Finite Group Databasebeta

← #12029582

Subgroups — #12029582

Order 1280.

1650 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×C5×#394C211yesmaximal, characteristic
2C2×#65240C212yesmaximal, complemented
3#10602924C212yesmaximal
4#10602358C211yesmaximal, characteristic, complemented
5#10602356C211yesmaximal, characteristic, complemented
6#10602339C212yesmaximal, complemented
7#10602338C212yesmaximal, complemented
8#10602338C212yesmaximal, complemented
9#10600194C212yesmaximal, complemented
10C23×C5×D4C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2212yes—
14C22×C22⋊Dic5C2212yes—
15C22×C22⋊Dic5C2212yes—
16C22×C22⋊Dic5C2212yes—
17C22×C22⋊Dic5C2212yes—
18C22×C4⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4×Dic5C2212yes—
21C22×C4×Dic5C2211yescharacteristic
22C5×#394C418yescomplemented
23C2×C5×#95C2211yescharacteristic
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2211yescharacteristic
31C2×#3963C2212yes—
32#65240—28no—
33#14589—51nomaximal, Sylow
34C25×C5C2312yes—
35C22×C5×D4—41no—
36C22×C5×D4—41no—
37C22×C5×D4—42no—
38C22×C5×D4—42no—
39C22×C5×D4C2×C414yes—
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×Dic5C2312yes—
45C23×Dic5C2312yes—
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C2×C5×C4⋊C4—41no—
49C2×C5×C4⋊C4—41no—
50C2×C5×C4⋊C4C2×C414yes—
51C2×C5×C22⋊C4—24no—
52C2×C5×C22⋊C4—24no—
53C2×C5×C22⋊C4—42no—
54C2×C5×C22⋊C4—42no—
55C2×C5×C22⋊C4C2×C418yes—
56C2×C5×C22⋊C4C2×C418yes—
57C2×C22⋊Dic5—24no—
58C2×C22⋊Dic5—24no—
59C2×C22⋊Dic5—24no—
60C2×C22⋊Dic5—24no—
61C2×C22⋊Dic5—24no—
62C2×C22⋊Dic5—24no—
63C2×C22⋊Dic5—42no—
64C2×C22⋊Dic5—42no—
65C2×C22⋊Dic5—42no—
66C2×C22⋊Dic5—42no—
67C2×C22⋊Dic5—42no—
68C2×C22⋊Dic5—42no—
69C2×C4⋊Dic5—41no—
70C2×C4⋊Dic5—41no—
71C2×C4⋊Dic5—41no—
72C2×C4⋊Dic5—42no—
73C2×C4⋊Dic5D414yescomplemented
74C2×C4×Dic5—22no—
75C2×C4×Dic5—24no—
76C2×C4×Dic5—24no—
77C2×C4×Dic5—42no—
78C2×C4×Dic5—41no—
79C2×C4×Dic5—41no—
80C5×#95C2×C414yes—
81#3963—24no—
82#3963—24no—
83#3963—24no—
84#3963—41no—
85#3963—42no—
86#3963—42no—
87#3963—42no—
88#3963—42no—
89C2×#394D511yescharacteristic
90C2×#388—52no—
91#1441—51no—
92#1439—52no—
93#1438—52no—
94#1437—52no—
95#1437—52no—
96C4⋊#95—51no—
97#1434—52no—
98C24×C5—22no—
99C24×C5—22no—
100C24×C5—22no—
101C24×C5—22no—
102C24×C5—22no—
103C24×C5—22no—
104C24×C5—22no—
105C24×C5—22no—
106C24×C5—22no—
107C24×C5—22no—
108C24×C5—22no—
109C24×C5—22no—
110C24×C5—22no—
111C24×C5—22no—
112C24×C5C22×C414yes—
113C24×C5C2411yescharacteristic
114C2×C5×D4—44no—
115C2×C5×D4—48no—
116C2×C5×D4—44no—
117C2×C5×D4—48no—
118C2×C5×D4—44no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5C22×C412yes—
138C22×C4×C5C22×C414yes—
139C22×C4×C5C22×C412yes—
140C22×C4×C5C22×C412yes—
141C22×C4×C5C2×D412yes—
142C22×C4×C5#4112yes—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5C2×D414yes—
169C22×Dic5#4114yes—
170C22×Dic5#4114yes—
171C5×C4⋊C4—44no—
172C5×C22⋊C4—216no—
173C5×C22⋊C4—48no—
174C22⋊Dic5—48no—
175C22⋊Dic5—48no—
176C22⋊Dic5—48no—
177C22⋊Dic5—48no—
178C4⋊Dic5—44no—
179C4⋊Dic5—44no—
180C4×Dic5—48no—
181C4×Dic5—44no—
182C23×D4C2×D511yescharacteristic
183C22×C4⋊C4—51no—
184C22×C4⋊C4—51no—
185C22×C4⋊C4C2×D511yescharacteristic
186C22×C22⋊C4—52no—
187C22×C22⋊C4—52no—
188C22×C22⋊C4—52no—
189C22×C22⋊C4—52no—
190C22×C22⋊C4C2×D512yes—
191C22×C22⋊C4C2×D512yes—
192C22×C42—52no—
193C22×C42—51no—
194#394Dic518yescomplemented
195#388—108no—
196C2×#95—52no—
197C2×#95—52no—
198C2×#95—52no—
199C2×#95—52no—
200C2×#95—52no—
201C2×#95—52no—
202C2×#95—52no—
203C2×#95—51no—
204C2×#95C2×D511yescharacteristic
205C23×C5—24no—
206C23×C5—24no—
207C23×C5—24no—
208C23×C5—24no—
209C23×C5—24no—
210C23×C5—24no—
211C23×C5—24no—
212C23×C5—42no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5—42no—
217C23×C5—42no—
218C23×C5—42no—
219C23×C5—42no—
220C23×C5—42no—
221C23×C5—42no—
222C23×C5—42no—
223C23×C5—42no—
224C23×C5—42no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5—42no—
229C23×C5—42no—
230C23×C5—42no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—42no—
234C23×C5—42no—
235C23×C5—42no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5C23×C411yescharacteristic
241C23×C5C22×D411yescharacteristic
242C23×C5C2×#4111yescharacteristic
243C23×C5C2×#4112yes—
244C23×C5C2×#4112yes—
245C23×C5H(5,𝔽2)11yescharacteristic
246C23×C5H(5,𝔽2)11yescharacteristic
247C23×C5H(5,𝔽2)12yes—
248C23×C5H(5,𝔽2)12yes—
249C23×C5H(5,𝔽2)11yescharacteristic
250C23×C52−1+411yescharacteristic
251C5×D4—416no—
252C2×C4×C5—22no—
253C2×C4×C5—22no—
254C2×C4×C5—22no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—24no—
259C2×C4×C5—24no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—24no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—41no—
270C2×C4×C5—42no—
271C2×C4×C5—41no—
272C2×C4×C5—42no—
273C2×C4×C5—41no—
274C2×C4×C5—41no—
275C2×C4×C5C4×D414yes—
276C2×Dic5—24no—
277C2×Dic5—24no—
278C2×Dic5—24no—
279C2×Dic5—24no—
280C2×Dic5—24no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—24no—
284C2×Dic5—24no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
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—
304C25C22×D512yes—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4—41no—
308C22×D4—41no—
309C22×D4C2×Dic514yes—
310C23×C4—52no—
311C23×C4—52no—
312C23×C4—52no—
313C23×C4—52no—
314C23×C4C22×D511yescharacteristic
315C23×C4C22×D512yes—
316C23×C4C22×D511yescharacteristic
317C23×C4C22×D511yescharacteristic
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—54no—
321C2×C4⋊C4—201no—
322C2×C4⋊C4—201no—
323C2×C4⋊C4—202no—
324C2×C4⋊C4—201no—
325C2×C4⋊C4C2×Dic514yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—104no—
331C2×C22⋊C4—104no—
332C2×C22⋊C4—104no—
333C2×C22⋊C4—104no—
334C2×C22⋊C4—104no—
335C2×C22⋊C4—104no—
336C2×C22⋊C4—202no—
337C2×C22⋊C4—202no—
338C2×C22⋊C4—202no—
339C2×C22⋊C4—202no—
340C2×C22⋊C4—202no—
341C2×C22⋊C4—202no—
342C2×C22⋊C4C2×Dic518yes—
343C2×C22⋊C4C2×Dic518yes—
344C2×C42—104no—
345C2×C42—104no—
346C2×C42—102no—
347C2×C42—201no—
348C2×C42—201no—
349C2×C42—202no—
350#95—104no—
351#95—104no—
352#95—104no—
353#95—202no—
354#95—202no—
355#95—201no—
356#95—202no—
357#95—202no—
358#95C2×Dic514yes—
359C22×C5—44no—
360C22×C5—44no—
361C22×C5—44no—
362C22×C5—44no—
363C22×C5—44no—
364C22×C5—44no—
365C22×C5—44no—
366C22×C5—82no—
367C22×C5—82no—
368C22×C5—82no—
369C22×C5—82no—
370C22×C5—82no—
371C22×C5—82no—
372C22×C5—82no—
373C22×C5—82no—
374C22×C5C2×C4×D411yescharacteristic
375C22×C5C4×#4112yes—
376C22×C5#51811yescharacteristic
377C22×C5#51812yes—
378C22×C5#52011yescharacteristic
379C22×C5#53411yescharacteristic
380C22×C5#53711yescharacteristic
381C22×C5#53811yescharacteristic
382C22×C5#53812yes—
383C22×C5#53911yescharacteristic
384C22×C5#53912yes—
385C22×C5#54012yes—
386C22×C5#54212yes—
387C22×C5#54612yes—
388C22×C5#55012yes—
389C22×C5#55112yes—
390C22×C5#55312yes—
391C22×C5#55512yes—
392C22×C5#55511yescharacteristic
393C22×C5#55511yescharacteristic
394C22×C5#56011yescharacteristic
395C22×C5#56012yes—
396C22×C5H(3,𝔽4)11yescharacteristic
397C4×C5—24no—
398C4×C5—44no—
399C4×C5—42no—
400C4×C5—42no—
401Dic5—44no—
402Dic5—44no—
403Dic5—44no—
404Dic5—82no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24C22×Dic514yes—
420C24C23×D511yescharacteristic
421C2×D4—44no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—44no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—54no—
445C22×C4—54no—
446C22×C4—54no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4D4×D512yes—
473C22×C4#71112yes—
474C22×C4C22×Dic514yes—
475C22×C4C22×Dic512yes—
476C22×C4C22×Dic512yes—
477C22×C4C22×Dic512yes—
478C4⋊C4—44no—
479C4⋊C4—204no—
480C4⋊C4—204no—
481C22⋊C4—216no—
482C22⋊C4—48no—
483C22⋊C4—208no—
484C22⋊C4—208no—
485C22⋊C4—208no—
486C22⋊C4—208no—
487C42—204no—
488C42—208no—
489C2×C5—84no—
490C2×C5#232511yescharacteristic
491C2×C5#233512yes—
492C2×C5#236312yes—
493C2×C5#237211yescharacteristic
494C2×C5#237511yescharacteristic
495C2×C5#269911yescharacteristic
496C2×C5#270512yes—
497C2×C5#273311yescharacteristic
498C2×C5#275612yes—
499C2×C5#278511yescharacteristic
500C2×C5#279511yescharacteristic
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23C2×D4×D511yescharacteristic
537C23C2×#71111yescharacteristic
538C23#414412yes—
539C23#414411yescharacteristic
540C23#414411yescharacteristic
541C23#414412yes—
542C23D5×#4112yes—
543C23D5×#4112yes—
544C23#414911yescharacteristic
545C23#415011yescharacteristic
546C23C23×Dic511yescharacteristic
547D4—416no—
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—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—104no—
572C2×C4—104no—
573C2×C4—104no—
574C2×C4—104no—
575C2×C4—104no—
576C2×C4—104no—
577C2×C4—104no—
578C2×C4—104no—
579C2×C4—104no—
580C2×C4—202no—
581C2×C4—202no—
582C2×C4—202no—
583C2×C4—202no—
584C2×C4—202no—
585C2×C4—202no—
586C2×C4—202no—
587C2×C4—202no—
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×C4D4×Dic514yes—
600C5#1458911yescharacteristic, complemented, Sylow
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22#6592811yescharacteristic
617C22#6592912yes—
618C22#6592911yescharacteristic
619C22#6593111yescharacteristic
620C22#6593312yes—
621C22#6593611yescharacteristic
622C22#6593911yescharacteristic
623C22#6594612yes—
624C22#6594812yes—
625C22#6595012yes—
626C22#6595111yescharacteristic
627C22#6599112yes—
628C22#6599412yes—
629C22#6599612yes—
630C22#6599712yes—
631C22#6600411yescharacteristic
632C22#6600411yescharacteristic
633C22#6601312yes—
634C22C2×D4×Dic511yescharacteristic
635C22#6613212yes—
636C22#6613211yescharacteristic
637C22#41×Dic512yes—
638C22#6616111yescharacteristic
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—204no—
644C4—204no—
645C4—204no—
646C4—402no—
647C2—84no—
648C2#1060875612yes—
649C2#1060877811yescharacteristic
650C2#1060879212yes—
651C2#1060880111yescharacteristic
652C2#1060880311yescharacteristic
653C2#1060887811yescharacteristic
654C2#1061431111yescharacteristic
655C2#1061436511yescharacteristic
656C2#1061436812yes—
657C2#1061456812yes—
658C2#1061468711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#394C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#394D5
hypocenterC5#14589
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#65240C2semidirect
4. #10602358C2semidirect
5. #10602356C2semidirect
6. #10602339C2semidirect
7. #10602338C2semidirect
8. #10602338C2semidirect
9. #10600194C2semidirect
22. C5×#394C4semidirect
73. C2×C4⋊Dic5D4semidirect
194. #394Dic5semidirect
600. C5#14589semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3942
C2×#652402
#106029242
#106023582
#106023562
#106023392
#106023382
#106001942
#145895