Finite Group Databasebeta

← #14424146

Subgroups — #14424146

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#239C211yesmaximal, characteristic
2C2×#91510C212yesmaximal, complemented
3D3×#4070C211yesmaximal, characteristic, complemented
4#11751329C211yesmaximal, characteristic, complemented
5C3×#65517C211yesmaximal, characteristic, complemented
6#11749305C212yesmaximal, complemented
7#11749300C212yesmaximal, complemented
8#11749201C212yesmaximal, complemented
9#11748543C211yesmaximal, characteristic, complemented
10#11748537C211yesmaximal, characteristic, complemented
11#11748505C211yesmaximal, characteristic, complemented
12#10615815—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C5×#239—28no—
15C2×C5×#239—21no—
16C2×C5×#239—21no—
17C2×C5×#239C2212yes—
18C2×C5×#239C2212yes—
19C22×C5×D12—21no—
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3—21no—
22C22×C4×C5×D3C2211yescharacteristic
23C2×D3×Dic10C2211yescharacteristic, complemented
24C2×#6718C2212yescomplemented
25#91813C2211yescharacteristic
26C2×C3×#689C2212yescomplemented
27C3×#4070C2211yescharacteristic
28#91575—21no—
29D3×C22⋊Dic5—21no—
30#91510—28no—
31D3×C4⋊Dic5C2211yescharacteristic, complemented
32D3×#683—21no—
33#91369C2211yescharacteristic, complemented
34#91365C2211yescharacteristic, complemented
35#91352—21no—
36C2×#6659C2212yescomplemented
37C2×#6656C2212yescomplemented
38C2×#6650C2212yescomplemented
39#91119C2212yescomplemented
40#91114C2211yescharacteristic
41C3×#3967C2212yescomplemented
42C3×C22⋊#168C2211yescharacteristic
43#90967C2212yescomplemented
44#90966C2212yescomplemented
45(C2×D3)⋊#168C2212yescomplemented
46#80184—51nomaximal, Hall
47C22×C5×#41—31no—
48C2×#4097—32no—
49C2×#4070—31no—
50#65528—32no—
51#65528—32no—
52#65521—32no—
53#65517—31no—
54#65517D311yescharacteristic, complemented
55#65507—31no—
56#65507—31no—
57#65496—31no—
58C23×C5×D3—21no—
59C23×C5×D3D411yescharacteristic
60C2×C3×C5×Q8—24no—
61C2×C3×C5×Q8—21no—
62C2×C3×C5×Q8C2312yes—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×Dic30C2311yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C5×#239—28no—
68C5×#239—28no—
69C5×#239—24no—
70C5×#239—24no—
71C5×#239—24no—
72C5×#239D418yes—
73C2×C5×D12—28no—
74C2×C5×D12—22no—
75C2×C5×D12—22no—
76C2×C5×D12—21no—
77C2×C5×D12—24no—
78C2×C5×D12C2312yes—
79C2×C4×C5×D3—28no—
80C2×C4×C5×D3—22no—
81C2×C4×C5×D3—22no—
82C2×C4×C5×D3—24no—
83C2×C4×C5×D3D411yescharacteristic
84C2×C4×C5×D3D411yescharacteristic
85C2×C4×C5×D3C2311yescharacteristic
86C2×C4×C5×D3C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C2×#1204—21no—
89C2×D3×Dic5—21no—
90C2×D3×Dic5—21no—
91D3×Dic10—24no—
92#6719—21no—
93#6718—24no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C2×C3⋊#168C2312yes—
97C3×C22⋊Dic5—21no—
98C3×#689—24no—
99C3×C4⋊Dic5C2311yescharacteristic
100C3×#683—21no—
101C2×C3×#168C2312yes—
102Dic3⋊Dic5—21no—
103#6669—21no—
104#6668—21no—
105(C2×D3)⋊Dic5—21no—
106(C2×D3)⋊Dic5—21no—
107#6659—24no—
108#6656—24no—
109#6650—24no—
110C22×#239D511yescharacteristic
111C2×#918—52no—
112D3×C22⋊Q8—51no—
113C3×#451—51no—
114#5228—51no—
115#5187—52no—
116#5046—51no—
117#4808—52no—
118#4803—52no—
119#4731—51no—
120#4726—51no—
121C2×C5×#41—32no—
122C2×C5×#41—32no—
123C2×C5×#41—61no—
124C2×C5×#41—61no—
125C2×C5×#41—68no—
126C22×C5×Q8C2×D311yescharacteristic
127C22×C5×D4—31no—
128C22×C5×D4—61no—
129C23×C4×C5—31no—
130C23×C4×C5—61no—
131C22×Dic10—31no—
132C2×C22⋊Dic5—61no—
133#4097—68no—
134C2×#689—32no—
135C2×#689C2×D312yescomplemented
136C2×#687—32no—
137C2×#687—32no—
138C2×C4⋊Dic5—31no—
139#4070—31no—
140#4070—31no—
141#4070—31no—
142#4070—61no—
143#4070—61no—
144#4070C2×D311yescharacteristic
145C2×#683—61no—
146C2×#681—32no—
147#3967—32no—
148#3967C2×D312yescomplemented
149#3964—32no—
150#3964—32no—
151C22⋊#168—31no—
152C22⋊#168—32no—
153C22⋊#168C2×D311yescharacteristic
154#3007—151noSylow
155C23×C3×C5C2×D411yescharacteristic
156C22×C5×D3—24no—
157C22×C5×D3—22no—
158C22×C5×D3—22no—
159C22×C5×D3—22no—
160C22×C5×D3—41no—
161C22×C5×D3—42no—
162C22×C5×D3—42no—
163C22×C5×D3C2×D411yescharacteristic
164C22×C5×D3C2×D411yescharacteristic
165C3×C5×Q8—24no—
166C3×C5×Q8—22no—
167C3×C5×Q8C2×D414yes—
168C2×C3×C4×C5—24no—
169C2×C3×C4×C5—22no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5C2×D411yescharacteristic
172C2×C3×C4×C5C2411yescharacteristic
173C2×Dic15—21no—
174C2×Dic15—21no—
175Dic30—22no—
176C2×C5×Dic3—22no—
177C2×C5×Dic3C2×D411yescharacteristic
178C2×C5×Dic3C2×D411yescharacteristic
179C5×D12—28no—
180C5×D12—24no—
181C5×D12—28no—
182C5×D12—22no—
183C5×D12C2×D414yes—
184C4×C5×D3—28no—
185C4×C5×D3—22no—
186C4×C5×D3—22no—
187C4×C5×D3—28no—
188C4×C5×D3—22no—
189C4×C5×D3C2×D414yes—
190C2×C3×Dic5—21no—
191C2×C3×Dic5—21no—
192C3×Dic10—22no—
193#1204—42no—
194D3×Dic5—42no—
195D3×Dic5—42no—
196C3⋊#168—22no—
197C3×#168—22no—
198C22×C3×Q8C2×D511yescharacteristic
199C2×#239—28no—
200C2×#239—21no—
201C2×#239—21no—
202C2×#239C2×D512yes—
203C2×#239C2×D512yes—
204C2×D3×Q8—51no—
205C22×D12—21no—
206C22×D12C2×D511yescharacteristic
207C22×C4×D3—21no—
208C22×C4×D3C2×D511yescharacteristic
209C2×C3×Q16—52no—
210C3×C22⋊Q8—51no—
211#946—51no—
212C2×#216—52no—
213C2×#215—52no—
214#924—51no—
215#918—108no—
216C2×#204—52no—
217C2×ΓL(1,𝔽25)—52no—
218#897—51no—
219#896—101no—
220D3×C4⋊C4—51no—
221D3×C4⋊C4—101no—
222D3×C22⋊C4—101no—
223#878—101no—
224C3×#103—52no—
225C3×C22⋊C8—51no—
226#835—52no—
227#830—51no—
228#821—52no—
229(C2×D3)⋊C8—52no—
230#809—52no—
231C24×C5—31no—
232C24×C5—61no—
233C5×#41—38no—
234C5×#41—64no—
235C5×#41—64no—
236C5×#41—68no—
237C5×#41—68no—
238C5×#41—64no—
239C2×C5×Q8—24no—
240C2×C5×Q8—21no—
241C2×C5×Q8C22×D312yes—
242C2×C5×D4—32no—
243C2×C5×D4—64no—
244C2×C5×D4—62no—
245C2×C5×D4—62no—
246C2×C5×D4—68no—
247C2×C5×D4—61no—
248C22×C4×C5—21no—
249C22×C4×C5—31no—
250C22×C4×C5—31no—
251C22×C4×C5—31no—
252C22×C4×C5—31no—
253C22×C4×C5—31no—
254C22×C4×C5—64no—
255C22×C4×C5—62no—
256C22×C4×C5—62no—
257C22×C4×C5—68no—
258C22×C4×C5C22×D311yescharacteristic
259C22×Dic5—61no—
260C22×Dic5—61no—
261C2×Dic10—31no—
262C2×Dic10—64no—
263C2×Dic10—61no—
264C2×Dic10C22×D311yescharacteristic
265C22⋊Dic5—21no—
266C22⋊Dic5—61no—
267C22⋊Dic5—61no—
268C22⋊Dic5—61no—
269#689—24no—
270#689—64no—
271#687—64no—
272#687—64no—
273C4⋊Dic5—31no—
274C4⋊Dic5—61no—
275C4⋊Dic5C22×D311yescharacteristic
276#683—21no—
277#683—61no—
278#683—61no—
279#683—61no—
280#681—64no—
281C2×#168—32no—
282C2×#168C22×D312yes—
283C22×#41—31no—
284C2×#137—152no—
285C2×C22⋊Q8—151no—
286#452—152no—
287#452—152no—
288#451—51no—
289#451—151no—
290#450—151no—
291#450—151no—
292#417—152no—
293#407—151no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5#13712yescomplemented
297C22×C3×C5C22×D411yescharacteristic
298C2×C5×D3—21no—
299C2×C5×D3—21no—
300C2×C5×D3—21no—
301C2×C5×D3—24no—
302C2×C5×D3—21no—
303C2×C5×D3—21no—
304C2×C5×D3—44no—
305C2×C5×D3—48no—
306C2×C5×D3—42no—
307C2×C5×D3—42no—
308C2×C5×D3#12012yes—
309C3×C4×C5—24no—
310C3×C4×C5—21no—
311C3×C4×C5C22×D412yes—
312Dic15—41no—
313Dic15—41no—
314C3×Dic5—41no—
315C3×Dic5—41no—
316C5×Dic3—21no—
317C5×Dic3#12012yes—
318C23×D3—21no—
319C23×D3C22⋊D511yescharacteristic
320C2×C3×Q8—24no—
321C2×C3×Q8—21no—
322C2×C3×Q8—51no—
323C2×C3×Q8C22×D512yes—
324C22×C3×C4—21no—
325C22×C3×C4C22×D511yescharacteristic
326C22×Dic3C22⋊D511yescharacteristic
327#239—28no—
328#239—28no—
329#239—24no—
330#239—24no—
331#239—24no—
332#239C22⋊D518yes—
333D3×Q8—104no—
334C2×D12—28no—
335C2×D12—22no—
336C2×D12—22no—
337C2×D12—21no—
338C2×D12—24no—
339C2×D12C22×D512yes—
340C2×C4×D3—28no—
341C2×C4×D3—22no—
342C2×C4×D3—22no—
343C2×C4×D3—24no—
344C2×C4×D3—101no—
345C2×C4×D3—101no—
346C2×C4×D3C22⋊D511yescharacteristic
347C2×C4×D3C22⋊D511yescharacteristic
348C2×C4×D3C22×D511yescharacteristic
349C2×C4×D3C22×D511yescharacteristic
350C2×Dic6—51no—
351C2×Dic6—101no—
352C3×Q16—104no—
353C2×C3×C8—52no—
354C3×C4⋊C4—51no—
355C3×C4⋊C4—101no—
356C3×C22⋊C4—101no—
357#217—101no—
358#216—104no—
359#215—104no—
360(C2×D3)⋊C4—101no—
361(C2×D3)⋊C4—101no—
362C4⋊Dic3—51no—
363C4⋊Dic3—101no—
364Dic3⋊C4—101no—
365Dic3⋊C4—101no—
366Dic3⋊C4—101no—
367C2×C3⋊C8—52no—
368#204—104no—
369ΓL(1,𝔽25)—104no—
370C23×C5—31no—
371C23×C5—31no—
372C23×C5—62no—
373C23×C5—64no—
374C23×C5—62no—
375C23×C5—62no—
376C23×C5—121no—
377C23×C5—122no—
378C23×C5—122no—
379C23×C5D3×D411yescharacteristic
380C5×Q8—24no—
381C5×Q8—22no—
382C5×Q8D3×D414yes—
383C5×D4—34no—
384C5×D4—68no—
385C5×D4—68no—
386C5×D4—64no—
387C5×D4—62no—
388C2×C4×C5—24no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—31no—
392C2×C4×C5—34no—
393C2×C4×C5—31no—
394C2×C4×C5—62no—
395C2×C4×C5—68no—
396C2×C4×C5—62no—
397C2×C4×C5—68no—
398C2×C4×C5—62no—
399C2×C4×C5—62no—
400C2×C4×C5D3×D411yescharacteristic
401C2×C4×C5C23×D311yescharacteristic
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—122no—
407C2×Dic5—122no—
408Dic10—22no—
409Dic10—62no—
410Dic10—122no—
411#168—22no—
412#168—62no—
413C2×#41—32no—
414C2×#41—32no—
415C2×#41—61no—
416C2×#41—61no—
417C2×#41—68no—
418C22×Q8—151no—
419C22×Q8D3×D511yescharacteristic
420C22×D4—31no—
421C22×D4—61no—
422C23×C4—31no—
423C23×C4—61no—
424#137—308no—
425C2×Q16—52no—
426C2×Q16—152no—
427C2×SD16—152no—
428C2×SD16—152no—
429C2×M16—152no—
430C22⋊Q8—51no—
431C22⋊Q8—151no—
432C22⋊Q8—151no—
433C22⋊Q8—151no—
434C22⋊Q8—301no—
435C22⋊Q8—301no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—301no—
438C2×C22⋊C4—301no—
439#103—52no—
440#103—152no—
441#102—152no—
442#102—152no—
443C22⋊C8—51no—
444C22⋊C8—152no—
445C22⋊C8—151no—
446C2×C3×C5—22no—
447C2×C3×C5C2×#12011yescharacteristic
448C2×C3×C5C2×#13711yescharacteristic
449C2×C3×C5#57511yescharacteristic
450C5×D3—22no—
451C5×D3—41no—
452C5×D3—44no—
453C23×C3C2×C22⋊D511yescharacteristic
454C22×D3—24no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—41no—
459C22×D3—42no—
460C22×D3—42no—
461C22×D3C2×C22⋊D511yescharacteristic
462C22×D3C2×C22⋊D511yescharacteristic
463C3×Q8—24no—
464C3×Q8—22no—
465C3×Q8—102no—
466C3×Q8C2×C22⋊D514yes—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4C2×C22⋊D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—22no—
475C2×Dic3—101no—
476C2×Dic3—101no—
477C2×Dic3C2×C22⋊D511yescharacteristic
478C2×Dic3C2×C22⋊D511yescharacteristic
479D12—28no—
480D12—24no—
481D12—28no—
482D12—22no—
483D12C2×C22⋊D514yes—
484C4×D3—28no—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—28no—
488C4×D3—22no—
489C4×D3—202no—
490C4×D3—202no—
491C4×D3C2×C22⋊D514yes—
492Dic6—102no—
493Dic6—202no—
494C3×C8—102no—
495C3⋊C8—102no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5—32no—
499C22×C5—61no—
500C22×C5—61no—
501C22×C5—61no—
502C22×C5—61no—
503C22×C5—64no—
504C22×C5—61no—
505C22×C5—124no—
506C22×C5—128no—
507C22×C5—122no—
508C22×C5—122no—
509C22×C5#91812yescomplemented
510C22×C5C2×D3×D411yescharacteristic
511C4×C5—24no—
512C4×C5—21no—
513C4×C5—32no—
514C4×C5—61no—
515C4×C5C2×D3×D412yes—
516Dic5—41no—
517Dic5—41no—
518Dic5—121no—
519Dic5—121no—
520C24—31no—
521C24—61no—
522#41—38no—
523#41—64no—
524#41—64no—
525#41—68no—
526#41—68no—
527#41—64no—
528C2×Q8—24no—
529C2×Q8—21no—
530C2×Q8—51no—
531C2×Q8—151no—
532C2×Q8—301no—
533C2×Q8—304no—
534C2×Q8C2×D3×D512yes—
535C2×D4—32no—
536C2×D4—64no—
537C2×D4—62no—
538C2×D4—62no—
539C2×D4—68no—
540C2×D4—61no—
541C22×C4—21no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—64no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—68no—
551C22×C4—301no—
552C22×C4—301no—
553C22×C4C2×D3×D511yescharacteristic
554Q16—104no—
555Q16—304no—
556SD16—304no—
557SD16—304no—
558M16—304no—
559C2×C8—52no—
560C2×C8—152no—
561C4⋊C4—51no—
562C4⋊C4—101no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C22⋊C4—101no—
569C22⋊C4—301no—
570C22⋊C4—301no—
571C22⋊C4—301no—
572C3×C5#300711yescharacteristic, complemented, Hall
573C22×C3—21no—
574C22×C3—21no—
575C22×C3#409712yescomplemented
576C22×C3C22×C22⋊D511yescharacteristic
577C2×D3—21no—
578C2×D3—21no—
579C2×D3—21no—
580C2×D3—21no—
581C2×D3—21no—
582C2×D3—24no—
583C2×D3—44no—
584C2×D3—48no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3#409912yes—
588C3×C4—24no—
589C3×C4—21no—
590C3×C4—201no—
591C3×C4—201no—
592C3×C4C22×C22⋊D512yes—
593Dic3—21no—
594Dic3—201no—
595Dic3—201no—
596Dic3#409912yes—
597C2×C5—22no—
598C2×C5—62no—
599C2×C5—121no—
600C2×C5—124no—
601C2×C5D3×#12011yescharacteristic
602C2×C5C2×#91811yescharacteristic
603C2×C5#577711yescharacteristic
604C23—31no—
605C23—31no—
606C23—62no—
607C23—64no—
608C23—62no—
609C23—62no—
610C23—121no—
611C23—122no—
612C23—122no—
613C23D3×C22⋊D511yescharacteristic
614Q8—24no—
615Q8—22no—
616Q8—102no—
617Q8—302no—
618Q8—602no—
619Q8D3×C22⋊D514yes—
620D4—34no—
621D4—68no—
622D4—68no—
623D4—64no—
624D4—62no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—31no—
629C2×C4—34no—
630C2×C4—31no—
631C2×C4—62no—
632C2×C4—68no—
633C2×C4—62no—
634C2×C4—68no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D3×C22⋊D511yescharacteristic
644C2×C4C22×D3×D511yescharacteristic
645C8—102no—
646C8—302no—
647C2×C3—22no—
648C2×C3#6615611yescharacteristic
649C2×C3C2×#409711yescharacteristic
650C2×C3C2×#409911yescharacteristic
651D3—22no—
652D3—41no—
653D3—44no—
654C5#8018411yescharacteristic, complemented, Sylow
655C22—21no—
656C22—21no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22—61no—
661C22—61no—
662C22—64no—
663C22—61no—
664C22—124no—
665C22—128no—
666C22—122no—
667C22—122no—
668C22#9151012yescomplemented
669C22C2×D3×C22⋊D511yescharacteristic
670C4—24no—
671C4—21no—
672C4—32no—
673C4—61no—
674C4—201no—
675C4—201no—
676C4—601no—
677C4—601no—
678C4C2×D3×C22⋊D512yes—
679C3#1061581511yescharacteristic, complemented, Sylow
680C2—22no—
681C2—62no—
682C2—121no—
683C2—124no—
684C2#1175509011yescharacteristic
685C2C2×#9151011yescharacteristic
686C2D3×#409911yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC22×C5×#239C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91510C2semidirect
3. D3×#4070C2semidirect
4. #11751329C2semidirect
5. C3×#65517C2semidirect
6. #11749305C2semidirect
7. #11749300C2semidirect
8. #11749201C2semidirect
9. #11748543C2semidirect
10. #11748537C2semidirect
11. #11748505C2semidirect
23. C2×D3×Dic10C22semidirect
24. C2×#6718C22semidirect
26. C2×C3×#689C22semidirect
31. D3×C4⋊Dic5C22semidirect
33. #91369C22semidirect
34. #91365C22semidirect
36. C2×#6659C22semidirect
37. C2×#6656C22semidirect
38. C2×#6650C22semidirect
39. #91119C22semidirect
41. C3×#3967C22semidirect
43. #90967C22semidirect
44. #90966C22semidirect
45. (C2×D3)⋊#168C22semidirect
54. #65517D3semidirect
135. C2×#689C2×D3semidirect
148. #3967C2×D3semidirect
296. C22×C3×C5#137semidirect
509. C22×C5#918semidirect
572. C3×C5#3007semidirect
575. C22×C3#4097semidirect
654. C5#80184semidirect
668. C22#91510semidirect
679. C3#10615815semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2392
C2×#915102
D3×#40702
#117513292
C3×#655172
#117493052
#117493002
#117492012
#117485432
#117485372
#117485052
#106158153
#801845