Finite Group Databasebeta

← #12117058

Subgroups — #12117058

Order 1280.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65410C211yesmaximal, characteristic
2#10605191C211yesmaximal, characteristic
3#10605188C211yesmaximal, characteristic
4C5×#1753C211yesmaximal, characteristic
5#10602781C211yesmaximal, characteristic
6#10600719C211yesmaximal, characteristic
7#10600717C211yesmaximal, characteristic
8#10600613C211yesmaximal, characteristic, complemented
9#10600607C211yesmaximal, characteristic, complemented
10#10600562C211yesmaximal, characteristic, complemented
11C4×#3950C211yesmaximal, characteristic, complemented
12#10599417C211yesmaximal, characteristic, complemented
13#10599416C211yesmaximal, characteristic, complemented
14#10599415C211yesmaximal, characteristic, complemented
15#10599414C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C2×C5×C22⋊C8C2211yescharacteristic
20C2×C5×#97C2211yescharacteristic
21C2×C4×C5×C8C2211yescharacteristic
22C4×C5×C22⋊C4C2211yescharacteristic
23#65501C2211yescharacteristic
24#65501C2211yescharacteristic
25#65410C418yescomplemented
26C2×#3950C2211yescharacteristic
27C2×#3950C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3949C2211yescharacteristic
31C2×#3949C2211yescharacteristic
32#65234—21no—
33#65234—21no—
34#65231—21no—
35C22⋊C4×Dic5—21no—
36C4×C4⋊Dic5C2211yescharacteristic
37C4×C4⋊Dic5C2211yescharacteristic
38C4×C4⋊Dic5C2211yescharacteristic
39C4×C4⋊Dic5C2211yescharacteristic
40#65217C2211yescharacteristic
41#65217C2211yescharacteristic
42#65217C2211yescharacteristic
43#65217C2211yescharacteristic
44#64943—21no—
45#64943—21no—
46#64940—21no—
47#64938—21no—
48C5×#336C2211yescharacteristic
49C5×#336C2211yescharacteristic
50#64771C2211yescharacteristic
51#64771C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64771C2211yescharacteristic
59#64771C2211yescharacteristic
60#22623—51nomaximal, Sylow
61C23×C4×C5C2311yescharacteristic
62C23×Dic5—21no—
63C2×C5×M16—22no—
64C2×C5×M16—22no—
65C2×C5×M16C2×C414yes—
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C22×C5×C8C2311yescharacteristic
70C2×C5×C22⋊C4D411yescharacteristic
71C2×C5×C22⋊C4D411yescharacteristic
72C2×C42×C5C2311yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C22⋊Dic5—21no—
75C2×C22⋊Dic5—21no—
76C2×C22⋊Dic5—21no—
77#4072—22no—
78#4072C2×C414yes—
79C2×C4⋊Dic5—21no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5C2×C414yes—
82C2×C4⋊Dic5C2311yescharacteristic
83C2×C4⋊Dic5C2311yescharacteristic
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×#683—21no—
91C2×#683—21no—
92C2×#683—21no—
93C2×#683—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—21no—
96C2×C4×Dic5—21no—
97C2×C4×Dic5—21no—
98C2×C4×Dic5—21no—
99C5×C22⋊C8—22no—
100C5×#97—22no—
101C4×C5×C8—22no—
102C5×#95D411yescharacteristic
103C5×#95D411yescharacteristic
104#3963—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3950—22no—
115#3950C2×C414yes—
116#3950C2×C414yes—
117#3949—22no—
118#3949C2×C414yes—
119#3949C2×C414yes—
120C2×#428—51no—
121#2347—51no—
122#2345—51no—
123#1944—51no—
124#1941—51no—
125#1921—51no—
126#1920—51no—
127#1919—51no—
128#1918—51no—
129#1825—51no—
130#1823—51no—
131#1809—51no—
132#1776—51no—
133C4×#107—51no—
134#1753D511yescharacteristic
135C24×C5C2×D411yescharacteristic
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5C22×C412yes—
141C22×C4×C5C2×D411yescharacteristic
142C22×C4×C5C2×D411yescharacteristic
143C22×C4×C5C2×D411yescharacteristic
144C22×C4×C5C2×D411yescharacteristic
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5#4112yes—
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—24no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—81no—
158C22×Dic5—81no—
159C5×M16—28no—
160C2×C5×C8—21no—
161C2×C5×C8—21no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8C22×C412yes—
169C2×C5×C8C22×C412yes—
170C2×C5×C8#4112yes—
171C2×C5×C8#4112yes—
172C5×C22⋊C4—22no—
173C5×C22⋊C4—41no—
174C42×C5—21no—
175C42×C5—21no—
176C42×C5—21no—
177C42×C5—21no—
178C22⋊Dic5—24no—
179C22⋊Dic5—42no—
180C22⋊Dic5—81no—
181C4⋊Dic5—24no—
182C4⋊Dic5—21no—
183C4⋊Dic5—21no—
184C4⋊Dic5—21no—
185C4⋊Dic5—21no—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5C22×C412yes—
195C4⋊Dic5C22×C412yes—
196C4⋊Dic5C22×C412yes—
197C4⋊Dic5C22×C412yes—
198#683—42no—
199#683—42no—
200#683—81no—
201#683—81no—
202C4×Dic5—24no—
203C4×Dic5—81no—
204C4×Dic5—81no—
205C4×Dic5—81no—
206C4×Dic5—81no—
207C22×M16C2×D511yescharacteristic
208C2×#117—51no—
209C22×C4⋊C4—51no—
210#428—58no—
211C2×#107—51no—
212C2×#107—51no—
213C2×#107—51no—
214C2×#106—51no—
215C2×#106—51no—
216C2×#106—51no—
217C2×C22⋊C8C2×D511yescharacteristic
218C2×#97C2×D511yescharacteristic
219C2×C4×C8C2×D511yescharacteristic
220#389—51no—
221#389—51no—
222#389—51no—
223#389—51no—
224#388—101no—
225#388—101no—
226#387—101no—
227#387—101no—
228#383—101no—
229#380—51no—
230#380—51no—
231#380—101no—
232C4×C4⋊C4—51no—
233C4×C4⋊C4—51no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C4⋊C4—101no—
237C4×C22⋊C4—101no—
238C4×C22⋊C4C2×D511yescharacteristic
239#340—51no—
240#340—51no—
241#340—51no—
242#340—51no—
243#340—51no—
244#340—51no—
245#340—51no—
246#340—51no—
247#340—51no—
248#340—51no—
249#336C2×D511yescharacteristic
250#336C2×D511yescharacteristic
251C23×C5—21no—
252C23×C5—21no—
253C23×C5—21no—
254C23×C5—21no—
255C23×C5—21no—
256C23×C5—21no—
257C23×C5C4×D412yes—
258C23×C5C22×D411yescharacteristic
259C2×C4×C5—21no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
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×C5C4×D412yes—
277C2×C4×C5#13712yes—
278C2×C4×C5C23×C411yescharacteristic
279C2×C4×C5C2×#4111yescharacteristic
280C2×C4×C5C2×#4111yescharacteristic
281C2×C4×C5C2×#4111yescharacteristic
282C2×C4×C52−1+411yescharacteristic
283C2×C4×C52−1+411yescharacteristic
284C2×Dic5—22no—
285C2×Dic5—22no—
286C2×Dic5—22no—
287C2×Dic5—22no—
288C2×Dic5—41no—
289C2×Dic5—41no—
290C2×Dic5—41no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—84no—
309C5×C8—22no—
310C5×C8—41no—
311C5×C8—41no—
312C5×C8#11714yes—
313C23×C4—101no—
314C23×C4C22×D511yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16C4×D514yes—
318C22×C8C22×D511yescharacteristic
319C22×C8C22×D511yescharacteristic
320C22×C8C22×D511yescharacteristic
321C22×C8C22×D511yescharacteristic
322#117—54no—
323#117—102no—
324C2×C4⋊C4—54no—
325C2×C4⋊C4—51no—
326C2×C4⋊C4—51no—
327C2×C4⋊C4—51no—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—101no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—101no—
336C2×C4⋊C4—101no—
337C2×C4⋊C4—101no—
338C2×C4⋊C4—101no—
339C2×C22⋊C4—101no—
340C2×C22⋊C4—101no—
341C2×C22⋊C4—101no—
342C2×C22⋊C4D2011yescharacteristic
343C2×C22⋊C4D2011yescharacteristic
344C2×C42—101no—
345C2×C42—101no—
346C2×C42—101no—
347C2×C42—101no—
348C2×C42—101no—
349C2×C42C22×D511yescharacteristic
350C2×C42C22×D511yescharacteristic
351#107—54no—
352#107—54no—
353#107—102no—
354#106—54no—
355#106—54no—
356#106—102no—
357C22⋊C8—22no—
358#97—22no—
359C4×C8—22no—
360#95—101no—
361#95—101no—
362#95—101no—
363#95—101no—
364#95—101no—
365#95—101no—
366#95—101no—
367#95—101no—
368#95—101no—
369#95—101no—
370#95D2011yescharacteristic
371#95D2011yescharacteristic
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5C2×C4×D411yescharacteristic
380C22×C5#54711yescharacteristic
381C22×C5#54711yescharacteristic
382C22×C5C2×#13711yescharacteristic
383C22×C5#57511yescharacteristic
384C22×C5#57611yescharacteristic
385C22×C5#57711yescharacteristic
386C4×C5—22no—
387C4×C5—22no—
388C4×C5—41no—
389C4×C5—41no—
390C4×C5—41no—
391C4×C5C2×#11711yescharacteristic
392C4×C5#51911yescharacteristic
393C4×C5#55211yescharacteristic
394C4×C5#55211yescharacteristic
395Dic5—42no—
396Dic5—42no—
397Dic5—42no—
398Dic5—42no—
399Dic5—81no—
400Dic5—81no—
401Dic5—81no—
402Dic5—81no—
403C24C2×D2011yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—101no—
409C22×C4—101no—
410C22×C4—101no—
411C22×C4—101no—
412C22×C4—104no—
413C22×C4—101no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4—401no—
418C22×C4—401no—
419C22×C4C2×C4×D512yes—
420C22×C4C2×D2011yescharacteristic
421C22×C4C2×D2011yescharacteristic
422C22×C4C2×D2011yescharacteristic
423C22×C4C2×D2011yescharacteristic
424C22×C4C2×D2011yescharacteristic
425C22×C4#70912yes—
426C22×C4C23×D511yescharacteristic
427M16—28no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×C4×D512yes—
437C2×C8C2×C4×D512yes—
438C2×C8#71112yes—
439C2×C8#71112yes—
440C4⋊C4—52no—
441C4⋊C4—52no—
442C4⋊C4—52no—
443C4⋊C4—52no—
444C4⋊C4—101no—
445C4⋊C4—101no—
446C4⋊C4—101no—
447C4⋊C4—101no—
448C4⋊C4—104no—
449C4⋊C4—101no—
450C4⋊C4—101no—
451C4⋊C4—101no—
452C4⋊C4—101no—
453C4⋊C4—101no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—101no—
457C4⋊C4—202no—
458C4⋊C4—202no—
459C4⋊C4—401no—
460C4⋊C4—401no—
461C22⋊C4—22no—
462C22⋊C4—41no—
463C22⋊C4—104no—
464C22⋊C4—202no—
465C22⋊C4—401no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—104no—
471C42—401no—
472C42—401no—
473C42—401no—
474C42—401no—
475C2×C5—42no—
476C2×C5#234411yescharacteristic
477C2×C5C4×#13711yescharacteristic
478C2×C5#294611yescharacteristic
479C2×C5#334611yescharacteristic
480C2×C5#335011yescharacteristic
481C2×C5#335511yescharacteristic
482C2×C5#335611yescharacteristic
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23C4×D2012yes—
490C23C22×D2011yescharacteristic
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
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—102no—
509C2×C4—102no—
510C2×C4—102no—
511C2×C4—102no—
512C2×C4—201no—
513C2×C4—201no—
514C2×C4—201no—
515C2×C4—201no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—201no—
519C2×C4—201no—
520C2×C4—201no—
521C2×C4—201no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—404no—
533C2×C4C4×D2012yes—
534C2×C4#405512yes—
535C2×C4C22×C4×D511yescharacteristic
536C2×C4C2×#70911yescharacteristic
537C2×C4C2×#71111yescharacteristic
538C2×C4C2×#71111yescharacteristic
539C2×C4#415011yescharacteristic
540C2×C4#415011yescharacteristic
541C8—22no—
542C8—41no—
543C8—41no—
544C8#402314yes—
545C5#2262311yescharacteristic, complemented, Sylow
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×D2011yescharacteristic
554C22#6588911yescharacteristic
555C22#6588911yescharacteristic
556C22C2×#405511yescharacteristic
557C22#6608211yescharacteristic
558C22#6608511yescharacteristic
559C22#6608611yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—202no—
566C4—202no—
567C4—202no—
568C4—202no—
569C4—401no—
570C4—401no—
571C4—401no—
572C4—401no—
573C4C2×#402311yescharacteristic
574C4#6585011yescharacteristic
575C4#6587511yescharacteristic
576C4#6587511yescharacteristic
577C2—42no—
578C2#1060518711yescharacteristic
579C2C4×#405511yescharacteristic
580C2#1061029111yescharacteristic
581C2#1061120311yescharacteristic
582C2#1061120711yescharacteristic
583C2#1061126411yescharacteristic
584C2#1061126511yescharacteristic
subgroupG/H
centerC23C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1753C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenter#1753D5
hypocenterC5#22623
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
8. #10600613C2semidirect
9. #10600607C2semidirect
10. #10600562C2semidirect
11. C4×#3950C2semidirect
12. #10599417C2semidirect
13. #10599416C2semidirect
14. #10599415C2semidirect
15. #10599414C2semidirect
25. #65410C4semidirect
545. C5#22623semidirect

Maximal subgroups

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

subgroupindex
C2×#654102
#106051912
#106051882
C5×#17532
#106027812
#106007192
#106007172
#106006132
#106006072
#106005622
C4×#39502
#105994172
#105994162
#105994152
#105994142
#226235