Finite Group Databasebeta

← #12021506

Subgroups — #12021506

Order 1280.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#383C211yesmaximal, characteristic, complemented
2C2×C4×#685C211yesmaximal, characteristic
3C2×D5×#95C211yesmaximal, characteristic
4#10602327C211yesmaximal, characteristic, complemented
5#10600218C211yesmaximal, characteristic
6#10600218C212yesmaximal
7#10600218C212yesmaximal
8#10600211C212yesmaximal, complemented
9#10600210C212yesmaximal, complemented
10#10600196C211yesmaximal, characteristic, complemented
11#10600194C211yesmaximal, characteristic, complemented
12C23×C4×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×#685C2212yes—
16C22×#685C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×C4×Dic5C2211yescharacteristic
19C5×#383—24no—
20C2×C5×#95C2211yescharacteristic
21C2×C5×#95C2212yes—
22C2×C5×#95C2212yes—
23C2×C5×#95C2211yescharacteristic
24C2×#3963C2211yescharacteristic
25C2×#3963C2212yes—
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C4×#685C418yescomplemented
37D5×#95—24no—
38#13901—51nomaximal, Sylow
39C24×D5C2311yescharacteristic
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×Dic5C2312yes—
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2312yes—
50C22×C4×D5—24no—
51C22×C4×D5—24no—
52C22×C4×D5—24no—
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—24no—
56C22×C4×D5—24no—
57C22×C4×D5—24no—
58C22×C4×D5—42no—
59C22×C4×D5—42no—
60C22×C4×D5—42no—
61C22×C4×D5C2×C414yes—
62C2×C42×C5—22no—
63C2×C42×C5—22no—
64C2×C42×C5C2×C414yescomplemented
65C2×#685—22no—
66C2×#685—24no—
67C2×#685—22no—
68C2×#685—24no—
69C2×#685—24no—
70C2×#685—24no—
71C2×#685C2×C414yes—
72C2×#685C2×C414yes—
73C2×C4×Dic5—42no—
74C2×C4×Dic5C2×C414yescomplemented
75C5×#95—24no—
76C5×#95—24no—
77C5×#95—22no—
78C5×#95D414yes—
79#3963—24no—
80#3963—22no—
81#3963—22no—
82#3963—24no—
83#3963—24no—
84#3963—42no—
85#3963—42no—
86#3963—42no—
87#3963—42no—
88#3963—42no—
89#3963C2×C414yescomplemented
90#3963C2×C414yescomplemented
91C2×#383D511yescharacteristic, complemented
92C2×C4×C22⋊C4—51no—
93C22×#95—51no—
94#1443—52no—
95#1443—52no—
96#1434—51no—
97#1434—51no—
98#1434—51no—
99C22⋊#95—52no—
100C22⋊#95—52no—
101C22⋊#95—51no—
102C24×C5C2411yescharacteristic
103C23×D5—21no—
104C23×D5—21no—
105C23×D5—22no—
106C23×D5—22no—
107C23×D5—21no—
108C23×D5—21no—
109C23×D5C22×C412yes—
110C23×D5#4112yes—
111C23×D5#4114yes—
112C23×D5#4114yes—
113C23×D5#4112yes—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5C22×C412yes—
140C22×C4×C5C22×C412yes—
141C22×C4×C5C22×C412yes—
142C22×C4×C5C2×D414yes—
143C22×C4×C5C2×D412yes—
144C22×C4×C5#4112yes—
145C22×Dic5—21no—
146C22×Dic5—22no—
147C22×Dic5—21no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—21no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—21no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5C22×C412yes—
171C22×Dic5C22×C412yes—
172C22×Dic5C22×C412yes—
173C22×Dic5#4114yes—
174C2×C4×D5—216no—
175C2×C4×D5—28no—
176C2×C4×D5—28no—
177C2×C4×D5—44no—
178C2×C4×D5—48no—
179C2×C4×D5—48no—
180C2×C4×D5—48no—
181C2×C4×D5—48no—
182C2×C4×D5—48no—
183C2×C4×D5—48no—
184C2×C4×D5—48no—
185C2×C4×D5—48no—
186C42×C5—28no—
187#685—28no—
188#685—28no—
189#685—48no—
190C4×Dic5—44no—
191C24×C4—51no—
192C24×C4—52no—
193C22×C22⋊C4—51no—
194C22×C22⋊C4—51no—
195C22×C22⋊C4—52no—
196C22×C42—51no—
197C22×C42C2×D511yescharacteristic
198#383—24no—
199C4×C22⋊C4—58no—
200C2×#95—51no—
201C2×#95—51no—
202C2×#95—51no—
203C2×#95—52no—
204C2×#95—52no—
205C2×#95—51no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95—52no—
211C2×#95—52no—
212C2×#95—104no—
213C2×#95C2×D511yescharacteristic
214C2×#95C2×D512yes—
215C2×#95C2×D512yes—
216C2×#95C2×D511yescharacteristic
217C23×C5C23×C411yescharacteristic
218C23×C5C22×D411yescharacteristic
219C23×C5C2×#4111yescharacteristic
220C23×C5C2×#4112yes—
221C23×C5C2×#4112yes—
222C23×C5C2×#4111yescharacteristic
223C23×C5C2×#4111yescharacteristic
224C23×C5C2×#4112yes—
225C23×C5H(5,𝔽2)12yes—
226C23×C5H(5,𝔽2)11yescharacteristic
227C23×C52−1+411yescharacteristic
228C22×D5—22no—
229C22×D5—22no—
230C22×D5—22no—
231C22×D5—22no—
232C22×D5—24no—
233C22×D5—24no—
234C22×D5—24no—
235C22×D5—24no—
236C22×D5—24no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—24no—
240C22×D5—24no—
241C22×D5—24no—
242C22×D5—22no—
243C22×D5—24no—
244C22×D5—22no—
245C22×D5—24no—
246C22×D5#11714yes—
247C22×D5#11714yes—
248C22×D5#11714yes—
249C22×D5#12618yes—
250C22×D5#12618yes—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—24no—
262C2×C4×C5—24no—
263C2×C4×C5—24no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—41no—
273C2×C4×C5—41no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5C4×D414yes—
282C2×Dic5—22no—
283C2×Dic5—22no—
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—24no—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C2×Dic5—42no—
309C2×Dic5—42no—
310C2×Dic5—42no—
311C4×D5—416no—
312C4×D5—432no—
313C25—51no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—52no—
318C23×C4—54no—
319C23×C4—52no—
320C23×C4—104no—
321C23×C4—104no—
322C23×C4—104no—
323C23×C4—104no—
324C23×C4—104no—
325C23×C4—102no—
326C23×C4—104no—
327C23×C4—102no—
328C23×C4—202no—
329C23×C4—202no—
330C23×C4—202no—
331C23×C4C22×D512yes—
332C23×C4C22×D511yescharacteristic
333C23×C4C22×D511yescharacteristic
334C23×C4C22×D512yes—
335C23×C4C22×D511yescharacteristic
336C2×C22⋊C4—54no—
337C2×C22⋊C4—54no—
338C2×C22⋊C4—102no—
339C2×C22⋊C4—104no—
340C2×C22⋊C4—102no—
341C2×C22⋊C4—104no—
342C2×C22⋊C4—104no—
343C2×C22⋊C4—104no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—54no—
347C2×C42—202no—
348C2×C42C4×D514yescomplemented
349#95—24no—
350#95—24no—
351#95—22no—
352#95—54no—
353#95—54no—
354#95—104no—
355#95—104no—
356#95—102no—
357#95—104no—
358#95—102no—
359#95—202no—
360#95—202no—
361#95—202no—
362#95—202no—
363#95—202no—
364#95C22⋊D514yes—
365C22×C5C2×#11711yescharacteristic
366C22×C5C2×#11711yescharacteristic
367C22×C5C2×#11711yescharacteristic
368C22×C5C2×C4×D411yescharacteristic
369C22×C5C4×#4111yescharacteristic
370C22×C5#51811yescharacteristic
371C22×C5#52011yescharacteristic
372C22×C5#52512yes—
373C22×C5C2×#12612yes—
374C22×C5C2×#12612yes—
375C22×C5#52912yes—
376C22×C5#53812yes—
377C22×C5#53912yes—
378C22×C5#54612yes—
379C22×C5#54611yescharacteristic
380C22×C5#54811yescharacteristic
381C22×C5#55112yes—
382C22×C5#55112yes—
383C22×C5#55112yes—
384C22×C5#55211yescharacteristic
385C22×C5#55212yes—
386C22×C5#55311yescharacteristic
387C22×C5#55312yes—
388C2×D5—24no—
389C2×D5—24no—
390C2×D5—24no—
391C2×D5—24no—
392C2×D5—24no—
393C2×D5—28no—
394C2×D5—28no—
395C2×D5—28no—
396C2×D5—28no—
397C2×D5—24no—
398C2×D5#38318yescomplemented
399C4×C5—24no—
400C4×C5—42no—
401C4×C5—44no—
402C4×C5—42no—
403C4×C5—82no—
404Dic5—42no—
405Dic5—42no—
406Dic5—42no—
407Dic5—44no—
408Dic5—82no—
409C24—52no—
410C24—52no—
411C24—54no—
412C24—52no—
413C24—54no—
414C24—101no—
415C24—102no—
416C24—102no—
417C24—101no—
418C24—101no—
419C24—101no—
420C24C23×D511yescharacteristic
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—54no—
450C22×C4—108no—
451C22×C4—1016no—
452C22×C4—101no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—101no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4—101no—
469C22×C4—102no—
470C22×C4—108no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—204no—
479C22×C4—208no—
480C22×C4—208no—
481C22×C4—208no—
482C22×C4—208no—
483C22×C4—208no—
484C22×C4—208no—
485C22×C4—208no—
486C22×C4—208no—
487C22×C4C2×C4×D512yes—
488C22×C4C2×C4×D512yes—
489C22×C4C2×C4×D512yes—
490C22×C4#70912yes—
491C22×C4C2×C22⋊D514yes—
492C22×C4C2×C22⋊D512yes—
493C22⋊C4—108no—
494C22⋊C4—108no—
495C22⋊C4—208no—
496C42—28no—
497C42—204no—
498C2×C5C2×#38311yescharacteristic
499C2×C5#229011yescharacteristic
500C2×C5#231811yescharacteristic
501C2×C5#234211yescharacteristic
502C2×C5#234311yescharacteristic
503C2×C5#235211yescharacteristic
504C2×C5#235311yescharacteristic
505C2×C5#248012yes—
506C2×C5#248112yes—
507C2×C5#249312yes—
508C2×C5#251012yes—
509D5—28no—
510C23—54no—
511C23—54no—
512C23—54no—
513C23—58no—
514C23—58no—
515C23—102no—
516C23—102no—
517C23—102no—
518C23—104no—
519C23—104no—
520C23—102no—
521C23—102no—
522C23—102no—
523C23—104no—
524C23—102no—
525C23—104no—
526C23—102no—
527C23—104no—
528C23—104no—
529C23—104no—
530C23—104no—
531C23—104no—
532C23—104no—
533C23C22×C4×D511yescharacteristic
534C23C2×#70911yescharacteristic
535C23D5×#4112yes—
536C23D5×#4112yes—
537C23D5×#4111yescharacteristic
538C23D5×#4111yescharacteristic
539C23D5×#4112yes—
540C23#414912yes—
541C23#414911yescharacteristic
542C23#415011yescharacteristic
543C23C22×C22⋊D511yescharacteristic
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—102no—
575C2×C4—102no—
576C2×C4—102no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—104no—
584C2×C4—104no—
585C2×C4—104no—
586C2×C4—2016no—
587C2×C4—2032no—
588C2×C4—202no—
589C2×C4—202no—
590C2×C4—202no—
591C2×C4—202no—
592C2×C4—202no—
593C2×C4—202no—
594C2×C4—202no—
595C2×C4—202no—
596C2×C4—202no—
597C2×C4—202no—
598C2×C4—202no—
599C2×C4—202no—
600C2×C4—202no—
601C2×C4—202no—
602C2×C4—202no—
603C2×C4—202no—
604C2×C4—202no—
605C2×C4C4×C22⋊D514yes—
606C5#1390111yescharacteristic, complemented, Sylow
607C22—58no—
608C22—108no—
609C22—108no—
610C22—104no—
611C22—104no—
612C22—104no—
613C22—108no—
614C22—108no—
615C22—104no—
616C22—104no—
617C22—104no—
618C22D5×#11711yescharacteristic
619C22D5×#11711yescharacteristic
620C22D5×#11711yescharacteristic
621C22#6585511yescharacteristic
622C22#6585611yescharacteristic
623C22#6585711yescharacteristic
624C22#6586112yes—
625C22#6586212yes—
626C22#6586311yescharacteristic
627C22#6586411yescharacteristic
628C22D5×#12612yes—
629C22D5×#12612yes—
630C22#6603812yes—
631C22#6603912yes—
632C22#6603912yes—
633C22#6604112yes—
634C22#6604212yes—
635C22#6604312yes—
636C22C2×C4×C22⋊D511yescharacteristic
637C22#6616212yes—
638C22#6616311yescharacteristic
639C22#6616312yes—
640C22#6616511yescharacteristic
641C4—24no—
642C4—44no—
643C4—42no—
644C4—42no—
645C4—82no—
646C4—204no—
647C4—202no—
648C4—202no—
649C4—202no—
650C4—402no—
651C2—108no—
652C2D5×#38311yescharacteristic
653C2#1060602611yescharacteristic
654C2#1060602711yescharacteristic
655C2#1060602811yescharacteristic
656C2#1060603112yes—
657C2#1060603212yes—
658C2#1061399911yescharacteristic
659C2#1061400211yescharacteristic
660C2#1061400311yescharacteristic
661C2#1061481212yes—
662C2#1061481312yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#383C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#383D5
hypocenterC5#13901
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C2×C5×#383C2semidirect
4. #10602327C2semidirect
8. #10600211C2semidirect
9. #10600210C2semidirect
10. #10600196C2semidirect
11. #10600194C2semidirect
36. C4×#685C4semidirect
64. C2×C42×C5C2×C4semidirect
74. C2×C4×Dic5C2×C4semidirect
89. #3963C2×C4semidirect
90. #3963C2×C4semidirect
91. C2×#383D5semidirect
348. C2×C42C4×D5semidirect
398. C2×D5#383semidirect
606. C5#13901semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3832
C2×C4×#6852
C2×D5×#952
#106023272
#106002182
#106002112
#106002102
#106001962
#106001942
#139015