Finite Group Databasebeta

← #14425734

Subgroups — #14425734

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1004C211yesmaximal, characteristic, complemented
2C3×#66138C211yesmaximal, characteristic, complemented
3#11755426C212yesmaximal, complemented
4C2×#91118C211yesmaximal, characteristic, complemented
5C2×#90996C212yesmaximal, complemented
6#11749183C214yesmaximal, complemented
7#11749177C214yesmaximal, complemented
8#10615841—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×#67—21no—
11C22×C5×#67C2212yes—
12C5×#1004—22no—
13C5×#1004—24no—
14C5×#1004C2214yes—
15C2×C5×#237—22no—
16C2×C5×D3×D4—22no—
17C2×C5×#235—21no—
18C22×C3×C22⋊D5C2211yescharacteristic, complemented
19C2×#6719C2212yescomplemented
20C3×#4099—21no—
21C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
22C3×#4085—22no—
23C3×#4083C2212yescomplemented
24C3×#4081C2212yescomplemented
25C3×#4075—21no—
26#91571—24no—
27#91568—22no—
28#91563C2214yescomplemented
29#91539C2214yescomplemented
30#91536—22no—
31#91118C2214yescomplemented
32#90996C2218yescomplemented
33#83375—51nomaximal, Hall
34C2×C5×H(5,𝔽2)—31no—
35#66138—32no—
36#66138D311yescharacteristic, complemented
37#65533—34no—
38#65532—34no—
39C2×#3966—31no—
40C2×#3966—32no—
41C24×C3×C5D411yescharacteristic, complemented
42C24×C3×C5C2311yescharacteristic
43C23×C5×D3—21no—
44C23×C5×D3D412yescomplemented
45C23×C3×D5C2311yescharacteristic, complemented
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D412yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5D411yescharacteristic, complemented
51C22×Dic15—22no—
52C2×C5×#67—22no—
53C2×C5×#67—24no—
54C2×C5×#67—22no—
55C2×C5×#67—22no—
56C2×C5×#67—22no—
57C2×C5×#67—22no—
58C2×C5×#67—24no—
59C2×C5×#67D414yescomplemented
60C2×C5×#67C2314yes—
61C22×C5×Dic3—21no—
62C22×C5×Dic3D412yescomplemented
63C5×#237—28no—
64C5×#237—28no—
65C5×D3×D4—28no—
66C5×D3×D4—28no—
67C5×#235—24no—
68C5×#235—24no—
69C2×C5×D12—21no—
70C2×C4×C5×D3—22no—
71C2×C5×Dic6—21no—
72C2×C3×C22⋊D5—21no—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—22no—
75C2×C3×C22⋊D5—22no—
76C2×C3×C22⋊D5—22no—
77C22×C3×Dic5—21no—
78C22×C3×Dic5C2311yescharacteristic, complemented
79C2×#1201—24no—
80#6719—22no—
81#6719C2314yescomplemented
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5—21no—
84C3×C22⋊Dic5C2312yescomplemented
85C3×#685—22no—
86C3×#683—22no—
87#6669—24no—
88(C2×D3)⋊Dic5—24no—
89#6665—24no—
90C2×#1004D511yescharacteristic, complemented
91C3×#534—51no—
92#5804—52no—
93C2×#834—51no—
94#5053—54no—
95#5032—54no—
96C2×#806—52no—
97C5×H(5,𝔽2)—34no—
98C5×H(5,𝔽2)—64no—
99C5×H(5,𝔽2)—62no—
100C2×C5×#41—62no—
101C2×C5×#41—61no—
102C22×C5×D4—32no—
103C22×C5×D4—62no—
104C22×C5×D4—61no—
105C22×C5×D4C2×D311yescharacteristic
106C22×C22⋊D5C2×D311yescharacteristic, complemented
107#4099—21no—
108#4099—62no—
109C2×C22⋊Dic5—32no—
110C2×C22⋊Dic5C2×D311yescharacteristic, complemented
111#4085—22no—
112#4085—64no—
113#4083—34no—
114#4083C2×D312yescomplemented
115#4081—34no—
116#4081C2×D312yescomplemented
117#4075—21no—
118#4075—62no—
119#3966—34no—
120#3966—38no—
121#3026—151noSylow
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—81no—
125C23×C3×C5—81no—
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×D412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5C2×D411yescharacteristic
130C23×C3×C5C2×D411yescharacteristic
131C23×C3×C5C2411yescharacteristic
132C22×C5×D3—22no—
133C22×C5×D3—24no—
134C22×C5×D3—22no—
135C22×C5×D3—82no—
136C22×C5×D3—82no—
137C22×C5×D3C2×D414yes—
138C22×C3×D5—22no—
139C22×C3×D5—21no—
140C22×C3×D5—81no—
141C3×C5×D4—24no—
142C3×C5×D4—24no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D412yes—
146C2×Dic15—24no—
147C2×Dic15—82no—
148C5×#67—28no—
149C5×#67—24no—
150C5×#67—24no—
151C5×#67—24no—
152C5×#67—24no—
153C2×C5×Dic3—24no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3C2×D414yes—
157C5×D12—24no—
158C4×C5×D3—28no—
159C5×Dic6—24no—
160C3×C22⋊D5—41no—
161C3×C22⋊D5—42no—
162C3×C22⋊D5—41no—
163C3×C22⋊D5—82no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—81no—
168#1201—84no—
169C22×C3×D4—51no—
170C22×C3×D4C2×D511yescharacteristic
171C22×#67—21no—
172C22×#67C2×D512yes—
173#1004—22no—
174#1004—24no—
175#1004C2×D514yes—
176C2×#237—22no—
177C2×D3×D4—22no—
178C2×#235—21no—
179C3×#123—52no—
180C3×#123—101no—
181C3×#121—102no—
182C3×#120—52no—
183C3×#120—101no—
184C2×C3×C22⋊C4—51no—
185#953—54no—
186C2×#217—52no—
187#939—104no—
188#937—102no—
189#935—102no—
190#929—54no—
191#834—54no—
192#806—58no—
193C24×C5—32no—
194C24×C5—61no—
195C24×C5#6711yescharacteristic, complemented
196C24×C5C22×D311yescharacteristic
197C23×D5C22×D311yescharacteristic, complemented
198C5×#41—64no—
199C5×#41—68no—
200C5×#41—68no—
201C5×#41—64no—
202C2×C5×Q8—61no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—34no—
206C2×C5×D4—34no—
207C2×C5×D4—61no—
208C2×C5×D4—68no—
209C2×C5×D4—68no—
210C2×C5×D4—62no—
211C2×C5×D4—64no—
212C2×C5×D4—62no—
213C2×C5×D4—62no—
214C2×C5×D4—62no—
215C2×C5×D4—62no—
216C2×C5×D4—64no—
217C2×C5×D4#6712yescomplemented
218C2×C5×D4C22×D312yes—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—61no—
222C22×C4×C5#6711yescharacteristic, complemented
223C2×C22⋊D5—22no—
224C2×C22⋊D5—22no—
225C2×C22⋊D5—21no—
226C2×C22⋊D5—21no—
227C2×C22⋊D5—22no—
228C2×C22⋊D5—64no—
229C22×Dic5—21no—
230C22×Dic5—62no—
231C22×Dic5C22×D311yescharacteristic, complemented
232C22⋊Dic5—21no—
233C22⋊Dic5—22no—
234C22⋊Dic5—34no—
235C22⋊Dic5—64no—
236C22⋊Dic5—62no—
237C22⋊Dic5C22×D312yescomplemented
238#685—22no—
239#685—64no—
240#683—22no—
241#683—64no—
242C2×H(5,𝔽2)—31no—
243#534—51no—
244#534—152no—
245#458—154no—
246B(4,𝔽2)—154no—
247C2×#99—152no—
248C2×#99—151no—
249C22×C3×C5—22no—
250C22×C3×C5—41no—
251C22×C3×C5—42no—
252C22×C3×C5—41no—
253C22×C3×C5—42no—
254C22×C3×C5—41no—
255C22×C3×C5—42no—
256C22×C3×C5—42no—
257C22×C3×C5—81no—
258C22×C3×C5#12011yescharacteristic
259C22×C3×C5#12012yes—
260C22×C3×C5#12011yescharacteristic
261C22×C3×C5C22×D412yes—
262C22×C3×C5C22×D411yescharacteristic
263C2×C5×D3—24no—
264C2×C5×D3—44no—
265C2×C5×D3—44no—
266C2×C5×D3—82no—
267C2×C5×D3—84no—
268C2×C3×D5—44no—
269C2×C3×D5—42no—
270C2×C3×D5—41no—
271C3×C4×C5—22no—
272Dic15—44no—
273C3×Dic5—42no—
274C3×Dic5—41no—
275C5×Dic3—24no—
276C24×C3—51no—
277C24×C3C22⋊D511yescharacteristic, complemented
278C24×C3C22×D511yescharacteristic
279C23×D3—21no—
280C23×D3C22⋊D512yescomplemented
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—102no—
284C2×C3×D4—102no—
285C2×C3×D4—101no—
286C2×C3×D4—101no—
287C2×C3×D4—102no—
288C2×C3×D4C22⋊D512yescomplemented
289C2×C3×D4C22×D512yes—
290C22×C3×C4—51no—
291C22×C3×C4—101no—
292C22×C3×C4C22⋊D511yescharacteristic, complemented
293C2×#67—22no—
294C2×#67—24no—
295C2×#67—22no—
296C2×#67—22no—
297C2×#67—22no—
298C2×#67—22no—
299C2×#67—24no—
300C2×#67—104no—
301C2×#67C22⋊D514yescomplemented
302C2×#67C22×D514yes—
303C22×Dic3—21no—
304C22×Dic3—102no—
305C22×Dic3C22⋊D512yescomplemented
306#237—28no—
307#237—28no—
308D3×D4—28no—
309D3×D4—28no—
310#235—24no—
311#235—24no—
312C2×D12—21no—
313C2×C4×D3—22no—
314C2×Dic6—21no—
315C3×C4⋊C4—102no—
316C3×C22⋊C4—52no—
317C3×C22⋊C4—101no—
318C3×C22⋊C4—102no—
319C3×C22⋊C4—102no—
320#217—54no—
321#217—102no—
322#217—104no—
323(C2×D3)⋊C4—104no—
324Dic3⋊C4—104no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—34no—
328C23×C5—64no—
329C23×C5—62no—
330C23×C5—62no—
331C23×C5—81no—
332C23×C5—81no—
333C23×C5—242no—
334C23×C5—242no—
335C23×C5D3×D412yes—
336C23×C5D3×D412yes—
337C23×C5C2×#6712yes—
338C23×C5C2×#6711yescharacteristic
339C23×C5C2×#6711yescharacteristic
340C23×C5C23×D311yescharacteristic
341C22×D5—22no—
342C22×D5—21no—
343C22×D5—81no—
344C5×Q8—64no—
345C5×D4—24no—
346C5×D4—24no—
347C5×D4—64no—
348C5×D4—68no—
349C5×D4—64no—
350C5×D4—64no—
351C5×D4—64no—
352C5×D4—64no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—34no—
356C2×C4×C5—68no—
357C2×C4×C5—64no—
358C2×C4×C5—62no—
359C2×C4×C5—62no—
360C2×C4×C5C2×#6712yes—
361C22⋊D5—41no—
362C22⋊D5—41no—
363C22⋊D5—42no—
364C22⋊D5—82no—
365C22⋊D5—244no—
366C2×Dic5—22no—
367C2×Dic5—21no—
368C2×Dic5—22no—
369C2×Dic5—64no—
370C2×Dic5—81no—
371C2×Dic5—242no—
372H(5,𝔽2)—34no—
373H(5,𝔽2)—64no—
374H(5,𝔽2)—62no—
375C2×#41—62no—
376C2×#41—61no—
377C22×D4—32no—
378C22×D4—51no—
379C22×D4—62no—
380C22×D4—61no—
381C22×D4D3×D511yescharacteristic
382#123—52no—
383#123—101no—
384#123—154no—
385#123—302no—
386#121—102no—
387#121—304no—
388#120—52no—
389#120—101no—
390#120—154no—
391#120—302no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4—152no—
394#99—158no—
395#99—154no—
396C2×C3×C5—21no—
397C2×C3×C5—22no—
398C2×C3×C5—21no—
399C2×C3×C5—22no—
400C2×C3×C5—21no—
401C2×C3×C5—42no—
402C2×C3×C5C2×#12011yescharacteristic
403C3×D5—81no—
404C5×D3—44no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—81no—
408C23×C3—81no—
409C23×C3—102no—
410C23×C3—101no—
411C23×C3—401no—
412C23×C3C2×C22⋊D512yes—
413C23×C3C2×C22⋊D511yescharacteristic
414C23×C3C2×C22⋊D511yescharacteristic
415C23×C3C2×C22⋊D512yes—
416C23×C3C2×C22⋊D512yes—
417C23×C3C23×D511yescharacteristic
418C22×D3—22no—
419C22×D3—24no—
420C22×D3—22no—
421C22×D3—82no—
422C22×D3—82no—
423C22×D3C2×C22⋊D514yes—
424C3×D4—24no—
425C3×D4—24no—
426C3×D4—201no—
427C3×D4—202no—
428C3×D4—201no—
429C3×D4—402no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—101no—
435C2×C3×C4—401no—
436C2×C3×C4C2×C22⋊D512yes—
437#67—28no—
438#67—24no—
439#67—24no—
440#67—24no—
441#67—24no—
442#67—404no—
443C2×Dic3—24no—
444C2×Dic3—22no—
445C2×Dic3—22no—
446C2×Dic3—104no—
447C2×Dic3—402no—
448C2×Dic3C2×C22⋊D514yes—
449D12—24no—
450C4×D3—28no—
451Dic6—24no—
452C22×C5—22no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5—42no—
460C22×C5—64no—
461C22×C5—81no—
462C22×C5—124no—
463C22×C5—124no—
464C22×C5—242no—
465C22×C5—244no—
466C22×C5#93711yescharacteristic
467C22×C5#93711yescharacteristic
468C22×C5#93712yes—
469C22×C5C2×D3×D412yes—
470C22×C5C22×#6711yescharacteristic
471C2×D5—42no—
472C2×D5—44no—
473C2×D5—41no—
474C4×C5—22no—
475C4×C5—64no—
476Dic5—42no—
477Dic5—41no—
478Dic5—124no—
479C24—32no—
480C24—51no—
481C24—61no—
482C24#120111yescharacteristic, complemented
483C24C2×D3×D511yescharacteristic
484#41—64no—
485#41—68no—
486#41—68no—
487#41—64no—
488C2×Q8—61no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—34no—
492C2×D4—34no—
493C2×D4—61no—
494C2×D4—68no—
495C2×D4—68no—
496C2×D4—62no—
497C2×D4—64no—
498C2×D4—62no—
499C2×D4—62no—
500C2×D4—64no—
501C2×D4—62no—
502C2×D4—62no—
503C2×D4—101no—
504C2×D4—101no—
505C2×D4—102no—
506C2×D4—102no—
507C2×D4—102no—
508C2×D4—304no—
509C2×D4#120112yescomplemented
510C2×D4C2×D3×D512yes—
511C22×C4—32no—
512C22×C4—51no—
513C22×C4—62no—
514C22×C4—61no—
515C22×C4—101no—
516C22×C4—302no—
517C22×C4#120111yescharacteristic, complemented
518C4⋊C4—102no—
519C4⋊C4—304no—
520C22⋊C4—52no—
521C22⋊C4—101no—
522C22⋊C4—102no—
523C22⋊C4—102no—
524C22⋊C4—154no—
525C22⋊C4—304no—
526C22⋊C4—304no—
527C22⋊C4—302no—
528C3×C5#302611yescharacteristic, complemented, Hall
529C22×C3—22no—
530C22×C3—42no—
531C22×C3—41no—
532C22×C3—42no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—81no—
538C22×C3—204no—
539C22×C3—202no—
540C22×C3—201no—
541C22×C3#409911yescharacteristic
542C22×C3#409912yes—
543C22×C3#409911yescharacteristic
544C22×C3C22×C22⋊D511yescharacteristic
545C22×C3C22×C22⋊D512yes—
546C2×D3—24no—
547C2×D3—44no—
548C2×D3—44no—
549C2×D3—82no—
550C2×D3—84no—
551C3×C4—22no—
552C3×C4—202no—
553C3×C4—201no—
554Dic3—24no—
555Dic3—204no—
556C2×C5—21no—
557C2×C5—22no—
558C2×C5—21no—
559C2×C5—21no—
560C2×C5—22no—
561C2×C5—42no—
562C2×C5—124no—
563C2×C5C2×#93711yescharacteristic
564D5—81no—
565C23—21no—
566C23—21no—
567C23—34no—
568C23—64no—
569C23—62no—
570C23—62no—
571C23—81no—
572C23—81no—
573C23—101no—
574C23—102no—
575C23—242no—
576C23—242no—
577C23—401no—
578C23C2×#120112yes—
579C23C2×#120111yescharacteristic
580C23C2×#120111yescharacteristic
581C23D3×C22⋊D512yes—
582C23D3×C22⋊D512yes—
583C23C22×D3×D511yescharacteristic
584Q8—64no—
585D4—24no—
586D4—24no—
587D4—64no—
588D4—68no—
589D4—64no—
590D4—64no—
591D4—64no—
592D4—64no—
593D4—201no—
594D4—201no—
595D4—202no—
596D4—402no—
597D4—1204no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—34no—
601C2×C4—68no—
602C2×C4—64no—
603C2×C4—62no—
604C2×C4—62no—
605C2×C4—102no—
606C2×C4—101no—
607C2×C4—102no—
608C2×C4—304no—
609C2×C4—401no—
610C2×C4—1202no—
611C2×C4C2×#120112yes—
612C2×C3—22no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3—401no—
619C2×C3C2×#409911yescharacteristic
620D3—44no—
621C5#8337511yescharacteristic, complemented, Sylow
622C22—22no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—41no—
628C22—42no—
629C22—42no—
630C22—64no—
631C22—81no—
632C22—124no—
633C22—124no—
634C22—202no—
635C22—204no—
636C22—201no—
637C22—242no—
638C22—244no—
639C22#9156811yescharacteristic
640C22#9156811yescharacteristic
641C22#9156812yes—
642C22C22×#120111yescharacteristic
643C22C2×D3×C22⋊D512yes—
644C4—22no—
645C4—64no—
646C4—202no—
647C4—201no—
648C4—604no—
649C3#1061584111yescharacteristic, complemented, Sylow
650C2—21no—
651C2—22no—
652C2—21no—
653C2—21no—
654C2—22no—
655C2—42no—
656C2—124no—
657C2—401no—
658C2C2×#9156811yescharacteristic
subgroupG/H
centerC2C2×#91568
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C2×#120
hypercenterC22×D4D3×D5
hypocenterC3×C5#3026
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1004C2semidirect
2. C3×#66138C2semidirect
3. #11755426C2semidirect
4. C2×#91118C2semidirect
5. C2×#90996C2semidirect
6. #11749183C2semidirect
7. #11749177C2semidirect
18. C22×C3×C22⋊D5C22semidirect
19. C2×#6719C22semidirect
21. C2×C3×C22⋊Dic5C22semidirect
23. C3×#4083C22semidirect
24. C3×#4081C22semidirect
28. #91563C22semidirect
29. #91539C22semidirect
31. #91118C22semidirect
32. #90996C22semidirect
36. #66138D3semidirect
41. C24×C3×C5D4semidirect
44. C23×C5×D3D4semidirect
45. C23×C3×D5C23semidirect
48. C2×C3×C5×D4D4semidirect
50. C22×C3×C4×C5D4semidirect
59. C2×C5×#67D4semidirect
62. C22×C5×Dic3D4semidirect
78. C22×C3×Dic5C23semidirect
81. #6719C23semidirect
84. C3×C22⋊Dic5C23semidirect
90. C2×#1004D5semidirect
106. C22×C22⋊D5C2×D3semidirect
110. C2×C22⋊Dic5C2×D3semidirect
114. #4083C2×D3semidirect
116. #4081C2×D3semidirect
195. C24×C5#67semidirect
197. C23×D5C22×D3semidirect
217. C2×C5×D4#67semidirect
222. C22×C4×C5#67semidirect
231. C22×Dic5C22×D3semidirect
237. C22⋊Dic5C22×D3semidirect
277. C24×C3C22⋊D5semidirect
280. C23×D3C22⋊D5semidirect
288. C2×C3×D4C22⋊D5semidirect
292. C22×C3×C4C22⋊D5semidirect
301. C2×#67C22⋊D5semidirect
305. C22×Dic3C22⋊D5semidirect
482. C24#1201semidirect
509. C2×D4#1201semidirect
517. C22×C4#1201semidirect
528. C3×C5#3026semidirect
621. C5#83375semidirect
649. C3#10615841semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10042
C3×#661382
#117554262
C2×#911182
C2×#909962
#117491832
#117491772
#106158413
#833755