Finite Group Databasebeta

← #12021572

Subgroups — #12021572

Order 1280.

1774 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65261C212yesmaximal
2C2×#65265C212yesmaximal
3C2×#65265C211yesmaximal, characteristic
4C2×#64936C212yesmaximal
5C2×#64938C211yesmaximal, characteristic
6C2×#64938C211yesmaximal, characteristic
7C5×#1444C211yesmaximal, characteristic
8#10602361C211yesmaximal, characteristic
9#10600213C211yesmaximal, characteristic
10#10600212C211yesmaximal, characteristic
11#10600197C212yesmaximal
12C22×C5×C4⋊C4C2212yes—
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic5C2212yes—
15C22×C4⋊Dic5C2211yescharacteristic
16C22×#683C2212yes—
17C22×#683C2212yes—
18C22×#683C2212yes—
19C22×#683C2212yes—
20C22×#683C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×#683C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2212yes—
26C22×C4×Dic5C2211yescharacteristic
27C2×C5×#95C2212yes—
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35#65265—28no—
36#65265—24no—
37#65261—28no—
38#64938—24no—
39#64938C418yescomplemented
40#64936—28no—
41#13910—51nomaximal, Sylow
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—24no—
55C2×C5×C4⋊C4—22no—
56C2×C5×C4⋊C4—42no—
57C2×C5×C4⋊C4—42no—
58C2×C4⋊Dic5—24no—
59C2×C4⋊Dic5—22no—
60C2×C4⋊Dic5—24no—
61C2×C4⋊Dic5—42no—
62C2×C4⋊Dic5—42no—
63C2×#683—22no—
64C2×#683—22no—
65C2×#683—22no—
66C2×#683—22no—
67C2×#683—24no—
68C2×#683—24no—
69C2×#683—24no—
70C2×#683—24no—
71C2×#683—24no—
72C2×#683—24no—
73C2×#683—24no—
74C2×#683—24no—
75C2×#683—24no—
76C2×#683—24no—
77C2×#683—42no—
78C2×#683—42no—
79C2×#683C2×C418yes—
80C2×#683D414yes—
81C2×#683D418yes—
82C2×#683Q814yes—
83C2×#683Q818yes—
84C2×C4×Dic5—24no—
85C2×C4×Dic5—24no—
86C2×C4×Dic5—24no—
87C2×C4×Dic5—22no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—24no—
90C2×C4×Dic5C2×C418yes—
91C2×C4×Dic5C2×C414yes—
92C2×C4×Dic5D414yes—
93C2×C4×Dic5Q814yes—
94C5×#95—24no—
95C5×#95—22no—
96C5×#95C2×C414yes—
97#3963—22no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963C2×C414yes—
102C2×#389—52no—
103C2×#389—52no—
104C2×#384—52no—
105C2×#384—51no—
106C2×C4×C4⋊C4—51no—
107C2×C4×C4⋊C4—51no—
108#1444—51no—
109#1444—51no—
110#1444—51no—
111#1444D511yescharacteristic
112C4⋊#95—52no—
113C24×C5C2411yescharacteristic
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×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
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×C414yes—
137C22×C4×C5C2×D412yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D414yes—
140C22×C4×C5C2×Q812yes—
141C22×C4×C5C2×Q812yes—
142C22×C4×C5C2×Q814yes—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—22no—
151C22×Dic5—21no—
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×Dic5C22×C414yes—
163C22×Dic5C22×C412yes—
164C22×Dic5C22×C412yes—
165C22×Dic5C2×D412yes—
166C22×Dic5C2×D414yes—
167C22×Dic5C2×D412yes—
168C22×Dic5C2×D412yes—
169C22×Dic5C2×D414yes—
170C22×Dic5C2×D412yes—
171C22×Dic5C2×Q812yes—
172C22×Dic5C2×Q814yes—
173C22×Dic5C2×Q812yes—
174C22×Dic5C2×Q812yes—
175C22×Dic5C2×Q814yes—
176C22×Dic5C2×Q812yes—
177C22×Dic5#4112yes—
178C22×Dic5#4112yes—
179C5×C4⋊C4—48no—
180C5×C4⋊C4—44no—
181C4⋊Dic5—48no—
182C4⋊Dic5—44no—
183#683—28no—
184#683—28no—
185#683—48no—
186#683—48no—
187#683—48no—
188#683—48no—
189#683C4⋊C4132yescomplemented
190C4×Dic5—216no—
191C4×Dic5—44no—
192C4×Dic5—44no—
193C4×Dic5C4⋊C4116yescomplemented
194C22×C4⋊C4—52no—
195C22×C4⋊C4—51no—
196C22×C4⋊C4—51no—
197C22×C4⋊C4—52no—
198C22×C4⋊C4—52no—
199C22×C4⋊C4—52no—
200C22×C4⋊C4—52no—
201C22×C4⋊C4—52no—
202C22×C4⋊C4—51no—
203C22×C4⋊C4C2×D512yes—
204C22×C4⋊C4C2×D511yescharacteristic
205C22×C42—51no—
206C22×C42—52no—
207C22×C42—51no—
208C22×C42—51no—
209#389—108no—
210#389—108no—
211#384—104no—
212#384—108no—
213C4×C4⋊C4—58no—
214C4×C4⋊C4—104no—
215C2×#95—51no—
216C2×#95—52no—
217C2×#95—52no—
218C2×#95—52no—
219C2×#95—51no—
220C2×#95C2×D512yes—
221C2×#95C2×D511yescharacteristic
222C2×#95C2×D511yescharacteristic
223C23×C5C23×C411yescharacteristic
224C23×C5C22×D411yescharacteristic
225C23×C5C22×D412yes—
226C23×C5C22×D411yescharacteristic
227C23×C5C22×Q811yescharacteristic
228C23×C5C22×Q812yes—
229C23×C5C22×Q811yescharacteristic
230C23×C5C2×#4111yescharacteristic
231C23×C5C2×#4111yescharacteristic
232C23×C5H(5,𝔽2)12yes—
233C23×C52−1+412yes—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—24no—
237C2×C4×C5—22no—
238C2×C4×C5—22no—
239C2×C4×C5—24no—
240C2×C4×C5—24no—
241C2×C4×C5—24no—
242C2×C4×C5—24no—
243C2×C4×C5—24no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
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×C5—42no—
261C2×C4×C5C2×C4⋊C414yes—
262C2×C4×C5C2×C4⋊C418yes—
263C2×Dic5—24no—
264C2×Dic5—24no—
265C2×Dic5—24no—
266C2×Dic5—24no—
267C2×Dic5—24no—
268C2×Dic5—24no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—24no—
272C2×Dic5—24no—
273C2×Dic5—41no—
274C2×Dic5—41no—
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×Dic5C2×C4⋊C418yes—
287C2×Dic5C2×C4⋊C414yes—
288C2×Dic5C2×C4⋊C418yes—
289C2×Dic5C2×C4⋊C414yes—
290C2×Dic5C4×D414yes—
291C2×Dic5C4×Q814yes—
292C2×Dic5#12114yes—
293C2×Dic5C22⋊Q814yes—
294C2×Dic5#12514yes—
295C2×Dic5#12714yes—
296C2×Dic5C4⋊Q814yes—
297C2×Dic5C4⋊Q818yes—
298C2×Dic5C4⋊Q814yes—
299C23×C4—51no—
300C23×C4—51no—
301C23×C4—52no—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4—52no—
305C23×C4C22×D512yes—
306C23×C4C22×D511yescharacteristic
307C23×C4C22×D511yescharacteristic
308C23×C4C22×D512yes—
309C23×C4C22×D511yescharacteristic
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—58no—
316C2×C4⋊C4—58no—
317C2×C4⋊C4—58no—
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—104no—
325C2×C4⋊C4—104no—
326C2×C4⋊C4—104no—
327C2×C4⋊C4—104no—
328C2×C4⋊C4—104no—
329C2×C4⋊C4—104no—
330C2×C4⋊C4—104no—
331C2×C4⋊C4—104no—
332C2×C4⋊C4—104no—
333C2×C4⋊C4—104no—
334C2×C4⋊C4—104no—
335C2×C4⋊C4—102no—
336C2×C4⋊C4—104no—
337C2×C4⋊C4—202no—
338C2×C4⋊C4—202no—
339C2×C4⋊C4—202no—
340C2×C4⋊C4—202no—
341C2×C42—54no—
342C2×C42—54no—
343C2×C42—54no—
344C2×C42—58no—
345C2×C42—104no—
346C2×C42—104no—
347C2×C42—102no—
348C2×C42—102no—
349C2×C42—104no—
350C2×C42—104no—
351#95—22no—
352#95—24no—
353#95—54no—
354#95—104no—
355#95—104no—
356#95—102no—
357#95—104no—
358#95C4×D514yes—
359C22×C5C22×C4⋊C411yescharacteristic
360C22×C5C22×C4⋊C412yes—
361C22×C5C2×C4×D411yescharacteristic
362C22×C5C2×C4×Q811yescharacteristic
363C22×C5#52012yes—
364C22×C5C2×#12111yescharacteristic
365C22×C5C2×C22⋊Q811yescharacteristic
366C22×C5C2×#12511yescharacteristic
367C22×C5C2×#12711yescharacteristic
368C22×C5C2×C4⋊Q811yescharacteristic
369C22×C5C2×C4⋊Q812yes—
370C22×C5C2×C4⋊Q811yescharacteristic
371C22×C5#53511yescharacteristic
372C22×C5#53611yescharacteristic
373C22×C5#54412yes—
374C22×C5D4212yes—
375C22×C5#54712yes—
376C22×C5D4×Q812yes—
377C22×C5D4×Q812yes—
378C22×C5#55012yes—
379C22×C5#55412yes—
380C22×C5#55712yes—
381C22×C5Q8212yes—
382C4×C5—24no—
383C4×C5—28no—
384C4×C5—42no—
385C4×C5—42no—
386C4×C5—82no—
387Dic5—28no—
388Dic5—42no—
389Dic5—42no—
390Dic5—82no—
391Dic5#38418yescomplemented
392Dic5#38918yescomplemented
393C24C23×D511yescharacteristic
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
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—52no—
416C22×C4—52no—
417C22×C4—52no—
418C22×C4—52no—
419C22×C4—54no—
420C22×C4—52no—
421C22×C4—52no—
422C22×C4—52no—
423C22×C4—54no—
424C22×C4—52no—
425C22×C4—52no—
426C22×C4—52no—
427C22×C4—54no—
428C22×C4—54no—
429C22×C4—54no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—102no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4C2×C4×D512yes—
452C22×C4C2×C4×D514yes—
453C22×C4D4×D512yes—
454C22×C4D4×D512yes—
455C22×C4D4×D514yes—
456C22×C4Q8×D512yes—
457C22×C4Q8×D512yes—
458C22×C4Q8×D514yes—
459C4⋊C4—48no—
460C4⋊C4—44no—
461C4⋊C4—532no—
462C4⋊C4—108no—
463C4⋊C4—108no—
464C4⋊C4—208no—
465C4⋊C4—208no—
466C4⋊C4—204no—
467C4⋊C4—208no—
468C4⋊C4—208no—
469C4⋊C4—208no—
470C42—516no—
471C42—1016no—
472C42—204no—
473C42—204no—
474C2×C5C2×#38411yescharacteristic
475C2×C5C2×#38911yescharacteristic
476C2×C5#231711yescharacteristic
477C2×C5D4×C4⋊C412yes—
478C2×C5Q8×C4⋊C412yes—
479C2×C5#254111yescharacteristic
480C2×C5#254211yescharacteristic
481C2×C5#254611yescharacteristic
482C2×C5#255112yes—
483C2×C5#255212yes—
484C2×C5#256711yescharacteristic
485C23C22×C4×D511yescharacteristic
486C23C2×D4×D512yes—
487C23C2×D4×D511yescharacteristic
488C23C2×D4×D511yescharacteristic
489C23#414412yes—
490C23C2×Q8×D511yescharacteristic
491C23C2×Q8×D512yes—
492C23C2×Q8×D511yescharacteristic
493C23D5×#4111yescharacteristic
494C23D5×#4111yescharacteristic
495C23#415012yes—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—54no—
524C2×C4—58no—
525C2×C4—54no—
526C2×C4—54no—
527C2×C4—54no—
528C2×C4—54no—
529C2×C4—58no—
530C2×C4—54no—
531C2×C4—54no—
532C2×C4—54no—
533C2×C4—54no—
534C2×C4—54no—
535C2×C4—58no—
536C2×C4—104no—
537C2×C4—104no—
538C2×C4—104no—
539C2×C4—104no—
540C2×C4—104no—
541C2×C4—104no—
542C2×C4—104no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—104no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—202no—
550C2×C4—201no—
551C2×C4—202no—
552C2×C4—202no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—202no—
558C2×C4—202no—
559C2×C4D5×C4⋊C414yes—
560C2×C4D5×C4⋊C418yes—
561C5#1391011yescharacteristic, complemented, Sylow
562C22C2×D5×C4⋊C411yescharacteristic
563C22C2×D5×C4⋊C412yes—
564C22C4×D4×D511yescharacteristic
565C22#6588012yes—
566C22C4×Q8×D511yescharacteristic
567C22#6592412yes—
568C22#6592611yescharacteristic
569C22#6593312yes—
570C22D5×#12111yescharacteristic
571C22#6595712yes—
572C22D5×C22⋊Q811yescharacteristic
573C22#6596612yes—
574C22#6596612yes—
575C22#6597012yes—
576C22#6598211yescharacteristic
577C22#6598912yes—
578C22#6601912yes—
579C22D5×#12511yescharacteristic
580C22D5×#12711yescharacteristic
581C22#6605612yes—
582C22D5×C4⋊Q812yes—
583C22D5×C4⋊Q811yescharacteristic
584C22D5×C4⋊Q811yescharacteristic
585C4—24no—
586C4—28no—
587C4—42no—
588C4—42no—
589C4—58no—
590C4—58no—
591C4—82no—
592C4—108no—
593C4—202no—
594C4—202no—
595C4—402no—
596C2D5×#38411yescharacteristic
597C2#1060611311yescharacteristic
598C2#1060612412yes—
599C2#1060771212yes—
600C2D5×#38911yescharacteristic
601C2#1060841911yescharacteristic
602C2#1060891712yes—
603C2#1060892011yescharacteristic
604C2#1060951611yescharacteristic
605C2#1060951812yes—
606C2#1060976811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1444C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1444D5
hypocenterC5#13910
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
39. #64938C4semidirect
189. #683C4⋊C4semidirect
193. C4×Dic5C4⋊C4semidirect
391. Dic5#384semidirect
392. Dic5#389semidirect
561. C5#13910semidirect

Maximal subgroups

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

subgroupindex
C2×#652612
C2×#652652
C2×#649362
C2×#649382
C5×#14442
#106023612
#106002132
#106002122
#106001972
#139105