Finite Group Databasebeta

← #11994886

Subgroups — #11994886

Order 1280.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2847C211yesmaximal, characteristic
2C2×#65496C211yesmaximal, characteristic, complemented
3#10602920C211yesmaximal, characteristic, complemented
4C2×#64757C212yesmaximal, complemented
5#10598115C212yesmaximal, complemented
6C24×C4×C5C2211yescharacteristic
7C2×C5×#121C411yescharacteristic, complemented
8C2×C5×#121C411yescharacteristic, complemented
9C2×C5×#121C2211yescharacteristic
10C2×C5×#120—21no—
11C22×C22⋊Dic5—21no—
12C22×#681—21no—
13C5×#386—21no—
14C5×#386—21no—
15C5×#386—21no—
16C5×#380C411yescharacteristic, complemented
17C5×#380C411yescharacteristic, complemented
18C5×#380C2211yescharacteristic
19C2×#3963—21no—
20C2×#3963C2212yes—
21#65496—24no—
22C2×C22⋊#168—21no—
23C2×C22⋊#168C2212yes—
24#64757—24no—
25#9117—51nomaximal, Sylow
26C25×C5D411yescharacteristic
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×C5×D4C2×C411yescharacteristic
31C23×C4×C5—22no—
32C23×C4×C5—22no—
33C23×C4×C5—42no—
34C23×C4×C5—42no—
35C23×C4×C5C2×C411yescharacteristic
36C23×C4×C5C2×C411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5D411yescharacteristic
39C23×C4×C5D411yescharacteristic
40C23×C4×C5C2311yescharacteristic
41C23×Dic5—22no—
42C5×#121—22no—
43C5×#121—22no—
44C5×#121—42no—
45C5×#121—42no—
46C5×#120—44no—
47C2×C5×C4⋊C4C2×C411yescharacteristic
48C2×C5×C4⋊C4C2×C411yescharacteristic
49C2×C5×C4⋊C4C2×C411yescharacteristic
50C2×C5×C22⋊C4—21no—
51C2×C5×C22⋊C4—21no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C22⋊Dic5—24no—
57C2×C22⋊Dic5—42no—
58C2×C22⋊Dic5—42no—
59C2×#681—24no—
60C2×#681—42no—
61C2×#681—42no—
62C22×#168—22no—
63C5×#95—21no—
64C5×#95—21no—
65C5×#95—21no—
66#3963—22no—
67#3963—22no—
68#3963—42no—
69C22⋊#168—24no—
70C22⋊#168—22no—
71C22⋊#168D414yescomplemented
72C2×#407—51no—
73#2847D511yescharacteristic
74C2×#327—52no—
75C22⋊#95—51no—
76#1294—52no—
77C24×C5—22no—
78C24×C5—22no—
79C24×C5—21no—
80C24×C5—21no—
81C24×C5—22no—
82C24×C5—22no—
83C24×C5—21no—
84C24×C5—41no—
85C24×C5—41no—
86C24×C5C22⋊C411yescharacteristic
87C24×C5C22⋊C411yescharacteristic
88C24×C5C2×D411yescharacteristic
89C2×C5×D4—22no—
90C2×C5×D4—41no—
91C2×C5×D4—41no—
92C2×C5×D4—42no—
93C2×C5×D4—42no—
94C2×C5×D4—42no—
95C2×C5×D4—42no—
96C2×C5×D4—42no—
97C2×C5×D4—42no—
98C2×C5×D4—42no—
99C2×C5×D4—42no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
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—21no—
113C22×C4×C5—21no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5—41no—
124C22×C4×C5—48no—
125C22×C4×C5—48no—
126C22×C4×C5C22⋊C411yescharacteristic
127C22×C4×C5C22⋊C411yescharacteristic
128C22×C4×C5C22×C411yescharacteristic
129C22×C4×C5C2×D412yes—
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5#4112yes—
132C22×Dic5—24no—
133C22×Dic5—42no—
134C22×Dic5—42no—
135C22×Dic5—42no—
136C22×Dic5—42no—
137C22×Dic5—42no—
138C22×Dic5—42no—
139C5×C4⋊C4—22no—
140C5×C4⋊C4—41no—
141C5×C4⋊C4—41no—
142C5×C22⋊C4—42no—
143C5×C22⋊C4—42no—
144C5×C22⋊C4—42no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—41no—
148C5×C22⋊C4—41no—
149C22⋊Dic5—48no—
150#681—48no—
151C2×#168—24no—
152C2×#168—42no—
153C2×#168—42no—
154C24×C4C2×D511yescharacteristic
155C22×M16—101no—
156C2×#121Dic511yescharacteristic, complemented
157C2×#121Dic511yescharacteristic, complemented
158C2×#121C2×D511yescharacteristic
159C2×#120—21no—
160C22×C22⋊C4—101no—
161#407—104no—
162C2×C22⋊C8—52no—
163C2×C22⋊C8—101no—
164#386—21no—
165#386—21no—
166#386—21no—
167#380Dic511yescharacteristic, complemented
168#380Dic511yescharacteristic, complemented
169#380C2×D511yescharacteristic
170C2×#95—52no—
171C2×#95—101no—
172#327—104no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—24no—
178C23×C5—24no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—21no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—21no—
190C23×C5—21no—
191C23×C5—44no—
192C23×C5—44no—
193C23×C5—44no—
194C23×C5—44no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5—42no—
198C23×C5—42no—
199C23×C5—41no—
200C23×C5—41no—
201C23×C5—41no—
202C23×C5—41no—
203C23×C5—41no—
204C23×C5—41no—
205C23×C5—41no—
206C23×C5#9912yes—
207C23×C5#10412yes—
208C23×C5C2×C22⋊C411yescharacteristic
209C23×C5#12112yes—
210C23×C5AGL(1,ℤ/8)12yes—
211C23×C5AGL(1,ℤ/8)11yescharacteristic
212C23×C5#13711yescharacteristic
213C5×D4—82no—
214C5×D4—84no—
215C5×D4—84no—
216C5×D4—82no—
217C5×D4—82no—
218C2×C4×C5—24no—
219C2×C4×C5—24no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—44no—
232C2×C4×C5—44no—
233C2×C4×C5—44no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5#9912yes—
246C2×C4×C5C4×D412yes—
247C2×C4×C5#12011yescharacteristic
248C2×C4×C5#12311yescharacteristic
249C2×Dic5—44no—
250C2×Dic5—44no—
251C2×Dic5—44no—
252C2×Dic5—82no—
253C2×Dic5—82no—
254C2×Dic5—82no—
255C2×Dic5—82no—
256#168—44no—
257C25C22⋊D511yescharacteristic
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4C2×Dic511yescharacteristic
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—102no—
267C23×C4C2×Dic511yescharacteristic
268C23×C4C2×Dic511yescharacteristic
269C23×C4C22⋊D511yescharacteristic
270C23×C4C22⋊D511yescharacteristic
271C23×C4C22⋊D511yescharacteristic
272C23×C4C22×D511yescharacteristic
273C2×M16—104no—
274C2×M16—202no—
275C2×M16—202no—
276C22×C8—102no—
277#121—22no—
278#121—22no—
279#121—42no—
280#121—42no—
281#120—44no—
282C2×C4⋊C4C2×Dic511yescharacteristic
283C2×C4⋊C4C2×Dic511yescharacteristic
284C2×C4⋊C4C2×Dic511yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—104no—
292C2×C22⋊C4—202no—
293C2×C22⋊C4—202no—
294C22⋊C8—54no—
295C22⋊C8—104no—
296C22⋊C8—102no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—102no—
301#95—102no—
302#95—202no—
303C22×C5—22no—
304C22×C5—22no—
305C22×C5—21no—
306C22×C5—21no—
307C22×C5—22no—
308C22×C5—22no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—22no—
312C22×C5—22no—
313C22×C5—22no—
314C22×C5—22no—
315C22×C5—22no—
316C22×C5—22no—
317C22×C5—48no—
318C22×C5—48no—
319C22×C5—41no—
320C22×C5—41no—
321C22×C5—41no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5—41no—
327C22×C5—81no—
328C22×C5—81no—
329C22×C5—81no—
330C22×C5—81no—
331C22×C5—81no—
332C22×C5—81no—
333C22×C5—81no—
334C22×C5#38611yescharacteristic
335C22×C5C2×#9911yescharacteristic
336C22×C5C2×#9911yescharacteristic
337C22×C5#41711yescharacteristic
338C22×C5#41811yescharacteristic
339C22×C5C2×#10411yescharacteristic
340C22×C5#42111yescharacteristic
341C22×C5#46812yes—
342C22×C5#46912yes—
343C4×C5—21no—
344C4×C5—22no—
345C4×C5—21no—
346C4×C5—22no—
347C4×C5—41no—
348C4×C5—81no—
349C4×C5—81no—
350C4×C5—81no—
351Dic5—84no—
352C24—21no—
353C24—22no—
354C24—22no—
355C24—21no—
356C24—22no—
357C24—22no—
358C24—21no—
359C24—41no—
360C24—41no—
361C24C22⋊Dic511yescharacteristic
362C24C22⋊Dic511yescharacteristic
363C24C2×C22⋊D511yescharacteristic
364C2×D4—22no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—42no—
376C2×D4—41no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—48no—
400C22×C4—48no—
401C22×C4—104no—
402C22×C4—202no—
403C22×C4—202no—
404C22×C4—202no—
405C22×C4—202no—
406C22×C4—202no—
407C22×C4—202no—
408C22×C4C22⋊Dic511yescharacteristic
409C22×C4C22⋊Dic511yescharacteristic
410C22×C4D4×D512yes—
411C22×C4#71112yes—
412C22×C4C22×Dic511yescharacteristic
413C22×C4C2×C22⋊D511yescharacteristic
414M16—208no—
415C2×C8—104no—
416C2×C8—202no—
417C2×C8—202no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—208no—
429C2×C5—22no—
430C2×C5—22no—
431C2×C5—42no—
432C2×C5—42no—
433C2×C5—161no—
434C2×C5#150411yescharacteristic
435C2×C5#150711yescharacteristic
436C2×C5#151011yescharacteristic
437C2×C5#151311yescharacteristic
438C2×C5#187111yescharacteristic
439C2×C5#189511yescharacteristic
440C2×C5#189811yescharacteristic
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—24no—
446C23—24no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—44no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23#396612yes—
475C23#396912yes—
476C23#407812yes—
477C23#408512yes—
478C23#409511yescharacteristic
479C23#409711yescharacteristic
480C23C2×C22⋊Dic511yescharacteristic
481D4—82no—
482D4—84no—
483D4—84no—
484D4—82no—
485D4—82no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—204no—
514C2×C4—204no—
515C2×C4—204no—
516C2×C4—402no—
517C2×C4—402no—
518C2×C4—402no—
519C2×C4—402no—
520C2×C4#396612yes—
521C2×C4D4×Dic512yes—
522C2×C4#408111yescharacteristic
523C2×C4#408311yescharacteristic
524C8—204no—
525C5#911711yescharacteristic, complemented, Sylow
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22#6532812yes—
558C22#6533112yes—
559C22#6550411yescharacteristic
560C22C2×#396611yescharacteristic
561C22C2×#396611yescharacteristic
562C22#6550911yescharacteristic
563C22#6552111yescharacteristic
564C22C2×#396911yescharacteristic
565C22#6552511yescharacteristic
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—404no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2#1060246311yescharacteristic
581C2#1060246611yescharacteristic
582C2#1060246711yescharacteristic
583C2#1060247511yescharacteristic
584C2#1060250111yescharacteristic
585C2#1060250211yescharacteristic
586C2#1060250611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
Fitting, prime radicalC5×#2847C2
socleC23×C5C2×C22⋊C4
cosocleC23×C4×C5C23
hypercenter#2847D5
hypocenterC5#9117
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
2. C2×#65496C2semidirect
3. #10602920C2semidirect
4. C2×#64757C2semidirect
5. #10598115C2semidirect
7. C2×C5×#121C4semidirect
8. C2×C5×#121C4semidirect
16. C5×#380C4semidirect
17. C5×#380C4semidirect
71. C22⋊#168D4semidirect
156. C2×#121Dic5semidirect
157. C2×#121Dic5semidirect
167. #380Dic5semidirect
168. #380Dic5semidirect
525. C5#9117semidirect

Maximal subgroups

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

subgroupindex
C5×#28472
C2×#654962
#106029202
C2×#647572
#105981152
#91175