Finite Group Databasebeta

← #14297185

Subgroups — #14297185

Order 1920.

1240 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
1C2×#92100C211yesmaximal, characteristic
2C2×C3×C5×#104C211yesmaximal, characteristic, complemented
3#11751333C211yesmaximal, characteristic, complemented
4#11751234C211yesmaximal, characteristic, complemented
5C2×#91107C211yesmaximal, characteristic, complemented
6#11751040C211yesmaximal, characteristic, complemented
7C2×#91089C211yesmaximal, characteristic, complemented
8#10601177—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92100—22no—
11#92100—22no—
12#92100—22no—
13#92100C414yescomplemented
14C2×#6821—21no—
15C2×D4×D15—22no—
16C2×D4×D15—21no—
17C2×#6817—21no—
18C2×#6817C2211yescharacteristic
19C22×D60—21no—
20C22×D60C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic, complemented
22C2×C3×C42×C5C2211yescharacteristic, complemented
23C2×#6714—22no—
24C2×C4⋊Dic15C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C3×C5×#104—22no—
27#91119—21no—
28#91116—21no—
29#91107—22no—
30#91105—21no—
31#91100—21no—
32#91089—22no—
33#70384—51nomaximal, Hall
34C2×#4149—31no—
35C2×C5×#104D311yescharacteristic, complemented
36#65521—31no—
37#65422—31no—
38C2×#3955—31no—
39#65228—31no—
40C2×#3937—31no—
41C23×D15—22no—
42C23×D15D412yes—
43C3×C5×#41—21no—
44C3×C5×#41—21no—
45C3×C5×#41C2×C412yes—
46C3×C5×#41D412yes—
47C2×C3×C5×Q8D411yescharacteristic
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4D411yescharacteristic
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×#1220—22no—
54C2×#1220—21no—
55C22×Dic15—21no—
56#6821—24no—
57#6821—24no—
58D4×D15—28no—
59D4×D15—24no—
60D4×D15—28no—
61D4×D15—24no—
62#6817—24no—
63#6817—21no—
64#6817—21no—
65#6817—24no—
66#6817C2×C412yes—
67#6817D412yes—
68C2×D60—22no—
69C2×D60—24no—
70C2×D60—21no—
71C2×D60—21no—
72C2×D60—21no—
73C2×D60—21no—
74C2×D60—24no—
75C2×D60C2×C412yes—
76C2×D60D412yes—
77C2×D60D411yescharacteristic
78C2×C4×D15—22no—
79C2×C4×D15—21no—
80C2×Dic30D411yescharacteristic
81C3×C5×M16—21no—
82C3×C5×M16—21no—
83C2×C3×C5×C8—21no—
84C3×C42×C5—21no—
85C3×C42×C5—21no—
86#6714—44no—
87C4⋊Dic15—21no—
88C4⋊Dic15—21no—
89#6710—21no—
90#6710—21no—
91C2×C3⋊#168—21no—
92C2×#1009—51no—
93C2×C3×#104D511yescharacteristic, complemented
94#5232—51no—
95#5133—51no—
96C2×#823—51no—
97#4939—51no—
98C2×#805—51no—
99C2×C5×#41C2×D311yescharacteristic
100#4149—34no—
101#4149—62no—
102#4149—62no—
103#4149—62no—
104C2×#713—61no—
105C2×D4×D5—62no—
106C2×D4×D5—61no—
107C2×#709—31no—
108C2×#709—61no—
109C22×D20—31no—
110C22×D20—61no—
111C2×C5×M16C2×D311yescharacteristic, complemented
112C2×C42×C5C2×D311yescharacteristic, complemented
113C2×#685—62no—
114C2×C4⋊Dic5—31no—
115C2×#681—31no—
116C5×#104—22no—
117#3967—61no—
118#3964—61no—
119#3955—62no—
120#3953—61no—
121#3948—61no—
122#3937—62no—
123#1792—151noSylow
124C23×C3×C5—21no—
125C23×C3×C5C2×D411yescharacteristic
126C22×D15—22no—
127C22×D15—21no—
128C22×D15—28no—
129C22×D15—22no—
130C22×D15—42no—
131C22×D15—42no—
132C22×D15—82no—
133C22×D15—82no—
134C22×D15C22⋊C414yes—
135C3×C5×Q8—21no—
136C3×C5×Q8C22⋊C412yescomplemented
137C3×C5×D4—22no—
138C3×C5×D4—22no—
139C3×C5×D4—21no—
140C3×C5×D4C22⋊C412yescomplemented
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—41no—
146C2×C3×C4×C5—41no—
147C2×C3×C4×C5C22×C411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5C2×D411yescharacteristic
153#1220—28no—
154#1220—22no—
155#1220—22no—
156C2×Dic15—21no—
157C2×Dic15—42no—
158C2×Dic15—41no—
159D60—28no—
160D60—22no—
161D60—22no—
162D60—22no—
163D60—21no—
164D60—22no—
165D60C22⋊C412yescomplemented
166C4×D15—28no—
167C4×D15—22no—
168C4×D15—22no—
169Dic30—21no—
170Dic30C22⋊C412yescomplemented
171C3×C5×C8—41no—
172C3⋊#168—41no—
173C2×C3×#41C2×D511yescharacteristic
174#1009—54no—
175#1009—102no—
176#1009—102no—
177#1009—102no—
178C2×#239—101no—
179C2×D3×D4—102no—
180C2×D3×D4—101no—
181C2×#235—51no—
182C2×#235—101no—
183C22×D12—51no—
184C22×D12—101no—
185C2×C3×M16C2×D511yescharacteristic, complemented
186C2×C3×C42C2×D511yescharacteristic, complemented
187C2×(C2×D3)⋊C4—102no—
188C2×C4⋊Dic3—51no—
189C2×#208—51no—
190C3×#104—22no—
191#835—101no—
192#832—101no—
193#823—102no—
194#821—101no—
195#816—101no—
196#805—102no—
197C23×D5—32no—
198C23×D5—62no—
199C5×#41—21no—
200C5×#41—21no—
201C5×#41C4×D312yes—
202C5×#41#6712yes—
203C2×C5×Q8D1211yescharacteristic
204C2×C5×D4—21no—
205C2×C5×D4D1211yescharacteristic
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—62no—
210C2×C22⋊D5—61no—
211C22×Dic5—61no—
212#713—64no—
213#713—64no—
214D4×D5—68no—
215D4×D5—68no—
216D4×D5—64no—
217D4×D5—64no—
218#709—32no—
219#709—32no—
220#709—64no—
221#709—64no—
222#709—61no—
223#709—61no—
224C2×D20—31no—
225C2×D20—32no—
226C2×D20—32no—
227C2×D20—64no—
228C2×D20—62no—
229C2×D20—64no—
230C2×D20—61no—
231C2×D20—61no—
232C2×D20—61no—
233C2×D20—61no—
234C2×C4×D5—62no—
235C2×C4×D5—61no—
236C2×Dic10—31no—
237C5×M16—21no—
238C5×M16—21no—
239C2×C5×C8—21no—
240C42×C5—21no—
241C42×C5—21no—
242#685—124no—
243C4⋊Dic5—61no—
244C4⋊Dic5—61no—
245#681—61no—
246#681—61no—
247C2×#168—61no—
248C2×H(5,𝔽2)—151no—
249C2×#104—151no—
250C2×#104D1511yescharacteristic, complemented
251#417—151no—
252#417—151no—
253C2×#100—151no—
254#390—151no—
255C22×C3×C5—21no—
256C22×C3×C5—21no—
257C22×C3×C5—22no—
258C22×C3×C5—41no—
259C22×C3×C5—41no—
260C22×C3×C5C2×C22⋊C411yescharacteristic
261C22×C3×C5#12011yescharacteristic
262C22×C3×C5#12011yescharacteristic
263C2×D15—24no—
264C2×D15—22no—
265C2×D15—42no—
266C2×D15—41no—
267C2×D15—42no—
268C2×D15—41no—
269C2×D15—44no—
270C2×D15—82no—
271C2×D15—88no—
272C3×C4×C5—22no—
273C3×C4×C5—42no—
274C3×C4×C5C2×C22⋊C411yescharacteristic
275C3×C4×C5C2×C22⋊C411yescharacteristic
276C3×C4×C5#12011yescharacteristic
277C3×C4×C5#12011yescharacteristic
278Dic15—22no—
279Dic15—81no—
280C23×D3—52no—
281C23×D3—102no—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41C4×D512yes—
285C3×#41C22⋊D512yes—
286C2×C3×Q8D2011yescharacteristic
287C2×C3×D4—21no—
288C2×C3×D4D2011yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—102no—
293C2×#67—101no—
294C22×Dic3—101no—
295#239—104no—
296#239—104no—
297D3×D4—108no—
298D3×D4—108no—
299D3×D4—104no—
300D3×D4—104no—
301#235—52no—
302#235—52no—
303#235—104no—
304#235—104no—
305#235—101no—
306#235—101no—
307C2×D12—51no—
308C2×D12—52no—
309C2×D12—52no—
310C2×D12—104no—
311C2×D12—102no—
312C2×D12—104no—
313C2×D12—101no—
314C2×D12—101no—
315C2×D12—101no—
316C2×D12—101no—
317C2×C4×D3—102no—
318C2×C4×D3—101no—
319C2×Dic6—51no—
320C3×M16—21no—
321C3×M16—21no—
322C2×C3×C8—21no—
323C3×C42—21no—
324C3×C42—21no—
325(C2×D3)⋊C4—204no—
326C4⋊Dic3—101no—
327C4⋊Dic3—101no—
328#208—101no—
329#208—101no—
330C2×C3⋊C8—101no—
331C23×C5—21no—
332C23×C5D3×D411yescharacteristic
333C22×D5—34no—
334C22×D5—61no—
335C22×D5—62no—
336C22×D5—68no—
337C22×D5—62no—
338C22×D5—122no—
339C22×D5—122no—
340C22×D5—242no—
341C22×D5—242no—
342C5×Q8—21no—
343C5×Q8(C2×D3)⋊C412yescomplemented
344C5×D4—22no—
345C5×D4—22no—
346C5×D4—21no—
347C5×D4(C2×D3)⋊C412yescomplemented
348C2×C4×C5—21no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5C2×C4×D311yescharacteristic
355C2×C4×C5C2×D1211yescharacteristic
356C2×C4×C5D3×D411yescharacteristic
357C2×C4×C5D3×D411yescharacteristic
358C2×C4×C5D3×D411yescharacteristic
359C2×C4×C5C2×#6711yescharacteristic
360C22⋊D5—68no—
361C22⋊D5—62no—
362C22⋊D5—62no—
363C2×Dic5—61no—
364C2×Dic5—122no—
365C2×Dic5—121no—
366D20—32no—
367D20—68no—
368D20—62no—
369D20—62no—
370D20—62no—
371D20—61no—
372D20—62no—
373C4×D5—68no—
374C4×D5—62no—
375C4×D5—62no—
376Dic10—32no—
377Dic10—61no—
378C5×C8—41no—
379#168—121no—
380H(5,𝔽2)—154no—
381H(5,𝔽2)—302no—
382H(5,𝔽2)—302no—
383H(5,𝔽2)—302no—
384C2×#41—151no—
385C2×#41—301no—
386C2×#41—301no—
387C2×#41C2×D1511yescharacteristic
388C22×D4—151no—
389C22×D4—301no—
390C22×D4—302no—
391C22×D4—301no—
392C2×M16—151no—
393C2×M16C2×D1511yescharacteristic, complemented
394C2×C4⋊C4—151no—
395C2×C22⋊C4—302no—
396C2×C42C2×D1511yescharacteristic, complemented
397#104—22no—
398#104—302no—
399#103—301no—
400#103—301no—
401#102—301no—
402#102—301no—
403#100—302no—
404C2×C3×C5—21no—
405C2×C3×C5—21no—
406C2×C3×C5—42no—
407C2×C3×C5#37911yescharacteristic
408C2×C3×C5#45311yescharacteristic
409C2×C3×C5#45511yescharacteristic
410D15—44no—
411D15—42no—
412C23×C3—21no—
413C23×C3D4×D511yescharacteristic
414C22×D3—54no—
415C22×D3—101no—
416C22×D3—102no—
417C22×D3—108no—
418C22×D3—102no—
419C22×D3—202no—
420C22×D3—202no—
421C22×D3—402no—
422C22×D3—402no—
423C3×Q8—21no—
424C3×Q8#68512yescomplemented
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—21no—
428C3×D4#68512yescomplemented
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4C2×C4×D511yescharacteristic
436C2×C3×C4C2×D2011yescharacteristic
437C2×C3×C4D4×D511yescharacteristic
438C2×C3×C4D4×D511yescharacteristic
439C2×C3×C4D4×D511yescharacteristic
440C2×C3×C4C2×C22⋊D511yescharacteristic
441#67—108no—
442#67—102no—
443#67—102no—
444C2×Dic3—101no—
445C2×Dic3—202no—
446C2×Dic3—201no—
447D12—52no—
448D12—108no—
449D12—102no—
450D12—102no—
451D12—102no—
452D12—101no—
453D12—102no—
454C4×D3—108no—
455C4×D3—102no—
456C4×D3—102no—
457Dic6—52no—
458Dic6—101no—
459C3×C8—41no—
460C3⋊C8—201no—
461C22×C5—21no—
462C22×C5—21no—
463C22×C5—22no—
464C22×C5—41no—
465C22×C5—41no—
466C22×C5D3×C22⋊C411yescharacteristic
467C22×C5#88211yescharacteristic
468C22×C5#93711yescharacteristic
469C2×D5—62no—
470C2×D5—64no—
471C2×D5—122no—
472C2×D5—121no—
473C2×D5—122no—
474C2×D5—121no—
475C2×D5—124no—
476C2×D5—242no—
477C2×D5—248no—
478C4×C5—22no—
479C4×C5—42no—
480C4×C5D3×C22⋊C411yescharacteristic
481C4×C5#88211yescharacteristic
482C4×C5C2×(C2×D3)⋊C411yescharacteristic
483C4×C5#93711yescharacteristic
484Dic5—62no—
485Dic5—241no—
486C24—152no—
487C24—302no—
488#41—21no—
489#41—21no—
490#41—152no—
491#41—152no—
492#41—304no—
493#41—304no—
494#41—304no—
495#41—304no—
496#41—301no—
497#41—301no—
498#41C4×D1512yes—
499#41#122012yes—
500C2×Q8—151no—
501C2×Q8D6011yescharacteristic
502C2×D4—21no—
503C2×D4—152no—
504C2×D4—151no—
505C2×D4—152no—
506C2×D4—304no—
507C2×D4—302no—
508C2×D4—304no—
509C2×D4—308no—
510C2×D4—308no—
511C2×D4—304no—
512C2×D4—302no—
513C2×D4—301no—
514C2×D4—304no—
515C2×D4—301no—
516C2×D4—301no—
517C2×D4—301no—
518C2×D4—301no—
519C2×D4D6011yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—302no—
523C22×C4—301no—
524C22×C4—301no—
525C22×C4C22×D1511yescharacteristic
526M16—21no—
527M16—21no—
528M16—301no—
529M16—301no—
530C2×C8—21no—
531C2×C8—301no—
532C4⋊C4—301no—
533C4⋊C4—301no—
534C22⋊C4—604no—
535C42—21no—
536C42—21no—
537C3×C5#179211yescharacteristic, complemented, Hall
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—22no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3D5×C22⋊C411yescharacteristic
544C22×C3#402811yescharacteristic
545C22×C3#408311yescharacteristic
546C2×D3—102no—
547C2×D3—104no—
548C2×D3—202no—
549C2×D3—201no—
550C2×D3—202no—
551C2×D3—201no—
552C2×D3—204no—
553C2×D3—402no—
554C2×D3—408no—
555C3×C4—22no—
556C3×C4—42no—
557C3×C4D5×C22⋊C411yescharacteristic
558C3×C4#402811yescharacteristic
559C3×C4C2×#68511yescharacteristic
560C3×C4#408311yescharacteristic
561Dic3—102no—
562Dic3—401no—
563C2×C5—21no—
564C2×C5—21no—
565C2×C5—42no—
566C2×C5#482211yescharacteristic
567C2×C5#482511yescharacteristic
568C2×C5#495511yescharacteristic
569D5—124no—
570D5—122no—
571C23—21no—
572C23—154no—
573C23—308no—
574C23—301no—
575C23—302no—
576C23—302no—
577C23—602no—
578C23—602no—
579C23—1202no—
580C23—1202no—
581C23D4×D1511yescharacteristic
582Q8—21no—
583Q8—152no—
584Q8—301no—
585Q8#671412yescomplemented
586D4—22no—
587D4—22no—
588D4—21no—
589D4—152no—
590D4—308no—
591D4—308no—
592D4—302no—
593D4—302no—
594D4—302no—
595D4—302no—
596D4—302no—
597D4—301no—
598D4—302no—
599D4#671412yescomplemented
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—308no—
607C2×C4—301no—
608C2×C4—302no—
609C2×C4—302no—
610C2×C4—602no—
611C2×C4—601no—
612C2×C4C2×C4×D1511yescharacteristic
613C2×C4C2×D6011yescharacteristic
614C2×C4D4×D1511yescharacteristic
615C2×C4D4×D1511yescharacteristic
616C2×C4D4×D1511yescharacteristic
617C2×C4C2×#122011yescharacteristic
618C8—41no—
619C8—601no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—42no—
623C2×C3#6511111yescharacteristic
624C2×C3#6511411yescharacteristic
625C2×C3#6524411yescharacteristic
626D3—204no—
627D3—202no—
628C5#7038411yescharacteristic, complemented, Sylow
629C22—21no—
630C22—21no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—302no—
635C22—304no—
636C22—604no—
637C22—602no—
638C22—601no—
639C22—602no—
640C22—601no—
641C22—1202no—
642C22—1208no—
643C22C22⋊C4×D1511yescharacteristic
644C22#9177111yescharacteristic
645C22#9182611yescharacteristic
646C4—22no—
647C4—42no—
648C4—302no—
649C4—1201no—
650C4C22⋊C4×D1511yescharacteristic
651C4#9177111yescharacteristic
652C4C2×#671411yescharacteristic
653C4#9182611yescharacteristic
654C3#1060117711yescharacteristic, complemented, Sylow
655C2—21no—
656C2—21no—
657C2—42no—
658C2—604no—
659C2—602no—
660C2#1175092311yescharacteristic
661C2#1175092611yescharacteristic
662C2#1175105611yescharacteristic
subgroupG/H
centerC22#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5#120
prime radicalC2×#92100C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1792
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#104C2semidirect
3. #11751333C2semidirect
4. #11751234C2semidirect
5. C2×#91107C2semidirect
6. #11751040C2semidirect
7. C2×#91089C2semidirect
13. #92100C4semidirect
21. C2×C3×C5×M16C22semidirect
22. C2×C3×C42×C5C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. C2×#6710C22semidirect
35. C2×C5×#104D3semidirect
93. C2×C3×#104D5semidirect
111. C2×C5×M16C2×D3semidirect
112. C2×C42×C5C2×D3semidirect
136. C3×C5×Q8C22⋊C4semidirect
140. C3×C5×D4C22⋊C4semidirect
165. D60C22⋊C4semidirect
170. Dic30C22⋊C4semidirect
185. C2×C3×M16C2×D5semidirect
186. C2×C3×C42C2×D5semidirect
250. C2×#104D15semidirect
343. C5×Q8(C2×D3)⋊C4semidirect
347. C5×D4(C2×D3)⋊C4semidirect
393. C2×M16C2×D15semidirect
396. C2×C42C2×D15semidirect
424. C3×Q8#685semidirect
428. C3×D4#685semidirect
537. C3×C5#1792semidirect
585. Q8#6714semidirect
599. D4#6714semidirect
628. C5#70384semidirect
654. C3#10601177semidirect

Maximal subgroups

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

subgroupindex
C2×#921002
C2×C3×C5×#1042
#117513332
#117512342
C2×#911072
#117510402
C2×#910892
#106011773
#703845