Finite Group Databasebeta

← #13035124

Subgroups — #13035124

Order 1280.

906 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65696C211yesmaximal, characteristic
2C2×#65691C211yesmaximal, characteristic
3#10605595C211yesmaximal, characteristic
4#10604895C211yesmaximal, characteristic
5C2×#64918C211yesmaximal, characteristic
6#10604324C211yesmaximal, characteristic, complemented
7#10604323C211yesmaximal, characteristic, complemented
8#10604322C211yesmaximal, characteristic, complemented
9#10604321C211yesmaximal, characteristic, complemented
10#10604223C211yesmaximal, characteristic
11#10604223C211yesmaximal, characteristic
12#10603791C211yesmaximal, characteristic, complemented
13#10603790C211yesmaximal, characteristic, complemented
14#10603789C211yesmaximal, characteristic, complemented
15#10603788C211yesmaximal, characteristic, complemented
16C22×#704C2211yescharacteristic
17C22×#704C2211yescharacteristic
18C23×#170C2211yescharacteristic
19C23×#170C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C2×#4023C2211yescharacteristic
22C2×#4023C2211yescharacteristic
23C2×#4004C2211yescharacteristic
24C2×#4004C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4×#170C2211yescharacteristic
30C2×C4×#170C2211yescharacteristic
31#65696—24no—
32#65691—24no—
33C5×#380C411yescharacteristic
34#65501C411yescharacteristic
35#65265C411yescharacteristic
36#65265C411yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38C4⋊C4×Dic5C2211yescharacteristic
39#65231C411yescharacteristic
40#65231C411yescharacteristic
41#64939C411yescharacteristic
42#64939C411yescharacteristic
43#64938C2211yescharacteristic
44#64938C2211yescharacteristic
45#64918C2211yescharacteristic
46#64918C2211yescharacteristic
47#64918C2211yescharacteristic
48#64918C2211yescharacteristic
49#64918C2211yescharacteristic
50#64918C2211yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#21026—51nomaximal, Sylow
62C23×C4×C5C2×C411yescharacteristic
63C23×Dic5C2×C411yescharacteristic
64C23×Dic5C2311yescharacteristic
65C2×#704—22no—
66C2×#704—22no—
67C2×#704—22no—
68C2×#704—22no—
69C2×#704—22no—
70C2×#704D414yes—
71C22×#170—22no—
72C22×#170—22no—
73C22×#170—22no—
74C22×#170—22no—
75C22×#170—22no—
76C22×#170Q814yes—
77C22×#170C2311yescharacteristic
78C22×#170C2311yescharacteristic
79C22×#170C2311yescharacteristic
80C22×#170C2311yescharacteristic
81C22×#170C2311yescharacteristic
82C22×#170C2311yescharacteristic
83C22×#170C2311yescharacteristic
84C22×#170C2311yescharacteristic
85C2×C5×C4⋊C4C2×C411yescharacteristic
86C2×C5×C4⋊C4C2×C411yescharacteristic
87C2×C5×C22⋊C4C2×C411yescharacteristic
88C2×C5×C22⋊C4C2×C411yescharacteristic
89C2×C22⋊Dic5C2×C411yescharacteristic
90C2×C22⋊Dic5C2×C411yescharacteristic
91C2×C4⋊Dic5C2×C411yescharacteristic
92C2×C4⋊Dic5C2×C411yescharacteristic
93C2×#683C2×C411yescharacteristic
94C2×#683C2×C411yescharacteristic
95C2×#683C2×C411yescharacteristic
96C2×#683C2×C411yescharacteristic
97C2×#683C2×C411yescharacteristic
98C2×#683C2×C411yescharacteristic
99C2×#683C2×C411yescharacteristic
100C2×#683C2×C411yescharacteristic
101C2×C4×Dic5—22no—
102C2×C4×Dic5—22no—
103C2×C4×Dic5C2×C411yescharacteristic
104C2×C4×Dic5C2×C411yescharacteristic
105C2×C4×Dic5C2311yescharacteristic
106C2×C4×Dic5C2311yescharacteristic
107C2×C4×Dic5C2311yescharacteristic
108C2×C4×Dic5C2311yescharacteristic
109C2×C4×Dic5C2311yescharacteristic
110C2×C4×Dic5C2311yescharacteristic
111#4023—22no—
112#4023—22no—
113#4023—22no—
114#4023—22no—
115#4004—22no—
116#4004—22no—
117#4002—22no—
118#4002—22no—
119C4⋊#170—22no—
120C4⋊#170—22no—
121C4×#170—22no—
122C4×#170—22no—
123C5×#95C2×C411yescharacteristic
124C5×#95C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131C2×#424—51no—
132C2×#405—51no—
133#2285—51no—
134#1917—51no—
135#1917—51no—
136#1917—51no—
137#1917—51no—
138#1916—51no—
139#1916—51no—
140#1916—51no—
141#1916—51no—
142#1729—51no—
143#1729—51no—
144#1728—51no—
145C2×#336—51no—
146C24×C5C22×C411yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—41no—
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C22×C411yescharacteristic
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C22×C411yescharacteristic
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—41no—
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C22×Dic5C22×C411yescharacteristic
162C22×Dic5C22×C411yescharacteristic
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C411yescharacteristic
165C22×Dic5C22×C411yescharacteristic
166C22×Dic5C2×D412yes—
167C22×Dic5C2×Q812yes—
168C22×Dic5#4112yes—
169C22×Dic5#4112yes—
170C22×Dic5#4112yes—
171C22×Dic5#4112yes—
172C22×Dic5C2411yescharacteristic
173#704—28no—
174#704—44no—
175C2×#170—28no—
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×#170—21no—
194C2×#170—21no—
195C2×#170—21no—
196C2×#170—44no—
197C2×#170C2×D412yes—
198C2×#170C2×D412yes—
199C2×#170C2×Q812yes—
200C2×#170C2×Q812yes—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—41no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C22⋊Dic5—22no—
206C22⋊Dic5—22no—
207C4⋊Dic5—22no—
208C4⋊Dic5—41no—
209#683—22no—
210#683—22no—
211#683—22no—
212#683—22no—
213#683—22no—
214#683—22no—
215#683—41no—
216#683—41no—
217C4×Dic5—22no—
218C4×Dic5—22no—
219C4×Dic5—21no—
220C4×Dic5—21no—
221C4×Dic5—21no—
222C4×Dic5—21no—
223C4×Dic5—21no—
224C4×Dic5—21no—
225C4×Dic5—21no—
226C4×Dic5—21no—
227C4×Dic5—21no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5—21no—
231C22×M16—51no—
232C22×M16—51no—
233C23×C8—51no—
234C23×C8—51no—
235C2×#117—51no—
236C2×#117—51no—
237C22×C42—51no—
238#424—104no—
239C2×C4⋊C8—51no—
240C2×C4⋊C8—51no—
241C2×C4⋊C8—51no—
242C2×C4⋊C8—51no—
243#405—104no—
244C2×#97—51no—
245C2×#97—51no—
246C2×C4×C8—51no—
247C2×C4×C8—51no—
248#384—51no—
249#384—51no—
250#382—51no—
251#382—51no—
252#380—51no—
253#380—51no—
254#380—51no—
255#380AGL(1,𝔽5)11yescharacteristic
256C4×C4⋊C4—51no—
257C4×C4⋊C4—51no—
258C4×C4⋊C4—51no—
259C4×C4⋊C4—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—
269#336—51no—
270#336—51no—
271#336—51no—
272#336—51no—
273#336—51no—
274#336—51no—
275#336—51no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5#11712yes—
281C23×C5C4×D412yes—
282C23×C5C4×Q812yes—
283C23×C5C23×C411yescharacteristic
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×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—44no—
302C2×C4×C5#13112yes—
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×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—44no—
321C2×Dic5#11712yes—
322C2×Dic5C4×D412yes—
323C2×Dic5C4×Q812yes—
324C2×Dic5C22⋊Q814yes—
325C2×Dic5#12314yes—
326C2×Dic5#12514yes—
327C2×Dic5#12614yes—
328C2×Dic5#13112yes—
329C2×Dic5C22×D411yescharacteristic
330C2×Dic5C22×Q811yescharacteristic
331C2×Dic5C2×#4111yescharacteristic
332C2×Dic5C2×#4111yescharacteristic
333C2×Dic5C2×#4111yescharacteristic
334C2×Dic5C2×#4111yescharacteristic
335#170—22no—
336#170—22no—
337#170—22no—
338#170—22no—
339#170—41no—
340#170—41no—
341#170—41no—
342#170—41no—
343C23×C4—51no—
344C23×C4—51no—
345C23×C4C2×AGL(1,𝔽5)11yescharacteristic
346C2×M16—54no—
347C2×M16—102no—
348C2×M16—102no—
349C2×M16—102no—
350C2×M16—102no—
351C2×M16—102no—
352C22×C8—54no—
353C22×C8—51no—
354C22×C8—51no—
355C22×C8—51no—
356C22×C8—51no—
357C22×C8—51no—
358C22×C8—51no—
359C22×C8—51no—
360C22×C8—51no—
361C22×C8—102no—
362C22×C8—102no—
363C22×C8—102no—
364C22×C8—102no—
365C22×C8—102no—
366#117—102no—
367#117—102no—
368#117—102no—
369#117—102no—
370C2×C4⋊C4—51no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—51no—
376C2×C4⋊C4—51no—
377C2×C4⋊C4—51no—
378C2×C4⋊C4—51no—
379C2×C4⋊C4—51no—
380C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
381C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
382C2×C22⋊C4—51no—
383C2×C22⋊C4—51no—
384C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
385C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
386C2×C42—51no—
387C2×C42—51no—
388C2×C42—51no—
389C2×C42—51no—
390C2×C42—51no—
391C2×C42—51no—
392C2×C42—51no—
393C2×C42—51no—
394C2×C42—102no—
395C2×C42—102no—
396C4⋊C8—102no—
397C4⋊C8—102no—
398C4⋊C8—102no—
399C4⋊C8—102no—
400#97—102no—
401#97—102no—
402C4×C8—102no—
403C4×C8—102no—
404#95—51no—
405#95—51no—
406#95—51no—
407#95—51no—
408#95—51no—
409#95—51no—
410#95C2×AGL(1,𝔽5)11yescharacteristic
411#95C2×AGL(1,𝔽5)11yescharacteristic
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5#38714yes—
419C22×C5C2×#11711yescharacteristic
420C22×C5C2×C4×D411yescharacteristic
421C22×C5C2×C4×Q811yescharacteristic
422C22×C5C2×#13111yescharacteristic
423C22×C5C2×#13111yescharacteristic
424C22×C5#56811yescharacteristic
425C22×C5#56811yescharacteristic
426C4×C5—22no—
427C4×C5—41no—
428C4×C5—41no—
429C4×C5—41no—
430C4×C5—41no—
431C4×C5—41no—
432Dic5—22no—
433Dic5—41no—
434Dic5—41no—
435Dic5—41no—
436Dic5—41no—
437Dic5—41no—
438Dic5#38714yes—
439Dic5C2×C22⋊Q811yescharacteristic
440Dic5C2×#12311yescharacteristic
441Dic5C2×#12511yescharacteristic
442Dic5C2×#12611yescharacteristic
443C24C22×AGL(1,𝔽5)11yescharacteristic
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—41no—
447C22×C4—52no—
448C22×C4—52no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—52no—
453C22×C4—51no—
454C22×C4—51no—
455C22×C4—51no—
456C22×C4—51no—
457C22×C4—51no—
458C22×C4—51no—
459C22×C4—51no—
460C22×C4—51no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—201no—
464C22×C4C22×AGL(1,𝔽5)11yescharacteristic
465C22×C4C22×AGL(1,𝔽5)11yescharacteristic
466C22×C4C22×AGL(1,𝔽5)11yescharacteristic
467C22×C4C22×AGL(1,𝔽5)11yescharacteristic
468C22×C4C22×AGL(1,𝔽5)11yescharacteristic
469C22×C4C22×AGL(1,𝔽5)11yescharacteristic
470M16—108no—
471M16—204no—
472C2×C8—52no—
473C2×C8—52no—
474C2×C8—52no—
475C2×C8—52no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—108no—
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—
488C2×C8—101no—
489C2×C8—101no—
490C2×C8—101no—
491C2×C8—101no—
492C2×C8—101no—
493C2×C8—101no—
494C2×C8—101no—
495C2×C8—101no—
496C2×C8—101no—
497C2×C8—204no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—102no—
501C4⋊C4—102no—
502C4⋊C4—102no—
503C4⋊C4—102no—
504C4⋊C4—102no—
505C4⋊C4—102no—
506C4⋊C4—102no—
507C4⋊C4—201no—
508C4⋊C4—201no—
509C4⋊C4—201no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—102no—
513C22⋊C4—102no—
514C42—101no—
515C42—101no—
516C42—101no—
517C42—101no—
518C42—101no—
519C42—101no—
520C42—102no—
521C42—101no—
522C42—101no—
523C42—102no—
524C42—101no—
525C42—101no—
526C42—101no—
527C42—101no—
528C2×C5—24no—
529C2×C5C2×#38711yescharacteristic
530C2×C5#292411yescharacteristic
531C2×C5#292411yescharacteristic
532C2×C5#293511yescharacteristic
533C2×C5#293511yescharacteristic
534C2×C5#296011yescharacteristic
535C2×C5#296111yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23#413012yes—
541C23D4×AGL(1,𝔽5)12yes—
542C23Q8×AGL(1,𝔽5)12yes—
543C23C23×AGL(1,𝔽5)11yescharacteristic
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
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—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—44no—
562C2×C4—54no—
563C2×C4—54no—
564C2×C4—54no—
565C2×C4—54no—
566C2×C4—51no—
567C2×C4—51no—
568C2×C4—52no—
569C2×C4—51no—
570C2×C4—51no—
571C2×C4—52no—
572C2×C4—51no—
573C2×C4—51no—
574C2×C4—52no—
575C2×C4—52no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—101no—
580C2×C4—101no—
581C2×C4—101no—
582C2×C4—101no—
583C2×C4—101no—
584C2×C4—101no—
585C2×C4—101no—
586C2×C4—101no—
587C2×C4—101no—
588C2×C4—101no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—101no—
593C2×C4—204no—
594C2×C4#413112yes—
595C8—102no—
596C8—102no—
597C8—102no—
598C8—102no—
599C8—201no—
600C8—201no—
601C8—201no—
602C8—201no—
603C5#2102611yescharacteristic, complemented, Sylow
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#6571114yes—
611C22C2×#413011yescharacteristic
612C22C2×#413111yescharacteristic
613C22#6625611yescharacteristic
614C22C2×D4×AGL(1,𝔽5)11yescharacteristic
615C22C2×Q8×AGL(1,𝔽5)11yescharacteristic
616C22D5⋊#13111yescharacteristic
617C22#6626411yescharacteristic
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—51no—
625C4—51no—
626C4—51no—
627C4—51no—
628C4—54no—
629C4—102no—
630C4—201no—
631C4—201no—
632C4—201no—
633C4—201no—
634C4—201no—
635C2—24no—
636C2#1061705511yescharacteristic
637C2C2×#6571111yescharacteristic
638C2#1061711111yescharacteristic
639C2#1061723111yescharacteristic
640C2#1061723211yescharacteristic
641C2#1061726111yescharacteristic
642C2#1061726211yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#380C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenter#380AGL(1,𝔽5)
hypocenterC5#21026
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
6. #10604324C2semidirect
7. #10604323C2semidirect
8. #10604322C2semidirect
9. #10604321C2semidirect
12. #10603791C2semidirect
13. #10603790C2semidirect
14. #10603789C2semidirect
15. #10603788C2semidirect
603. C5#21026semidirect

Maximal subgroups

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

subgroupindex
C2×#656962
C2×#656912
#106055952
#106048952
C2×#649182
#106043242
#106043232
#106043222
#106043212
#106042232
#106037912
#106037902
#106037892
#106037882
#210265