Finite Group Databasebeta

← #14327385

Subgroups — #14327385

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#4038C211yesmaximal, characteristic, complemented
3C2×C4×#1201C211yesmaximal, characteristic
4C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
5#11748910C212yesmaximal
6#11748813C212yesmaximal, complemented
7#11748786C211yesmaximal, characteristic, complemented
8#11748759C211yesmaximal, characteristic, complemented
9C4×(C2×D3)⋊Dic5C212yesmaximal, complemented
10#11748709C212yesmaximal, complemented
11#11748623C211yesmaximal, characteristic, complemented
12#10613892—31nomaximal, Hall
13C22×C4×C5×D3C2212yes—
14C22×C4×C5×D3C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1201C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yes—
23C5×D3×C4⋊C4—24no—
24C2×C3×#685C2212yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C3×#4038—24no—
28C2×#6669C2211yescharacteristic
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2211yescharacteristic
31C2×#6665C2212yes—
32C2×#6665C2211yescharacteristic
33C4×#1201C418yescomplemented
34#91115C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82272—51nomaximal, Hall
40C22×C5×C4⋊C4—31no—
41C2×C4×C22⋊D5—31no—
42C2×#4038D311yescharacteristic, complemented
43#65502—32no—
44#65501—31no—
45C4×C22⋊Dic5—32no—
46#65279—32no—
47#65276—31no—
48#65267—32no—
49#65266—31no—
50C4⋊C4×Dic5—31no—
51C23×C5×D3C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3—24no—
63C2×C4×C5×D3—24no—
64C2×C4×C5×D3—42no—
65C2×C4×C5×D3C2×C414yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2311yescharacteristic
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5C2×C414yescomplemented
71C2×#1201—22no—
72C2×#1201—22no—
73C2×#1201C2×C414yes—
74C3×C5×C4⋊C4D414yescomplemented
75C4⋊Dic15—22no—
76C4×Dic15—42no—
77C4×Dic15C2×C414yescomplemented
78C5×C4⋊Dic3—22no—
79C5×Dic3⋊C4—24no—
80C3×#685—24no—
81C3×C4⋊Dic5—22no—
82C3×C4×Dic5—24no—
83#6669C2×C414yescomplemented
84(C2×D3)⋊Dic5—24no—
85(C2×D3)⋊Dic5C2×C414yes—
86#6665—42no—
87#6665C2×C414yescomplemented
88C2×C3×#117—51no—
89C2×C4×#67—51no—
90C2×D3×C4⋊C4D511yescharacteristic, complemented
91#5212—51no—
92#4987—51no—
93#4977—51no—
94Dic3×C4⋊C4—51no—
95#4956—52no—
96#4945—52no—
97C4×(C2×D3)⋊C4—52no—
98#4933—52no—
99C23×C4×C5—31no—
100C23×C4×C5—32no—
101C22×C22⋊D5—31no—
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×C4⋊C4—32no—
104C2×C5×C4⋊C4—31no—
105C2×C5×C4⋊C4—64no—
106C2×C5×C4⋊C4C2×D311yescharacteristic
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5—32no—
109C4×C22⋊D5—38no—
110C2×#685—31no—
111C2×#685—32no—
112C2×#685C2×D312yes—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5C2×D311yescharacteristic
115C2×#683—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5C2×D312yes—
119#4038—24no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#3963—32no—
125#2352—151noSylow
126C23×C3×C5C2411yescharacteristic
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3—21no—
130C22×C5×D3—21no—
131C22×C5×D3C22×C412yes—
132C22×C5×D3#4112yes—
133C22×C5×D3#4112yes—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5C22×C412yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D414yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×Dic15—21no—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15C22×C412yes—
155C2×Dic15C22×C412yes—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3C22×C412yes—
162C4×C5×D3—28no—
163C4×C5×D3—48no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C22×C412yes—
170C3×C4×D5—28no—
171#1201—28no—
172C23×C3×C4—51no—
173C22×#67—51no—
174C22×C4×D3C2×D512yes—
175C22×C4×D3C2×D511yescharacteristic
176C3×#117—104no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4C2×D511yescharacteristic
179C2×C3×C22⋊C4—52no—
180C2×C3×C42—52no—
181C2×#217—51no—
182C2×#217—52no—
183C4×#67—58no—
184C2×(C2×D3)⋊C4—51no—
185C2×(C2×D3)⋊C4—52no—
186C2×C4⋊Dic3—51no—
187C2×C4⋊Dic3C2×D511yescharacteristic
188C2×Dic3⋊C4—51no—
189C2×Dic3⋊C4C2×D512yes—
190C2×C4×Dic3—51no—
191C2×C4×Dic3—52no—
192D3×C4⋊C4—24no—
193C3⋊#95—52no—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C3⋊#95—52no—
198C24×C5—31no—
199C23×D5C22×D311yescharacteristic
200C22×C4×C5—31no—
201C22×C4×C5—34no—
202C22×C4×C5—32no—
203C22×C4×C5—64no—
204C22×C4×C5—62no—
205C22×C4×C5—62no—
206C22×C4×C5—64no—
207C22×C4×C5—122no—
208C22×C4×C5C22×D312yes—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—34no—
211C2×C22⋊D5—62no—
212C2×C22⋊D5—62no—
213C22×Dic5—31no—
214C22×Dic5—31no—
215C22×Dic5—32no—
216C22×Dic5C22×D312yes—
217C22×Dic5C22×D311yescharacteristic
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5C4×D314yescomplemented
221C5×C4⋊C4—64no—
222C5×C4⋊C4—62no—
223C5×C4⋊C4#6714yescomplemented
224C22⋊Dic5—34no—
225C22⋊Dic5—64no—
226#685—24no—
227#685—34no—
228#685—122no—
229C4⋊Dic5—22no—
230C4⋊Dic5—62no—
231#683—34no—
232C4×Dic5—24no—
233C4×Dic5—34no—
234C4×Dic5—122no—
235C2×C4×D4—151no—
236C2×#117—51no—
237C22×C4⋊C4—31no—
238#388—152no—
239#387—152no—
240#386—152no—
241#382—151no—
242#380—151no—
243#380—151no—
244C4×C4⋊C4—151no—
245C4×C22⋊C4—152no—
246C22×C3×C5C23×C411yescharacteristic
247C22×C3×C5C22×D411yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5H(5,𝔽2)11yescharacteristic
252C22×C3×C52−1+411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—22no—
255C2×C5×D3—22no—
256C2×C5×D3—22no—
257C2×C5×D3—22no—
258C2×C5×D3—22no—
259C2×C5×D3#11714yescomplemented
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—41no—
264C2×C3×D5—41no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C3×C4×C5—24no—
268C3×C4×C5C4×D414yes—
269Dic15—22no—
270Dic15—22no—
271Dic15—42no—
272C3×Dic5—22no—
273C3×Dic5—42no—
274C5×Dic3—22no—
275C5×Dic3—42no—
276C24×C3—51no—
277C23×D3C22×D511yescharacteristic
278C22×C3×C4—51no—
279C22×C3×C4—54no—
280C22×C3×C4—52no—
281C22×C3×C4—102no—
282C22×C3×C4—102no—
283C22×C3×C4C22×D512yes—
284C22×C3×C4C22×D511yescharacteristic
285C2×#67—54no—
286C2×#67—102no—
287C2×#67—102no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3—52no—
291C22×Dic3C22×D512yes—
292C22×Dic3C22×D511yescharacteristic
293C2×C4×D3—22no—
294C2×C4×D3—22no—
295C2×C4×D3—24no—
296C2×C4×D3—24no—
297C2×C4×D3—42no—
298C2×C4×D3C4×D514yes—
299C3×C4⋊C4—102no—
300C3×C4⋊C4C22⋊D514yescomplemented
301C3×C22⋊C4—104no—
302C3×C42—104no—
303#217—54no—
304#217—202no—
305(C2×D3)⋊C4—54no—
306(C2×D3)⋊C4—104no—
307C4⋊Dic3—22no—
308C4⋊Dic3—102no—
309Dic3⋊C4—24no—
310Dic3⋊C4—54no—
311C4×Dic3—54no—
312C4×Dic3—202no—
313C23×C5—32no—
314C23×C5—32no—
315C23×C5—32no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5—61no—
319C23×C5—61no—
320C23×C5C23×D311yescharacteristic
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—21no—
325C22×D5—21no—
326C22×D5—21no—
327C22×D5C2×C4×D312yes—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—32no—
331C2×C4×C5—61no—
332C2×C4×C5—61no—
333C2×C4×C5—68no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5—62no—
337C2×C4×C5—128no—
338C2×C4×C5C2×C4×D312yes—
339C2×C4×C5#23512yes—
340C2×C4×C5C2×#6714yes—
341C2×C4×C5C2×#6712yes—
342C22⋊D5—68no—
343C2×Dic5—21no—
344C2×Dic5—21no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—32no—
349C2×Dic5—32no—
350C2×Dic5—61no—
351C2×Dic5—61no—
352C2×Dic5—61no—
353C2×Dic5—61no—
354C2×Dic5—62no—
355C2×Dic5—62no—
356C2×Dic5—62no—
357C2×Dic5C2×C4×D312yes—
358C4×D5—28no—
359C22×D4—151no—
360C23×C4—31no—
361C23×C4—32no—
362C23×C4—51no—
363C4×D4—158no—
364#117—104no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—32no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—64no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4D3×D511yescharacteristic
372C2×C22⋊C4—52no—
373C2×C22⋊C4—151no—
374C2×C22⋊C4—151no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C42—52no—
378C2×C42—151no—
379C2×C42—152no—
380#95—152no—
381#95—152no—
382#95—152no—
383#95—152no—
384#95—152no—
385C2×C3×C5C2×#11711yescharacteristic
386C2×C3×C5C2×C4×D411yescharacteristic
387C2×C3×C5#52011yescharacteristic
388C2×C3×C5#54611yescharacteristic
389C2×C3×C5#54811yescharacteristic
390C2×C3×C5#55211yescharacteristic
391C2×C3×C5#55311yescharacteristic
392C3×D5—42no—
393C5×D3—24no—
394C23×C3—52no—
395C23×C3—101no—
396C23×C3—101no—
397C23×C3—101no—
398C23×C3—101no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3C23×D511yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3C2×C4×D512yes—
407C22×D3#71112yes—
408C22×D3#71312yes—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—52no—
412C2×C3×C4—101no—
413C2×C3×C4—101no—
414C2×C3×C4—108no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4C2×C4×D512yes—
419C2×C3×C4#70912yes—
420C2×C3×C4C2×C22⋊D514yes—
421C2×C3×C4C2×C22⋊D512yes—
422#67—108no—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—101no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3C2×C4×D512yes—
438C4×D3—28no—
439C4×D3—48no—
440C22×C5—34no—
441C22×C5—62no—
442C22×C5—62no—
443C22×C5—62no—
444C22×C5—62no—
445C22×C5—62no—
446C22×C5—62no—
447C22×C5C22×C4×D311yescharacteristic
448C22×C5C2×#23511yescharacteristic
449C22×C5D3×#4111yescharacteristic
450C22×C5D3×#4111yescharacteristic
451C22×C5#100911yescharacteristic
452C22×C5#101011yescharacteristic
453C22×C5C22×#6711yescharacteristic
454C2×D5—22no—
455C2×D5—22no—
456C2×D5—22no—
457C2×D5—41no—
458C2×D5—41no—
459C2×D5—41no—
460C2×D5—41no—
461C4×C5—24no—
462C4×C5—62no—
463C4×C5—122no—
464C4×C5C4×#6714yes—
465Dic5—22no—
466Dic5—42no—
467Dic5—62no—
468Dic5—62no—
469Dic5—122no—
470C24—31no—
471C24—51no—
472C2×D4—154no—
473C2×D4—302no—
474C2×D4—302no—
475C22×C4—31no—
476C22×C4—34no—
477C22×C4—32no—
478C22×C4—51no—
479C22×C4—54no—
480C22×C4—52no—
481C22×C4—64no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—64no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—122no—
488C22×C4—151no—
489C22×C4—151no—
490C22×C4—152no—
491C22×C4C2×D3×D512yes—
492C22×C4C2×D3×D511yescharacteristic
493C4⋊C4—64no—
494C4⋊C4—62no—
495C4⋊C4—102no—
496C4⋊C4—154no—
497C4⋊C4—302no—
498C4⋊C4#120114yescomplemented
499C22⋊C4—104no—
500C22⋊C4—154no—
501C22⋊C4—154no—
502C22⋊C4—304no—
503C22⋊C4—602no—
504C42—104no—
505C42—154no—
506C42—602no—
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—102no—
509C22×C3—102no—
510C22×C3—102no—
511C22×C3—201no—
512C22×C3—201no—
513C22×C3—201no—
514C22×C3—201no—
515C22×C3C22×C4×D511yescharacteristic
516C22×C3C2×#70911yescharacteristic
517C22×C3C2×#71111yescharacteristic
518C22×C3#414411yescharacteristic
519C22×C3C2×#71311yescharacteristic
520C22×C3#414711yescharacteristic
521C22×C3C22×C22⋊D511yescharacteristic
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—22no—
527C2×D3—22no—
528C2×D3#403814yescomplemented
529C3×C4—24no—
530C3×C4—102no—
531C3×C4—202no—
532C3×C4C4×C22⋊D514yes—
533Dic3—22no—
534Dic3—42no—
535Dic3—102no—
536Dic3—102no—
537Dic3—202no—
538C2×C5—64no—
539C2×C5D3×#11711yescharacteristic
540C2×C5#552311yescharacteristic
541C2×C5#552911yescharacteristic
542C2×C5#553011yescharacteristic
543C2×C5C2×C4×#6711yescharacteristic
544C2×C5#582911yescharacteristic
545C2×C5#583111yescharacteristic
546D5—42no—
547C23—32no—
548C23—32no—
549C23—32no—
550C23—52no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—61no—
555C23—101no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23C22×D3×D511yescharacteristic
562D4—308no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—32no—
566C2×C4—52no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—68no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—108no—
576C2×C4—102no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—128no—
580C2×C4—152no—
581C2×C4—152no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4—302no—
587C2×C4—302no—
588C2×C4—302no—
589C2×C4#677112yes—
590C2×C4C4×D3×D512yes—
591C2×C4C2×#120114yes—
592C2×C4C2×#120112yes—
593C2×C3—202no—
594C2×C3C2×#403811yescharacteristic
595C2×C3#6583811yescharacteristic
596C2×C3#6584711yescharacteristic
597C2×C3#6584811yescharacteristic
598C2×C3C2×C4×C22⋊D511yescharacteristic
599C2×C3#6614011yescharacteristic
600C2×C3#6615111yescharacteristic
601D3—24no—
602C5#8227211yescharacteristic, complemented, Sylow
603C22—34no—
604C22—62no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—201no—
614C22—201no—
615C22—201no—
616C22—201no—
617C22C2×#677111yescharacteristic
618C22C2×C4×D3×D511yescharacteristic
619C22D3×#71111yescharacteristic
620C22#9202711yescharacteristic
621C22#9202811yescharacteristic
622C22D3×#71311yescharacteristic
623C22C22×#120111yescharacteristic
624C4—24no—
625C4—62no—
626C4—102no—
627C4—122no—
628C4—202no—
629C4—302no—
630C4—302no—
631C4—602no—
632C4C4×#120114yes—
633C3#1061389211yescharacteristic, complemented, Sylow
634C2—64no—
635C2—202no—
636C2#1175366911yescharacteristic
637C2#1175376211yescharacteristic
638C2#1175377311yescharacteristic
639C2D3×#403811yescharacteristic
640C2C2×C4×#120111yescharacteristic
641C2#1175496811yescharacteristic
642C2#1175524711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×C4⋊C4C2semidirect
2. C2×C3×#4038C2semidirect
4. C4⋊C4×Dic15C2semidirect
6. #11748813C2semidirect
7. #11748786C2semidirect
8. #11748759C2semidirect
9. C4×(C2×D3)⋊Dic5C2semidirect
10. #11748709C2semidirect
11. #11748623C2semidirect
33. C4×#1201C4semidirect
42. C2×#4038D3semidirect
70. C2×C3×C4×D5C2×C4semidirect
74. C3×C5×C4⋊C4D4semidirect
77. C4×Dic15C2×C4semidirect
83. #6669C2×C4semidirect
87. #6665C2×C4semidirect
90. C2×D3×C4⋊C4D5semidirect
220. C2×C4×D5C4×D3semidirect
223. C5×C4⋊C4#67semidirect
259. C2×C5×D3#117semidirect
300. C3×C4⋊C4C22⋊D5semidirect
498. C4⋊C4#1201semidirect
507. C3×C5#2352semidirect
528. C2×D3#4038semidirect
602. C5#82272semidirect
633. C3#10613892semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C2×C3×#40382
C2×C4×#12012
C4⋊C4×Dic152
#117489102
#117488132
#117487862
#117487592
C4×(C2×D3)⋊Dic52
#117487092
#117486232
#106138923
#822725