—61no—
456C24—61no—
457C24—61no—
458C24—61no—
459C24—124no—
460C24C2×D3×D511yescharacteristic
461C2×D4—52no—
462C2×D4—52no—
463C2×D4—101no—
464C2×D4—101no—
465C2×D4—101no—
466C2×D4—101no—
467C2×D4—304no—
468C2×D4—604no—
469C22×C4—51no—
470C22×C4—52no—
471C22×C4—61no—
472C22×C4—102no—
473C22×C4—301no—
474C22×C4—301no—
475C22×C4#120112yescomplemented
476C4⋊C4—102no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—61no—
480C22⋊C4—61no—
481C22⋊C4—102no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—124no—
485C22⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C22⋊C4—301no—
489C22⋊C4—301no—
490C22⋊C4—604no—
491C42—102no—
492C3×C5#188911yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—102no—
501C22×C3—202no—
502C22×C3—202no—
503C22×C3—401no—
504C22×C3D5×C22⋊C411yescharacteristic
505C22×C3#402711yescharacteristic
506C22×C3#402911yescharacteristic
507C22×C3#403011yescharacteristic
508C22×C3C4×C22⋊D511yescharacteristic
509C22×C3#408311yescharacteristic
510C22×C3#408411yescharacteristic
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—24no—
514C2×D3—44no—
515C2×D3—42no—
516C2×D3—44no—
517C2×D3—42no—
518C2×D3—42no—
519C2×D3—44no—
520C2×D3—44no—
521C2×D3—42no—
522C3×C4—42no—
523C3×C4—102no—
524C3×C4—202no—
525Dic3—81no—
526Dic3—202no—
527Dic3—401no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—21no—
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—21no—
534C2×C5—124no—
535C2×C5#521311yescharacteristic
536C2×C5#524412yes—
537D5—42no—
538C23—42no—
539C23—52no—
540C23—64no—
541C23—64no—
542C23—64no—
543C23—62no—
544C23—62no—
545C23—62no—
546C23—101no—
547C23—101no—
548C23—122no—
549C23—122no—
550C23—122no—
551C23—124no—
552C23—124no—
553C23—124no—
554C23—124no—
555C23—121no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23—202no—
560C23#677111yescharacteristic
561C23#677211yescharacteristic
562C23C4×D3×D511yescharacteristic
563C23D5×D1211yescharacteristic
564C23C2×#120111yescharacteristic
565C23D5×#6711yescharacteristic
566C23D5×#6711yescharacteristic
567D4—102no—
568D4—102no—
569D4—102no—
570D4—102no—
571D4—608no—
572C2×C4—22no—
573C2×C4—42no—
574C2×C4—52no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—102no—
578C2×C4—122no—
579C2×C4—121no—
580C2×C4—202no—
581C2×C4—302no—
582C2×C4—402no—
583C2×C4—602no—
584C2×C4—602no—
585C2×C4—601no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—202no—
593C2×C3#6524511yescharacteristic
594C2×C3#6532112yes—
595D3—44no—
596C5#7165411yescharacteristic, complemented, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—64no—
605C22—64no—
606C22—64no—
607C22—102no—
608C22—124no—
609C22—122no—
610C22—124no—
611C22—122no—
612C22—122no—
613C22—124no—
614C22—122no—
615C22—124no—
616C22—202no—
617C22—202no—
618C22—401no—
619C22C4×#120111yescharacteristic
620C22#9144011yescharacteristic
621C22#9144711yescharacteristic
622C22#9144811yescharacteristic
623C22#9144911yescharacteristic
624C22D5×(C2×D3)⋊C411yescharacteristic
625C22#9156311yescharacteristic
626C4—42no—
627C4—102no—
628C4—202no—
629C4—241no—
630C4—602no—
631C4—1201no—
632C3#1060029211yescharacteristic, complemented, Sylow
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—124no—
640C2—202no—
641C2#1174890511yescharacteristic
642C2#1174917512yes—
subgroupG/H
centerC22#91563
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91568C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1889
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65820C2semidirect
3. C5×#4955C2semidirect
4. #11749496C2semidirect
5. C2×#90995C2semidirect
6. #11746347C2semidirect
7. #11746019C2semidirect
23. #91568C4semidirect
29. #65820D3semidirect
43. C23×C5×D3C2×C4semidirect
45. C22×C3×C4×C5D4semidirect
56. C22×C3×Dic5D4semidirect
65. #6719C2×C4semidirect
80. #4955D5semidirect
130. C22×C3×D5C22⋊C4semidirect
147. C2×C3×Dic5C22⋊C4semidirect
179. C22×C4×C5#67semidirect
191. C22×Dic5#67semidirect
260. C23×D3C4×D5semidirect
270. C22×C3×C4C22⋊D5semidirect
320. C22×D5(C2×D3)⋊C4semidirect
338. C2×Dic5(C2×D3)⋊C4semidirect
475. C22×C4#1201semidirect
492. C3×C5#1889semidirect
596. C5#71654semidirect
632. C3#10600292semidirect

Maximal subgroups

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

subgroupindex
C3×#658202
C2×#915682
C5×#49552
#117494962
C2×#909952
#117463472
#117460192
#106002923
#716545