Finite Group Databasebeta

← #13036096

Subgroups — #13036096

Order 1280.

688 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10607182C211yesmaximal, characteristic
2#10604324C211yesmaximal, characteristic, complemented
3#10604322C211yesmaximal, characteristic, complemented
4#10604240C211yesmaximal, characteristic
5#10604239C211yesmaximal, characteristic
6#10604238C211yesmaximal, characteristic
7#10604237C211yesmaximal, characteristic
8#10604224C211yesmaximal, characteristic
9#10604224C211yesmaximal, characteristic
10#10604180C211yesmaximal, characteristic, complemented
11C4×C4⋊#170C211yesmaximal, characteristic, complemented
12#10603791C211yesmaximal, characteristic, complemented
13#10603789C211yesmaximal, characteristic, complemented
14#10603774C211yesmaximal, characteristic, complemented
15#10603773C211yesmaximal, characteristic, complemented
16C2×#4023C2211yescharacteristic
17C2×C22⋊#170C2211yescharacteristic
18C2×C22⋊#170C2211yescharacteristic
19C2×C22⋊#170C2211yescharacteristic
20C2×C22⋊#170C2211yescharacteristic
21C2×#4004C2211yescharacteristic
22C2×#4004C2211yescharacteristic
23C2×#4002C2211yescharacteristic
24C2×#4002C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×C4⋊#170C2211yescharacteristic
28C2×C4⋊#170C2211yescharacteristic
29C2×C4×#170C2211yescharacteristic
30C2×C4×#170C2211yescharacteristic
31C2×C4×#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C5×#388C411yescharacteristic
34#65267C411yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36#65240C411yescharacteristic
37#65234C411yescharacteristic
38#65233C411yescharacteristic
39C22⋊C4×Dic5C2211yescharacteristic
40C22⋊C4×Dic5C2211yescharacteristic
41#65222C411yescharacteristic
42C42×Dic5C2211yescharacteristic
43#64944C411yescharacteristic
44#64941C411yescharacteristic
45#64938C2211yescharacteristic
46#64937C2211yescharacteristic
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#21436—51nomaximal, Sylow
60C23×Dic5C2311yescharacteristic
61C22×#170C2311yescharacteristic
62C22×#170C2311yescharacteristic
63C22×#170C2311yescharacteristic
64C22×#170C2311yescharacteristic
65C22×#170C2311yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C2×C5×C4⋊C4C2×C411yescharacteristic
70C2×C5×C22⋊C4C2×C411yescharacteristic
71C2×C5×C22⋊C4C2×C411yescharacteristic
72C2×C5×C22⋊C4C2×C411yescharacteristic
73C2×C42×C5C2×C411yescharacteristic
74C2×C22⋊Dic5C2×C411yescharacteristic
75C2×C22⋊Dic5C2×C411yescharacteristic
76C2×C22⋊Dic5C2×C411yescharacteristic
77C2×C4⋊Dic5C2×C411yescharacteristic
78C2×#683C2×C411yescharacteristic
79C2×#683C2×C411yescharacteristic
80C2×#683C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×C4×Dic5C2×C411yescharacteristic
83C2×C4×Dic5C2×C411yescharacteristic
84C2×C4×Dic5C2×C411yescharacteristic
85C2×C4×Dic5C2311yescharacteristic
86C2×C4×Dic5C2311yescharacteristic
87C2×C4×Dic5C2311yescharacteristic
88C2×C4×Dic5C2311yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C2×C4×Dic5C2311yescharacteristic
91#4023—22no—
92#4023—22no—
93C22⋊#170—22no—
94C22⋊#170—22no—
95C22⋊#170—22no—
96C22⋊#170—22no—
97#4004—22no—
98#4004—22no—
99#4002—22no—
100#4002—22no—
101#4002—22no—
102#4002—22no—
103C4⋊#170—22no—
104C4⋊#170—22no—
105C4×#170—22no—
106C4×#170—22no—
107C4×#170—22no—
108C4×#170—22no—
109C5×#95C2×C411yescharacteristic
110C5×#95C2×C411yescharacteristic
111#3963C2×C411yescharacteristic
112#3963C2×C411yescharacteristic
113#3963C2×C411yescharacteristic
114#3963C2×C411yescharacteristic
115#3963C2×C411yescharacteristic
116#3963C2×C411yescharacteristic
117#3963C2×C411yescharacteristic
118#3963C2×C411yescharacteristic
119#3963C2×C411yescharacteristic
120#3963C2×C411yescharacteristic
121#2298—51no—
122#1924—51no—
123#1924—51no—
124#1923—51no—
125#1923—51no—
126#1917—51no—
127#1917—51no—
128#1916—51no—
129#1916—51no—
130#1767—51no—
131C4×C4⋊C8—51no—
132#1750—51no—
133#1750—51no—
134#1746—51no—
135#1726—51no—
136C24×C5C22×C411yescharacteristic
137C22×C4×C5C22×C411yescharacteristic
138C22×C4×C5C22×C411yescharacteristic
139C22×C4×C5C22×C411yescharacteristic
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5C22×C411yescharacteristic
150C22×Dic5C22×C411yescharacteristic
151C22×Dic5C22×C411yescharacteristic
152C22×Dic5C22×C411yescharacteristic
153C22×Dic5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C2411yescharacteristic
157C2×#170—21no—
158C2×#170—21no—
159C2×#170—21no—
160C2×#170—21no—
161C2×#170—21no—
162C2×#170—21no—
163C2×#170—21no—
164C2×#170—21no—
165C2×#170—21no—
166C2×#170—21no—
167C2×#170—21no—
168C2×#170—21no—
169C2×#170—21no—
170C2×#170—21no—
171C2×#170—21no—
172C2×#170—21no—
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170#4112yes—
178C2×#170#4112yes—
179C2×#170#4112yes—
180C2×#170#4112yes—
181C5×C4⋊C4—41no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—22no—
184C5×C22⋊C4—41no—
185C42×C5—22no—
186C22⋊Dic5—22no—
187C22⋊Dic5—22no—
188C22⋊Dic5—41no—
189C4⋊Dic5—22no—
190#683—22no—
191#683—22no—
192#683—22no—
193#683—41no—
194C4×Dic5—22no—
195C4×Dic5—21no—
196C4×Dic5—21no—
197C4×Dic5—21no—
198C4×Dic5—21no—
199C4×Dic5—21no—
200C4×Dic5—21no—
201C4×Dic5—21no—
202C4×Dic5—21no—
203C4×Dic5—21no—
204C4×Dic5—21no—
205C4×Dic5—41no—
206C4×Dic5—41no—
207C4×Dic5#4112yes—
208C4×Dic5#4112yes—
209C2×#117—51no—
210C2×C4⋊C8—51no—
211C2×C4⋊C8—51no—
212C2×C4⋊C8—51no—
213C2×C4⋊C8—51no—
214C2×C22⋊C8—51no—
215C2×C22⋊C8—51no—
216C2×C22⋊C8—51no—
217C2×C22⋊C8—51no—
218C2×#97—51no—
219C2×#97—51no—
220C2×#97—51no—
221C2×#97—51no—
222C2×C4×C8—51no—
223C2×C4×C8—51no—
224C2×C4×C8—51no—
225C2×C4×C8—51no—
226#388—51no—
227#388—51no—
228#388—51no—
229#388AGL(1,𝔽5)11yescharacteristic
230#387—51no—
231#387—51no—
232#387—51no—
233#387—51no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C22⋊C4—51no—
237C4×C22⋊C4—51no—
238#376—51no—
239C43—51no—
240#336—51no—
241#336—51no—
242#336—51no—
243#336—51no—
244#336—51no—
245#336—51no—
246#336—51no—
247#336—51no—
248#336—51no—
249#336—51no—
250#336—51no—
251#336—51no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5C23×C411yescharacteristic
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5#11712yes—
277C2×C4×C5#13112yes—
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—21no—
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—21no—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5#11712yes—
302C2×Dic5#13112yes—
303C2×Dic5C2×#4111yescharacteristic
304C2×Dic5C2×#4111yescharacteristic
305C2×Dic5C2×#4111yescharacteristic
306C2×Dic5C2×#4111yescharacteristic
307C2×Dic5C2×#4111yescharacteristic
308C2×Dic5C2×#4111yescharacteristic
309#170—22no—
310#170—22no—
311#170—22no—
312#170—22no—
313#170—41no—
314#170—41no—
315#170—41no—
316#170—41no—
317C23×C4—51no—
318C22×C8—51no—
319C22×C8—51no—
320C22×C8—51no—
321C22×C8—51no—
322C22×C8—51no—
323C22×C8—51no—
324C22×C8—51no—
325C22×C8—51no—
326#117—102no—
327#117—102no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
334C2×C22⋊C4—51no—
335C2×C22⋊C4—51no—
336C2×C22⋊C4—51no—
337C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
338C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
339C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
340C2×C42—51no—
341C2×C42—51no—
342C2×C42—51no—
343C2×C42—51no—
344C2×C42—51no—
345C2×C42—51no—
346C2×C42—51no—
347C2×C42—51no—
348C2×C42—51no—
349C2×C42C2×AGL(1,𝔽5)11yescharacteristic
350C4⋊C8—102no—
351C4⋊C8—102no—
352C4⋊C8—102no—
353C4⋊C8—102no—
354C22⋊C8—102no—
355C22⋊C8—102no—
356C22⋊C8—102no—
357C22⋊C8—102no—
358#97—102no—
359#97—102no—
360#97—102no—
361#97—102no—
362C4×C8—102no—
363C4×C8—102no—
364C4×C8—102no—
365C4×C8—102no—
366#95—51no—
367#95—51no—
368#95—51no—
369#95—51no—
370#95—51no—
371#95—51no—
372#95—51no—
373#95—51no—
374#95—51no—
375#95—51no—
376#95C2×AGL(1,𝔽5)11yescharacteristic
377#95C2×AGL(1,𝔽5)11yescharacteristic
378C22×C5—41no—
379C22×C5—41no—
380C22×C5—41no—
381C22×C5—41no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—41no—
385C22×C5C2×#11711yescharacteristic
386C22×C5C4×#4111yescharacteristic
387C22×C5C4×#4111yescharacteristic
388C22×C5C2×#13111yescharacteristic
389C22×C5C2×#13111yescharacteristic
390C22×C5#56811yescharacteristic
391C22×C5#56811yescharacteristic
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—41no—
395C4×C5—41no—
396C4×C5—41no—
397C4×C5—41no—
398Dic5—22no—
399Dic5—22no—
400Dic5—41no—
401Dic5—41no—
402Dic5—41no—
403Dic5—41no—
404Dic5—41no—
405Dic5#52911yescharacteristic
406Dic5#52911yescharacteristic
407Dic5#52911yescharacteristic
408Dic5#52911yescharacteristic
409C24C22×AGL(1,𝔽5)11yescharacteristic
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—51no—
413C22×C4—51no—
414C22×C4—51no—
415C22×C4—51no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4C22×AGL(1,𝔽5)11yescharacteristic
425C22×C4C22×AGL(1,𝔽5)11yescharacteristic
426C22×C4C22×AGL(1,𝔽5)11yescharacteristic
427C22×C4C22×AGL(1,𝔽5)11yescharacteristic
428C22×C4C22×AGL(1,𝔽5)11yescharacteristic
429C22×C4C22×AGL(1,𝔽5)11yescharacteristic
430C2×C8—52no—
431C2×C8—52no—
432C2×C8—52no—
433C2×C8—52no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—101no—
437C2×C8—101no—
438C2×C8—101no—
439C2×C8—101no—
440C2×C8—101no—
441C2×C8—101no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C2×C8—101no—
449C2×C8—101no—
450C2×C8—101no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C4⋊C4—41no—
455C4⋊C4—102no—
456C4⋊C4—102no—
457C4⋊C4—102no—
458C4⋊C4—102no—
459C4⋊C4—201no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—41no—
463C22⋊C4—102no—
464C22⋊C4—102no—
465C22⋊C4—201no—
466C42—22no—
467C42—52no—
468C42—52no—
469C42—101no—
470C42—101no—
471C42—101no—
472C42—101no—
473C42—101no—
474C42—101no—
475C42—101no—
476C42—101no—
477C42—101no—
478C42—101no—
479C42—102no—
480C42—201no—
481C42—201no—
482C2×C5—81no—
483C2×C5#229811yescharacteristic
484C2×C5#292511yescharacteristic
485C2×C5#292511yescharacteristic
486C2×C5#296611yescharacteristic
487C2×C5#296711yescharacteristic
488C2×C5#296811yescharacteristic
489C2×C5#296911yescharacteristic
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23C23×AGL(1,𝔽5)11yescharacteristic
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—51no—
515C2×C4—51no—
516C2×C4—51no—
517C2×C4—51no—
518C2×C4—51no—
519C2×C4—51no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—101no—
525C2×C4—101no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4#413012yes—
546C2×C4#413112yes—
547C8—102no—
548C8—102no—
549C8—102no—
550C8—102no—
551C8—201no—
552C8—201no—
553C8—201no—
554C8—201no—
555C5#2143611yescharacteristic, complemented, Sylow
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×#413011yescharacteristic
564C22C2×#413111yescharacteristic
565C22#6625611yescharacteristic
566C22D5⋊#13111yescharacteristic
567C22#6626411yescharacteristic
568C22#41×AGL(1,𝔽5)11yescharacteristic
569C22#41×AGL(1,𝔽5)11yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—51no—
577C4—51no—
578C4—51no—
579C4—51no—
580C4—102no—
581C4—102no—
582C4—201no—
583C4—201no—
584C4—201no—
585C4—201no—
586C4—201no—
587C2—81no—
588C2#1061712911yescharacteristic
589C2#1061714311yescharacteristic
590C2#1061714611yescharacteristic
591C2#1061723611yescharacteristic
592C2#1061729211yescharacteristic
593C2#1061731311yescharacteristic
594C2#1061735111yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC5×#388C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenter#388AGL(1,𝔽5)
hypocenterC5#21436
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #10604324C2semidirect
3. #10604322C2semidirect
10. #10604180C2semidirect
11. C4×C4⋊#170C2semidirect
12. #10603791C2semidirect
13. #10603789C2semidirect
14. #10603774C2semidirect
15. #10603773C2semidirect
555. C5#21436semidirect

Maximal subgroups

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

subgroupindex
#106071822
#106043242
#106043222
#106042402
#106042392
#106042382
#106042372
#106042242
#106041802
C4×C4⋊#1702
#106037912
#106037892
#106037742
#106037732
#214365