Finite Group Databasebeta

← #12030060

Subgroups — #12030060

Order 1280.

1586 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#10602339C212yesmaximal, complemented
8#10602339C212yesmaximal, complemented
9#10600205C212yesmaximal, 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⋊Dic5C2212yes—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C5×#394C418yescomplemented
23C2×C5×#95C2211yescharacteristic
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32#65240—28no—
33#14632—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—42no—
60C2×C22⋊Dic5—42no—
61C2×C22⋊Dic5—42no—
62C2×C22⋊Dic5—42no—
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—22no—
70C2×C4⋊Dic5—24no—
71C2×C4⋊Dic5—42no—
72C2×C4⋊Dic5—42no—
73C2×C4⋊Dic5—41no—
74C2×C4⋊Dic5—41no—
75C2×C4⋊Dic5—41no—
76C2×C4⋊Dic5—42no—
77C2×C4×Dic5—41no—
78C2×C4×Dic5—41no—
79C2×C4×Dic5D414yescomplemented
80C5×#95C2×C414yes—
81#3963—24no—
82#3963—24no—
83#3963—42no—
84#3963—42no—
85#3963—41no—
86#3963—42no—
87#3963—42no—
88#3963—42no—
89C2×#394D511yescharacteristic
90C2×#388—52no—
91#1442—52no—
92#1441—51no—
93#1439—52no—
94#1439—52no—
95#1439—52no—
96#1438—52no—
97C4⋊#95—51no—
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—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
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×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5C2×D414yes—
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—48no—
179C4⋊Dic5—44no—
180C4⋊Dic5—44no—
181C4×Dic5—44no—
182C23×D4C2×D511yescharacteristic
183C22×C4⋊C4—51no—
184C22×C4⋊C4—52no—
185C22×C4⋊C4—51no—
186C22×C4⋊C4C2×D511yescharacteristic
187C22×C22⋊C4—52no—
188C22×C22⋊C4—52no—
189C22×C22⋊C4—52no—
190C22×C22⋊C4—52no—
191C22×C22⋊C4C2×D512yes—
192C22×C22⋊C4C2×D512yes—
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—51no—
202C2×#95—52no—
203C2×#95—52no—
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×C5H(5,𝔽2)11yescharacteristic
244C23×C5H(5,𝔽2)12yes—
245C23×C5H(5,𝔽2)11yescharacteristic
246C23×C5H(5,𝔽2)12yes—
247C23×C5H(5,𝔽2)11yescharacteristic
248C23×C5H(5,𝔽2)12yes—
249C23×C52−1+411yescharacteristic
250C23×C52−1+412yes—
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—22no—
262C2×C4×C5—22no—
263C2×C4×C5—24no—
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—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5—42no—
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—104no—
321C2×C4⋊C4—102no—
322C2×C4⋊C4—201no—
323C2×C4⋊C4—201no—
324C2×C4⋊C4—202no—
325C2×C4⋊C4—202no—
326C2×C4⋊C4—202no—
327C2×C4⋊C4—201no—
328C2×C4⋊C4C2×Dic514yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—104no—
334C2×C22⋊C4—104no—
335C2×C22⋊C4—202no—
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⋊C4—202no—
343C2×C22⋊C4—202no—
344C2×C22⋊C4—202no—
345C2×C22⋊C4C2×Dic518yes—
346C2×C22⋊C4C2×Dic518yes—
347C2×C42—54no—
348C2×C42—201no—
349C2×C42—201no—
350#95—104no—
351#95—104no—
352#95—202no—
353#95—202no—
354#95—201no—
355#95—202no—
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×C5#51812yes—
376C22×C5#51811yescharacteristic
377C22×C5#52012yes—
378C22×C5#52011yescharacteristic
379C22×C5#53411yescharacteristic
380C22×C5#53512yes—
381C22×C5#53711yescharacteristic
382C22×C5#53712yes—
383C22×C5#53811yescharacteristic
384C22×C5#53911yescharacteristic
385C22×C5#54012yes—
386C22×C5#54212yes—
387C22×C5#56011yescharacteristic
388C22×C5#56012yes—
389C22×C5#56012yes—
390C22×C5H(3,𝔽4)11yescharacteristic
391C22×C5H(3,𝔽4)11yescharacteristic
392C22×C5#56212yes—
393C22×C5#56212yes—
394C22×C5#56212yes—
395C22×C5#56312yes—
396C22×C5#56311yescharacteristic
397C4×C5—24no—
398C4×C5—44no—
399C4×C5—42no—
400C4×C5—42no—
401Dic5—44no—
402Dic5—82no—
403Dic5—82no—
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—44no—
425C2×D4—48no—
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—102no—
446C22×C4—102no—
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—208no—
481C4⋊C4—204no—
482C22⋊C4—216no—
483C22⋊C4—48no—
484C22⋊C4—208no—
485C22⋊C4—208no—
486C22⋊C4—208no—
487C22⋊C4—208no—
488C42—204no—
489C2×C5—84no—
490C2×C5#232412yes—
491C2×C5#232511yescharacteristic
492C2×C5#237511yescharacteristic
493C2×C5#237612yes—
494C2×C5#237911yescharacteristic
495C2×C5#281312yes—
496C2×C5#281911yescharacteristic
497C2×C5#282311yescharacteristic
498C2×C5#282811yescharacteristic
499C2×C5#283211yescharacteristic
500C2×C5#283712yes—
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#414411yescharacteristic
539C23#414412yes—
540C23#414411yescharacteristic
541C23#414412yes—
542C23#414911yescharacteristic
543C23#414912yes—
544C23#415011yescharacteristic
545C23#415012yes—
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—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—104no—
572C2×C4—104no—
573C2×C4—104no—
574C2×C4—202no—
575C2×C4—202no—
576C2×C4—202no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4—202no—
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#1463211yescharacteristic, 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#6592911yescharacteristic
618C22#6592912yes—
619C22#6593111yescharacteristic
620C22#6593611yescharacteristic
621C22#6593712yes—
622C22#6593911yescharacteristic
623C22#6594112yes—
624C22#6594212yes—
625C22#6595111yescharacteristic
626C22#6595312yes—
627C22#6598512yes—
628C22#6600012yes—
629C22#6600112yes—
630C22#6600112yes—
631C22#6600611yescharacteristic
632C22#6601711yescharacteristic
633C22#6601812yes—
634C22C2×D4×Dic511yescharacteristic
635C22#6613212yes—
636C22#6613211yescharacteristic
637C22#6616111yescharacteristic
638C22#6616112yes—
639C4—24no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—204no—
644C4—402no—
645C4—402no—
646C4—402no—
647C2—84no—
648C2#1060881811yescharacteristic
649C2#1060882011yescharacteristic
650C2#1060883111yescharacteristic
651C2#1060883312yes—
652C2#1060889112yes—
653C2#1060889811yescharacteristic
654C2#1061431111yescharacteristic
655C2#1061436412yes—
656C2#1061436511yescharacteristic
657C2#1061457112yes—
658C2#1061468811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#394C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#394D5
hypocenterC5#14632
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. #10602339C2semidirect
8. #10602339C2semidirect
9. #10600205C2semidirect
22. C5×#394C4semidirect
79. C2×C4×Dic5D4semidirect
194. #394Dic5semidirect
600. C5#14632semidirect

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
#106002052
#146325