Finite Group Databasebeta

← #12025586

Subgroups — #12025586

Order 1280.

1594 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#397C211yesmaximal, characteristic
2C2×C22⋊C4×Dic5C212yesmaximal
3#10602357C212yesmaximal, complemented
4#10602341C212yesmaximal
5#10602339C211yesmaximal, characteristic
6#10602337C211yesmaximal, characteristic
7#10600200C212yesmaximal, complemented
8#10600194C212yesmaximal, complemented
9#10600194C212yesmaximal, complemented
10C24×Dic5C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic5C2212yes—
15C22×C22⋊Dic5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C22×C4×Dic5C2212yes—
18C22×C4×Dic5C2212yes—
19C5×#397C418yescomplemented
20C2×C5×#95C2211yescharacteristic
21C2×C5×#95C2212yes—
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C22⋊C4×Dic5—28no—
33#14248—51nomaximal, Sylow
34C25×C5C2311yescharacteristic
35C23×C4×C5C2312yes—
36C23×C4×C5C2311yescharacteristic
37C23×C4×C5C2312yes—
38C23×C4×C5C2311yescharacteristic
39C23×Dic5—24no—
40C23×Dic5—24no—
41C23×Dic5—41no—
42C23×Dic5—41no—
43C23×Dic5D414yes—
44C23×Dic5C2312yes—
45C23×Dic5C2312yes—
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C2×C5×C4⋊C4—41no—
49C2×C5×C4⋊C4—41no—
50C2×C5×C4⋊C4C2×C414yescomplemented
51C2×C5×C22⋊C4—24no—
52C2×C5×C22⋊C4—24no—
53C2×C5×C22⋊C4—41no—
54C2×C5×C22⋊C4—41no—
55C2×C5×C22⋊C4C2×C418yes—
56C2×C5×C22⋊C4C2×C414yes—
57C2×C22⋊Dic5—24no—
58C2×C22⋊Dic5—24no—
59C2×C22⋊Dic5—24no—
60C2×C22⋊Dic5—22no—
61C2×C22⋊Dic5—41no—
62C2×C22⋊Dic5—41no—
63C2×C4⋊Dic5—24no—
64C2×C4⋊Dic5—41no—
65C2×C4×Dic5—24no—
66C2×C4×Dic5—24no—
67C2×C4×Dic5—24no—
68C2×C4×Dic5—24no—
69C2×C4×Dic5—42no—
70C2×C4×Dic5—42no—
71C5×#95C2×C414yescomplemented
72C5×#95C2×C418yescomplemented
73#3963—24no—
74#3963—24no—
75#3963—24no—
76#3963—24no—
77#3963—24no—
78#3963—24no—
79#3963—24no—
80#3963—41no—
81#3963—42no—
82#3963—42no—
83C2×#397D511yescharacteristic
84C2×C4×C22⋊C4—52no—
85#1440—52no—
86#1439—51no—
87#1436—52no—
88#1436—52no—
89#1434—52no—
90#1434—52no—
91C22⋊#95—51no—
92C24×C5—22no—
93C24×C5—22no—
94C24×C5—22no—
95C24×C5—22no—
96C24×C5—21no—
97C24×C5—21no—
98C24×C5—21no—
99C24×C5—21no—
100C24×C5C22×C412yes—
101C24×C5C2×D412yes—
102C24×C5#4112yes—
103C24×C5C2411yescharacteristic
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5C22×C414yes—
125C22×C4×C5C22×C412yes—
126C22×C4×C5C22×C414yes—
127C22×C4×C5C22×C412yes—
128C22×Dic5—22no—
129C22×Dic5—22no—
130C22×Dic5—22no—
131C22×Dic5—22no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—216no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—44no—
153C22×Dic5—44no—
154C22×Dic5—44no—
155C22×Dic5—48no—
156C22×Dic5C2×D414yes—
157C22×Dic5#4114yes—
158C22×Dic5#4114yes—
159C22×Dic5#4114yes—
160C22×Dic5#4114yes—
161C5×C4⋊C4—44no—
162C5×C22⋊C4—216no—
163C5×C22⋊C4—44no—
164C22⋊Dic5—216no—
165C22⋊Dic5—44no—
166C4⋊Dic5—44no—
167C4×Dic5—48no—
168C4×Dic5—48no—
169C24×C4—51no—
170C22×C4⋊C4—51no—
171C22×C4⋊C4C2×D511yescharacteristic
172C22×C22⋊C4—52no—
173C22×C22⋊C4—51no—
174C22×C22⋊C4C2×D512yes—
175C22×C22⋊C4C2×D511yescharacteristic
176C22×C42—52no—
177C22×C42—52no—
178#397Dic518yescomplemented
179C4×C22⋊C4—108no—
180C2×#95—52no—
181C2×#95—52no—
182C2×#95—52no—
183C2×#95—52no—
184C2×#95—52no—
185C2×#95—52no—
186C2×#95—52no—
187C2×#95—51no—
188C2×#95—52no—
189C2×#95—52no—
190C2×#95C2×D511yescharacteristic
191C2×#95C2×D512yes—
192C23×C5—24no—
193C23×C5—24no—
194C23×C5—22no—
195C23×C5—22no—
196C23×C5—24no—
197C23×C5—24no—
198C23×C5—24no—
199C23×C5—24no—
200C23×C5—22no—
201C23×C5—22no—
202C23×C5—22no—
203C23×C5—22no—
204C23×C5—41no—
205C23×C5—41no—
206C23×C5—42no—
207C23×C5—41no—
208C23×C5—42no—
209C23×C5—42no—
210C23×C5—42no—
211C23×C5—42no—
212C23×C5—42no—
213C23×C5—41no—
214C23×C5C4×D414yes—
215C23×C5C23×C411yescharacteristic
216C23×C5C22×D411yescharacteristic
217C23×C5C2×#4111yescharacteristic
218C23×C5C2×#4112yes—
219C23×C5C2×#4112yes—
220C23×C5C2×#4112yes—
221C23×C5C2×#4112yes—
222C23×C5H(5,𝔽2)11yescharacteristic
223C23×C5H(5,𝔽2)11yescharacteristic
224C23×C5H(5,𝔽2)11yescharacteristic
225C23×C52−1+411yescharacteristic
226C2×C4×C5—24no—
227C2×C4×C5—24no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—41no—
250C2×Dic5—24no—
251C2×Dic5—24no—
252C2×Dic5—24no—
253C2×Dic5—24no—
254C2×Dic5—24no—
255C2×Dic5—24no—
256C2×Dic5—24no—
257C2×Dic5—24no—
258C2×Dic5—24no—
259C2×Dic5—24no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—416no—
263C2×Dic5—42no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—42no—
274C2×Dic5—42no—
275C2×Dic5—42no—
276C2×Dic5—42no—
277C2×Dic5—42no—
278C2×Dic5#12318yes—
279C25C22×D511yescharacteristic
280C23×C4—52no—
281C23×C4—52no—
282C23×C4—52no—
283C23×C4—54no—
284C23×C4—52no—
285C23×C4—104no—
286C23×C4—104no—
287C23×C4—201no—
288C23×C4—201no—
289C23×C4C22×D511yescharacteristic
290C23×C4C22×D511yescharacteristic
291C23×C4C22×D512yes—
292C23×C4C22×D512yes—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—104no—
296C2×C4⋊C4—201no—
297C2×C4⋊C4C2×Dic514yescomplemented
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—41no—
301C2×C22⋊C4—41no—
302C2×C22⋊C4—104no—
303C2×C22⋊C4—104no—
304C2×C22⋊C4—104no—
305C2×C22⋊C4—102no—
306C2×C22⋊C4—201no—
307C2×C22⋊C4—201no—
308C2×C22⋊C4C2×Dic518yes—
309C2×C22⋊C4C2×Dic514yes—
310C2×C42—104no—
311C2×C42—104no—
312C2×C42—104no—
313C2×C42—104no—
314C2×C42—202no—
315C2×C42—202no—
316#95—104no—
317#95—104no—
318#95—104no—
319#95—104no—
320#95—104no—
321#95—104no—
322#95—104no—
323#95—201no—
324#95—202no—
325#95—202no—
326#95C2×Dic514yescomplemented
327#95C2×Dic518yescomplemented
328C22×C5—24no—
329C22×C5—28no—
330C22×C5—42no—
331C22×C5—42no—
332C22×C5—44no—
333C22×C5—42no—
334C22×C5—42no—
335C22×C5—44no—
336C22×C5—42no—
337C22×C5—44no—
338C22×C5—42no—
339C22×C5C2×C4×D411yescharacteristic
340C22×C5C4×#4112yes—
341C22×C5C4×#4112yes—
342C22×C5#51811yescharacteristic
343C22×C5#52011yescharacteristic
344C22×C5C2×#12312yes—
345C22×C5#52512yes—
346C22×C5#52912yes—
347C22×C5#52912yes—
348C22×C5#53411yescharacteristic
349C22×C5#53711yescharacteristic
350C22×C5#53811yescharacteristic
351C22×C5#53911yescharacteristic
352C22×C5#55111yescharacteristic
353C22×C5#55111yescharacteristic
354C22×C5#55111yescharacteristic
355C22×C5#55112yes—
356C22×C5#55212yes—
357C22×C5#55312yes—
358C22×C5#55312yes—
359C22×C5#55512yes—
360C22×C5#55612yes—
361C22×C5#55911yescharacteristic
362C4×C5—44no—
363C4×C5—42no—
364C4×C5—42no—
365C4×C5—44no—
366Dic5—28no—
367Dic5—44no—
368Dic5—44no—
369Dic5—82no—
370C24—21no—
371C24—21no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24—21no—
377C24—21no—
378C24D4×D512yes—
379C24#71112yes—
380C24C22×Dic512yes—
381C24C23×D511yescharacteristic
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—54no—
403C22×C4—54no—
404C22×C4—54no—
405C22×C4—54no—
406C22×C4—54no—
407C22×C4—1016no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—102no—
413C22×C4—102no—
414C22×C4—102no—
415C22×C4—102no—
416C22×C4—102no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—204no—
432C22×C4—204no—
433C22×C4—204no—
434C22×C4—208no—
435C22×C4C22×Dic514yes—
436C22×C4C22×Dic512yes—
437C22×C4C22×Dic514yes—
438C22×C4C22×Dic512yes—
439C4⋊C4—44no—
440C4⋊C4—204no—
441C22⋊C4—216no—
442C22⋊C4—44no—
443C22⋊C4—1016no—
444C22⋊C4—204no—
445C42—208no—
446C42—208no—
447C2×C5—44no—
448C2×C5C4×#12312yes—
449C2×C5#232511yescharacteristic
450C2×C5#237211yescharacteristic
451C2×C5#237312yes—
452C2×C5#237411yescharacteristic
453C2×C5#248311yescharacteristic
454C2×C5#248512yes—
455C2×C5#251711yescharacteristic
456C2×C5#251812yes—
457C2×C5#252311yescharacteristic
458C2×C5#260011yescharacteristic
459C23—22no—
460C23—24no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—24no—
468C23—24no—
469C23—24no—
470C23—24no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23D4×Dic514yes—
482C23C2×D4×D511yescharacteristic
483C23C2×#71111yescharacteristic
484C23#414411yescharacteristic
485C23#414411yescharacteristic
486C23D5×#4112yes—
487C23D5×#4112yes—
488C23D5×#4112yes—
489C23D5×#4112yes—
490C23#414911yescharacteristic
491C23#415011yescharacteristic
492C23C23×Dic511yescharacteristic
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—58no—
518C2×C4—104no—
519C2×C4—104no—
520C2×C4—104no—
521C2×C4—104no—
522C2×C4—104no—
523C2×C4—104no—
524C2×C4—104no—
525C2×C4—104no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—104no—
529C2×C4—104no—
530C2×C4—2016no—
531C2×C4—202no—
532C2×C4—202no—
533C2×C4—202no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4—202no—
537C2×C4—202no—
538C2×C4—202no—
539C2×C4—202no—
540C2×C4—202no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4—202no—
544C2×C4—202no—
545C2×C4—202no—
546C5#1424811yescharacteristic, complemented, Sylow
547C22—28no—
548C22—24no—
549C22—42no—
550C22—44no—
551C22—42no—
552C22—44no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22#6593111yescharacteristic
559C22#6593611yescharacteristic
560C22#6593911yescharacteristic
561C22#6595111yescharacteristic
562C22#6598312yes—
563C22#6598312yes—
564C22D5×#12312yes—
565C22#6599012yes—
566C22#6599311yescharacteristic
567C22#6599512yes—
568C22#6599811yescharacteristic
569C22#6600412yes—
570C22#6601311yescharacteristic
571C22#6601311yescharacteristic
572C22#6603612yes—
573C22#6603912yes—
574C22#6604212yes—
575C22#6604312yes—
576C22C2×D4×Dic511yescharacteristic
577C22#6613211yescharacteristic
578C22#41×Dic512yes—
579C22#41×Dic512yes—
580C22#6616111yescharacteristic
581C4—44no—
582C4—42no—
583C4—44no—
584C4—42no—
585C4—108no—
586C4—204no—
587C4—204no—
588C4—402no—
589C2—44no—
590C2#1060921512yes—
591C2#1060922911yescharacteristic
592C2#1060923112yes—
593C2#1060923311yescharacteristic
594C2#1060926511yescharacteristic
595C2#1060940811yescharacteristic
596C2#1061436511yescharacteristic
597C2Dic5×#12312yes—
598C2#1061457011yescharacteristic
599C2#1061468711yescharacteristic
600C2#1061480612yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#397C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#397D5
hypocenterC5#14248
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #10602357C2semidirect
7. #10600200C2semidirect
8. #10600194C2semidirect
9. #10600194C2semidirect
19. C5×#397C4semidirect
50. C2×C5×C4⋊C4C2×C4semidirect
71. C5×#95C2×C4semidirect
72. C5×#95C2×C4semidirect
178. #397Dic5semidirect
297. C2×C4⋊C4C2×Dic5semidirect
326. #95C2×Dic5semidirect
327. #95C2×Dic5semidirect
546. C5#14248semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3972
C2×C22⋊C4×Dic52
#106023572
#106023412
#106023392
#106023372
#106002002
#106001942
#142485