Finite Group Databasebeta

← #12266644

Subgroups — #12266644

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2643C211yesmaximal, characteristic, complemented
2#10610147C211yesmaximal, characteristic, complemented
3#10610140C211yesmaximal, characteristic, complemented
4#10609946C213yesmaximal, complemented
5#10609863C213yesmaximal, complemented
6#10609279C213yesmaximal, complemented
7#10609192C213yesmaximal, complemented
8#10609068C211yesmaximal, characteristic, complemented
9#10609014C211yesmaximal, characteristic, complemented
10#10606517C213yesmaximal, complemented
11#10606389C213yesmaximal
12#10606356C213yesmaximal, complemented
13#10606109C213yesmaximal, complemented
14#10605111C211yesmaximal, characteristic, complemented
15C2×#64937C211yesmaximal, characteristic, complemented
16C22×#711C2211yescharacteristic
17C22×C4×Dic5C2213yes—
18C2×#4023C2213yes—
19C5×#401C2211yescharacteristic
20C5×#400C2213yes—
21C5×#397C2213yes—
22C5×#396C2211yescharacteristic
23C5×#386C2213yes—
24C5×#385C2213yes—
25C2×C5×#95C2211yescharacteristic
26#65509C2213yes—
27#65502C2213yes—
28#65499C2213yes—
29C2×#3963C2213yes—
30#65283C2213yes—
31#65282C2213yes—
32#65275C2213yes—
33#65271C2213yes—
34C4⋊C4×Dic5C2213yes—
35C4⋊C4×Dic5C2213yes—
36#65261C2213yes—
37#65261C2213yes—
38#65247C2213yes—
39#65246C2213yes—
40#65246C2213yes—
41#65242C2213yes—
42#65241C2213yes—
43#65241C2213yes—
44#65239C2213yes—
45#65237C2213yes—
46#65235C2213yes—
47C22⋊C4×Dic5C2213yes—
48C22⋊C4×Dic5C2213yes—
49#64965C2211yescharacteristic
50#64964C2213yes—
51#64964C2213yes—
52#64963C2213yes—
53#64955C2213yes—
54#64955C2213yes—
55C5⋊#401C2213yes—
56C5⋊#401C2213yes—
57C5⋊#401C2211yescharacteristic
58#64949C2213yes—
59#64949C2213yes—
60#64948C2213yes—
61#64947C2213yes—
62#64947C2213yes—
63#64938C2213yes—
64#64938C2213yes—
65#64937C2213yes—
66#64937C2213yes—
67#64937C2211yescharacteristic
68#64937C2211yescharacteristic
69#64936C2213yes—
70#64936C2213yes—
71#64935C2213yes—
72#64935C2213yes—
73#34639—51nomaximal, Sylow
74C22×C5×D4C2311yescharacteristic
75C23×C4×C5C2313yes—
76C22×C22⋊D5C2311yescharacteristic
77C22×C22⋊D5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2313yes—
80C23×Dic5C2311yescharacteristic
81C2×#711—212no—
82C22×C4×D5C2311yescharacteristic
83C22×Dic10C2311yescharacteristic
84C2×C5×C4⋊C4C2313yes—
85C2×C5×C4⋊C4C2313yes—
86C2×C5×C22⋊C4C2313yes—
87C2×C5×C22⋊C4C2313yes—
88C2×C5×C22⋊C4C2313yes—
89C2×C22⋊Dic5C2313yes—
90C2×C22⋊Dic5C2313yes—
91C2×C22⋊Dic5C2313yes—
92C2×#685C2313yes—
93C2×#685C2313yes—
94C2×#685C2313yes—
95C2×#685C2313yes—
96C2×C4⋊Dic5C2313yes—
97C2×C4⋊Dic5C2313yes—
98C2×#683C2313yes—
99C2×#683C2313yes—
100C2×#683C2313yes—
101C2×#683C2313yes—
102C2×#683C2313yes—
103C2×#683C2313yes—
104C2×C4×Dic5—212no—
105C2×C4×Dic5C2313yes—
106C2×C4×Dic5C2313yes—
107C2×C4×Dic5C2313yes—
108C2×C4×Dic5C2313yes—
109C2×C4×Dic5C2313yes—
110C2×C4×Dic5C2313yes—
111#4023—212no—
112C5×#95C2311yescharacteristic
113C5×#95C2313yes—
114C5×#95C2313yes—
115C5×#95C2313yes—
116C5×#95C2313yes—
117C5×#95C2313yes—
118#3963C2313yes—
119#3963C2313yes—
120#3963C2313yes—
121#3963C2313yes—
122#3963C2313yes—
123#3963C2313yes—
124#3963C2313yes—
125#3963C2313yes—
126#3963C2313yes—
127#3963C2313yes—
128#3963C2313yes—
129#3963C2313yes—
130#3963C2313yes—
131#3963C2313yes—
132#3963C2313yes—
133#3963C2313yes—
134#2645—51no—
135#2645—53no—
136#2644—53no—
137#2644—51no—
138#2643—53no—
139#2643—53no—
140#2643—51no—
141#2643D511yescharacteristic, complemented
142#2401—51no—
143#2401—53no—
144#2401—53no—
145#2401—51no—
146#2297—53no—
147#2296—53no—
148C2×#376—51no—
149C24×C5C2411yescharacteristic
150C24×C5C2411yescharacteristic
151C23×D5C2411yescharacteristic
152C2×C5×D4—26no—
153C22×C4×C5—26no—
154C22×C4×C5—43no—
155C22×C4×C5—43no—
156C22×C4×C5C2413yes—
157C22×C4×C5C2413yes—
158C22×C4×C5C2413yes—
159C22×C4×C5C2413yes—
160C22×C4×C5C2411yescharacteristic
161C2×C22⋊D5—26no—
162C2×C22⋊D5—26no—
163C22×Dic5—26no—
164C22×Dic5—26no—
165C22×Dic5—43no—
166C22×Dic5—43no—
167C22×Dic5#41112yes—
168C22×Dic5C2413yes—
169C22×Dic5C2413yes—
170C22×Dic5C2413yes—
171C22×Dic5C2413yes—
172C22×Dic5C2411yescharacteristic
173C22×Dic5C2411yescharacteristic
174C22×Dic5C2411yescharacteristic
175#711—416no—
176C2×C4×D5—26no—
177C2×Dic10—26no—
178C5×C4⋊C4—43no—
179C5×C4⋊C4—43no—
180C5×C22⋊C4—26no—
181C5×C22⋊C4—43no—
182C5×C22⋊C4—43no—
183C22⋊Dic5—26no—
184C22⋊Dic5—43no—
185C22⋊Dic5—43no—
186#685—43no—
187#685—43no—
188#685—43no—
189#685—43no—
190C4⋊Dic5—43no—
191C4⋊Dic5—43no—
192#683—26no—
193#683—26no—
194#683—43no—
195#683—43no—
196#683—43no—
197#683—43no—
198C4×Dic5—26no—
199C4×Dic5—26no—
200C4×Dic5—26no—
201C4×Dic5—26no—
202C4×Dic5—26no—
203C4×Dic5—26no—
204C22×#41—51no—
205C2×#117—53no—
206C22×C42—53no—
207#401—53no—
208#401—53no—
209#401—51no—
210#401C2×D511yescharacteristic
211#400—53no—
212#400—53no—
213#400—53no—
214#400—53no—
215#400—53no—
216#400—53no—
217#400—53no—
218#400C2×D513yes—
219#397—53no—
220#397—53no—
221#397—53no—
222#397—53no—
223#397—53no—
224#397—53no—
225#397—53no—
226#397C2×D513yes—
227#396—53no—
228#396—53no—
229#396—51no—
230#396C2×D511yescharacteristic
231#391—53no—
232#391—53no—
233#390—53no—
234#390—53no—
235#389—53no—
236#389—53no—
237#389—53no—
238#389—53no—
239#386—53no—
240#386—53no—
241#386—53no—
242#386C2×D513yes—
243#385—53no—
244#385—53no—
245#385—53no—
246#385C2×D513yes—
247C4×C4⋊C4—53no—
248C4×C4⋊C4—53no—
249C4×C4⋊C4—53no—
250C4×C4⋊C4—53no—
251C4×C22⋊C4—53no—
252C4×C22⋊C4—53no—
253C4×C22⋊C4—53no—
254C4×C22⋊C4—53no—
255#376—53no—
256#376—51no—
257#376—53no—
258#376—51no—
259C2×#95—53no—
260C2×#95C2×D511yescharacteristic
261C23×C5—21no—
262C23×C5—23no—
263C23×C5—23no—
264C23×C5—21no—
265C23×C5—23no—
266C23×C5C2×#4116yes—
267C23×C5C2511yescharacteristic
268C22×D5—23no—
269C22×D5—23no—
270C22×D5—21no—
271C5×D4—44no—
272C2×C4×C5—23no—
273C2×C4×C5—23no—
274C2×C4×C5—23no—
275C2×C4×C5—23no—
276C2×C4×C5—23no—
277C2×C4×C5—23no—
278C2×C4×C5—23no—
279C2×C4×C5—23no—
280C2×C4×C5—23no—
281C2×C4×C5—23no—
282C2×C4×C5—23no—
283C2×C4×C5—23no—
284C2×C4×C5—23no—
285C2×C4×C5—412no—
286C22⋊D5—44no—
287C22⋊D5—44no—
288C2×Dic5—23no—
289C2×Dic5—23no—
290C2×Dic5—23no—
291C2×Dic5—23no—
292C2×Dic5—23no—
293C2×Dic5—23no—
294C2×Dic5—23no—
295C2×Dic5—23no—
296C2×Dic5—23no—
297C2×Dic5—23no—
298C2×Dic5—23no—
299C2×Dic5—23no—
300C2×Dic5—23no—
301C2×Dic5—412no—
302C2×Dic5—44no—
303C2×Dic5#126116yes—
304C2×Dic5C2×#4116yes—
305C2×Dic5C2×#4116yes—
306C4×D5—44no—
307Dic10—44no—
308C2×#41—1012no—
309C22×Q8—51no—
310C22×D4—51no—
311C22×D4—51no—
312C22×D4C22×D511yescharacteristic
313C23×C4—51no—
314C23×C4—51no—
315C23×C4—53no—
316C23×C4—51no—
317C23×C4C22×D513yes—
318#117—1012no—
319C2×C4⋊C4—53no—
320C2×C4⋊C4—53no—
321C2×C4⋊C4—53no—
322C2×C4⋊C4—53no—
323C2×C4⋊C4—53no—
324C2×C4⋊C4—53no—
325C2×C4⋊C4—53no—
326C2×C4⋊C4—53no—
327C2×C4⋊C4C22×D513yes—
328C2×C4⋊C4C22×D513yes—
329C2×C22⋊C4—53no—
330C2×C22⋊C4—53no—
331C2×C22⋊C4—53no—
332C2×C22⋊C4—53no—
333C2×C22⋊C4—53no—
334C2×C22⋊C4—53no—
335C2×C22⋊C4—53no—
336C2×C22⋊C4C22×D513yes—
337C2×C22⋊C4C22×D513yes—
338C2×C22⋊C4C22×D513yes—
339C2×C42—53no—
340C2×C42—53no—
341C2×C42—53no—
342C2×C42—53no—
343C2×C42—53no—
344C2×C42—53no—
345C2×C42—1012no—
346#95—53no—
347#95—53no—
348#95—53no—
349#95—53no—
350#95—53no—
351#95—53no—
352#95—53no—
353#95—53no—
354#95—53no—
355#95—53no—
356#95—53no—
357#95—53no—
358#95—53no—
359#95—53no—
360#95—53no—
361#95—53no—
362#95C22×D511yescharacteristic
363#95C22×D513yes—
364#95C22×D513yes—
365#95C22×D513yes—
366#95C22×D513yes—
367#95C22×D513yes—
368C22×C5—26no—
369C22×C5—26no—
370C22×C5—41no—
371C22×C5—43no—
372C22×C5—43no—
373C22×C5C2×#12614yes—
374C22×C5C22×#4113yes—
375C22×C5#58513yes—
376C22×C5#58511yescharacteristic
377C2×D5—41no—
378C2×D5—43no—
379C2×D5—43no—
380C4×C5—41no—
381C4×C5—43no—
382C4×C5—43no—
383C4×C5—43no—
384C4×C5—43no—
385Dic5—41no—
386Dic5—43no—
387Dic5—43no—
388Dic5—43no—
389Dic5—43no—
390Dic5C2×#12614yes—
391Dic5C2×#12614yes—
392C24—51no—
393C24C23×D511yescharacteristic
394C24C23×D511yescharacteristic
395#41—2016no—
396C2×Q8—106no—
397C2×D4—26no—
398C2×D4—106no—
399C2×D4—106no—
400C22×C4—26no—
401C22×C4—43no—
402C22×C4—43no—
403C22×C4—512no—
404C22×C4—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—53no—
408C22×C4—53no—
409C22×C4—53no—
410C22×C4—53no—
411C22×C4—106no—
412C22×C4—106no—
413C22×C4—106no—
414C22×C4—203no—
415C22×C4—203no—
416C22×C4C23×D511yescharacteristic
417C22×C4C23×D513yes—
418C22×C4C23×D513yes—
419C22×C4C23×D513yes—
420C22×C4C23×D513yes—
421C4⋊C4—43no—
422C4⋊C4—43no—
423C4⋊C4—106no—
424C4⋊C4—106no—
425C4⋊C4—203no—
426C4⋊C4—203no—
427C4⋊C4—203no—
428C4⋊C4—203no—
429C4⋊C4—203no—
430C4⋊C4—203no—
431C22⋊C4—26no—
432C22⋊C4—43no—
433C22⋊C4—43no—
434C22⋊C4—106no—
435C22⋊C4—203no—
436C22⋊C4—203no—
437C22⋊C4—203no—
438C22⋊C4—203no—
439C22⋊C4—203no—
440C22⋊C4—203no—
441C42—106no—
442C42—106no—
443C42—106no—
444C42—106no—
445C42—106no—
446C42—106no—
447C2×C5—24no—
448C2×C5—81no—
449C2×C5C22×#12611yescharacteristic
450C2×C5#345513yes—
451C2×C5#345513yes—
452D5—81no—
453C23—23no—
454C23—21no—
455C23—23no—
456C23—23no—
457C23—21no—
458C23—103no—
459C23—103no—
460C23—101no—
461C23D5×#4116yes—
462C23C24×D511yescharacteristic
463Q8—204no—
464D4—44no—
465D4—204no—
466D4—204no—
467C2×C4—23no—
468C2×C4—23no—
469C2×C4—23no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—23no—
477C2×C4—23no—
478C2×C4—23no—
479C2×C4—23no—
480C2×C4—412no—
481C2×C4—56no—
482C2×C4—56no—
483C2×C4—516no—
484C2×C4—103no—
485C2×C4—103no—
486C2×C4—103no—
487C2×C4—103no—
488C2×C4—103no—
489C2×C4—103no—
490C2×C4—103no—
491C2×C4—103no—
492C2×C4—103no—
493C2×C4—103no—
494C2×C4—103no—
495C2×C4—103no—
496C2×C4—103no—
497C2×C4—204no—
498C2×C4—204no—
499C2×C4—2012no—
500C5#3463911yescharacteristic, complemented, Sylow
501C22—26no—
502C22—26no—
503C22—41no—
504C22—43no—
505C22—43no—
506C22—201no—
507C22—203no—
508C22—203no—
509C22D5×#12614yes—
510C22C2×D5×#4113yes—
511C22#6628513yes—
512C22#6628711yescharacteristic
513C4—41no—
514C4—43no—
515C4—43no—
516C4—43no—
517C4—43no—
518C4—54no—
519C4—54no—
520C4—201no—
521C4—203no—
522C4—203no—
523C4—203no—
524C4—203no—
525C2—24no—
526C2—81no—
527C2—401no—
528C2C2×D5×#12611yescharacteristic
529C2#1061828813yes—
530C2#1061832813yes—
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2643C2
prime radicalC22×#711C22
hypercenter#2643D5
hypocenterC5#34639
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. C5×#2643C2semidirect
2. #10610147C2semidirect
3. #10610140C2semidirect
4. #10609946C2semidirect
5. #10609863C2semidirect
6. #10609279C2semidirect
7. #10609192C2semidirect
8. #10609068C2semidirect
9. #10609014C2semidirect
10. #10606517C2semidirect
12. #10606356C2semidirect
13. #10606109C2semidirect
14. #10605111C2semidirect
15. C2×#64937C2semidirect
141. #2643D5semidirect
500. C5#34639semidirect

Maximal subgroups

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

subgroupindex
C5×#26432
#106101472
#106101402
#106099462
#106098632
#106092792
#106091922
#106090682
#106090142
#106065172
#106063892
#106063562
#106061092
#106051112
C2×#649372
#346395