Finite Group Databasebeta

← #12030349

Subgroups — #12030349

Order 1280.

1334 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4035C211yesmaximal, characteristic
2C2×#65266C211yesmaximal, characteristic
3C2×#64939C211yesmaximal, characteristic
4C5×#1441C211yesmaximal, characteristic
5#10602359C211yesmaximal, characteristic
6#10602358C211yesmaximal, characteristic
7#10600214C212yesmaximal
8#10600214C212yesmaximal
9#10600204C212yesmaximal
10#10600203C211yesmaximal, characteristic
11#10600202C212yesmaximal
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×#683C2211yescharacteristic
17C22×#683C2211yescharacteristic
18C22×#683C2211yescharacteristic
19C22×#683C2211yescharacteristic
20C22×#683C2212yes—
21C22×C4×Dic5C2211yescharacteristic
22C2×#4035—24no—
23C2×#4035—24no—
24C2×#4035C418yescomplemented
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65266—24no—
39#64939—24no—
40#14664—51nomaximal, Sylow
41C23×C4×C5C2312yes—
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4—42no—
56C2×C5×C4⋊C4C2×C414yes—
57C2×C4⋊Dic5—22no—
58C2×C4⋊Dic5—22no—
59C2×C4⋊Dic5—22no—
60C2×C4⋊Dic5—42no—
61C2×C4⋊Dic5C2×C414yes—
62C2×#683—22no—
63C2×#683—22no—
64C2×#683—22no—
65C2×#683—22no—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—22no—
70C2×#683—24no—
71C2×#683—42no—
72C2×#683—42no—
73C2×#683C2×C414yes—
74C2×#683C2×C414yes—
75C2×#683C2×C414yes—
76C2×#683C2×C414yes—
77C2×C4×Dic5C2×C414yes—
78C2×C4×Dic5D414yes—
79C2×C4×Dic5D414yes—
80#4035—232no—
81C5×#95—22no—
82C5×#95—42no—
83C5×#95—42no—
84#3963—22no—
85#3963—24no—
86#3963—24no—
87#3963—24no—
88#3963—42no—
89#3963—42no—
90#3963—42no—
91#3963—42no—
92#3963—42no—
93#3963—42no—
94C22×#125—51no—
95C2×#382—51no—
96C2×#382—51no—
97#1445—52no—
98#1445—52no—
99#1441—52no—
100#1441—51no—
101#1441—52no—
102#1441—51no—
103#1441—51no—
104#1441D511yescharacteristic
105C24×C5C2411yescharacteristic
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5C22×C412yes—
133C22×C4×C5C22×C412yes—
134C22×C4×C5C22×C412yes—
135C22×C4×C5C2×D412yes—
136C22×C4×C5C2×D412yes—
137C22×Dic5—21no—
138C22×Dic5—21no—
139C22×Dic5—22no—
140C22×Dic5—21no—
141C22×Dic5—22no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—22no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5C22×C412yes—
168C22×Dic5C22×C412yes—
169C22×Dic5C22×C412yes—
170C22×Dic5C22×C412yes—
171C22×Dic5C2×D412yes—
172C22×Dic5C2×D412yes—
173C22×Dic5C2×D412yes—
174C22×Dic5C2×D412yes—
175C5×C4⋊C4—28no—
176C5×C4⋊C4—44no—
177C4⋊Dic5—28no—
178C4⋊Dic5—44no—
179#683—28no—
180#683—28no—
181#683—28no—
182#683—28no—
183#683—48no—
184C4×Dic5C22⋊C4116yes—
185C2×#125—58no—
186C2×#125—104no—
187C2×#125—104no—
188C22×C4⋊C4—51no—
189C22×C4⋊C4—51no—
190C22×C4⋊C4—51no—
191C22×C4⋊C4—51no—
192C22×C4⋊C4—51no—
193C22×C4⋊C4—52no—
194C22×C4⋊C4—51no—
195C22×C4⋊C4C2×D511yescharacteristic
196C22×C4⋊C4C2×D511yescharacteristic
197C22×C42—51no—
198#382—104no—
199#382—104no—
200C2×#95—52no—
201C2×#95—51no—
202C2×#95—52no—
203C2×#95—52no—
204C2×#95—52no—
205C2×#95—52no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95C2×D511yescharacteristic
211C2×#95C2×D512yes—
212C2×#95C2×D512yes—
213C23×C5C23×C411yescharacteristic
214C23×C5C22×D411yescharacteristic
215C23×C5C22×D411yescharacteristic
216C23×C5H(5,𝔽2)12yes—
217C23×C5H(5,𝔽2)11yescharacteristic
218C23×C5H(5,𝔽2)11yescharacteristic
219C23×C52−1+412yes—
220C23×C52−1+411yescharacteristic
221C23×C52−1+412yes—
222C23×C52−1+411yescharacteristic
223C23×C52−1+412yes—
224C2×C4×C5—24no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—24no—
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—24no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—42no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5C2×C22⋊C414yes—
255C2×Dic5—24no—
256C2×Dic5—22no—
257C2×Dic5—22no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—24no—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—22no—
267C2×Dic5—22no—
268C2×Dic5—22no—
269C2×Dic5—24no—
270C2×Dic5—41no—
271C2×Dic5—41no—
272C2×Dic5—41no—
273C2×Dic5—41no—
274C2×Dic5—42no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5C2×C22⋊C414yes—
292C2×Dic5C2×C22⋊C414yes—
293C23×C4—51no—
294C23×C4—51no—
295C23×C4—51no—
296C23×C4—51no—
297C23×C4—52no—
298C23×C4—52no—
299C23×C4C22×D512yes—
300C23×C4C22×D512yes—
301C23×C4C22×D511yescharacteristic
302C23×C4C22×D511yescharacteristic
303C23×C4C22×D511yescharacteristic
304#125—1032no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—54no—
310C2×C4⋊C4—54no—
311C2×C4⋊C4—54no—
312C2×C4⋊C4—54no—
313C2×C4⋊C4—54no—
314C2×C4⋊C4—102no—
315C2×C4⋊C4—102no—
316C2×C4⋊C4—102no—
317C2×C4⋊C4—102no—
318C2×C4⋊C4—102no—
319C2×C4⋊C4—102no—
320C2×C4⋊C4—102no—
321C2×C4⋊C4—102no—
322C2×C4⋊C4—102no—
323C2×C4⋊C4—102no—
324C2×C4⋊C4—104no—
325C2×C4⋊C4—102no—
326C2×C4⋊C4—202no—
327C2×C4⋊C4—202no—
328C2×C4⋊C4—202no—
329C2×C4⋊C4C4×D514yes—
330C2×C42—54no—
331C2×C42—54no—
332C2×C42—54no—
333#95—22no—
334#95—42no—
335#95—42no—
336#95—104no—
337#95—104no—
338#95—104no—
339#95—102no—
340#95—202no—
341#95—202no—
342#95—202no—
343#95—202no—
344#95—202no—
345#95—202no—
346C22×C5C22×C22⋊C411yescharacteristic
347C22×C5#51912yes—
348C22×C5#52011yescharacteristic
349C22×C5#52011yescharacteristic
350C22×C5#52012yes—
351C22×C5#53511yescharacteristic
352C22×C5#53511yescharacteristic
353C22×C5#53611yescharacteristic
354C22×C5#53612yes—
355C22×C5#53611yescharacteristic
356C22×C5#53611yescharacteristic
357C22×C5#53611yescharacteristic
358C22×C5#53712yes—
359C22×C5#53711yescharacteristic
360C22×C5#53711yescharacteristic
361C22×C5#56212yes—
362C22×C5#56212yes—
363C22×C5#56312yes—
364C22×C5#56312yes—
365C22×C5#56312yes—
366C22×C5#56312yes—
367C22×C5#56412yes—
368C22×C5#56412yes—
369C4×C5—24no—
370C4×C5—42no—
371C4×C5—42no—
372C4×C5—82no—
373C4×C5—82no—
374Dic5—24no—
375Dic5—24no—
376Dic5—42no—
377Dic5—42no—
378Dic5—82no—
379Dic5—82no—
380C24C23×D511yescharacteristic
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
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—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—52no—
408C22×C4—52no—
409C22×C4—52no—
410C22×C4—52no—
411C22×C4—52no—
412C22×C4—52no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—101no—
416C22×C4—102no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—102no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—102no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4C2×C4×D512yes—
446C22×C4C2×C4×D512yes—
447C22×C4C2×C4×D512yes—
448C22×C4D4×D512yes—
449C22×C4D4×D512yes—
450C4⋊C4—28no—
451C4⋊C4—44no—
452C4⋊C4—108no—
453C4⋊C4—108no—
454C4⋊C4—108no—
455C4⋊C4—108no—
456C4⋊C4—108no—
457C4⋊C4—204no—
458C4⋊C4—208no—
459C42—516no—
460C2×C5#231011yescharacteristic
461C2×C5#231111yescharacteristic
462C2×C5#231111yescharacteristic
463C2×C5#238212yes—
464C2×C5#238212yes—
465C2×C5#282011yescharacteristic
466C2×C5#282011yescharacteristic
467C2×C5#282012yes—
468C2×C5#282211yescharacteristic
469C2×C5#282211yescharacteristic
470C2×C5#282212yes—
471C23C22×C4×D511yescharacteristic
472C23C2×D4×D511yescharacteristic
473C23C2×D4×D511yescharacteristic
474C23#414412yes—
475C23#414411yescharacteristic
476C23#414712yes—
477C23#414711yescharacteristic
478C23#414911yescharacteristic
479C23#415011yescharacteristic
480C23#415012yes—
481C23#415012yes—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
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—42no—
512C2×C4—54no—
513C2×C4—54no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—104no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—102no—
521C2×C4—104no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—104no—
529C2×C4—201no—
530C2×C4—202no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
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—
546C2×C4—202no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—202no—
550C2×C4D5×C22⋊C414yes—
551C5#1466411yescharacteristic, complemented, Sylow
552C22C2×D5×C22⋊C411yescharacteristic
553C22#6583811yescharacteristic
554C22#6585711yescharacteristic
555C22#6588012yes—
556C22#6590612yes—
557C22#6592611yescharacteristic
558C22#6593112yes—
559C22#6594111yescharacteristic
560C22#6594211yescharacteristic
561C22#6595512yes—
562C22#6596211yescharacteristic
563C22#6596212yes—
564C22#6596311yescharacteristic
565C22#6598012yes—
566C22#6598112yes—
567C22#6598211yescharacteristic
568C22#6598512yes—
569C22#6600911yescharacteristic
570C22C5⋊#56412yes—
571C22C5⋊#56412yes—
572C22#6604612yes—
573C22#6605811yescharacteristic
574C22#6606912yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—82no—
580C4—104no—
581C4—104no—
582C4—202no—
583C4—202no—
584C4—402no—
585C4—402no—
586C2#1060573411yescharacteristic
587C2#1060639311yescharacteristic
588C2#1060671012yes—
589C2#1060772412yes—
590C2#1060834111yescharacteristic
591C2#1060881911yescharacteristic
592C2#1060900611yescharacteristic
593C2#1060913312yes—
594C2#1060965711yescharacteristic
595C2#1060965812yes—
596C2#1061004911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1441C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1441D5
hypocenterC5#14664
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
24. C2×#4035C4semidirect
551. C5#14664semidirect

Maximal subgroups

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

subgroupindex
C22×#40352
C2×#652662
C2×#649392
C5×#14412
#106023592
#106023582
#106002142
#106002042
#106002032
#106002022
#146645