Finite Group Databasebeta

← #12026040

Subgroups — #12026040

Order 1280.

1262 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65266C211yesmaximal, characteristic
2C2×#64940C211yesmaximal, characteristic
3C2×#64938C211yesmaximal, characteristic
4C5×#1444C211yesmaximal, characteristic
5#10602361C212yesmaximal
6#10602361C211yesmaximal, characteristic
7#10602357C212yesmaximal
8#10600208C211yesmaximal, characteristic
9#10600206C212yesmaximal
10#10600205C211yesmaximal, characteristic
11#10600199C212yesmaximal
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×#683C2211yescharacteristic
16C22×#683C2211yescharacteristic
17C22×#683C2212yes—
18C22×C4×Dic5C2211yescharacteristic
19C22×C4×Dic5C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C2×C5×#95C2211yescharacteristic
22C2×C5×#95C2212yes—
23C2×C5×#95C2211yescharacteristic
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35#65266—24no—
36#64940C418yescomplemented
37#64938—24no—
38#14298—51nomaximal, Sylow
39C23×C4×C5C2312yes—
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×Dic5C2312yes—
45C23×Dic5C2312yes—
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—24no—
52C2×C5×C4⋊C4—42no—
53C2×C5×C4⋊C4—42no—
54C2×C5×C4⋊C4—42no—
55C2×C4⋊Dic5—22no—
56C2×C4⋊Dic5—42no—
57C2×#683—22no—
58C2×#683—22no—
59C2×#683—22no—
60C2×#683—22no—
61C2×#683—22no—
62C2×#683—22no—
63C2×#683—24no—
64C2×#683—42no—
65C2×#683—42no—
66C2×C4×Dic5—22no—
67C2×C4×Dic5—22no—
68C2×C4×Dic5—42no—
69C2×C4×Dic5—42no—
70C2×C4×Dic5C2×C414yes—
71C2×C4×Dic5D414yes—
72C2×C4×Dic5Q814yes—
73C5×#95—22no—
74C5×#95—42no—
75C5×#95C2×C414yes—
76#3963—22no—
77#3963—24no—
78#3963—24no—
79#3963—24no—
80#3963—24no—
81#3963—42no—
82#3963—42no—
83#3963—42no—
84#3963C2×C414yes—
85#3963C2×C418yes—
86#3963C2×C418yes—
87C2×#383—51no—
88C2×#382—51no—
89C2×C4×C4⋊C4—51no—
90#1444—52no—
91#1444—51no—
92#1444D511yescharacteristic
93#1442—51no—
94#1442—52no—
95#1442—51no—
96#1436—52no—
97#1436—52no—
98C24×C5C2411yescharacteristic
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
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—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5C22×C414yes—
123C22×C4×C5C22×C412yes—
124C22×C4×C5C2×D412yes—
125C22×C4×C5C2×Q812yes—
126C22×C4×C5#4112yes—
127C22×C4×C5#4112yes—
128C22×Dic5—21no—
129C22×Dic5—21no—
130C22×Dic5—21no—
131C22×Dic5—21no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—21no—
135C22×Dic5—21no—
136C22×Dic5—22no—
137C22×Dic5—21no—
138C22×Dic5—21no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5C22×C414yes—
156C22×Dic5C22×C412yes—
157C22×Dic5C22×C412yes—
158C22×Dic5C2×D412yes—
159C22×Dic5C2×D412yes—
160C22×Dic5C2×Q812yes—
161C22×Dic5C2×Q812yes—
162C22×Dic5#4112yes—
163C22×Dic5#4112yes—
164C5×C4⋊C4—44no—
165C5×C4⋊C4—48no—
166C4⋊Dic5—44no—
167#683—28no—
168#683—28no—
169#683—48no—
170C4×Dic5—44no—
171C4×Dic5—44no—
172C4×Dic5C4⋊C4116yescomplemented
173C22×C4⋊C4—51no—
174C22×C4⋊C4—51no—
175C22×C4⋊C4—52no—
176C22×C4⋊C4—51no—
177C22×C4⋊C4C2×D512yes—
178C22×C4⋊C4C2×D511yescharacteristic
179C22×C42—51no—
180C22×C42—51no—
181C22×C42—51no—
182#383—58no—
183#382—104no—
184C4×C4⋊C4—104no—
185C2×#95—52no—
186C2×#95—52no—
187C2×#95—51no—
188C2×#95—52no—
189C2×#95—52no—
190C2×#95—52no—
191C2×#95—51no—
192C2×#95—52no—
193C2×#95—52no—
194C2×#95—52no—
195C2×#95—52no—
196C2×#95C2×D511yescharacteristic
197C2×#95C2×D512yes—
198C2×#95C2×D511yescharacteristic
199C23×C5C23×C411yescharacteristic
200C23×C5C22×D411yescharacteristic
201C23×C5C22×Q811yescharacteristic
202C23×C5C2×#4111yescharacteristic
203C23×C5C2×#4111yescharacteristic
204C23×C5C2×#4111yescharacteristic
205C23×C5C2×#4111yescharacteristic
206C23×C5H(5,𝔽2)12yes—
207C23×C5H(5,𝔽2)12yes—
208C23×C52−1+412yes—
209C23×C52−1+412yes—
210C2×C4×C5—24no—
211C2×C4×C5—22no—
212C2×C4×C5—22no—
213C2×C4×C5—24no—
214C2×C4×C5—24no—
215C2×C4×C5—24no—
216C2×C4×C5—24no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—24no—
220C2×C4×C5—24no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5C2×C4⋊C414yes—
239C2×Dic5—22no—
240C2×Dic5—22no—
241C2×Dic5—24no—
242C2×Dic5—22no—
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—22no—
248C2×Dic5—24no—
249C2×Dic5—24no—
250C2×Dic5—24no—
251C2×Dic5—24no—
252C2×Dic5—22no—
253C2×Dic5—22no—
254C2×Dic5—24no—
255C2×Dic5—24no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—42no—
261C2×Dic5—42no—
262C2×Dic5—42no—
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×Dic5C2×C4⋊C414yes—
274C2×Dic5C2×C4⋊C414yes—
275C23×C4—51no—
276C23×C4—51no—
277C23×C4—51no—
278C23×C4—52no—
279C23×C4—51no—
280C23×C4—52no—
281C23×C4C22×D512yes—
282C23×C4C22×D512yes—
283C23×C4C22×D511yescharacteristic
284C23×C4C22×D511yescharacteristic
285C23×C4C22×D511yescharacteristic
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—102no—
292C2×C4⋊C4—102no—
293C2×C4⋊C4—102no—
294C2×C4⋊C4—102no—
295C2×C4⋊C4—102no—
296C2×C4⋊C4—102no—
297C2×C4⋊C4—104no—
298C2×C4⋊C4—102no—
299C2×C4⋊C4—202no—
300C2×C4⋊C4—202no—
301C2×C4⋊C4—202no—
302C2×C42—54no—
303C2×C42—54no—
304C2×C42—54no—
305C2×C42—102no—
306C2×C42—102no—
307C2×C42—202no—
308C2×C42—202no—
309#95—22no—
310#95—42no—
311#95—58no—
312#95—58no—
313#95—54no—
314#95—104no—
315#95—104no—
316#95—104no—
317#95—102no—
318#95—104no—
319#95—202no—
320#95—202no—
321#95—202no—
322#95C4×D514yes—
323C22×C5C22×C4⋊C411yescharacteristic
324C22×C5C4×#4111yescharacteristic
325C22×C5C4×#4111yescharacteristic
326C22×C5#52012yes—
327C22×C5#52012yes—
328C22×C5#52511yescharacteristic
329C22×C5#52511yescharacteristic
330C22×C5#53311yescharacteristic
331C22×C5#53311yescharacteristic
332C22×C5#53511yescharacteristic
333C22×C5#53511yescharacteristic
334C22×C5#53611yescharacteristic
335C22×C5#53611yescharacteristic
336C22×C5#53812yes—
337C22×C5#53812yes—
338C22×C5#53912yes—
339C22×C5#53912yes—
340C22×C5#54112yes—
341C22×C5#54112yes—
342C22×C5#54212yes—
343C22×C5#54212yes—
344C22×C5#54412yes—
345C22×C5#54412yes—
346C4×C5—24no—
347C4×C5—44no—
348C4×C5—42no—
349C4×C5—42no—
350C4×C5—82no—
351Dic5—24no—
352Dic5—24no—
353Dic5—44no—
354Dic5—42no—
355Dic5—42no—
356Dic5—82no—
357C24C23×D511yescharacteristic
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—52no—
382C22×C4—52no—
383C22×C4—52no—
384C22×C4—52no—
385C22×C4—52no—
386C22×C4—52no—
387C22×C4—54no—
388C22×C4—52no—
389C22×C4—52no—
390C22×C4—101no—
391C22×C4—102no—
392C22×C4—101no—
393C22×C4—102no—
394C22×C4—101no—
395C22×C4—101no—
396C22×C4—101no—
397C22×C4—101no—
398C22×C4—101no—
399C22×C4—102no—
400C22×C4—102no—
401C22×C4—102no—
402C22×C4—102no—
403C22×C4—102no—
404C22×C4—102no—
405C22×C4—101no—
406C22×C4—102no—
407C22×C4—102no—
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×C4C2×C4×D514yes—
418C22×C4C2×C4×D512yes—
419C22×C4D4×D512yes—
420C22×C4#71112yes—
421C22×C4Q8×D512yes—
422C22×C4#71312yes—
423C4⋊C4—44no—
424C4⋊C4—48no—
425C4⋊C4—108no—
426C4⋊C4—108no—
427C4⋊C4—204no—
428C4⋊C4—208no—
429C42—516no—
430C42—204no—
431C42—204no—
432C2×C5#229611yescharacteristic
433C2×C5#231711yescharacteristic
434C2×C5#231711yescharacteristic
435C2×C5#233412yes—
436C2×C5#233412yes—
437C2×C5#263111yescharacteristic
438C2×C5#263211yescharacteristic
439C2×C5#263311yescharacteristic
440C2×C5#263411yescharacteristic
441C2×C5#266612yes—
442C2×C5#266612yes—
443C23C22×C4×D511yescharacteristic
444C23C2×D4×D511yescharacteristic
445C23C2×#71111yescharacteristic
446C23#414412yes—
447C23#414412yes—
448C23C2×Q8×D511yescharacteristic
449C23C2×#71311yescharacteristic
450C23#414712yes—
451C23D5×#4111yescharacteristic
452C23D5×#4111yescharacteristic
453C23#415012yes—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—54no—
483C2×C4—54no—
484C2×C4—102no—
485C2×C4—102no—
486C2×C4—102no—
487C2×C4—104no—
488C2×C4—104no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—104no—
495C2×C4—104no—
496C2×C4—104no—
497C2×C4—102no—
498C2×C4—104no—
499C2×C4—102no—
500C2×C4—104no—
501C2×C4—201no—
502C2×C4—201no—
503C2×C4—202no—
504C2×C4—201no—
505C2×C4—202no—
506C2×C4—202no—
507C2×C4—202no—
508C2×C4—202no—
509C2×C4—201no—
510C2×C4—202no—
511C2×C4—202no—
512C2×C4—202no—
513C2×C4—202no—
514C2×C4—202no—
515C2×C4—202no—
516C2×C4—202no—
517C2×C4—202no—
518C2×C4D5×C4⋊C414yes—
519C5#1429811yescharacteristic, complemented, Sylow
520C22C2×D5×C4⋊C411yescharacteristic
521C22#6583812yes—
522C22C4×#71111yescharacteristic
523C22#6588012yes—
524C22C4×#71311yescharacteristic
525C22#6592611yescharacteristic
526C22#6592712yes—
527C22#6594011yescharacteristic
528C22#6594712yes—
529C22#6595712yes—
530C22#6595912yes—
531C22#6596111yescharacteristic
532C22#6597412yes—
533C22#6597912yes—
534C22#6598211yescharacteristic
535C22#6599412yes—
536C22#6602211yescharacteristic
537C22#6603012yes—
538C22#6604911yescharacteristic
539C22#6605811yescharacteristic
540C22#6606211yescharacteristic
541C22#6606312yes—
542C22#6606712yes—
543C4—24no—
544C4—44no—
545C4—42no—
546C4—42no—
547C4—82no—
548C4—104no—
549C4—104no—
550C4—202no—
551C4—204no—
552C4—202no—
553C4—402no—
554C2#1060609011yescharacteristic
555C2#1060611311yescharacteristic
556C2#1060612012yes—
557C2#1060769411yescharacteristic
558C2#1060770712yes—
559C2#1060843211yescharacteristic
560C2#1060893411yescharacteristic
561C2#1060894412yes—
562C2#1060955411yescharacteristic
563C2#1060957212yes—
564C2#1060978211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1444C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1444D5
hypocenterC5#14298
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
36. #64940C4semidirect
172. C4×Dic5C4⋊C4semidirect
519. C5#14298semidirect

Maximal subgroups

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

subgroupindex
C2×#652662
C2×#649402
C2×#649382
C5×#14442
#106023612
#106023572
#106002082
#106002062
#106002052
#106001992
#142985