Finite Group Databasebeta

← #12021622

Subgroups — #12021622

Order 1280.

1730 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#382C211yesmaximal, characteristic, complemented
2C2×#65279C212yesmaximal
3C2×C4×#685C211yesmaximal, characteristic
4C2×#64956C211yesmaximal, characteristic
5#10602361C212yesmaximal, complemented
6#10602327C211yesmaximal, characteristic, complemented
7#10600221C212yesmaximal
8#10600218C211yesmaximal, characteristic
9#10600198C212yesmaximal, complemented
10#10600197C211yesmaximal, characteristic, complemented
11Dic5×#95C211yesmaximal, characteristic, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C42×C5C2211yescharacteristic
15C22×#685C2212yes—
16C22×#685C2212yes—
17C22×#685C2211yescharacteristic
18C22×#685C2211yescharacteristic
19C22×#683C2212yes—
20C22×#683C2212yes—
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C5×#382—24no—
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2212yes—
26C2×C5×#95C2211yescharacteristic
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2211yescharacteristic
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36#65279—28no—
37C4×#685C418yescomplemented
38#64956—24no—
39#13915—51nomaximal, Sylow
40C24×D5C2311yescharacteristic
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C22×C4×D5—22no—
52C22×C4×D5—22no—
53C22×C4×D5—24no—
54C22×C4×D5—42no—
55C22×C4×D5C2×C414yes—
56C2×C5×C4⋊C4—24no—
57C2×C5×C4⋊C4—24no—
58C2×C5×C4⋊C4—42no—
59C2×C42×C5—22no—
60C2×C42×C5—22no—
61C2×C42×C5C2×C414yes—
62C2×#685—24no—
63C2×#685—24no—
64C2×#685—24no—
65C2×#685—24no—
66C2×#685—24no—
67C2×#685—42no—
68C2×#685—42no—
69C2×#685C2×C414yes—
70C2×#685C2×C414yes—
71C2×#685D414yes—
72C2×#685Q814yes—
73C2×#683—24no—
74C2×#683—24no—
75C2×#683—24no—
76C2×#683—42no—
77C2×#683—42no—
78C2×#683—42no—
79C2×C4×Dic5—24no—
80C2×C4×Dic5—24no—
81C2×C4×Dic5—42no—
82C2×C4×Dic5—42no—
83C2×C4×Dic5C2×C414yes—
84C5×#95—24no—
85C5×#95—22no—
86C5×#95D414yes—
87#3963—22no—
88#3963—24no—
89#3963—22no—
90#3963—24no—
91#3963—24no—
92#3963—24no—
93#3963—24no—
94#3963C2×C414yes—
95#3963C2×C414yes—
96C2×#388—52no—
97C2×#382D511yescharacteristic, complemented
98C2×#380—51no—
99C2×C4×C22⋊C4—51no—
100#1444—52no—
101#1439—52no—
102#1436—52no—
103C4⋊#95—51no—
104#1434—51no—
105C22⋊#95—51no—
106C4×#95—51no—
107C24×C5C2411yescharacteristic
108C23×D5—21no—
109C23×D5—21no—
110C23×D5—22no—
111C23×D5—22no—
112C23×D5—22no—
113C23×D5—22no—
114C23×D5—21no—
115C23×D5—21no—
116C23×D5C22×C412yes—
117C23×D5C2×D412yes—
118C23×D5C2×Q812yes—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—22no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
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×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5C22×C412yes—
143C22×C4×C5C22×C412yes—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C2×D412yes—
146C22×C4×C5C2×D414yes—
147C22×C4×C5C2×D412yes—
148C22×C4×C5C2×Q812yes—
149C22×C4×C5#4112yes—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—21no—
157C22×Dic5—21no—
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×Dic5—22no—
171C22×Dic5C22×C412yes—
172C22×Dic5C22×C412yes—
173C22×Dic5C22×C412yes—
174C22×Dic5C2×D412yes—
175C22×Dic5C2×Q812yes—
176C22×Dic5#4114yes—
177C22×Dic5#4114yes—
178C22×Dic5#4114yes—
179C2×C4×D5—28no—
180C2×C4×D5—28no—
181C2×C4×D5—44no—
182C2×C4×D5—48no—
183C2×C4×D5—48no—
184C5×C4⋊C4—48no—
185C42×C5—28no—
186#685—28no—
187#685—48no—
188#685—48no—
189#685C4⋊C4116yescomplemented
190#683—48no—
191#683—48no—
192C4×Dic5—44no—
193C4×Dic5—48no—
194C24×C4—51no—
195C22×C4⋊C4—52no—
196C22×C4⋊C4—52no—
197C22×C4⋊C4C2×D512yes—
198C22×C22⋊C4—51no—
199C22×C22⋊C4—51no—
200C22×C22⋊C4—52no—
201C22×C22⋊C4—52no—
202C22×C42—51no—
203C22×C42—52no—
204C22×C42C2×D511yescharacteristic
205#388—108no—
206#382—24no—
207#380—104no—
208C4×C22⋊C4—58no—
209C2×#95—51no—
210C2×#95—51no—
211C2×#95—51no—
212C2×#95—52no—
213C2×#95—52no—
214C2×#95—51no—
215C2×#95—52no—
216C2×#95—52no—
217C2×#95—52no—
218C2×#95C2×D511yescharacteristic
219C2×#95C2×D512yes—
220C2×#95C2×D511yescharacteristic
221C23×C5C23×C411yescharacteristic
222C23×C5C22×D411yescharacteristic
223C23×C5C22×D411yescharacteristic
224C23×C5C22×Q811yescharacteristic
225C23×C5C2×#4111yescharacteristic
226C23×C5C2×#4112yes—
227C23×C5C2×#4112yes—
228C23×C5C2×#4112yes—
229C23×C5H(5,𝔽2)11yescharacteristic
230C23×C5H(5,𝔽2)12yes—
231C23×C52−1+411yescharacteristic
232C22×D5—22no—
233C22×D5—22no—
234C22×D5—22no—
235C22×D5—22no—
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—24no—
239C22×D5—24no—
240C22×D5—22no—
241C22×D5—24no—
242C22×D5—22no—
243C22×D5—22no—
244C22×D5—22no—
245C22×D5—24no—
246C22×D5—42no—
247C22×D5—42no—
248C22×D5—42no—
249C22×D5—42no—
250C22×D5—42no—
251C22×D5—42no—
252C22×D5—42no—
253C22×D5—42no—
254C22×D5C2×C4⋊C414yes—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—24no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—24no—
269C2×C4×C5—24no—
270C2×C4×C5—24no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
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×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5C2×C4⋊C414yes—
285C2×C4×C5C4×D414yes—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—24no—
293C2×Dic5—24no—
294C2×Dic5—24no—
295C2×Dic5—24no—
296C2×Dic5—24no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5—24no—
300C2×Dic5—24no—
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—
311C2×Dic5—42no—
312C2×Dic5C2×C4⋊C414yes—
313C2×Dic5#11714yes—
314C2×Dic5#11714yes—
315C4×D5—416no—
316C25—51no—
317C23×C4—51no—
318C23×C4—51no—
319C23×C4—51no—
320C23×C4—52no—
321C23×C4—54no—
322C23×C4—52no—
323C23×C4—104no—
324C23×C4—102no—
325C23×C4—102no—
326C23×C4—202no—
327C23×C4C22×D512yes—
328C23×C4C22×D511yescharacteristic
329C23×C4C22×D512yes—
330C23×C4C22×D511yescharacteristic
331C23×C4C22×D511yescharacteristic
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—104no—
336C2×C4⋊C4—104no—
337C2×C4⋊C4—104no—
338C2×C4⋊C4—202no—
339C2×C4⋊C4—202no—
340C2×C4⋊C4—202no—
341C2×C22⋊C4—54no—
342C2×C22⋊C4—54no—
343C2×C22⋊C4—54no—
344C2×C22⋊C4—54no—
345C2×C22⋊C4—104no—
346C2×C22⋊C4—104no—
347C2×C22⋊C4—104no—
348C2×C22⋊C4—104no—
349C2×C22⋊C4—104no—
350C2×C22⋊C4—202no—
351C2×C22⋊C4—202no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—54no—
355C2×C42—104no—
356C2×C42—104no—
357C2×C42—202no—
358C2×C42—202no—
359C2×C42C4×D514yes—
360#95—24no—
361#95—22no—
362#95—54no—
363#95—54no—
364#95—104no—
365#95—104no—
366#95—104no—
367#95—104no—
368#95—102no—
369#95—104no—
370#95—102no—
371#95C22⋊D514yes—
372C22×C5C22×C4⋊C411yescharacteristic
373C22×C5C2×#11711yescharacteristic
374C22×C5C2×#11711yescharacteristic
375C22×C5C2×C4×D411yescharacteristic
376C22×C5C4×#4111yescharacteristic
377C22×C5#51811yescharacteristic
378C22×C5#52011yescharacteristic
379C22×C5#52912yes—
380C22×C5#53212yes—
381C22×C5#53212yes—
382C22×C5#53312yes—
383C22×C5#53812yes—
384C22×C5#53912yes—
385C22×C5D4211yescharacteristic
386C22×C5#54612yes—
387C22×C5#54612yes—
388C22×C5#54711yescharacteristic
389C22×C5D4×Q811yescharacteristic
390C22×C5#55112yes—
391C22×C5#55212yes—
392C22×C5#55411yescharacteristic
393C22×C5#55412yes—
394C22×C5#55512yes—
395C2×D5—24no—
396C2×D5—24no—
397C2×D5—24no—
398C2×D5—42no—
399C2×D5—44no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—44no—
404C2×D5—44no—
405C2×D5—44no—
406C4×C5—24no—
407C4×C5—24no—
408C4×C5—42no—
409C4×C5—44no—
410C4×C5—82no—
411Dic5—24no—
412Dic5—24no—
413Dic5—24no—
414Dic5—44no—
415Dic5—82no—
416C24—52no—
417C24—52no—
418C24—52no—
419C24—101no—
420C24—101no—
421C24—101no—
422C24—102no—
423C24—102no—
424C24—102no—
425C24—102no—
426C24—101no—
427C24C23×D511yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—52no—
452C22×C4—52no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—52no—
456C22×C4—54no—
457C22×C4—54no—
458C22×C4—54no—
459C22×C4—108no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—101no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—101no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4—102no—
471C22×C4—102no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—108no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—102no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—204no—
483C22×C4—208no—
484C22×C4—208no—
485C22×C4C2×C4×D512yes—
486C22×C4C2×C4×D512yes—
487C22×C4C2×C4×D512yes—
488C22×C4#70912yes—
489C22×C4D4×D512yes—
490C22×C4Q8×D512yes—
491C22×C4C2×C22⋊D514yes—
492C22×C4C2×C22⋊D512yes—
493C4⋊C4—48no—
494C4⋊C4—208no—
495C4⋊C4—208no—
496C22⋊C4—516no—
497C22⋊C4—108no—
498C22⋊C4—208no—
499C22⋊C4—208no—
500C42—28no—
501C42—204no—
502C42—208no—
503C2×C5#228511yescharacteristic
504C2×C5#229311yescharacteristic
505C2×C5#231811yescharacteristic
506C2×C5#234211yescharacteristic
507C2×C5#234611yescharacteristic
508C2×C5D4×C4⋊C411yescharacteristic
509C2×C5#234911yescharacteristic
510C2×C5#255312yes—
511C2×C5#255512yes—
512C2×C5#255612yes—
513C2×C5#257412yes—
514D5—44no—
515C23—54no—
516C23—102no—
517C23—102no—
518C23—102no—
519C23—102no—
520C23—102no—
521C23—102no—
522C23—102no—
523C23—102no—
524C23—102no—
525C23—102no—
526C23—104no—
527C23—104no—
528C23—104no—
529C23—104no—
530C23—202no—
531C23—202no—
532C23—202no—
533C23—202no—
534C23—202no—
535C23—202no—
536C23—202no—
537C23—202no—
538C23C22×C4×D511yescharacteristic
539C23C2×#70911yescharacteristic
540C23C2×D4×D511yescharacteristic
541C23#414411yescharacteristic
542C23C2×Q8×D511yescharacteristic
543C23#414711yescharacteristic
544C23D5×#4112yes—
545C23D5×#4112yes—
546C23D5×#4112yes—
547C23#414912yes—
548C23C22×C22⋊D511yescharacteristic
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
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—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—54no—
579C2×C4—54no—
580C2×C4—54no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—102no—
586C2×C4—104no—
587C2×C4—102no—
588C2×C4—104no—
589C2×C4—104no—
590C2×C4—104no—
591C2×C4—104no—
592C2×C4—104no—
593C2×C4—104no—
594C2×C4—104no—
595C2×C4—104no—
596C2×C4—2016no—
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×C4—202no—
606C2×C4—202no—
607C2×C4—202no—
608C2×C4D5×C4⋊C414yes—
609C2×C4C4×C22⋊D514yes—
610C5#1391511yescharacteristic, complemented, Sylow
611C22—104no—
612C22—104no—
613C22—104no—
614C22—202no—
615C22—204no—
616C22—204no—
617C22—202no—
618C22—204no—
619C22—202no—
620C22—204no—
621C22—202no—
622C22C2×D5×C4⋊C411yescharacteristic
623C22#6583811yescharacteristic
624C22#6584111yescharacteristic
625C22#6584511yescharacteristic
626C22D5×#11711yescharacteristic
627C22D5×#11711yescharacteristic
628C22#6585511yescharacteristic
629C22#6585611yescharacteristic
630C22#6586112yes—
631C22#6586212yes—
632C22#6600212yes—
633C22#6600412yes—
634C22#6601012yes—
635C22#6601212yes—
636C22#6602212yes—
637C22#6602412yes—
638C22#6602612yes—
639C22#6602712yes—
640C22C2×C4×C22⋊D511yescharacteristic
641C22D4×C22⋊D511yescharacteristic
642C22Q8×C22⋊D511yescharacteristic
643C22#6616312yes—
644C22#6616612yes—
645C4—24no—
646C4—24no—
647C4—44no—
648C4—42no—
649C4—82no—
650C4—104no—
651C4—104no—
652C4—104no—
653C4—204no—
654C4—402no—
655C2—204no—
656C2#1060587911yescharacteristic
657C2#1060588711yescharacteristic
658C2#1060591212yes—
659C2#1060592012yes—
660C2#1060595711yescharacteristic
661C2#1060595911yescharacteristic
662C2C4⋊C4×C22⋊D511yescharacteristic
663C2#1061395611yescharacteristic
664C2#1061400211yescharacteristic
665C2#1061470612yes—
666C2#1061476912yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#382C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#382D5
hypocenterC5#13915
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
1. C2×C5×#382C2semidirect
5. #10602361C2semidirect
6. #10602327C2semidirect
9. #10600198C2semidirect
10. #10600197C2semidirect
11. Dic5×#95C2semidirect
37. C4×#685C4semidirect
97. C2×#382D5semidirect
189. #685C4⋊C4semidirect
610. C5#13915semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3822
C2×#652792
C2×C4×#6852
C2×#649562
#106023612
#106023272
#106002212
#106002182
#106001982
#106001972
Dic5×#952
#139155