Finite Group Databasebeta

← #14495117

Subgroups — #14495117

Order 1920.

2060 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756331C211yesmaximal, characteristic, complemented
2C4×C5×#239C211yesmaximal, characteristic, complemented
3C3×#65908C211yesmaximal, characteristic, complemented
4#11755267C211yesmaximal, characteristic, complemented
5#11755257C211yesmaximal, characteristic, complemented
6#11755254C211yesmaximal, characteristic, complemented
7#11755134C211yesmaximal, characteristic, complemented
8#11753805C213yesmaximal, complemented
9#11753742C213yesmaximal, complemented
10#11753736C213yesmaximal, complemented
11#11753731C213yesmaximal, complemented
12#11752711C213yesmaximal, complemented
13#11752707C213yesmaximal, complemented
14#11752695C213yesmaximal, complemented
15#11752693C213yesmaximal, complemented
16#10617756—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21Q8×Dic15C2211yescharacteristic
22#91781C2213yes—
23#91776C2213yes—
24#91761C2213yes—
25C4×Dic30C2213yes—
26C5×Q8×Dic3C2211yescharacteristic
27C5×#893C2213yes—
28C5×#892C2213yes—
29C4×C5×D12C2213yes—
30C42×C5×D3C2213yes—
31C3×Q8×Dic5C2211yescharacteristic
32C3×#4039C2213yes—
33C3×D5×C4⋊C4C2213yes—
34C3×C4×D20C2213yes—
35C3×#4018C2213yes—
36#91468C2213yes—
37C4×#1204C2213yes—
38#91466C2213yes—
39#91465C2213yes—
40#91464C2216yes—
41#91463C2213yes—
42#91456C2213yes—
43#91454C2213yes—
44#91452C2216yes—
45#91452C2213yes—
46#91449C2213yes—
47#91448C2216yes—
48#91447C2216yes—
49C4×#1203C2213yes—
50C4×#1202C2213yes—
51C4×#1201C2213yes—
52C4×#1201C2216yes—
53#91384C2213yes—
54#91381C2213yes—
55#91380C2211yescharacteristic
56#91379C2213yes—
57#91373C2213yes—
58#91367C2216yes—
59#91365C2213yes—
60#91364C2213yes—
61#91363C2213yes—
62#91360C2213yes—
63#91357C2216yes—
64#91353C2213yes—
65#91352C2213yes—
66#91351C2213yes—
67#85898—51nomaximal, Hall
68C4×C5×#41—31no—
69#66168—31no—
70#66165—31no—
71#65910—31no—
72#65908D311yescharacteristic, complemented
73#65906—31no—
74#65903—31no—
75#65896—33no—
76#65895—33no—
77#65893—33no—
78#65892—33no—
79#65866—33no—
80#65863—33no—
81#65813—33no—
82#65813—33no—
83C2×C3×C5×Q8C2311yescharacteristic
84Q8×D15—24no—
85C2×C4×D15C2313yes—
86C2×Dic30C2313yes—
87C5×#239—24no—
88C2×C5×D12C2313yes—
89C2×C4×C5×D3C2313yes—
90C2×C4×C5×D3C2313yes—
91C2×C4×C5×D3C2313yes—
92C3×#713—24no—
93C2×C3×D20C2313yes—
94C2×C3×C4×D5C2313yes—
95C2×C3×C4×D5C2316yes—
96C2×#1204C2313yes—
97C2×#1203C2313yes—
98C2×#1202C2313yes—
99C2×#1201C2313yes—
100C2×#1201C2316yes—
101C3×C5×C4⋊C4C2313yes—
102C3×C42×C5C2313yes—
103#6714C2313yes—
104#6714C2311yescharacteristic
105C4⋊Dic15C2313yes—
106#6712C2313yes—
107#6712C2313yes—
108C4×Dic15C2313yes—
109C4×Dic15C2316yes—
110C5×(C2×D3)⋊C4C2316yes—
111C5×C4⋊Dic3C2313yes—
112C4×C5×Dic3C2311yescharacteristic
113C4×C5×Dic3C2313yes—
114C4×C5×Dic3C2313yes—
115C3×#685C2313yes—
116C3×#685C2313yes—
117C3×C4⋊Dic5C2313yes—
118C3×#683C2311yescharacteristic
119C3×#683C2313yes—
120C3×C4×Dic5C2313yes—
121Dic3⋊Dic5C2313yes—
122Dic3⋊Dic5C2313yes—
123#6669C2311yescharacteristic
124#6669C2313yes—
125#6668C2313yes—
126#6668C2316yes—
127#6668C2311yescharacteristic
128#6667C2311yescharacteristic
129#6667C2311yescharacteristic
130(C2×D3)⋊Dic5C2316yes—
131(C2×D3)⋊Dic5C2313yes—
132(C2×D3)⋊Dic5C2313yes—
133#6665C2313yes—
134#6665C2313yes—
135#6665C2316yes—
136C3×#520—51no—
137#5834—51no—
138#5831—51no—
139#5576—51no—
140C4×#239D511yescharacteristic, complemented
141#5572—51no—
142#5570—51no—
143#5563—53no—
144#5562—53no—
145#5559—53no—
146#5557—53no—
147#5534—53no—
148#5528—53no—
149#5514—53no—
150#5513—53no—
151C2×C5×#41—31no—
152C2×#713C2×D311yescharacteristic
153C2×Q8×D5—31no—
154C4×C5×Q8—31no—
155C4×C5×Q8C2×D311yescharacteristic
156C4×C5×D4—33no—
157C4×C5×D4—33no—
158C5×#117—33no—
159C2×C42×C5—33no—
160Q8×Dic5—31no—
161Q8×Dic5C2×D311yescharacteristic
162#4086—33no—
163#4084—33no—
164#4084—33no—
165#4082—33no—
166#4076—33no—
167#4076—33no—
168#4075—33no—
169#4075—36no—
170#4075—33no—
171C4×C22⋊D5—33no—
172C4×C22⋊D5—36no—
173C4×C22⋊D5—33no—
174#4070—33no—
175#4070—33no—
176#4043—33no—
177#4041—33no—
178#4039C2×D313yes—
179#4038—33no—
180D5×C4⋊C4C2×D313yes—
181#4036—33no—
182#4034—33no—
183#4033—33no—
184#4031—36no—
185#4030—36no—
186#4029—36no—
187#4025—36no—
188#4022—33no—
189#4022—31no—
190#4021—33no—
191#4021—33no—
192C4×D20—33no—
193C4×D20C2×D313yes—
194#4018—36no—
195#4018—33no—
196#4018C2×D313yes—
197#4016—33no—
198#4016—33no—
199C4×Dic10—33no—
200C4×Dic10—33no—
201#3524—151noSylow
202C22×D15C2411yescharacteristic
203C22×C5×D3C2413yes—
204C22×C3×D5C2413yes—
205C3×C5×Q8#4114yes—
206C2×C3×C4×C5C2411yescharacteristic
207C2×C3×C4×C5C2413yes—
208C2×C3×C4×C5C2413yes—
209C2×Dic15C2413yes—
210C2×Dic15C2413yes—
211C2×Dic15C2411yescharacteristic
212C4×D15—26no—
213Dic30—26no—
214C2×C5×Dic3C2411yescharacteristic
215C2×C5×Dic3C2411yescharacteristic
216C2×C5×Dic3C2413yes—
217C5×D12—26no—
218C4×C5×D3—26no—
219C4×C5×D3—43no—
220C4×C5×D3—43no—
221C2×C3×Dic5C2411yescharacteristic
222C2×C3×Dic5C2411yescharacteristic
223C2×C3×Dic5C2413yes—
224C3×D20—26no—
225C3×C4×D5—26no—
226C3×C4×D5—46no—
227#1204—43no—
228#1203—43no—
229#1202—43no—
230#1201—43no—
231#1201—46no—
232C2×C3×#41—51no—
233C2×#239C2×D511yescharacteristic
234C2×D3×Q8—51no—
235C3×C4×Q8—51no—
236C3×C4×Q8C2×D511yescharacteristic
237C3×C4×D4—53no—
238C3×C4×D4—53no—
239C3×#117—53no—
240C2×C3×C4⋊C4—53no—
241Q8×Dic3—51no—
242Q8×Dic3C2×D511yescharacteristic
243#940—53no—
244#938—53no—
245#938—53no—
246#936—53no—
247#930—53no—
248#930—56no—
249#929—56no—
250C4×#67—53no—
251C4×#67—56no—
252C4×#67—53no—
253#926—56no—
254#924—53no—
255#898—56no—
256#898—51no—
257#897—53no—
258#896—53no—
259#895—53no—
260#894—53no—
261#893C2×D513yes—
262#892—53no—
263#892C2×D513yes—
264#890—53no—
265#890—53no—
266#889—53no—
267#887—53no—
268#885—56no—
269#885—53no—
270#884—53no—
271#883—53no—
272#883—56no—
273#879—53no—
274#875—53no—
275C4×D12—53no—
276C4×D12C2×D513yes—
277#872—53no—
278C42×D3C2×D513yes—
279#869—53no—
280C4×Dic6—53no—
281C4×Dic6—53no—
282C5×#41—64no—
283C2×C5×Q8C22×D311yescharacteristic
284C2×C5×D4—33no—
285C22×C4×C5—33no—
286C22×C4×C5—33no—
287C22×C4×C5—33no—
288C2×C22⋊D5—33no—
289C2×C22⋊D5—36no—
290C2×C22⋊D5—33no—
291#713—24no—
292Q8×D5—64no—
293C2×D20—33no—
294C2×D20C22×D313yes—
295C2×C4×D5—33no—
296C2×C4×D5C22×D313yes—
297C2×C4×D5C22×D316yes—
298C2×Dic10—33no—
299C2×Dic10—33no—
300C5×C4⋊C4—33no—
301C5×C4⋊C4C22×D313yes—
302C5×C22⋊C4—36no—
303C42×C5—31no—
304C42×C5—33no—
305C42×C5—33no—
306C42×C5C22×D313yes—
307C22⋊Dic5—33no—
308C22⋊Dic5—36no—
309C22⋊Dic5—33no—
310#685—33no—
311#685—36no—
312#685—33no—
313#685—31no—
314#685—33no—
315#685—31no—
316#685—31no—
317#685C22×D313yes—
318#685C22×D313yes—
319C4⋊Dic5—33no—
320C4⋊Dic5—33no—
321C4⋊Dic5—33no—
322C4⋊Dic5C22×D313yes—
323#683—33no—
324#683—33no—
325#683—31no—
326#683—33no—
327#683—36no—
328#683—33no—
329#683—31no—
330#683C22×D313yes—
331#683C22×D311yescharacteristic
332C4×Dic5—36no—
333C4×Dic5—33no—
334C4×Dic5C22×D313yes—
335#559—153no—
336#557—151no—
337#555—153no—
338#553—153no—
339#552—153no—
340#550—151no—
341#548—151no—
342#548—151no—
343#542—153no—
344#540—153no—
345#529—153no—
346#529—153no—
347#520—51no—
348#519—151no—
349C4×#41—31no—
350C22×C3×C5C2511yescharacteristic
351C2×D15—21no—
352C2×D15—21no—
353C2×D15—21no—
354C2×C5×D3—23no—
355C2×C5×D3—23no—
356C2×C5×D3—23no—
357C2×C3×D5—23no—
358C2×C3×D5—23no—
359C2×C3×D5—23no—
360C3×C4×C5—23no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4116yes—
363Dic15—23no—
364Dic15—21no—
365Dic15—23no—
366C3×Dic5—21no—
367C3×Dic5—23no—
368C3×Dic5—21no—
369C5×Dic3—21no—
370C5×Dic3—23no—
371C5×Dic3—21no—
372C3×#41—104no—
373C2×C3×Q8C22×D511yescharacteristic
374C2×C3×D4—53no—
375C22×C3×C4—53no—
376C22×C3×C4—56no—
377C2×#67—53no—
378C2×#67—56no—
379C2×#67—53no—
380#239—24no—
381D3×Q8—104no—
382C2×D12—53no—
383C2×D12C22×D513yes—
384C2×C4×D3—53no—
385C2×C4×D3C22×D513yes—
386C2×C4×D3C22×D513yes—
387C2×C4×D3C22×D513yes—
388C2×Dic6—53no—
389C2×Dic6—53no—
390C3×C4⋊C4—53no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—53no—
393C3×C4⋊C4C22×D513yes—
394C3×C22⋊C4—53no—
395C3×C22⋊C4—53no—
396C3×C42—53no—
397C3×C42C22×D513yes—
398#217—53no—
399#217—53no—
400#217—56no—
401(C2×D3)⋊C4—53no—
402(C2×D3)⋊C4—56no—
403(C2×D3)⋊C4—53no—
404(C2×D3)⋊C4—51no—
405(C2×D3)⋊C4—53no—
406(C2×D3)⋊C4—51no—
407(C2×D3)⋊C4—51no—
408(C2×D3)⋊C4C22×D516yes—
409C4⋊Dic3—53no—
410C4⋊Dic3—51no—
411C4⋊Dic3—56no—
412C4⋊Dic3—53no—
413C4⋊Dic3C22×D513yes—
414Dic3⋊C4—53no—
415Dic3⋊C4—53no—
416Dic3⋊C4—53no—
417Dic3⋊C4—51no—
418Dic3⋊C4—53no—
419Dic3⋊C4—53no—
420C4×Dic3—53no—
421C4×Dic3—56no—
422C4×Dic3C22×D513yes—
423C4×Dic3C22×D511yescharacteristic
424C4×Dic3C22×D513yes—
425C23×C5—33no—
426C22×D5—31no—
427C22×D5C23×D313yes—
428C5×Q8#23514yes—
429C5×D4—66no—
430C2×C4×C5—31no—
431C2×C4×C5—31no—
432C2×C4×C5—33no—
433C2×C4×C5—66no—
434C2×C4×C5—123no—
435C2×C4×C5—123no—
436C2×C4×C5C23×D313yes—
437C2×C4×C5C23×D311yescharacteristic
438C2×C4×C5C23×D313yes—
439C22⋊D5—123no—
440C22⋊D5—123no—
441C22⋊D5—126no—
442C2×Dic5—31no—
443C2×Dic5—33no—
444C2×Dic5—33no—
445C2×Dic5C23×D311yescharacteristic
446C2×Dic5C23×D313yes—
447C2×Dic5C23×D311yescharacteristic
448D20—26no—
449D20—123no—
450C4×D5—26no—
451C4×D5—46no—
452C4×D5—66no—
453Dic10—66no—
454Dic10—123no—
455C2×#41—31no—
456C2×#41—51no—
457C22×Q8—151no—
458C4⋊Q8—153no—
459#127—153no—
460#126—153no—
461#126—151no—
462#126—156no—
463#125—153no—
464#125—153no—
465#125—153no—
466#124—153no—
467#124—153no—
468#124—153no—
469#124—156no—
470#123—156no—
471#123—156no—
472#123—153no—
473#123—153no—
474C22⋊Q8—153no—
475C22⋊Q8—153no—
476C22⋊Q8—153no—
477#121—156no—
478#121—153no—
479#121—153no—
480#121—153no—
481#121—153no—
482#121—153no—
483C4×Q8—31no—
484C4×Q8—51no—
485C4×Q8—153no—
486C4×Q8—151no—
487C4×Q8—153no—
488C4×Q8—153no—
489C4×Q8D3×D511yescharacteristic
490C4×D4—33no—
491C4×D4—33no—
492C4×D4—53no—
493C4×D4—53no—
494C4×D4—153no—
495C4×D4—153no—
496C4×D4—153no—
497C4×D4—156no—
498#117—33no—
499#117—53no—
500#117—156no—
501#117—153no—
502#117—153no—
503C2×C4⋊C4—53no—
504C2×C42—33no—
505C2×C3×C5C22×#4111yescharacteristic
506C2×C3×C5#58511yescharacteristic
507C2×C3×C5#58511yescharacteristic
508D15—41no—
509C3×D5—43no—
510C5×D3—43no—
511C23×C3—53no—
512C22×D3—51no—
513C22×D3C23×D513yes—
514C3×Q8#70914yes—
515C3×D4—106no—
516C2×C3×C4—51no—
517C2×C3×C4—53no—
518C2×C3×C4—51no—
519C2×C3×C4—106no—
520C2×C3×C4—206no—
521C2×C3×C4C23×D513yes—
522C2×C3×C4C23×D511yescharacteristic
523C2×C3×C4C23×D513yes—
524#67—203no—
525#67—206no—
526#67—203no—
527C2×Dic3—51no—
528C2×Dic3—53no—
529C2×Dic3—53no—
530C2×Dic3C23×D511yescharacteristic
531C2×Dic3C23×D511yescharacteristic
532C2×Dic3C23×D513yes—
533D12—26no—
534D12—203no—
535C4×D3—26no—
536C4×D3—43no—
537C4×D3—43no—
538C4×D3—106no—
539Dic6—106no—
540Dic6—203no—
541C22×C5—63no—
542C22×C5—63no—
543C22×C5—63no—
544C22×C5C24×D311yescharacteristic
545C2×D5—23no—
546C2×D5—23no—
547C2×D5—23no—
548C2×D5—61no—
549C2×D5—61no—
550C2×D5—61no—
551C4×C5—23no—
552C4×C5—21no—
553C4×C5—61no—
554C4×C5—61no—
555C4×C5—63no—
556C4×C5C2×#23516yes—
557Dic5—21no—
558Dic5—23no—
559Dic5—21no—
560Dic5—63no—
561Dic5—61no—
562Dic5—63no—
563#41—64no—
564#41—104no—
565C2×Q8—153no—
566C2×Q8—153no—
567C2×Q8—304no—
568C2×Q8C2×D3×D511yescharacteristic
569C2×D4—33no—
570C2×D4—53no—
571C2×D4—153no—
572C2×D4—153no—
573C2×D4—156no—
574C2×D4—153no—
575C22×C4—33no—
576C22×C4—33no—
577C22×C4—33no—
578C22×C4—53no—
579C22×C4—56no—
580C22×C4—153no—
581C4⋊C4—33no—
582C4⋊C4—53no—
583C4⋊C4—53no—
584C4⋊C4—51no—
585C4⋊C4—153no—
586C4⋊C4—156no—
587C4⋊C4—151no—
588C4⋊C4—153no—
589C4⋊C4—153no—
590C4⋊C4—151no—
591C4⋊C4—153no—
592C4⋊C4—153no—
593C4⋊C4—153no—
594C4⋊C4—153no—
595C4⋊C4C2×D3×D513yes—
596C22⋊C4—36no—
597C22⋊C4—53no—
598C22⋊C4—53no—
599C22⋊C4—151no—
600C22⋊C4—151no—
601C22⋊C4—153no—
602C22⋊C4—156no—
603C22⋊C4—153no—
604C22⋊C4—153no—
605C22⋊C4—156no—
606C22⋊C4—153no—
607C22⋊C4—151no—
608C22⋊C4—153no—
609C42—31no—
610C42—33no—
611C42—33no—
612C42—53no—
613C42—156no—
614C42—153no—
615C42C2×D3×D513yes—
616C3×C5#352411yescharacteristic, complemented, Hall
617C22×C3—103no—
618C22×C3—103no—
619C22×C3—103no—
620C22×C3C24×D511yescharacteristic
621C2×D3—23no—
622C2×D3—23no—
623C2×D3—23no—
624C2×D3—101no—
625C2×D3—101no—
626C2×D3—101no—
627C3×C4—21no—
628C3×C4—23no—
629C3×C4—101no—
630C3×C4—101no—
631C3×C4—103no—
632C3×C4C2×#70916yes—
633Dic3—21no—
634Dic3—23no—
635Dic3—21no—
636Dic3—103no—
637Dic3—103no—
638Dic3—101no—
639C2×C5—123no—
640C2×C5C22×#23511yescharacteristic
641C2×C5#596611yescharacteristic
642C2×C5#596811yescharacteristic
643D5—43no—
644D5—121no—
645C23—33no—
646C23—53no—
647C23—151no—
648Q8—306no—
649Q8—603no—
650Q8#677114yes—
651D4—66no—
652D4—106no—
653D4—603no—
654D4—603no—
655D4—603no—
656D4—606no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—33no—
660C2×C4—51no—
661C2×C4—53no—
662C2×C4—51no—
663C2×C4—66no—
664C2×C4—106no—
665C2×C4—123no—
666C2×C4—123no—
667C2×C4—153no—
668C2×C4—151no—
669C2×C4—153no—
670C2×C4—206no—
671C2×C4—306no—
672C2×C4C22×D3×D513yes—
673C2×C4C22×D3×D511yescharacteristic
674C2×C4C22×D3×D513yes—
675C2×C3—203no—
676C2×C3C22×#70911yescharacteristic
677C2×C3#6628311yescharacteristic
678C2×C3#6628311yescharacteristic
679D3—43no—
680D3—201no—
681C5#8589811yescharacteristic, complemented, Sylow
682C22—63no—
683C22—63no—
684C22—63no—
685C22—103no—
686C22—103no—
687C22—103no—
688C22—301no—
689C22—301no—
690C22—301no—
691C22C23×D3×D511yescharacteristic
692C4—23no—
693C4—21no—
694C4—61no—
695C4—61no—
696C4—63no—
697C4—103no—
698C4—101no—
699C4—101no—
700C4—301no—
701C4—303no—
702C4—303no—
703C4C2×#677116yes—
704C3#1061775611yescharacteristic, complemented, Sylow
705C2—123no—
706C2—203no—
707C2—601no—
708C2C22×#677111yescharacteristic
709C2#1175704911yescharacteristic
710C2#1175706111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3524
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756331C2semidirect
2. C4×C5×#239C2semidirect
3. C3×#65908C2semidirect
4. #11755267C2semidirect
5. #11755257C2semidirect
6. #11755254C2semidirect
7. #11755134C2semidirect
8. #11753805C2semidirect
9. #11753742C2semidirect
10. #11753736C2semidirect
11. #11753731C2semidirect
12. #11752711C2semidirect
13. #11752707C2semidirect
14. #11752695C2semidirect
15. #11752693C2semidirect
72. #65908D3semidirect
140. C4×#239D5semidirect
616. C3×C5#3524semidirect
681. C5#85898semidirect
704. C3#10617756semidirect

Maximal subgroups

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

subgroupindex
#117563312
C4×C5×#2392
C3×#659082
#117552672
#117552572
#117552542
#117551342
#117538052
#117537422
#117537362
#117537312
#117527112
#117527072
#117526952
#117526932
#106177563
#858985