Finite Group Databasebeta

← #14319928

Subgroups — #14319928

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic5C211yesmaximal, characteristic
2C2×#91398C212yesmaximal, complemented
3#11751043C211yesmaximal, characteristic, complemented
4C5×#4955C211yesmaximal, characteristic
5C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#11749516C211yesmaximal, characteristic, complemented
7#11749496C211yesmaximal, characteristic
8Dic5×#217C211yesmaximal, characteristic, complemented
9#11748887C212yesmaximal, complemented
10#11748880C212yesmaximal, complemented
11Dic5×(C2×D3)⋊C4C212yesmaximal, complemented
12#10605548—31nomaximal, Hall
13C24×C5×D3C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C22×D3×Dic5—28no—
17C22×D3×Dic5C418yescomplemented
18C22×D3×Dic5C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×#6712C2212yescomplemented
25C2×C5×#217C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2212yes—
27C2×C5×(C2×D3)⋊C4C2212yes—
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2212yescomplemented
30C2×#6669C2212yescomplemented
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×Dic3×Dic5C2212yescomplemented
34#91398—28no—
35#91115C2212yescomplemented
36C3×#3963C2212yescomplemented
37#90994C2212yescomplemented
38#90994C2212yescomplemented
39#73561—51nomaximal, Hall
40C24×Dic5—31no—
41C2×#4023—32no—
42C5×#379—31no—
43#65536—31no—
44#65232—32no—
45#65231—32no—
46#65231—31no—
47#65231—31no—
48C22⋊C4×Dic5—32no—
49C22⋊C4×Dic5—31no—
50C22⋊C4×Dic5D311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—24no—
55C23×C5×D3—24no—
56C23×C5×D3C2×C414yes—
57C23×C5×D3C2311yescharacteristic
58C23×C5×D3C2311yescharacteristic
59C22×C3×C4×C5C2312yes—
60C22×Dic15—24no—
61C22×Dic15C2×C414yes—
62C22×Dic15C2312yes—
63C22×Dic15C2311yescharacteristic
64C22×Dic15C2311yescharacteristic
65C22×C5×Dic3C2312yes—
66C22×C3×Dic5—24no—
67C22×C3×Dic5C2×C414yes—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2311yescharacteristic
71C2×D3×Dic5—24no—
72C2×D3×Dic5—24no—
73C2×D3×Dic5—24no—
74C2×D3×Dic5—232no—
75C2×D3×Dic5C2×C414yes—
76C2×D3×Dic5C2×C414yes—
77C2×D3×Dic5C2×C414yes—
78C2×D3×Dic5C2×C414yes—
79C2×D3×Dic5D418yes—
80C3×C5×C22⋊C4—22no—
81#6719—22no—
82#6712—24no—
83C5×#217—22no—
84C5×(C2×D3)⋊C4—24no—
85C5×(C2×D3)⋊C4—24no—
86C3×C22⋊Dic5—22no—
87C3×C4×Dic5—24no—
88#6669—24no—
89(C2×D3)⋊Dic5—24no—
90(C2×D3)⋊Dic5—24no—
91Dic3×Dic5—24no—
92C23×C4×D3—51no—
93C2×#872—52no—
94C3×C4×C22⋊C4—51no—
95C4×#217—51no—
96#4955—51no—
97#4955D511yescharacteristic
98#4942—51no—
99#4942—51no—
100C4×(C2×D3)⋊C4—52no—
101#4667—52no—
102#4664—52no—
103C25×C5—31no—
104C23×Dic5—31no—
105C23×Dic5—31no—
106C23×Dic5—38no—
107C23×Dic5—31no—
108C23×Dic5—31no—
109C23×Dic5—31no—
110C23×Dic5—68no—
111C23×Dic5C2×D311yescharacteristic
112C2×C5×C22⋊C4—31no—
113C2×C5×C22⋊C4—32no—
114C2×C5×C22⋊C4—32no—
115C2×C5×C22⋊C4C2×D311yescharacteristic
116C2×C22⋊Dic5—31no—
117C2×C22⋊Dic5—32no—
118C2×C22⋊Dic5—32no—
119C2×C22⋊Dic5C2×D311yescharacteristic
120C2×#683—32no—
121C2×#683—32no—
122C2×C4×Dic5—32no—
123C2×C4×Dic5C2×D312yescomplemented
124#4023—68no—
125#3963—32no—
126#3963—32no—
127#3963—32no—
128#3963C2×D312yescomplemented
129#2280—151noSylow
130C23×C3×C5—22no—
131C23×C3×C5—22no—
132C23×C3×C5C22×C412yes—
133C23×C3×C5#4112yes—
134C23×C3×C5#4112yes—
135C23×C3×C5C2411yescharacteristic
136C22×C5×D3—216no—
137C22×C5×D3—216no—
138C22×C5×D3—28no—
139C22×C5×D3—22no—
140C22×C5×D3—21no—
141C22×C5×D3—21no—
142C22×C5×D3—22no—
143C22×C5×D3—21no—
144C22×C5×D3—21no—
145C22×C5×D3—28no—
146C22×C5×D3—28no—
147C22×C5×D3C22×C412yes—
148C22×C5×D3C22×C412yes—
149C22×C5×D3C2×D414yes—
150C22×C5×D3#4114yes—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×Dic15—22no—
155C2×Dic15—28no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15C22×C412yes—
160C2×Dic15C22×C412yes—
161C2×Dic15C2×D414yes—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—28no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5C22×C412yes—
171C2×C3×Dic5C22×C412yes—
172C2×C3×Dic5C2×D414yes—
173D3×Dic5—28no—
174D3×Dic5—28no—
175D3×Dic5—28no—
176D3×Dic5C22⋊C4116yescomplemented
177C24×D3C2×D511yescharacteristic
178C23×C3×C4—51no—
179C23×Dic3—51no—
180C22×C4×D3—51no—
181C22×C4×D3—58no—
182C22×C4×D3—51no—
183C22×C4×D3—51no—
184C22×C4×D3—51no—
185C22×C4×D3—108no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4C2×D511yescharacteristic
188C2×C3×C42—52no—
189C2×#217—51no—
190C2×#217C2×D511yescharacteristic
191C2×(C2×D3)⋊C4—52no—
192C2×(C2×D3)⋊C4—52no—
193C2×(C2×D3)⋊C4C2×D512yes—
194C2×(C2×D3)⋊C4C2×D512yes—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×C4×Dic3—52no—
198#872—108no—
199C3×#95—52no—
200C3⋊#95—52no—
201C3⋊#95—52no—
202C3⋊#95—52no—
203C24×C5—31no—
204C24×C5—31no—
205C24×C5—34no—
206C24×C5—64no—
207C24×C5—64no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5C22×D311yescharacteristic
211C22×C4×C5—32no—
212C22×C4×C5C22×D312yes—
213C22×Dic5—24no—
214C22×Dic5—31no—
215C22×Dic5—34no—
216C22×Dic5—38no—
217C22×Dic5—34no—
218C22×Dic5—31no—
219C22×Dic5—34no—
220C22×Dic5—34no—
221C22×Dic5—34no—
222C22×Dic5—32no—
223C22×Dic5—64no—
224C22×Dic5—632no—
225C22×Dic5—64no—
226C22×Dic5—64no—
227C22×Dic5—64no—
228C22×Dic5C4×D314yes—
229C22×Dic5C22×D312yes—
230C22×Dic5C22×D311yescharacteristic
231C22×Dic5C22×D311yescharacteristic
232C5×C22⋊C4—22no—
233C5×C22⋊C4—64no—
234C5×C22⋊C4—64no—
235C5×C22⋊C4—62no—
236C22⋊Dic5—22no—
237C22⋊Dic5—64no—
238C22⋊Dic5—64no—
239C22⋊Dic5—62no—
240#683—64no—
241#683—64no—
242C4×Dic5—24no—
243C4×Dic5—64no—
244C24×C4—151no—
245C2×#117—152no—
246#381—152no—
247#380—152no—
248#380—151no—
249#380—151no—
250#379—31no—
251#379—151no—
252C4×C22⋊C4—51no—
253C4×C22⋊C4—152no—
254C4×C22⋊C4—151no—
255C22×C3×C5—22no—
256C22×C3×C5—22no—
257C22×C3×C5—24no—
258C22×C3×C5—24no—
259C22×C3×C5#11714yescomplemented
260C22×C3×C5C23×C411yescharacteristic
261C22×C3×C5C22×D412yes—
262C22×C3×C5C2×#4111yescharacteristic
263C22×C3×C5C2×#4111yescharacteristic
264C22×C3×C5C2×#4112yes—
265C2×C5×D3—232no—
266C2×C5×D3—22no—
267C2×C5×D3—22no—
268C2×C5×D3—22no—
269C2×C5×D3—22no—
270C2×C5×D3—24no—
271C2×C5×D3—24no—
272C2×C5×D3—24no—
273C2×C5×D3—24no—
274C2×C5×D3C2×C22⋊C414yes—
275C2×C5×D3#11714yescomplemented
276C3×C4×C5—42no—
277Dic15—22no—
278Dic15—42no—
279Dic15C2×C22⋊C414yes—
280C3×Dic5—22no—
281C3×Dic5—42no—
282C3×Dic5C2×C22⋊C414yes—
283C5×Dic3—42no—
284C24×C3C22×D511yescharacteristic
285C23×D3—22no—
286C23×D3—22no—
287C23×D3—24no—
288C23×D3—24no—
289C23×D3C4×D514yes—
290C23×D3C22×D511yescharacteristic
291C23×D3C22×D511yescharacteristic
292C22×C3×C4—51no—
293C22×C3×C4—54no—
294C22×C3×C4—51no—
295C22×C3×C4—52no—
296C22×C3×C4—104no—
297C22×C3×C4C22×D512yes—
298C22×Dic3—51no—
299C22×Dic3—54no—
300C22×Dic3—51no—
301C22×Dic3—52no—
302C22×Dic3—104no—
303C22×Dic3C22×D512yes—
304C2×C4×D3—54no—
305C2×C4×D3—58no—
306C2×C4×D3—54no—
307C2×C4×D3—54no—
308C2×C4×D3—54no—
309C2×C4×D3—1032no—
310C2×C4×D3—104no—
311C2×C4×D3—104no—
312C2×C4×D3—104no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—102no—
315C3×C42—104no—
316#217—22no—
317#217—102no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—104no—
321(C2×D3)⋊C4—104no—
322Dic3⋊C4—104no—
323Dic3⋊C4—104no—
324C4×Dic3—104no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—32no—
328C23×C5—32no—
329C23×C5—34no—
330C23×C5—34no—
331C23×C5—68no—
332C23×C5—68no—
333C23×C5—616no—
334C23×C5—616no—
335C23×C5—68no—
336C23×C5—61no—
337C23×C5—61no—
338C23×C5—61no—
339C23×C5—61no—
340C23×C5—62no—
341C23×C5—62no—
342C23×C5C2×C4×D312yes—
343C23×C5#23512yes—
344C23×C5#23512yes—
345C23×C5C23×D311yescharacteristic
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5—62no—
352C2×Dic5—22no—
353C2×Dic5—28no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—32no—
358C2×Dic5—34no—
359C2×Dic5—316no—
360C2×Dic5—32no—
361C2×Dic5—68no—
362C2×Dic5—68no—
363C2×Dic5—68no—
364C2×Dic5—62no—
365C2×Dic5—68no—
366C2×Dic5—62no—
367C2×Dic5—62no—
368C2×Dic5—62no—
369C2×Dic5C2×C4×D312yes—
370C2×Dic5C2×C4×D312yes—
371C2×Dic5D3×D414yes—
372C25—31no—
373C23×C4—51no—
374C23×C4—151no—
375C23×C4—151no—
376C23×C4—151no—
377C23×C4—151no—
378C23×C4—158no—
379C23×C4—151no—
380C23×C4—308no—
381#117—308no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—152no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—51no—
388C2×C22⋊C4—152no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—151no—
391C2×C22⋊C4D3×D511yescharacteristic
392C2×C42—52no—
393C2×C42—152no—
394#95—52no—
395#95—152no—
396#95—152no—
397#95—152no—
398C2×C3×C5—24no—
399C2×C3×C5C22×C22⋊C411yescharacteristic
400C2×C3×C5C2×#11711yescharacteristic
401C2×C3×C5C2×#11711yescharacteristic
402C2×C3×C5#52512yes—
403C2×C3×C5#52512yes—
404C5×D3—24no—
405C5×D3—24no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3C2×C4×D512yes—
409C23×C3#71112yes—
410C23×C3#71112yes—
411C23×C3C23×D511yescharacteristic
412C22×D3—216no—
413C22×D3—216no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—28no—
421C22×D3—28no—
422C22×D3—28no—
423C22×D3C2×C4×D512yes—
424C22×D3C2×C4×D512yes—
425C22×D3D4×D514yes—
426C22×D3#71114yes—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—52no—
431C2×C3×C4—54no—
432C2×C3×C4—52no—
433C2×C3×C4—108no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—52no—
442C2×Dic3—54no—
443C2×Dic3—52no—
444C2×Dic3—108no—
445C2×Dic3—102no—
446C2×Dic3—102no—
447C2×Dic3—102no—
448C2×Dic3—102no—
449C4×D3—516no—
450C4×D3—108no—
451C4×D3—108no—
452C4×D3—108no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—24no—
456C22×C5—24no—
457C22×C5—34no—
458C22×C5—34no—
459C22×C5—632no—
460C22×C5—62no—
461C22×C5—62no—
462C22×C5—62no—
463C22×C5—62no—
464C22×C5—64no—
465C22×C5—64no—
466C22×C5—64no—
467C22×C5—64no—
468C22×C5#87214yescomplemented
469C22×C5C22×C4×D311yescharacteristic
470C22×C5C2×#23511yescharacteristic
471C22×C5C2×#23511yescharacteristic
472C22×C5C2×D3×D412yes—
473C22×C5D3×#4112yes—
474C4×C5—42no—
475C4×C5—122no—
476Dic5—22no—
477Dic5—34no—
478Dic5—42no—
479Dic5—62no—
480Dic5—122no—
481Dic5D3×C22⋊C414yes—
482C24—31no—
483C24—31no—
484C24—34no—
485C24—64no—
486C24—64no—
487C24—62no—
488C24—62no—
489C24C2×D3×D511yescharacteristic
490C22×C4—32no—
491C22×C4—51no—
492C22×C4—54no—
493C22×C4—51no—
494C22×C4—52no—
495C22×C4—104no—
496C22×C4—158no—
497C22×C4—154no—
498C22×C4—154no—
499C22×C4—154no—
500C22×C4—154no—
501C22×C4—151no—
502C22×C4—154no—
503C22×C4—151no—
504C22×C4—152no—
505C22×C4—304no—
506C22×C4—3032no—
507C22×C4—304no—
508C22×C4—304no—
509C22×C4—304no—
510C22×C4C2×D3×D512yes—
511C4⋊C4—304no—
512C4⋊C4—304no—
513C22⋊C4—22no—
514C22⋊C4—64no—
515C22⋊C4—64no—
516C22⋊C4—62no—
517C22⋊C4—102no—
518C22⋊C4—304no—
519C22⋊C4—304no—
520C22⋊C4—302no—
521C42—104no—
522C42—304no—
523C3×C5#228011yescharacteristic, complemented, Hall
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3#402314yescomplemented
529C22×C3C22×C4×D511yescharacteristic
530C22×C3C2×D4×D512yes—
531C22×C3C2×#71111yescharacteristic
532C22×C3C2×#71112yes—
533C22×C3C2×#71111yescharacteristic
534C2×D3—232no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3#402314yescomplemented
544C2×D3D5×C22⋊C414yes—
545C3×C4—42no—
546C3×C4—54no—
547C3×C4—102no—
548C3×C4—202no—
549Dic3—42no—
550Dic3—54no—
551Dic3—102no—
552Dic3—202no—
553C2×C5—24no—
554C2×C5—64no—
555C2×C5—64no—
556C2×C5C2×#87211yescharacteristic
557C2×C5C2×D3×C22⋊C411yescharacteristic
558C2×C5D3×#11711yescharacteristic
559C2×C5#554712yes—
560C2×C5#554712yes—
561C23—22no—
562C23—22no—
563C23—32no—
564C23—32no—
565C23—34no—
566C23—34no—
567C23—68no—
568C23—68no—
569C23—616no—
570C23—616no—
571C23—68no—
572C23—61no—
573C23—61no—
574C23—62no—
575C23—62no—
576C23—61no—
577C23—61no—
578C23#677212yes—
579C23C4×D3×D512yes—
580C23#678212yes—
581C23C22×D3×D511yescharacteristic
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—52no—
586C2×C4—54no—
587C2×C4—52no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—108no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—1516no—
597C2×C4—152no—
598C2×C4—154no—
599C2×C4—152no—
600C2×C4—308no—
601C2×C4—308no—
602C2×C4—308no—
603C2×C4—308no—
604C2×C4—302no—
605C2×C4—302no—
606C2×C4—302no—
607C2×C4—302no—
608C2×C3—24no—
609C2×C3C2×#402311yescharacteristic
610C2×C3C2×#402311yescharacteristic
611C2×C3C2×D5×C22⋊C411yescharacteristic
612C2×C3#6592012yes—
613C2×C3#6592012yes—
614D3—24no—
615D3—24no—
616C5#7356111yescharacteristic, complemented, Sylow
617C22—24no—
618C22—22no—
619C22—24no—
620C22—22no—
621C22—34no—
622C22—34no—
623C22—632no—
624C22—64no—
625C22—64no—
626C22—62no—
627C22—62no—
628C22—62no—
629C22—64no—
630C22—64no—
631C22—62no—
632C22#9139814yescomplemented
633C22C2×#677211yescharacteristic
634C22C2×C4×D3×D511yescharacteristic
635C22D3×D4×D512yes—
636C22D3×#71112yes—
637C22C2×#678211yescharacteristic
638C4—42no—
639C4—54no—
640C4—102no—
641C4—122no—
642C4—154no—
643C4—202no—
644C4—302no—
645C4—602no—
646C3#1060554811yescharacteristic, complemented, Sylow
647C2—24no—
648C2—64no—
649C2—64no—
650C2D3×#402311yescharacteristic
651C2#1175284012yes—
652C2D3×D5×C22⋊C411yescharacteristic
653C2C2×#9139811yescharacteristic
654C2#1175476712yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91398C2semidirect
3. #11751043C2semidirect
5. C3×C22⋊C4×Dic5C2semidirect
6. #11749516C2semidirect
8. Dic5×#217C2semidirect
9. #11748887C2semidirect
10. #11748880C2semidirect
11. Dic5×(C2×D3)⋊C4C2semidirect
17. C22×D3×Dic5C4semidirect
24. C2×#6712C22semidirect
29. C2×C3×C4×Dic5C22semidirect
30. C2×#6669C22semidirect
33. C2×Dic3×Dic5C22semidirect
35. #91115C22semidirect
36. C3×#3963C22semidirect
37. #90994C22semidirect
38. #90994C22semidirect
50. C22⋊C4×Dic5D3semidirect
123. C2×C4×Dic5C2×D3semidirect
128. #3963C2×D3semidirect
176. D3×Dic5C22⋊C4semidirect
259. C22×C3×C5#117semidirect
275. C2×C5×D3#117semidirect
468. C22×C5#872semidirect
523. C3×C5#2280semidirect
528. C22×C3#4023semidirect
543. C2×D3#4023semidirect
616. C5#73561semidirect
632. C22#91398semidirect
646. C3#10605548semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic52
C2×#913982
#117510432
C5×#49552
C3×C22⋊C4×Dic52
#117495162
#117494962
Dic5×#2172
#117488872
#117488802
Dic5×(C2×D3)⋊C42
#106055483
#735615