Finite Group Databasebeta

← #12171966

Subgroups — #12171966

Order 1280.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2361C211yesmaximal, characteristic
2#10605242C211yesmaximal, characteristic, complemented
3#10602473C211yesmaximal, characteristic
4#10602472C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic, complemented
6#10602400C211yesmaximal, characteristic, complemented
7#10602349C211yesmaximal, characteristic, complemented
8#10602347C211yesmaximal, characteristic, complemented
9#10600445C211yesmaximal, characteristic, complemented
10#10600434C211yesmaximal, characteristic, complemented
11#10600411C211yesmaximal, characteristic, complemented
12#10600393C211yesmaximal, characteristic, complemented
13#10600261C211yesmaximal, characteristic, complemented
14#10600252C211yesmaximal, characteristic, complemented
15#10600244C211yesmaximal, characteristic, complemented
16C2×C5×#121C2211yescharacteristic
17C2×C4×C5×D4—21no—
18C2×C4×C5×D4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C5×#390C2211yescharacteristic
21C5×#389C2211yescharacteristic
22C5×#388—21no—
23C5×#386—21no—
24C5×#385—21no—
25C4×C5×C4⋊C4C2211yescharacteristic
26C4×C5×C22⋊C4C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31#65501C2211yescharacteristic
32#65501C2211yescharacteristic
33C2×C22⋊#168C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39#65241—21no—
40#65233—21no—
41#65225C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65217C2211yescharacteristic
44#65217C2211yescharacteristic
45C2×C4⋊#168C2211yescharacteristic
46C2×C4×#168C2211yescharacteristic
47#64947—21no—
48#64940—21no—
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#27031—51nomaximal, Sylow
60C22×C5×D4—21no—
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5C2311yescharacteristic
65C5×#121—22no—
66C5×#121—22no—
67C4×C5×D4—22no—
68C4×C5×D4—41no—
69C4×C5×D4—44no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—41no—
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4D411yescharacteristic
82C2×C5×C22⋊C4D411yescharacteristic
83C2×C42×C5—21no—
84C2×C42×C5C2311yescharacteristic
85C2×C42×C5C2311yescharacteristic
86C2×C22⋊Dic5—21no—
87C2×C22⋊Dic5—21no—
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×#683—21no—
93C2×#683—21no—
94C2×C4×Dic5—21no—
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C5×#95—21no—
100C5×#95—21no—
101C5×#95D411yescharacteristic
102C5×#95D411yescharacteristic
103#3964—22no—
104#3964—22no—
105#3964—22no—
106#3964—41no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114C22⋊#168—22no—
115C22⋊#168—41no—
116#3940—22no—
117#3940—22no—
118#3940—41no—
119#3939—22no—
120C4⋊#168—22no—
121C4×#168—41no—
122#2495—51no—
123#2361D511yescharacteristic
124#2073—51no—
125#2065—51no—
126#2034—51no—
127#2033—51no—
128#1949—51no—
129#1941—51no—
130#1923—51no—
131#1919—51no—
132#1918—51no—
133#1864—51no—
134#1853—51no—
135#1824—51no—
136C4×#102—51no—
137C24×C5—21no—
138C24×C5C2×D411yescharacteristic
139C2×C5×D4—24no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—42no—
146C2×C5×D4—42no—
147C2×C5×D4#4112yes—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—42no—
158C22×C4×C5—42no—
159C22×C4×C5—42no—
160C22×C4×C5—42no—
161C22×C4×C5—81no—
162C22×C4×C5—81no—
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2411yescharacteristic
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—42no—
178C5×C4⋊C4—42no—
179C5×C4⋊C4#4112yes—
180C5×C4⋊C4#4112yes—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—42no—
185C5×C22⋊C4—42no—
186C5×C22⋊C4—81no—
187C42×C5—21no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5—21no—
191C42×C5—42no—
192C22⋊Dic5—42no—
193C22⋊Dic5—81no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202#683—81no—
203#683—81no—
204C4×Dic5—42no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168#4112yes—
217C2×#121C2×D511yescharacteristic
218C2×C4×D4—21no—
219C2×C4×D4C2×D511yescharacteristic
220C22×C4⋊C4C2×D511yescharacteristic
221C2×#107—51no—
222C2×#106—51no—
223C2×#106—51no—
224C2×#106—51no—
225C2×C4⋊C8—51no—
226C2×#102—51no—
227C2×#102—51no—
228C2×#102—51no—
229C2×#102—51no—
230C2×C22⋊C8—51no—
231C2×C22⋊C8—51no—
232C2×C4×C8—51no—
233#400—101no—
234#397—101no—
235#390C2×D511yescharacteristic
236#389—51no—
237#389—51no—
238#389C2×D511yescharacteristic
239#388—21no—
240#388—101no—
241#386—21no—
242#385—21no—
243#383—101no—
244#382—51no—
245#380—51no—
246#380—51no—
247C4×C4⋊C4—51no—
248C4×C4⋊C4C2×D511yescharacteristic
249C4×C22⋊C4C2×D511yescharacteristic
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#336—51no—
259#336—51no—
260C23×C5—21no—
261C23×C5—21no—
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—22no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5#13512yes—
274C23×C5C22×D411yescharacteristic
275C5×D4—22no—
276C5×D4—22no—
277C5×D4—48no—
278C5×D4—41no—
279C5×D4—41no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—22no—
284C2×C4×C5—21no—
285C2×C4×C5—22no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—84no—
308C2×C4×C5—84no—
309C2×C4×C5AGL(1,ℤ/8)12yes—
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5H(5,𝔽2)11yescharacteristic
315C2×C4×C52−1+411yescharacteristic
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—41no—
326C2×Dic5—41no—
327C2×Dic5—41no—
328#168—22no—
329#168—41no—
330#168—41no—
331#168—41no—
332C22×D4—21no—
333C22×D4C22×D511yescharacteristic
334C23×C4—21no—
335C23×C4—21no—
336C23×C4C22×D511yescharacteristic
337C22×C8—51no—
338C22×C8—51no—
339C22×C8—51no—
340C22×C8—51no—
341#121—22no—
342#121—22no—
343C4×D4—22no—
344C4×D4—41no—
345C4×D4—44no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4—101no—
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C4⋊C4C22×D511yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—101no—
364C2×C22⋊C4—101no—
365C2×C22⋊C4C22⋊D511yescharacteristic
366C2×C22⋊C4C22⋊D511yescharacteristic
367C2×C42—21no—
368C2×C42—101no—
369C2×C42C22×D511yescharacteristic
370C2×C42C22×D511yescharacteristic
371#107—102no—
372#106—102no—
373#106—102no—
374#106—201no—
375C4⋊C8—102no—
376#102—102no—
377#102—102no—
378#102—102no—
379#102—201no—
380C22⋊C8—102no—
381C22⋊C8—201no—
382C4×C8—201no—
383#95—21no—
384#95—21no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390#95—101no—
391#95—101no—
392#95C22⋊D511yescharacteristic
393#95C22⋊D511yescharacteristic
394C22×C5—22no—
395C22×C5—22no—
396C22×C5—22no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—42no—
402C22×C5—42no—
403C22×C5—42no—
404C22×C5—81no—
405C22×C5—81no—
406C22×C5—81no—
407C22×C5—81no—
408C22×C5#52511yescharacteristic
409C22×C5#54611yescharacteristic
410C22×C5#54711yescharacteristic
411C22×C5C2×#13511yescharacteristic
412C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C5#57711yescharacteristic
414C22×C5#57711yescharacteristic
415C4×C5—22no—
416C4×C5—41no—
417C4×C5—41no—
418C4×C5—42no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—42no—
422C4×C5—81no—
423C4×C5#52911yescharacteristic
424C4×C5#53911yescharacteristic
425C4×C5#55311yescharacteristic
426C4×C5#55611yescharacteristic
427Dic5—81no—
428Dic5—81no—
429Dic5—81no—
430Dic5—81no—
431C24—21no—
432C24C2×C22⋊D511yescharacteristic
433C2×D4—24no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4#70912yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4—101no—
458C22×C4—101no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4C2×C22⋊D511yescharacteristic
462C22×C4C2×C22⋊D511yescharacteristic
463C22×C4C2×C22⋊D511yescharacteristic
464C22×C4C2×C22⋊D511yescharacteristic
465C22×C4C2×C22⋊D511yescharacteristic
466C22×C4C23×D511yescharacteristic
467C2×C8—52no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—101no—
486C4⋊C4—101no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—401no—
494C4⋊C4—401no—
495C4⋊C4#70912yes—
496C4⋊C4#71112yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—81no—
503C22⋊C4—202no—
504C22⋊C4—401no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—202no—
511C2×C5—42no—
512C2×C5—82no—
513C2×C5#246611yescharacteristic
514C2×C5#310511yescharacteristic
515C2×C5#312511yescharacteristic
516C2×C5#330111yescharacteristic
517C2×C5#331011yescharacteristic
518C2×C5#333711yescharacteristic
519C2×C5#335411yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—22no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23#409612yes—
534C23C22×C22⋊D511yescharacteristic
535D4—22no—
536D4—22no—
537D4—48no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—84no—
569C2×C4—201no—
570C2×C4—201no—
571C2×C4—201no—
572C2×C4—201no—
573C2×C4—201no—
574C2×C4—201no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4#407812yes—
582C2×C4C2×#70911yescharacteristic
583C2×C4C2×#70911yescharacteristic
584C2×C4C2×#71111yescharacteristic
585C2×C4#414411yescharacteristic
586C2×C4D5×#4111yescharacteristic
587C2×C4#415011yescharacteristic
588C8—102no—
589C8—201no—
590C8—201no—
591C8—201no—
592C5#2703111yescharacteristic, complemented, Sylow
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#6612511yescharacteristic
608C22C2×#407811yescharacteristic
609C22#6614011yescharacteristic
610C22C2×#409611yescharacteristic
611C22#6615811yescharacteristic
612C22#6617011yescharacteristic
613C22#6617111yescharacteristic
614C4—22no—
615C4—42no—
616C4—41no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—401no—
623C4—401no—
624C4—401no—
625C4—401no—
626C4#6587211yescharacteristic
627C4#6587611yescharacteristic
628C4#6589211yescharacteristic
629C4#6589811yescharacteristic
630C2—42no—
631C2—82no—
632C2#1061404011yescharacteristic
633C2#1061410011yescharacteristic
634C2#1061430711yescharacteristic
635C2#1061521511yescharacteristic
636C2#1061525211yescharacteristic
637C2#1061526611yescharacteristic
638C2#1061533711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2361C2
socleC23×C5C22×D4
prime radicalC2×C5×#121C22
hypercenter#2361D5
hypocenterC5#27031
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #10605242C2semidirect
5. C4×#3964C2semidirect
6. #10602400C2semidirect
7. #10602349C2semidirect
8. #10602347C2semidirect
9. #10600445C2semidirect
10. #10600434C2semidirect
11. #10600411C2semidirect
12. #10600393C2semidirect
13. #10600261C2semidirect
14. #10600252C2semidirect
15. #10600244C2semidirect
592. C5#27031semidirect

Maximal subgroups

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

subgroupindex
C5×#23612
#106052422
#106024732
#106024722
C4×#39642
#106024002
#106023492
#106023472
#106004452
#106004342
#106004112
#106003932
#106002612
#106002522
#106002442
#270315