Finite Group Databasebeta

← #12021055

Subgroups — #12021055

Order 1280.

1790 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4033C211yesmaximal, characteristic
2C2×C4⋊C4×Dic5C211yesmaximal, characteristic
3C2×#64937C211yesmaximal, characteristic
4C5×#1441C211yesmaximal, characteristic
5#10602359C211yesmaximal, characteristic
6#10602358C211yesmaximal, characteristic
7#10600217C212yesmaximal
8#10600214C212yesmaximal
9#10600203C211yesmaximal, characteristic
10Dic5×#95C212yesmaximal
11Dic5×#95C212yesmaximal
12C23×Dic10C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×#683C2211yescharacteristic
17C22×#683C2211yescharacteristic
18C22×C4×Dic5C2212yes—
19C22×C4×Dic5C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2211yescharacteristic
23C2×#4033—24no—
24C2×#4033—24no—
25C2×#4033C418yescomplemented
26C2×C5×#95C2212yes—
27C2×C5×#95C2212yes—
28C2×C5×#95C2211yescharacteristic
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2211yescharacteristic
38C4⋊C4×Dic5—24no—
39#64937—24no—
40#13850—51nomaximal, Sylow
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C22×Dic10—22no—
53C22×Dic10—22no—
54C22×Dic10—22no—
55C22×Dic10—22no—
56C22×Dic10—22no—
57C22×Dic10—22no—
58C22×Dic10C2×C414yes—
59C2×C5×C4⋊C4—22no—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—24no—
63C2×C5×C4⋊C4C2×C414yes—
64C2×C4⋊Dic5—22no—
65C2×C4⋊Dic5—24no—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683—22no—
70C2×#683C2×C414yes—
71C2×#683C2×C414yes—
72C2×C4×Dic5—22no—
73C2×C4×Dic5—22no—
74C2×C4×Dic5—22no—
75C2×C4×Dic5—22no—
76C2×C4×Dic5—24no—
77C2×C4×Dic5—24no—
78C2×C4×Dic5—24no—
79C2×C4×Dic5—24no—
80C2×C4×Dic5—24no—
81C2×C4×Dic5C2×C414yes—
82C2×C4×Dic5C2×C414yes—
83C2×C4×Dic5C2×C414yes—
84C2×C4×Dic5D414yes—
85C2×C4×Dic5D414yes—
86C2×C4×Dic5Q818yescomplemented
87#4033—232no—
88C5×#95—22no—
89C5×#95—24no—
90C5×#95—24no—
91#3963—22no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963—24no—
96#3963—24no—
97#3963—24no—
98#3963—24no—
99#3963—24no—
100C22×C4×Q8—51no—
101C2×C4×C4⋊C4—51no—
102C2×#376—51no—
103#1446—52no—
104#1445—52no—
105#1441—51no—
106#1441—51no—
107#1441—51no—
108#1441D511yescharacteristic
109C4×#95—52no—
110C4×#95—52no—
111C24×C5C2411yescharacteristic
112C22×C4×C5—21no—
113C22×C4×C5—21no—
114C22×C4×C5—22no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
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×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5C22×C412yes—
135C22×C4×C5C22×C412yes—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C2×D412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×Q814yes—
140C22×C4×C5#4114yes—
141C22×C4×C5#4112yes—
142C22×C4×C5#4112yes—
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
147C22×Dic5—21no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—21no—
154C22×Dic5—21no—
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—
175C22×Dic5C2×Q814yes—
176C22×Dic5C2×Q814yes—
177C22×Dic5#4114yes—
178C22×Dic5#4112yes—
179C22×Dic5#4112yes—
180C22×Dic5#4114yes—
181C2×Dic10—28no—
182C2×Dic10—28no—
183C2×Dic10—28no—
184C2×Dic10—28no—
185C2×Dic10—28no—
186C2×Dic10—28no—
187C2×Dic10—28no—
188C5×C4⋊C4—28no—
189C5×C4⋊C4—28no—
190C4⋊Dic5—28no—
191#683—28no—
192#683—28no—
193C4×Dic5—28no—
194C4×Dic5—28no—
195C4×Dic5—216no—
196C4×Dic5—48no—
197C4×Dic5C22⋊C4116yes—
198C23×Q8—51no—
199C2×C4×Q8—58no—
200C2×C4×Q8—104no—
201C2×C4×Q8—104no—
202C22×C4⋊C4—51no—
203C22×C4⋊C4—51no—
204C22×C4⋊C4—51no—
205C22×C4⋊C4C2×D511yescharacteristic
206C22×C4⋊C4C2×D511yescharacteristic
207C22×C42—51no—
208C22×C42—51no—
209C22×C42—51no—
210C22×C42—52no—
211C22×C42—52no—
212C4×C4⋊C4—104no—
213#376—104no—
214C2×#95—52no—
215C2×#95—52no—
216C2×#95—52no—
217C2×#95—52no—
218C2×#95—52no—
219C2×#95—52no—
220C2×#95—51no—
221C2×#95—52no—
222C2×#95—52no—
223C2×#95C2×D512yes—
224C2×#95C2×D512yes—
225C2×#95C2×D511yescharacteristic
226C23×C5C23×C411yescharacteristic
227C23×C5C22×D411yescharacteristic
228C23×C5C22×D411yescharacteristic
229C23×C5C22×Q812yes—
230C23×C5C2×#4111yescharacteristic
231C23×C5C2×#4112yes—
232C23×C5C2×#4111yescharacteristic
233C23×C5C2×#4111yescharacteristic
234C23×C5C2×#4111yescharacteristic
235C23×C5C2×#4112yes—
236C23×C5C2×#4112yes—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—24no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—24no—
247C2×C4×C5—22no—
248C2×C4×C5—24no—
249C2×C4×C5—24no—
250C2×C4×C5—24no—
251C2×C4×C5—24no—
252C2×C4×C5—24no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—41no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—41no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5C2×C22⋊C414yes—
267C2×C4×C5#11714yes—
268C2×Dic5—22no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—24no—
284C2×Dic5—24no—
285C2×Dic5—24no—
286C2×Dic5—24no—
287C2×Dic5—24no—
288C2×Dic5—41no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—41no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5C2×C22⋊C414yes—
300C2×Dic5C2×C22⋊C414yes—
301C2×Dic5#11714yes—
302C2×Dic5C4×Q818yes—
303C2×Dic5C22⋊Q818yes—
304C2×Dic5#12414yes—
305C2×Dic5C4⋊Q814yes—
306Dic10—232no—
307C22×Q8—54no—
308C22×Q8—102no—
309C22×Q8—102no—
310C22×Q8—102no—
311C22×Q8—102no—
312C22×Q8—102no—
313C22×Q8—102no—
314C23×C4—51no—
315C23×C4—51no—
316C23×C4—51no—
317C23×C4—51no—
318C23×C4—52no—
319C23×C4—52no—
320C23×C4C22×D511yescharacteristic
321C23×C4C22×D512yes—
322C23×C4C22×D512yes—
323C23×C4C22×D511yescharacteristic
324C23×C4C22×D511yescharacteristic
325C4×Q8—1032no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—54no—
331C2×C4⋊C4—54no—
332C2×C4⋊C4—102no—
333C2×C4⋊C4—102no—
334C2×C4⋊C4—104no—
335C2×C4⋊C4—102no—
336C2×C4⋊C4—102no—
337C2×C4⋊C4—102no—
338C2×C4⋊C4C4×D514yes—
339C2×C42—54no—
340C2×C42—54no—
341C2×C42—54no—
342C2×C42—54no—
343C2×C42—54no—
344C2×C42—58no—
345C2×C42—102no—
346C2×C42—102no—
347C2×C42—102no—
348C2×C42—102no—
349C2×C42—104no—
350C2×C42—104no—
351C2×C42—104no—
352C2×C42—104no—
353C2×C42—104no—
354#95—22no—
355#95—24no—
356#95—24no—
357#95—104no—
358#95—104no—
359#95—104no—
360#95—104no—
361#95—104no—
362#95—104no—
363#95—102no—
364#95—104no—
365#95—104no—
366C22×C5C22×C22⋊C411yescharacteristic
367C22×C5C2×#11711yescharacteristic
368C22×C5C2×#11711yescharacteristic
369C22×C5C2×C4×Q812yes—
370C22×C5C4×#4112yes—
371C22×C5C2×C22⋊Q812yes—
372C22×C5#52511yescharacteristic
373C22×C5#52511yescharacteristic
374C22×C5#52511yescharacteristic
375C22×C5#52511yescharacteristic
376C22×C5#52511yescharacteristic
377C22×C5#52511yescharacteristic
378C22×C5C2×#12411yescharacteristic
379C22×C5#52912yes—
380C22×C5#52912yes—
381C22×C5#52912yes—
382C22×C5#52912yes—
383C22×C5C2×C4⋊Q811yescharacteristic
384C22×C5#53212yes—
385C22×C5#53312yes—
386C22×C5#53312yes—
387C22×C5#53312yes—
388C22×C5#53312yes—
389C4×C5—24no—
390C4×C5—24no—
391C4×C5—44no—
392C4×C5—44no—
393C4×C5—42no—
394Dic5—24no—
395Dic5—24no—
396Dic5—44no—
397Dic5—44no—
398Dic5—42no—
399Dic5#39118yes—
400C24C23×D511yescharacteristic
401C2×Q8—108no—
402C2×Q8—108no—
403C2×Q8—108no—
404C2×Q8—108no—
405C2×Q8—108no—
406C2×Q8—108no—
407C2×Q8—108no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—54no—
434C22×C4—54no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—52no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—52no—
442C22×C4—54no—
443C22×C4—54no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4C2×C4×D512yes—
469C22×C4C2×C4×D512yes—
470C22×C4C2×C4×D512yes—
471C22×C4D4×D512yes—
472C22×C4D4×D512yes—
473C22×C4#71114yes—
474C22×C4#71112yes—
475C22×C4Q8×D514yes—
476C22×C4#71312yes—
477C4⋊C4—28no—
478C4⋊C4—28no—
479C4⋊C4—108no—
480C4⋊C4—108no—
481C4⋊C4—108no—
482C42—516no—
483C42—108no—
484C42—108no—
485C42—1016no—
486C42—208no—
487C2×C5#228011yescharacteristic
488C2×C5C2×#39111yescharacteristic
489C2×C5#229512yes—
490C2×C5#229512yes—
491C2×C5#229711yescharacteristic
492C2×C5#239612yes—
493C2×C5#239612yes—
494C2×C5#239811yescharacteristic
495C2×C5#239811yescharacteristic
496C2×C5#239911yescharacteristic
497C2×C5#239911yescharacteristic
498C23C22×C4×D511yescharacteristic
499C23C2×D4×D511yescharacteristic
500C23C2×D4×D511yescharacteristic
501C23C2×#71112yes—
502C23C2×#71111yescharacteristic
503C23C2×Q8×D512yes—
504C23C2×#71311yescharacteristic
505C23D5×#4111yescharacteristic
506C23D5×#4111yescharacteristic
507C23D5×#4112yes—
508C23D5×#4112yes—
509Q8—1032no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—54no—
540C2×C4—54no—
541C2×C4—58no—
542C2×C4—58no—
543C2×C4—54no—
544C2×C4—54no—
545C2×C4—54no—
546C2×C4—102no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—102no—
558C2×C4—104no—
559C2×C4—102no—
560C2×C4—104no—
561C2×C4—104no—
562C2×C4—104no—
563C2×C4—104no—
564C2×C4—104no—
565C2×C4—104no—
566C2×C4—201no—
567C2×C4—202no—
568C2×C4—202no—
569C2×C4—202no—
570C2×C4—202no—
571C2×C4—202no—
572C2×C4—201no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4—202no—
576C2×C4—202no—
577C2×C4D5×C22⋊C414yes—
578C2×C4#403814yes—
579C5#1385011yescharacteristic, complemented, Sylow
580C22C2×D5×C22⋊C411yescharacteristic
581C22C2×#403811yescharacteristic
582C22D5×#11711yescharacteristic
583C22C4×#71112yes—
584C22C4×Q8×D512yes—
585C22#6592011yescharacteristic
586C22#6593012yes—
587C22#6593412yes—
588C22#6594011yescharacteristic
589C22#6594011yescharacteristic
590C22#6595612yes—
591C22#6595612yes—
592C22D5×C22⋊Q812yes—
593C22#6596111yescharacteristic
594C22#6596111yescharacteristic
595C22#6598312yes—
596C22#6599011yescharacteristic
597C22D5×#12411yescharacteristic
598C22#6602212yes—
599C22#6602512yes—
600C22#6604012yes—
601C22D5×C4⋊Q811yescharacteristic
602C22#6606212yes—
603C4—24no—
604C4—24no—
605C4—42no—
606C4—44no—
607C4—44no—
608C4—58no—
609C4—104no—
610C4—104no—
611C4—202no—
612C4—204no—
613C4—204no—
614C2#1060559311yescharacteristic
615C2#1060638911yescharacteristic
616C2#1060666912yes—
617C2#1060769312yes—
618C2D5×#39111yescharacteristic
619C2#1060862411yescharacteristic
620C2#1060890211yescharacteristic
621C2#1060901312yes—
622C2#1060947012yes—
623C2#1060947111yescharacteristic
624C2#1060986211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1441C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1441D5
hypocenterC5#13850
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
25. C2×#4033C4semidirect
86. C2×C4×Dic5Q8semidirect
579. C5#13850semidirect

Maximal subgroups

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

subgroupindex
C22×#40332
C2×C4⋊C4×Dic52
C2×#649372
C5×#14412
#106023592
#106023582
#106002172
#106002142
#106002032
Dic5×#952
#138505