Finite Group Databasebeta

← #12025903

Subgroups — #12025903

Order 1280.

1502 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4035C211yesmaximal, characteristic
2C2×#65265C211yesmaximal, characteristic
3C2×#64937C211yesmaximal, characteristic
4C5×#1441C211yesmaximal, characteristic
5#10602359C211yesmaximal, characteristic
6#10602358C211yesmaximal, characteristic
7#10600204C212yesmaximal
8#10600203C211yesmaximal, characteristic
9#10600202C212yesmaximal
10#10600197C212yesmaximal
11#10600197C212yesmaximal
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×#683C2212yes—
17C22×#683C2211yescharacteristic
18C22×#683C2211yescharacteristic
19C22×#683C2211yescharacteristic
20C22×#683C2211yescharacteristic
21C22×#683C2212yes—
22C22×C4×Dic5C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C2×#4035—24no—
25C2×#4035—24no—
26C2×#4035C418yescomplemented
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65265—24no—
39#64937—24no—
40#14283—51nomaximal, Sylow
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2312yes—
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—24no—
72C2×#683—24no—
73C2×#683—24no—
74C2×#683—42no—
75C2×#683—42no—
76C2×#683C2×C414yes—
77C2×#683C2×C414yes—
78C2×#683C2×C414yes—
79C2×#683C2×C414yes—
80C2×C4×Dic5—24no—
81C2×C4×Dic5—24no—
82C2×C4×Dic5C2×C414yes—
83C2×C4×Dic5D414yes—
84C2×C4×Dic5D414yes—
85C2×C4×Dic5Q818yes—
86#4035—232no—
87C5×#95—22no—
88C5×#95—42no—
89C5×#95—42no—
90#3963—22no—
91#3963—24no—
92#3963—42no—
93#3963—42no—
94#3963—42no—
95#3963—42no—
96#3963—42no—
97#3963—42no—
98C22×#125—51no—
99C2×#384—51no—
100C2×#376—51no—
101#1441—52no—
102#1441—51no—
103#1441—52no—
104#1441—51no—
105#1441—51no—
106#1441D511yescharacteristic
107C4⋊#95—52no—
108C4⋊#95—52no—
109C24×C5C2411yescharacteristic
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—22no—
117C22×C4×C5—22no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
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×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5C22×C412yes—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C22×C412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×Q814yes—
141C22×Dic5—21no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—22no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5—22no—
154C22×Dic5—21no—
155C22×Dic5—22no—
156C22×Dic5—21no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—21no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5C22×C412yes—
169C22×Dic5C22×C412yes—
170C22×Dic5C22×C412yes—
171C22×Dic5C22×C412yes—
172C22×Dic5C2×D412yes—
173C22×Dic5C2×D412yes—
174C22×Dic5C2×D412yes—
175C22×Dic5C2×D412yes—
176C22×Dic5C2×Q814yes—
177C22×Dic5C2×Q814yes—
178C22×Dic5#4114yes—
179C5×C4⋊C4—28no—
180C5×C4⋊C4—44no—
181C4⋊Dic5—28no—
182C4⋊Dic5—44no—
183#683—28no—
184#683—28no—
185#683—28no—
186#683—28no—
187#683—48no—
188#683—48no—
189C4×Dic5—216no—
190C4×Dic5C22⋊C4116yes—
191C2×#125—58no—
192C2×#125—104no—
193C2×#125—104no—
194C22×C4⋊C4—51no—
195C22×C4⋊C4—51no—
196C22×C4⋊C4—51no—
197C22×C4⋊C4—51no—
198C22×C4⋊C4—51no—
199C22×C4⋊C4—52no—
200C22×C4⋊C4—52no—
201C22×C4⋊C4—51no—
202C22×C4⋊C4C2×D511yescharacteristic
203C22×C4⋊C4C2×D511yescharacteristic
204C22×C42—51no—
205C22×C42—52no—
206#384—104no—
207#376—104no—
208C2×#95—52no—
209C2×#95—51no—
210C2×#95—52no—
211C2×#95—52no—
212C2×#95—52no—
213C2×#95—52no—
214C2×#95—52no—
215C2×#95—52no—
216C2×#95C2×D511yescharacteristic
217C2×#95C2×D512yes—
218C2×#95C2×D512yes—
219C23×C5C23×C411yescharacteristic
220C23×C5C22×D411yescharacteristic
221C23×C5C22×D411yescharacteristic
222C23×C5C22×Q812yes—
223C23×C5C2×#4112yes—
224C23×C5H(5,𝔽2)12yes—
225C23×C5H(5,𝔽2)11yescharacteristic
226C23×C5H(5,𝔽2)11yescharacteristic
227C23×C52−1+411yescharacteristic
228C23×C52−1+411yescharacteristic
229C23×C52−1+412yes—
230C2×C4×C5—24no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—24no—
239C2×C4×C5—24no—
240C2×C4×C5—24no—
241C2×C4×C5—24no—
242C2×C4×C5—41no—
243C2×C4×C5—41no—
244C2×C4×C5—41no—
245C2×C4×C5—41no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—41no—
249C2×C4×C5—42no—
250C2×C4×C5—41no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5C2×C22⋊C414yes—
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—22no—
270C2×Dic5—22no—
271C2×Dic5—24no—
272C2×Dic5—24no—
273C2×Dic5—24no—
274C2×Dic5—24no—
275C2×Dic5—41no—
276C2×Dic5—41no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—41no—
282C2×Dic5—41no—
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×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5C2×C22⋊C414yes—
294C2×Dic5C2×C22⋊C414yes—
295C2×Dic5C4×Q818yes—
296C2×Dic5C22⋊Q818yes—
297C2×Dic5#12414yes—
298C2×Dic5C4⋊Q814yes—
299C23×C4—51no—
300C23×C4—51no—
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—52no—
304C23×C4—52no—
305C23×C4C22×D512yes—
306C23×C4C22×D511yescharacteristic
307C23×C4C22×D511yescharacteristic
308C23×C4C22×D512yes—
309C23×C4C22×D511yescharacteristic
310#125—1032no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—54no—
316C2×C4⋊C4—54no—
317C2×C4⋊C4—54no—
318C2×C4⋊C4—54no—
319C2×C4⋊C4—54no—
320C2×C4⋊C4—102no—
321C2×C4⋊C4—102no—
322C2×C4⋊C4—102no—
323C2×C4⋊C4—102no—
324C2×C4⋊C4—102no—
325C2×C4⋊C4—102no—
326C2×C4⋊C4—102no—
327C2×C4⋊C4—102no—
328C2×C4⋊C4—102no—
329C2×C4⋊C4—102no—
330C2×C4⋊C4—104no—
331C2×C4⋊C4—104no—
332C2×C4⋊C4—104no—
333C2×C4⋊C4—104no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—202no—
336C2×C4⋊C4—202no—
337C2×C4⋊C4—202no—
338C2×C4⋊C4C4×D514yes—
339C2×C42—54no—
340C2×C42—54no—
341C2×C42—54no—
342C2×C42—58no—
343C2×C42—104no—
344C2×C42—104no—
345#95—22no—
346#95—42no—
347#95—42no—
348#95—104no—
349#95—102no—
350#95—202no—
351#95—202no—
352#95—202no—
353#95—202no—
354#95—202no—
355#95—202no—
356C22×C5C22×C22⋊C411yescharacteristic
357C22×C5C2×C4×Q812yes—
358C22×C5#52011yescharacteristic
359C22×C5#52011yescharacteristic
360C22×C5#52012yes—
361C22×C5C2×C22⋊Q812yes—
362C22×C5C2×#12411yescharacteristic
363C22×C5C2×C4⋊Q811yescharacteristic
364C22×C5#53511yescharacteristic
365C22×C5#53511yescharacteristic
366C22×C5#53611yescharacteristic
367C22×C5#53611yescharacteristic
368C22×C5#53712yes—
369C22×C5#53711yescharacteristic
370C22×C5#53711yescharacteristic
371C22×C5#54012yes—
372C22×C5#54012yes—
373C22×C5#54112yes—
374C22×C5#54112yes—
375C22×C5#54412yes—
376C22×C5#54412yes—
377C22×C5#54412yes—
378C22×C5#54412yes—
379C4×C5—24no—
380C4×C5—42no—
381C4×C5—42no—
382C4×C5—44no—
383C4×C5—82no—
384Dic5—24no—
385Dic5—42no—
386Dic5—42no—
387Dic5—44no—
388Dic5—82no—
389Dic5#39118yes—
390C24C23×D511yescharacteristic
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—52no—
417C22×C4—52no—
418C22×C4—52no—
419C22×C4—54no—
420C22×C4—54no—
421C22×C4—52no—
422C22×C4—52no—
423C22×C4—52no—
424C22×C4—52no—
425C22×C4—52no—
426C22×C4—54no—
427C22×C4—101no—
428C22×C4—101no—
429C22×C4—101no—
430C22×C4—101no—
431C22×C4—102no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—102no—
437C22×C4—101no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—101no—
441C22×C4—102no—
442C22×C4—101no—
443C22×C4—102no—
444C22×C4—101no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4C2×C4×D512yes—
455C22×C4C2×C4×D512yes—
456C22×C4C2×C4×D512yes—
457C22×C4D4×D512yes—
458C22×C4D4×D512yes—
459C22×C4Q8×D514yes—
460C4⋊C4—28no—
461C4⋊C4—44no—
462C4⋊C4—108no—
463C4⋊C4—108no—
464C4⋊C4—108no—
465C4⋊C4—108no—
466C4⋊C4—108no—
467C4⋊C4—204no—
468C4⋊C4—208no—
469C4⋊C4—208no—
470C42—516no—
471C42—1016no—
472C2×C5C2×#39111yescharacteristic
473C2×C5#231111yescharacteristic
474C2×C5#231111yescharacteristic
475C2×C5#233012yes—
476C2×C5#233012yes—
477C2×C5#262912yes—
478C2×C5#262912yes—
479C2×C5#264111yescharacteristic
480C2×C5#264211yescharacteristic
481C2×C5#266011yescharacteristic
482C2×C5#266011yescharacteristic
483C23C22×C4×D511yescharacteristic
484C23C2×D4×D511yescharacteristic
485C23C2×D4×D511yescharacteristic
486C23#414412yes—
487C23#414411yescharacteristic
488C23C2×Q8×D512yes—
489C23#414711yescharacteristic
490C23D5×#4112yes—
491C23#414911yescharacteristic
492C23#415011yescharacteristic
493C23#415012yes—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—54no—
525C2×C4—54no—
526C2×C4—58no—
527C2×C4—58no—
528C2×C4—54no—
529C2×C4—54no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—102no—
535C2×C4—102no—
536C2×C4—104no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—104no—
542C2×C4—104no—
543C2×C4—104no—
544C2×C4—201no—
545C2×C4—202no—
546C2×C4—202no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—202no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—202no—
558C2×C4—202no—
559C2×C4—202no—
560C2×C4—202no—
561C2×C4—202no—
562C2×C4D5×C22⋊C414yes—
563C5#1428311yescharacteristic, complemented, Sylow
564C22C2×D5×C22⋊C411yescharacteristic
565C22#6583811yescharacteristic
566C22#6585711yescharacteristic
567C22#6588012yes—
568C22C4×Q8×D512yes—
569C22#6592611yescharacteristic
570C22#6593112yes—
571C22#6594111yescharacteristic
572C22#6594211yescharacteristic
573C22#6594912yes—
574C22#6595712yes—
575C22#6595712yes—
576C22D5×C22⋊Q812yes—
577C22#6596211yescharacteristic
578C22#6596311yescharacteristic
579C22#6598211yescharacteristic
580C22#6599712yes—
581C22D5×#12411yescharacteristic
582C22#6602312yes—
583C22#6603012yes—
584C22#6603512yes—
585C22D5×C4⋊Q811yescharacteristic
586C22#6606312yes—
587C4—24no—
588C4—42no—
589C4—42no—
590C4—44no—
591C4—58no—
592C4—82no—
593C4—104no—
594C4—202no—
595C4—204no—
596C4—202no—
597C4—402no—
598C2#1060573411yescharacteristic
599C2#1060639311yescharacteristic
600C2#1060668012yes—
601C2#1060770412yes—
602C2D5×#39111yescharacteristic
603C2#1060871511yescharacteristic
604C2#1060893911yescharacteristic
605C2#1060906312yes—
606C2#1060955112yes—
607C2#1060956811yescharacteristic
608C2#1060994511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1441C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1441D5
hypocenterC5#14283
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
26. C2×#4035C4semidirect
563. C5#14283semidirect

Maximal subgroups

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

subgroupindex
C22×#40352
C2×#652652
C2×#649372
C5×#14412
#106023592
#106023582
#106002042
#106002032
#106002022
#106001972
#142835