Finite Group Databasebeta

← #14425733

Subgroups — #14425733

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×#92095C211yesmaximal, characteristic, complemented
2C5×#5804C211yesmaximal, characteristic, complemented
3#11755428C212yesmaximal, complemented
4C2×C3×#3966C211yesmaximal, characteristic, complemented
5C2×#90997C212yesmaximal, complemented
6#11749186C214yesmaximal, complemented
7#11749180C214yesmaximal, complemented
8#10615106—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C22×#1220C2212yes—
12#92095—22no—
13#92095—24no—
14#92095C2214yes—
15C2×#6819—22no—
16C2×D4×D15—22no—
17C2×#6817—21no—
18C22×C5×#67C2211yescharacteristic, complemented
19C5×#953—21no—
20C2×C5×#217C2211yescharacteristic, complemented
21C5×#939—22no—
22C5×#937C2212yescomplemented
23C5×#935C2212yescomplemented
24C5×#929—21no—
25C2×C3×C22⋊Dic5C2212yescomplemented
26#91573—22no—
27#91570C2214yescomplemented
28#91566—24no—
29#91543—22no—
30#91542C2214yescomplemented
31C3×#3966C2214yescomplemented
32#90997C2218yescomplemented
33#78686—51nomaximal, Hall
34C2×#4144—31no—
35C5×#534—31no—
36#66138—32no—
37C2×#3966D311yescharacteristic, complemented
38#65342—34no—
39#65321—34no—
40C2×#3938—32no—
41C24×C3×C5D411yescharacteristic, complemented
42C24×C3×C5C2311yescharacteristic
43C23×D15—21no—
44C23×D15D412yescomplemented
45C23×C5×D3C2311yescharacteristic, complemented
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4—22no—
48C2×C3×C5×D4D412yescomplemented
49C2×C3×C5×D4C2312yes—
50C22×C3×C4×C5D411yescharacteristic, complemented
51C2×#1220—22no—
52C2×#1220—24no—
53C2×#1220—22no—
54C2×#1220—22no—
55C2×#1220—22no—
56C2×#1220—22no—
57C2×#1220—24no—
58C2×#1220D414yescomplemented
59C2×#1220C2314yes—
60C22×Dic15—21no—
61C22×Dic15D412yescomplemented
62#6819—28no—
63#6819—28no—
64D4×D15—28no—
65D4×D15—28no—
66#6817—24no—
67#6817—24no—
68C2×D60—21no—
69C2×C4×D15—22no—
70C2×Dic30—21no—
71C2×C5×#67—21no—
72C2×C5×#67—21no—
73C2×C5×#67—22no—
74C2×C5×#67—22no—
75C2×C5×#67—22no—
76C22×C5×Dic3—21no—
77C22×C5×Dic3C2311yescharacteristic, complemented
78C22×C3×Dic5—22no—
79C2×#1203—24no—
80C5×#217—21no—
81C5×#217—22no—
82C5×#217C2312yescomplemented
83C5×(C2×D3)⋊C4—22no—
84C5×Dic3⋊C4—22no—
85C3×C22⋊Dic5—22no—
86C3×C22⋊Dic5C2314yescomplemented
87#6668—24no—
88#6667—24no—
89(C2×D3)⋊Dic5—24no—
90C2×#1004—51no—
91#5804D511yescharacteristic, complemented
92#5493—52no—
93C2×C3×#99—51no—
94C2×#806—52no—
95#4742—54no—
96#4741—54no—
97C22×C5×D4—31no—
98C22×C5×D4C2×D311yescharacteristic
99C22×C22⋊D5—32no—
100C22×C22⋊D5—61no—
101#4144—34no—
102#4144—64no—
103#4144—62no—
104C2×#711—62no—
105C2×D4×D5—62no—
106C2×#709—61no—
107C5×#123—32no—
108C5×#123—61no—
109C5×#121—62no—
110C5×#120—32no—
111C5×#120—61no—
112C2×C5×C22⋊C4—31no—
113#4099—34no—
114C2×C22⋊Dic5C2×D312yescomplemented
115#4085—64no—
116#4083—62no—
117#4081—62no—
118#4075—34no—
119#3966C2×D314yescomplemented
120#3938—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×D15—22no—
133C22×D15—24no—
134C22×D15—22no—
135C22×D15—82no—
136C22×D15—82no—
137C22×D15C2×D414yes—
138C22×C5×D3—22no—
139C22×C5×D3—21no—
140C22×C5×D3—81no—
141C3×C5×D4—24no—
142C3×C5×D4—24no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D412yes—
146#1220—28no—
147#1220—24no—
148#1220—24no—
149#1220—24no—
150#1220—24no—
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15C2×D414yes—
155D60—24no—
156C4×D15—28no—
157Dic30—24no—
158C5×#67—41no—
159C5×#67—42no—
160C5×#67—41no—
161C5×#67—82no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—21no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—81no—
166C2×C3×Dic5—24no—
167C2×C3×Dic5—82no—
168#1203—84no—
169C22×C3×D4C2×D511yescharacteristic
170C22×#67—52no—
171C22×#67—101no—
172C22×#67C2×D511yescharacteristic, complemented
173#1004—54no—
174#1004—104no—
175#1004—102no—
176C2×#237—102no—
177C2×D3×D4—102no—
178C2×#235—101no—
179C2×C3×C22⋊C4—52no—
180#953—21no—
181C2×#217C2×D511yescharacteristic, complemented
182#939—22no—
183#937C2×D512yescomplemented
184#935C2×D512yescomplemented
185#930—104no—
186#929—21no—
187#886—54no—
188#886—102no—
189#882—54no—
190#882—102no—
191C3×#99—54no—
192#806—58no—
193C24×C5—31no—
194C24×C5D1211yescharacteristic, complemented
195C24×C5C22×D311yescharacteristic
196C23×D5—32no—
197C23×D5—61no—
198C2×C5×D4—22no—
199C2×C5×D4—22no—
200C2×C5×D4—61no—
201C2×C5×D4—61no—
202C2×C5×D4—62no—
203C2×C5×D4—62no—
204C2×C5×D4—62no—
205C2×C5×D4D1212yescomplemented
206C2×C5×D4C22×D312yes—
207C22×C4×C5—31no—
208C22×C4×C5—61no—
209C22×C4×C5D1211yescharacteristic, complemented
210C2×C22⋊D5—34no—
211C2×C22⋊D5—34no—
212C2×C22⋊D5—64no—
213C2×C22⋊D5—62no—
214C2×C22⋊D5—64no—
215C2×C22⋊D5—62no—
216C2×C22⋊D5—64no—
217C2×C22⋊D5—62no—
218C2×C22⋊D5—62no—
219C2×C22⋊D5—62no—
220C22×Dic5—22no—
221C22×Dic5—32no—
222C22×Dic5—61no—
223#711—68no—
224#711—68no—
225D4×D5—68no—
226D4×D5—68no—
227#709—64no—
228#709—64no—
229C2×D20—61no—
230C2×C4×D5—62no—
231C2×Dic10—61no—
232C5×C4⋊C4—62no—
233C5×C22⋊C4—32no—
234C5×C22⋊C4—61no—
235C5×C22⋊C4—62no—
236C5×C22⋊C4—62no—
237C22⋊Dic5—22no—
238C22⋊Dic5—64no—
239C22⋊Dic5C22×D314yescomplemented
240#685—64no—
241#683—64no—
242C2×H(5,𝔽2)—151no—
243#534—31no—
244#534—152no—
245#458—154no—
246B(4,𝔽2)—154no—
247C2×#99—51no—
248C2×#99—152no—
249C22×C3×C5—22no—
250C22×C3×C5—42no—
251C22×C3×C5—41no—
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×D15—24no—
264C2×D15—44no—
265C2×D15—44no—
266C2×D15—82no—
267C2×D15—84no—
268C2×C5×D3—44no—
269C2×C5×D3—42no—
270C2×C5×D3—41no—
271C3×C4×C5—22no—
272Dic15—24no—
273C3×Dic5—44no—
274C5×Dic3—42no—
275C5×Dic3—41no—
276C24×C3C22⋊D511yescharacteristic, complemented
277C24×C3C22×D511yescharacteristic
278C23×D3—52no—
279C23×D3—101no—
280C23×D3C22×D511yescharacteristic, complemented
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4C22⋊D512yescomplemented
284C2×C3×D4C22×D512yes—
285C22×C3×C4—102no—
286C22×C3×C4C22⋊D511yescharacteristic, complemented
287C2×#67—22no—
288C2×#67—22no—
289C2×#67—21no—
290C2×#67—21no—
291C2×#67—22no—
292C2×#67—54no—
293C2×#67—54no—
294C2×#67—102no—
295C2×#67—104no—
296C2×#67—102no—
297C2×#67—102no—
298C2×#67—102no—
299C2×#67—104no—
300C2×#67—102no—
301C22×Dic3—21no—
302C22×Dic3—52no—
303C22×Dic3—101no—
304C22×Dic3C22×D511yescharacteristic, complemented
305#237—108no—
306#237—108no—
307D3×D4—108no—
308D3×D4—108no—
309#235—104no—
310#235—104no—
311C2×D12—101no—
312C2×D12—104no—
313C2×C4×D3—102no—
314C2×Dic6—101no—
315C3×C22⋊C4—54no—
316C3×C22⋊C4—102no—
317#217—21no—
318#217—22no—
319#217C22×D512yescomplemented
320(C2×D3)⋊C4—22no—
321(C2×D3)⋊C4—104no—
322(C2×D3)⋊C4—104no—
323C4⋊Dic3—104no—
324Dic3⋊C4—22no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—61no—
328C23×C5—62no—
329C23×C5—81no—
330C23×C5—81no—
331C23×C5—241no—
332C23×C5C2×D1212yes—
333C23×C5C2×D1211yescharacteristic
334C23×C5C2×D1211yescharacteristic
335C23×C5D3×D412yes—
336C23×C5D3×D412yes—
337C23×C5C23×D311yescharacteristic
338C22×D5—34no—
339C22×D5—62no—
340C22×D5—64no—
341C22×D5—62no—
342C22×D5—242no—
343C22×D5—242no—
344C5×D4—24no—
345C5×D4—24no—
346C5×D4—121no—
347C5×D4—122no—
348C5×D4—121no—
349C5×D4—242no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—62no—
353C2×C4×C5—61no—
354C2×C4×C5—62no—
355C2×C4×C5—241no—
356C2×C4×C5C2×D1212yes—
357C22⋊D5—68no—
358C22⋊D5—64no—
359C22⋊D5—64no—
360C22⋊D5—64no—
361C22⋊D5—64no—
362C22⋊D5—244no—
363C2×Dic5—24no—
364C2×Dic5—34no—
365C2×Dic5—64no—
366C2×Dic5—62no—
367C2×Dic5—62no—
368C2×Dic5—82no—
369D20—64no—
370C4×D5—68no—
371Dic10—64no—
372H(5,𝔽2)—154no—
373H(5,𝔽2)—304no—
374H(5,𝔽2)—302no—
375C2×#41—302no—
376C2×#41—301no—
377C22×D4—31no—
378C22×D4—152no—
379C22×D4—302no—
380C22×D4—301no—
381C22×D4D3×D511yescharacteristic
382#123—32no—
383#123—61no—
384#123—154no—
385#123—302no—
386#121—62no—
387#121—304no—
388#120—32no—
389#120—61no—
390#120—154no—
391#120—302no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—52no—
394#99—54no—
395#99—158no—
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
403D15—44no—
404C5×D3—81no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—81no—
408C23×C3—81no—
409C23×C3D4×D512yes—
410C23×C3D4×D512yes—
411C23×C3C2×C22⋊D512yes—
412C23×C3C2×C22⋊D511yescharacteristic
413C23×C3C2×C22⋊D511yescharacteristic
414C23×C3C23×D511yescharacteristic
415C22×D3—22no—
416C22×D3—21no—
417C22×D3—54no—
418C22×D3—81no—
419C22×D3—102no—
420C22×D3—104no—
421C22×D3—102no—
422C22×D3—402no—
423C22×D3—402no—
424C3×D4—24no—
425C3×D4—24no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—104no—
429C2×C3×C4—402no—
430C2×C3×C4C2×C22⋊D512yes—
431#67—41no—
432#67—42no—
433#67—41no—
434#67—82no—
435#67—108no—
436#67—104no—
437#67—104no—
438#67—104no—
439#67—104no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—22no—
443C2×Dic3—54no—
444C2×Dic3—81no—
445C2×Dic3—104no—
446C2×Dic3—102no—
447C2×Dic3—102no—
448D12—104no—
449D12—404no—
450C4×D3—108no—
451Dic6—104no—
452C22×C5—22no—
453C22×C5—42no—
454C22×C5—41no—
455C22×C5—42no—
456C22×C5—41no—
457C22×C5—41no—
458C22×C5—42no—
459C22×C5—42no—
460C22×C5—81no—
461C22×C5—124no—
462C22×C5—122no—
463C22×C5—121no—
464C22×C5#88211yescharacteristic
465C22×C5#88212yes—
466C22×C5#88211yescharacteristic
467C22×C5C22×D1211yescharacteristic
468C22×C5C2×D3×D412yes—
469C2×D5—64no—
470C2×D5—124no—
471C2×D5—124no—
472C2×D5—242no—
473C2×D5—244no—
474C4×C5—22no—
475C4×C5—122no—
476C4×C5—121no—
477Dic5—44no—
478Dic5—64no—
479C24—31no—
480C24—152no—
481C24—301no—
482C24#120311yescharacteristic, complemented
483C24C2×D3×D511yescharacteristic
484#41—304no—
485#41—308no—
486#41—308no—
487#41—304no—
488C2×Q8—301no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—61no—
492C2×D4—61no—
493C2×D4—62no—
494C2×D4—62no—
495C2×D4—62no—
496C2×D4—154no—
497C2×D4—154no—
498C2×D4—301no—
499C2×D4—304no—
500C2×D4—308no—
501C2×D4—308no—
502C2×D4—302no—
503C2×D4—304no—
504C2×D4—302no—
505C2×D4—302no—
506C2×D4—304no—
507C2×D4—302no—
508C2×D4—302no—
509C2×D4#120312yescomplemented
510C2×D4C2×D3×D512yes—
511C22×C4—31no—
512C22×C4—61no—
513C22×C4—102no—
514C22×C4—152no—
515C22×C4—302no—
516C22×C4—301no—
517C22×C4#120311yescharacteristic, complemented
518C4⋊C4—62no—
519C4⋊C4—304no—
520C22⋊C4—32no—
521C22⋊C4—54no—
522C22⋊C4—61no—
523C22⋊C4—62no—
524C22⋊C4—62no—
525C22⋊C4—102no—
526C22⋊C4—304no—
527C22⋊C4—304no—
528C3×C5#302611yescharacteristic, complemented, Hall
529C22×C3—22no—
530C22×C3—41no—
531C22×C3—42no—
532C22×C3—41no—
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—42no—
536C22×C3—42no—
537C22×C3—81no—
538C22×C3#408311yescharacteristic
539C22×C3#408312yes—
540C22×C3#408311yescharacteristic
541C22×C3C2×D4×D512yes—
542C22×C3C22×C22⋊D511yescharacteristic
543C2×D3—44no—
544C2×D3—42no—
545C2×D3—41no—
546C2×D3—104no—
547C2×D3—204no—
548C2×D3—204no—
549C2×D3—402no—
550C2×D3—404no—
551C3×C4—22no—
552C3×C4—204no—
553Dic3—42no—
554Dic3—41no—
555Dic3—104no—
556C2×C5—22no—
557C2×C5—21no—
558C2×C5—21no—
559C2×C5—22no—
560C2×C5—21no—
561C2×C5—42no—
562C2×C5—241no—
563C2×C5C2×#88211yescharacteristic
564D5—124no—
565C23—21no—
566C23—21no—
567C23—61no—
568C23—62no—
569C23—81no—
570C23—81no—
571C23—154no—
572C23—241no—
573C23—304no—
574C23—302no—
575C23—302no—
576C23—1202no—
577C23—1202no—
578C23C2×#120312yes—
579C23C2×#120311yescharacteristic
580C23C2×#120311yescharacteristic
581C23#679012yes—
582C23#679012yes—
583C23C22×D3×D511yescharacteristic
584Q8—304no—
585D4—24no—
586D4—24no—
587D4—121no—
588D4—121no—
589D4—122no—
590D4—242no—
591D4—304no—
592D4—308no—
593D4—304no—
594D4—304no—
595D4—304no—
596D4—304no—
597D4—1204no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—62no—
603C2×C4—104no—
604C2×C4—154no—
605C2×C4—241no—
606C2×C4—308no—
607C2×C4—304no—
608C2×C4—302no—
609C2×C4—302no—
610C2×C4—402no—
611C2×C4C2×#120312yes—
612C2×C3—21no—
613C2×C3—22no—
614C2×C3—21no—
615C2×C3—22no—
616C2×C3—21no—
617C2×C3—42no—
618C2×C3C2×#408311yescharacteristic
619D3—81no—
620D3—204no—
621C5#7868611yescharacteristic, complemented, Sylow
622C22—22no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—81no—
631C22—122no—
632C22—124no—
633C22—121no—
634C22—304no—
635C22—604no—
636C22—604no—
637C22—1202no—
638C22—1204no—
639C22#9157311yescharacteristic
640C22#9157311yescharacteristic
641C22#9157312yes—
642C22C22×#120311yescharacteristic
643C22C2×#679012yes—
644C4—22no—
645C4—122no—
646C4—121no—
647C4—204no—
648C4—304no—
649C3#1061510611yescharacteristic, complemented, Sylow
650C2—21no—
651C2—22no—
652C2—21no—
653C2—21no—
654C2—22no—
655C2—42no—
656C2—241no—
657C2—604no—
658C2C2×#9157311yescharacteristic
subgroupG/H
centerC2C2×#91573
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×#92095C2semidirect
2. C5×#5804C2semidirect
3. #11755428C2semidirect
4. C2×C3×#3966C2semidirect
5. C2×#90997C2semidirect
6. #11749186C2semidirect
7. #11749180C2semidirect
18. C22×C5×#67C22semidirect
20. C2×C5×#217C22semidirect
22. C5×#937C22semidirect
23. C5×#935C22semidirect
25. C2×C3×C22⋊Dic5C22semidirect
27. #91570C22semidirect
30. #91542C22semidirect
31. C3×#3966C22semidirect
32. #90997C22semidirect
37. C2×#3966D3semidirect
41. C24×C3×C5D4semidirect
44. C23×D15D4semidirect
45. C23×C5×D3C23semidirect
48. C2×C3×C5×D4D4semidirect
50. C22×C3×C4×C5D4semidirect
58. C2×#1220D4semidirect
61. C22×Dic15D4semidirect
77. C22×C5×Dic3C23semidirect
82. C5×#217C23semidirect
86. C3×C22⋊Dic5C23semidirect
91. #5804D5semidirect
114. C2×C22⋊Dic5C2×D3semidirect
119. #3966C2×D3semidirect
172. C22×#67C2×D5semidirect
181. C2×#217C2×D5semidirect
183. #937C2×D5semidirect
184. #935C2×D5semidirect
194. C24×C5D12semidirect
205. C2×C5×D4D12semidirect
209. C22×C4×C5D12semidirect
239. C22⋊Dic5C22×D3semidirect
276. C24×C3C22⋊D5semidirect
280. C23×D3C22×D5semidirect
283. C2×C3×D4C22⋊D5semidirect
286. C22×C3×C4C22⋊D5semidirect
304. C22×Dic3C22×D5semidirect
319. #217C22×D5semidirect
482. C24#1203semidirect
509. C2×D4#1203semidirect
517. C22×C4#1203semidirect
528. C3×C5#3026semidirect
621. C5#78686semidirect
649. C3#10615106semidirect

Maximal subgroups

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

subgroupindex
C2×#920952
C5×#58042
#117554282
C2×C3×#39662
C2×#909972
#117491862
#117491802
#106151063
#786865