Finite Group Databasebeta

← #13041567

Subgroups — #13041567

Order 1280.

880 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65703C211yesmaximal, characteristic, complemented
2C2×#65678C211yesmaximal, characteristic
3#10606672C211yesmaximal, characteristic
4#10604331C211yesmaximal, characteristic, complemented
5#10604321C211yesmaximal, characteristic, complemented
6C4⋊C4×#170C211yesmaximal, characteristic, complemented
7C4×#4003C211yesmaximal, characteristic
8#10603796C211yesmaximal, characteristic, complemented
9#10603793C211yesmaximal, characteristic
10#10603793C211yesmaximal, characteristic
11#10603792C211yesmaximal, characteristic
12#10603792C211yesmaximal, characteristic
13#10603788C211yesmaximal, characteristic, complemented
14#10603779C211yesmaximal, characteristic, complemented
15#10603779C211yesmaximal, characteristic, complemented
16C2×#4042C411yescharacteristic
17C2×#4033C2211yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×#4004C2211yescharacteristic
20C2×#4004C2211yescharacteristic
21C2×#4004C2211yescharacteristic
22C2×#4004C2211yescharacteristic
23C2×#4003C2211yescharacteristic
24C2×#4003C2211yescharacteristic
25C2×#4003C2211yescharacteristic
26C2×#4003C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4×#170C2211yescharacteristic
30C2×C4×#170C2211yescharacteristic
31C2×C4×#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65703—24no—
38#65678—24no—
39C5×#387C411yescharacteristic
40#65278C411yescharacteristic
41C4⋊C4×Dic5C2211yescharacteristic
42#65222C411yescharacteristic
43#64957C411yescharacteristic
44#64956C411yescharacteristic
45#64955C2211yescharacteristic
46#64955C2211yescharacteristic
47#64938C2211yescharacteristic
48#64938C2211yescharacteristic
49#64936C411yescharacteristic
50#64935C411yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#23050—51nomaximal, Sylow
62C22×C4×D5C2×C411yescharacteristic
63C22×C4×D5C2×C411yescharacteristic
64C22×C4×D5C2311yescharacteristic
65C22×Dic10C2×C411yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C22×#170C2311yescharacteristic
72C22×#170C2311yescharacteristic
73C22×#170C2311yescharacteristic
74C2×C5×C4⋊C4C2×C411yescharacteristic
75C2×C5×C4⋊C4C2×C411yescharacteristic
76C2×C42×C5C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×#685C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81C2×C4⋊Dic5C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×C4×Dic5C2×C411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95#4042C818yescomplemented
96#4033—22no—
97#4033—22no—
98C42×D5—22no—
99C42×D5—22no—
100#4004—22no—
101#4004—22no—
102#4004—22no—
103#4004D414yes—
104#4003—22no—
105#4003—22no—
106#4003—22no—
107#4003—22no—
108C4⋊#170—22no—
109C4⋊#170—22no—
110C4×#170—22no—
111C4×#170—22no—
112C4×#170—22no—
113C4×#170—22no—
114C4×#170—22no—
115C4×#170—22no—
116C4×#170—22no—
117C4×#170—22no—
118C5×#95C2×C411yescharacteristic
119C5×#95C2×C411yescharacteristic
120C5×#95C2×C411yescharacteristic
121C5×#95C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128C2×C8×Q8—51no—
129C2×#431—51no—
130C4×C22⋊Q8—51no—
131#1984—51no—
132#1939—51no—
133#1923—51no—
134#1923—51no—
135#1923—51no—
136#1923—51no—
137#1916—51no—
138#1916—51no—
139C8×C4⋊C4—51no—
140C8×C4⋊C4—51no—
141C8×C4⋊C4—51no—
142C4×C22⋊C8—51no—
143C23×D5C22×C411yescharacteristic
144C22×C4×C5C22×C411yescharacteristic
145C22×C4×C5C22×C411yescharacteristic
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C2411yescharacteristic
158C2×C4×D5—22no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—22no—
162C2×C4×D5—21no—
163C2×C4×D5—21no—
164C2×C4×D5—21no—
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—41no—
169C2×C4×D5C2×C814yes—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10C2×C814yes—
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—21no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—21no—
186C2×#170—21no—
187C2×#170—21no—
188C2×#170—21no—
189C2×#170—21no—
190C2×#170—21no—
191C2×#170—21no—
192C2×#170—21no—
193C2×#170C2×D412yes—
194C2×#170C2×D412yes—
195C2×#170#4112yes—
196C2×#170#4112yes—
197C5×C4⋊C4—22no—
198C5×C4⋊C4C2×C814yes—
199C42×C5—22no—
200#685—41no—
201#685—41no—
202#685C2×C814yes—
203#685C2×C814yes—
204C4⋊Dic5—22no—
205#683—22no—
206#683—22no—
207#683—22no—
208#683—22no—
209#683C2×C814yes—
210#683C2×C814yes—
211C4×Dic5—22no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—21no—
217C4×Dic5—21no—
218C4×Dic5—21no—
219C4×Dic5—21no—
220C4×Dic5—21no—
221C4×Dic5—21no—
222C4×Dic5C2×D412yes—
223C4×Dic5#4112yes—
224C2×C22⋊Q8—51no—
225C2×C4×Q8—51no—
226C22×C42—51no—
227C8×Q8—104no—
228#431—104no—
229C2×C4⋊C8—51no—
230C2×C4⋊C8—51no—
231C2×C4⋊C8—51no—
232C2×C4⋊C8—51no—
233C2×C4⋊C8—51no—
234C2×C4⋊C8—51no—
235C2×C22⋊C8—51no—
236C2×C22⋊C8—51no—
237C2×C22⋊C8—51no—
238C2×C22⋊C8—51no—
239C2×C4×C8—51no—
240C2×C4×C8—51no—
241C2×C4×C8—51no—
242C2×C4×C8—51no—
243C2×C4×C8—51no—
244C2×C4×C8—51no—
245C2×C4×C8—51no—
246C2×C4×C8—51no—
247#391—51no—
248#389—51no—
249#387—51no—
250#387AGL(1,𝔽5)11yescharacteristic
251#385—51no—
252#385—51no—
253#380—51no—
254C4×C4⋊C4—51no—
255C4×C4⋊C4—51no—
256C4×C4⋊C4—51no—
257C4×C22⋊C4—51no—
258C4×C22⋊C4—51no—
259#336—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263#336—51no—
264#336—51no—
265#336—51no—
266#336—51no—
267#336—51no—
268#336—51no—
269C23×C5C23×C411yescharacteristic
270C22×D5—21no—
271C22×D5—21no—
272C22×D5—21no—
273C22×D5—21no—
274C22×D5—21no—
275C22×D5—21no—
276C22×D5C22×C812yes—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
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×C5C4×D412yes—
295C2×C4×C5C22×C812yes—
296C2×C4×C5C22×C812yes—
297C2×C4×C5C22×C812yes—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5C4×D412yes—
311C2×Dic5C22×C812yes—
312C2×Dic5C22×C812yes—
313C2×Dic5C22×C812yes—
314C2×Dic5#13112yes—
315C2×Dic5#13112yes—
316C2×Dic5C22×D411yescharacteristic
317C2×Dic5C2×#4111yescharacteristic
318C2×Dic5C2×#4111yescharacteristic
319C2×Dic5C2×#4111yescharacteristic
320C2×Dic52−1+411yescharacteristic
321C2×Dic52−1+411yescharacteristic
322C4×D5—28no—
323C4×D5—44no—
324C4×D5—41no—
325C4×D5—41no—
326C4×D5—41no—
327C4×D5—41no—
328Dic10—28no—
329#170—22no—
330#170—22no—
331#170—22no—
332#170—22no—
333#170—41no—
334#170—41no—
335#170—41no—
336#170—41no—
337C22×Q8—51no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—51no—
345C22×C8—51no—
346C22×C8—51no—
347C22×C8—51no—
348C22×C8—51no—
349C22⋊Q8—58no—
350C4×Q8—102no—
351C4×Q8—102no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—51no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
360C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
361C2×C22⋊C4—51no—
362C2×C22⋊C4—51no—
363C2×C22⋊C4—51no—
364C2×C22⋊C4—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42—51no—
370C2×C42—51no—
371C2×C42—51no—
372C2×C42—102no—
373C2×C42—102no—
374C2×C42C2×AGL(1,𝔽5)11yescharacteristic
375C4⋊C8—54no—
376C4⋊C8—102no—
377C4⋊C8—102no—
378C4⋊C8—102no—
379C4⋊C8—102no—
380C4⋊C8—102no—
381C22⋊C8—102no—
382C22⋊C8—102no—
383C22⋊C8—102no—
384C22⋊C8—102no—
385C4×C8—102no—
386C4×C8—102no—
387C4×C8—102no—
388C4×C8—102no—
389C4×C8—102no—
390C4×C8—102no—
391C4×C8—102no—
392C4×C8—102no—
393#95—51no—
394#95—51no—
395#95—51no—
396#95—51no—
397#95—51no—
398#95—51no—
399#95C2×AGL(1,𝔽5)11yescharacteristic
400#95C2×AGL(1,𝔽5)11yescharacteristic
401#95C2×AGL(1,𝔽5)11yescharacteristic
402#95C2×AGL(1,𝔽5)11yescharacteristic
403C22×C5C2×C4×D411yescharacteristic
404C22×C5C4×#4111yescharacteristic
405C22×C5#51911yescharacteristic
406C22×C5C23×C811yescharacteristic
407C22×C5C2×#13111yescharacteristic
408C22×C5C2×#13111yescharacteristic
409C22×C5#56811yescharacteristic
410C2×D5—22no—
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—41no—
414C2×D5—41no—
415C2×D5—41no—
416C2×D5—41no—
417C4×C5—22no—
418C4×C5—22no—
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424Dic5—22no—
425Dic5—22no—
426Dic5—22no—
427Dic5—41no—
428Dic5—41no—
429Dic5C8×D414yes—
430Dic5#54711yescharacteristic
431Dic5#54811yescharacteristic
432Dic5#55211yescharacteristic
433Dic5#55611yescharacteristic
434C24—51no—
435C2×Q8—54no—
436C2×Q8—102no—
437C2×Q8—102no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—54no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—102no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—102no—
456C22×C4—201no—
457C22×C4C22×AGL(1,𝔽5)11yescharacteristic
458C22×C4C22×AGL(1,𝔽5)11yescharacteristic
459C22×C4C22×AGL(1,𝔽5)11yescharacteristic
460C22×C4C22×AGL(1,𝔽5)11yescharacteristic
461C22×C4C22×AGL(1,𝔽5)11yescharacteristic
462C22×C4C22×AGL(1,𝔽5)11yescharacteristic
463C22×C4C22×AGL(1,𝔽5)11yescharacteristic
464C2×C8—52no—
465C2×C8—52no—
466C2×C8—52no—
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—
479C2×C8—101no—
480C2×C8—101no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C2×C8—101no—
486C2×C8—101no—
487C2×C8—101no—
488C4⋊C4—22no—
489C4⋊C4—54no—
490C4⋊C4—54no—
491C4⋊C4—102no—
492C4⋊C4—102no—
493C4⋊C4—102no—
494C4⋊C4—102no—
495C4⋊C4—102no—
496C4⋊C4D5⋊C814yes—
497C22⋊C4—54no—
498C22⋊C4—54no—
499C22⋊C4—201no—
500C22⋊C4—201no—
501C42—22no—
502C42—52no—
503C42—52no—
504C42—101no—
505C42—101no—
506C42—101no—
507C42—101no—
508C42—101no—
509C42—101no—
510C42—101no—
511C42—101no—
512C42—102no—
513C42—101no—
514C42—101no—
515C2×C5#236211yescharacteristic
516C2×C5C2×C8×D411yescharacteristic
517C2×C5#293311yescharacteristic
518C2×C5C8×#4111yescharacteristic
519C2×C5#296911yescharacteristic
520C2×C5#298211yescharacteristic
521C2×C5#298611yescharacteristic
522D5—42no—
523C23—52no—
524C23—101no—
525C23—101no—
526C23—101no—
527C23—101no—
528C23—101no—
529C23—101no—
530C23C23×AGL(1,𝔽5)11yescharacteristic
531Q8—108no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—52no—
550C2×C4—51no—
551C2×C4—51no—
552C2×C4—52no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—52no—
556C2×C4—51no—
557C2×C4—51no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—108no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—204no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4C2×D5⋊C812yes—
580C2×C4C2×D5⋊C812yes—
581C2×C4C2×D5⋊C812yes—
582C2×C4D4×AGL(1,𝔽5)12yes—
583C8—102no—
584C8—102no—
585C8—102no—
586C8—102no—
587C8—201no—
588C8—201no—
589C8—201no—
590C8—201no—
591C5#2305011yescharacteristic, complemented, Sylow
592C22—102no—
593C22—102no—
594C22—102no—
595C22—201no—
596C22—201no—
597C22—201no—
598C22—201no—
599C22C22×D5⋊C811yescharacteristic
600C22C2×D4×AGL(1,𝔽5)11yescharacteristic
601C22#6626211yescharacteristic
602C22D5⋊#13111yescharacteristic
603C22D5⋊#13111yescharacteristic
604C22#6626411yescharacteristic
605C22#41×AGL(1,𝔽5)11yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—54no—
614C4—51no—
615C4—51no—
616C4—51no—
617C4—51no—
618C4—102no—
619C4—102no—
620C4—102no—
621C4—201no—
622C4—201no—
623C2—202no—
624C2#1061711411yescharacteristic
625C2D4×D5⋊C811yescharacteristic
626C2#1061719911yescharacteristic
627C2#1061728611yescharacteristic
628C2#1061729111yescharacteristic
629C2#1061733711yescharacteristic
630C2#1061735211yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C23×C8
FittingC5×#387C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#387AGL(1,𝔽5)
hypocenterC5#23050
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#65703C2semidirect
4. #10604331C2semidirect
5. #10604321C2semidirect
6. C4⋊C4×#170C2semidirect
8. #10603796C2semidirect
13. #10603788C2semidirect
14. #10603779C2semidirect
15. #10603779C2semidirect
95. #4042C8semidirect
591. C5#23050semidirect

Maximal subgroups

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

subgroupindex
C2×#657032
C2×#656782
#106066722
#106043312
#106043212
C4⋊C4×#1702
C4×#40032
#106037962
#106037932
#106037922
#106037882
#106037792
#230505