Finite Group Databasebeta

← #13041577

Subgroups — #13041577

Order 1280.

824 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×#65707C211yesmaximal, characteristic, complemented
2C2×#65678C211yesmaximal, characteristic
3#10607696C211yesmaximal, characteristic
4#10604333C211yesmaximal, characteristic, complemented
5#10604327C211yesmaximal, characteristic, complemented
6#10604322C211yesmaximal, characteristic, complemented
7#10604321C211yesmaximal, characteristic, complemented
8#10604316C211yesmaximal, characteristic, complemented
9#10604316C211yesmaximal, characteristic, complemented
10C4⋊C4×#170C211yesmaximal, characteristic, complemented
11#10604177C211yesmaximal, characteristic
12#10603795C211yesmaximal, characteristic
13#10603794C211yesmaximal, characteristic
14#10603793C211yesmaximal, characteristic
15#10603792C211yesmaximal, characteristic
16C2×#4043C411yescharacteristic
17C2×#4033C2211yescharacteristic
18C2×C42×D5C2211yescharacteristic
19C2×#4004C2211yescharacteristic
20C2×#4004C2211yescharacteristic
21C2×#4004C2211yescharacteristic
22C2×#4004C2211yescharacteristic
23C2×#4003C2211yescharacteristic
24C2×#4003C2211yescharacteristic
25C2×#4003C2211yescharacteristic
26C2×#4003C2211yescharacteristic
27C2×#4002C2211yescharacteristic
28C2×#4002C2211yescharacteristic
29C2×#4002C2211yescharacteristic
30C2×#4002C2211yescharacteristic
31C2×C4⋊#170C2211yescharacteristic
32C2×C4⋊#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65707—24no—
38#65678—24no—
39C5×#389C411yescharacteristic
40#65278C411yescharacteristic
41#65278C411yescharacteristic
42#65276C411yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C4⋊C4×Dic5C2211yescharacteristic
45C4⋊C4×Dic5C2211yescharacteristic
46#65218C411yescharacteristic
47#64955C2211yescharacteristic
48#64955C2211yescharacteristic
49#64943C411yescharacteristic
50#64943C411yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#23052—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×C5×C4⋊C4C2×C411yescharacteristic
77C2×C5×C4⋊C4C2×C411yescharacteristic
78C2×C42×C5C2×C411yescharacteristic
79C2×#685C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81C2×#685C2×C411yescharacteristic
82C2×#685C2×C411yescharacteristic
83C2×C4⋊Dic5C2×C411yescharacteristic
84C2×C4⋊Dic5C2×C411yescharacteristic
85C2×C4⋊Dic5C2×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#4043—24no—
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—
108#4002—22no—
109#4002—22no—
110#4002—22no—
111#4002—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
120#3963C2×C411yescharacteristic
121#3963C2×C411yescharacteristic
122#3963C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128C2×#446—51no—
129C2×#431—51no—
130C4×C22⋊Q8—51no—
131#1985—51no—
132#1940—51no—
133#1924—51no—
134#1924—51no—
135#1923—51no—
136#1923—51no—
137#1916—51no—
138#1916—51no—
139#1771—51no—
140#1771—51no—
141C8×C4⋊C4—51no—
142#1749—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—22no—
163C2×C4×D5—21no—
164C2×C4×D5—21no—
165C2×C4×D5—21no—
166C2×C4×D5—21no—
167C2×C4×D5—21no—
168C2×C4×D5—21no—
169C2×C4×D5—41no—
170C2×Dic10—22no—
171C2×Dic10—22no—
172C2×Dic10—41no—
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⋊C4—22no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C42×C5—22no—
202#685—22no—
203#685—22no—
204#685—22no—
205#685—22no—
206C4⋊Dic5—22no—
207C4⋊Dic5—41no—
208C4⋊Dic5M1614yes—
209#683—22no—
210#683—22no—
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—
227#446—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×#97—51no—
240C2×#97—51no—
241C2×#97—51no—
242C2×#97—51no—
243C2×C4×C8—51no—
244C2×C4×C8—51no—
245C2×C4×C8—51no—
246C2×C4×C8—51no—
247#391—51no—
248#389AGL(1,𝔽5)11yescharacteristic
249#387—51no—
250#387—51no—
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×D5#13112yes—
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×C5—21no—
295C2×C4×C5C4×D412yes—
296C2×C4×C5C2×M1612yes—
297C2×C4×C5#13112yes—
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×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5C4×D412yes—
314C2×Dic5C2×M1612yes—
315C2×Dic5C2×M1612yes—
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—44no—
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—104no—
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⋊C4C2×AGL(1,𝔽5)11yescharacteristic
358C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
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—
385#97—102no—
386#97—102no—
387#97—102no—
388#97—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#95—51no—
400#95—51no—
401#95C2×AGL(1,𝔽5)11yescharacteristic
402#95C2×AGL(1,𝔽5)11yescharacteristic
403C22×C5C2×C4×D411yescharacteristic
404C22×C5C4×#4111yescharacteristic
405C22×C5#51911yescharacteristic
406C22×C5C22×M1611yescharacteristic
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—41no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424Dic5—22no—
425Dic5—22no—
426Dic5—22no—
427Dic5—41no—
428Dic5—41no—
429Dic5—41no—
430Dic5#54711yescharacteristic
431Dic5#54811yescharacteristic
432Dic5#55211yescharacteristic
433Dic5#55611yescharacteristic
434C24—51no—
435C2×Q8—102no—
436C2×Q8—102no—
437C2×Q8—201no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—51no—
442C22×C4—51no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—102no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—102no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—102no—
454C22×C4—102no—
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—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—54no—
493C4⋊C4—102no—
494C4⋊C4—102no—
495C4⋊C4—102no—
496C4⋊C4—201no—
497C22⋊C4—102no—
498C22⋊C4—102no—
499C22⋊C4—102no—
500C22⋊C4—102no—
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×C5#292911yescharacteristic
517C2×C5D4×M1611yescharacteristic
518C2×C5#296511yescharacteristic
519C2×C5#296811yescharacteristic
520C2×C5#298411yescharacteristic
521C2×C5#298511yescharacteristic
522D5—42no—
523C23—52no—
524C23—101no—
525C23—101no—
526C23—101no—
527C23—101no—
528C23—101no—
529C23—101no—
530C23C23×AGL(1,𝔽5)11yescharacteristic
531Q8—204no—
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—21no—
550C2×C4—51no—
551C2×C4—51no—
552C2×C4—51no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—51no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—52no—
559C2×C4—108no—
560C2×C4—101no—
561C2×C4—101no—
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—101no—
575C2×C4—204no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4D5⋊M1612yes—
581C2×C4#413112yes—
582C2×C4D4×AGL(1,𝔽5)12yes—
583C8—102no—
584C8—102no—
585C8—102no—
586C8—102no—
587C8—201no—
588C8—201no—
589C8—201no—
590C8—201no—
591C5#2305211yescharacteristic, complemented, Sylow
592C22—102no—
593C22—102no—
594C22—102no—
595C22—201no—
596C22—201no—
597C22—201no—
598C22—201no—
599C22C2×D5⋊M1611yescharacteristic
600C22C2×#413111yescharacteristic
601C22C2×D4×AGL(1,𝔽5)11yescharacteristic
602C22#6626011yescharacteristic
603C22#6626211yescharacteristic
604C22D5⋊#13111yescharacteristic
605C22#41×AGL(1,𝔽5)11yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—51no—
614C4—51no—
615C4—51no—
616C4—51no—
617C4—102no—
618C4—102no—
619C4—102no—
620C4—201no—
621C4—201no—
622C4—201no—
623C2—202no—
624C2#1061708411yescharacteristic
625C2#1061715411yescharacteristic
626C2#1061720111yescharacteristic
627C2#1061722511yescharacteristic
628C2#1061728611yescharacteristic
629C2#1061733411yescharacteristic
630C2#1061738111yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#389C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#389AGL(1,𝔽5)
hypocenterC5#23052
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#65707C2semidirect
4. #10604333C2semidirect
5. #10604327C2semidirect
6. #10604322C2semidirect
7. #10604321C2semidirect
8. #10604316C2semidirect
9. #10604316C2semidirect
10. C4⋊C4×#170C2semidirect
591. C5#23052semidirect

Maximal subgroups

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

subgroupindex
C2×#657072
C2×#656782
#106076962
#106043332
#106043272
#106043222
#106043212
#106043162
C4⋊C4×#1702
#106041772
#106037952
#106037942
#106037932
#106037922
#230525