Finite Group Databasebeta

← #12021972

Subgroups — #12021972

Order 1280.

1630 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
1C2×#65261C212yesmaximal
2C2×C4⋊C4×Dic5C211yesmaximal, characteristic
3C2×#64936C212yesmaximal
4C2×#64939C211yesmaximal, characteristic
5C2×#64938C211yesmaximal, characteristic
6C5×#1444C211yesmaximal, characteristic
7#10602361C211yesmaximal, characteristic
8#10602356C212yesmaximal
9#10600213C211yesmaximal, characteristic
10#10600212C211yesmaximal, characteristic
11#10600197C212yesmaximal
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2212yes—
16C22×#683C2211yescharacteristic
17C22×#683C2211yescharacteristic
18C22×#683C2212yes—
19C22×#683C2212yes—
20C22×#683C2212yes—
21C22×C4×Dic5C2212yes—
22C22×C4×Dic5C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C2×C5×#95C2212yes—
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C4⋊C4×Dic5—24no—
36#65261—28no—
37#64939—24no—
38#64938C418yescomplemented
39#64936—28no—
40#13954—51nomaximal, Sylow
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C2×C5×C4⋊C4—22no—
53C2×C5×C4⋊C4—24no—
54C2×C5×C4⋊C4—24no—
55C2×C5×C4⋊C4—24no—
56C2×C5×C4⋊C4—42no—
57C2×C4⋊Dic5—22no—
58C2×C4⋊Dic5—24no—
59C2×C4⋊Dic5—24no—
60C2×C4⋊Dic5—24no—
61C2×C4⋊Dic5—42no—
62C2×#683—24no—
63C2×#683—24no—
64C2×#683—24no—
65C2×#683—22no—
66C2×#683—22no—
67C2×#683—24no—
68C2×#683—24no—
69C2×#683—24no—
70C2×#683—42no—
71C2×#683—42no—
72C2×#683C2×C418yes—
73C2×#683D418yes—
74C2×#683Q818yes—
75C2×C4×Dic5—24no—
76C2×C4×Dic5—24no—
77C2×C4×Dic5—24no—
78C2×C4×Dic5—42no—
79C2×C4×Dic5—42no—
80C2×C4×Dic5C2×C418yes—
81C2×C4×Dic5C2×C414yes—
82C2×C4×Dic5D414yes—
83C2×C4×Dic5Q814yes—
84C5×#95—24no—
85C5×#95—22no—
86C5×#95C2×C414yes—
87#3963—22no—
88#3963—24no—
89#3963—24no—
90#3963—22no—
91#3963—22no—
92#3963—24no—
93#3963—24no—
94#3963C2×C414yes—
95C2×#389—52no—
96C2×#389—52no—
97C2×#382—51no—
98C2×C4×C4⋊C4—51no—
99C2×C4×C4⋊C4—51no—
100#1444—51no—
101#1444—51no—
102#1444—51no—
103#1444D511yescharacteristic
104C4⋊#95—52no—
105C4⋊#95—52no—
106C24×C5C2411yescharacteristic
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—22no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
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—21no—
121C22×C4×C5—21no—
122C22×C4×C5—22no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5C22×C412yes—
130C22×C4×C5C22×C414yes—
131C22×C4×C5C2×D412yes—
132C22×C4×C5C2×D414yes—
133C22×C4×C5C2×Q812yes—
134C22×C4×C5C2×Q814yes—
135C22×C4×C5#4114yes—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—21no—
139C22×Dic5—21no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5C22×C414yes—
161C22×Dic5C22×C412yes—
162C22×Dic5C22×C412yes—
163C22×Dic5C2×D412yes—
164C22×Dic5C2×D414yes—
165C22×Dic5C2×D412yes—
166C22×Dic5C2×D414yes—
167C22×Dic5C2×Q812yes—
168C22×Dic5C2×Q814yes—
169C22×Dic5C2×Q812yes—
170C22×Dic5C2×Q814yes—
171C22×Dic5#4114yes—
172C5×C4⋊C4—28no—
173C5×C4⋊C4—48no—
174C4⋊Dic5—28no—
175C4⋊Dic5—48no—
176#683—48no—
177#683—48no—
178#683—44no—
179#683—44no—
180#683C4⋊C4132yescomplemented
181C4×Dic5—48no—
182C4×Dic5—48no—
183C4×Dic5C4⋊C4116yescomplemented
184C22×C4⋊C4—52no—
185C22×C4⋊C4—51no—
186C22×C4⋊C4—51no—
187C22×C4⋊C4—51no—
188C22×C4⋊C4—52no—
189C22×C4⋊C4—52no—
190C22×C4⋊C4—52no—
191C22×C4⋊C4C2×D511yescharacteristic
192C22×C4⋊C4C2×D512yes—
193C22×C42—51no—
194C22×C42—52no—
195C22×C42—52no—
196#389—108no—
197#389—108no—
198#382—104no—
199C4×C4⋊C4—58no—
200C4×C4⋊C4—104no—
201C2×#95—51no—
202C2×#95—52no—
203C2×#95—51no—
204C2×#95—51no—
205C2×#95—52no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—51no—
209C2×#95C2×D512yes—
210C2×#95C2×D511yescharacteristic
211C2×#95C2×D511yescharacteristic
212C23×C5C23×C411yescharacteristic
213C23×C5C22×D411yescharacteristic
214C23×C5C22×D412yes—
215C23×C5C22×Q811yescharacteristic
216C23×C5C22×Q812yes—
217C23×C5C2×#4112yes—
218C23×C5C2×#4112yes—
219C23×C5H(5,𝔽2)11yescharacteristic
220C23×C5H(5,𝔽2)11yescharacteristic
221C23×C52−1+411yescharacteristic
222C23×C52−1+411yescharacteristic
223C2×C4×C5—24no—
224C2×C4×C5—24no—
225C2×C4×C5—24no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—24no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—24no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
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—42no—
249C2×C4×C5—42no—
250C2×C4×C5C2×C4⋊C414yes—
251C2×C4×C5C2×C4⋊C418yes—
252C2×Dic5—24no—
253C2×Dic5—22no—
254C2×Dic5—24no—
255C2×Dic5—22no—
256C2×Dic5—22no—
257C2×Dic5—22no—
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—24no—
263C2×Dic5—24no—
264C2×Dic5—24no—
265C2×Dic5—24no—
266C2×Dic5—24no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—41no—
272C2×Dic5—41no—
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×Dic5C2×C4⋊C414yes—
282C2×Dic5C2×C4⋊C418yes—
283C2×Dic5C2×C4⋊C414yes—
284C2×Dic5C2×C4⋊C418yes—
285C2×Dic5#12714yes—
286C2×Dic5C4⋊Q814yes—
287C2×Dic5C4⋊Q818yes—
288C23×C4—51no—
289C23×C4—52no—
290C23×C4—51no—
291C23×C4—52no—
292C23×C4—51no—
293C23×C4—51no—
294C23×C4C22×D511yescharacteristic
295C23×C4C22×D511yescharacteristic
296C23×C4C22×D512yes—
297C23×C4C22×D512yes—
298C23×C4C22×D511yescharacteristic
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—58no—
305C2×C4⋊C4—58no—
306C2×C4⋊C4—58no—
307C2×C4⋊C4—104no—
308C2×C4⋊C4—102no—
309C2×C4⋊C4—102no—
310C2×C4⋊C4—102no—
311C2×C4⋊C4—104no—
312C2×C4⋊C4—104no—
313C2×C4⋊C4—104no—
314C2×C4⋊C4—104no—
315C2×C4⋊C4—104no—
316C2×C4⋊C4—104no—
317C2×C4⋊C4—104no—
318C2×C4⋊C4—104no—
319C2×C4⋊C4—202no—
320C2×C4⋊C4—202no—
321C2×C4⋊C4—202no—
322C2×C42—54no—
323C2×C42—54no—
324C2×C42—54no—
325C2×C42—58no—
326C2×C42—104no—
327C2×C42—104no—
328C2×C42—104no—
329C2×C42—202no—
330C2×C42—202no—
331#95—22no—
332#95—24no—
333#95—54no—
334#95—104no—
335#95—102no—
336#95—102no—
337#95—104no—
338#95—104no—
339#95—102no—
340#95—104no—
341#95C4×D514yes—
342C22×C5C22×C4⋊C411yescharacteristic
343C22×C5C22×C4⋊C412yes—
344C22×C5C4×#4112yes—
345C22×C5#51811yescharacteristic
346C22×C5#51911yescharacteristic
347C22×C5#52511yescharacteristic
348C22×C5#52511yescharacteristic
349C22×C5C2×#12711yescharacteristic
350C22×C5C2×C4⋊Q811yescharacteristic
351C22×C5C2×C4⋊Q812yes—
352C22×C5#53312yes—
353C22×C5#53711yescharacteristic
354C22×C5#53711yescharacteristic
355C22×C5#54411yescharacteristic
356C22×C5#54411yescharacteristic
357C22×C5#54612yes—
358C22×C5#54612yes—
359C22×C5#54812yes—
360C22×C5#54812yes—
361C22×C5#55412yes—
362C22×C5#55412yes—
363C22×C5#55712yes—
364C22×C5#55712yes—
365C4×C5—28no—
366C4×C5—24no—
367C4×C5—44no—
368C4×C5—81no—
369C4×C5—81no—
370Dic5—24no—
371Dic5—28no—
372Dic5—44no—
373Dic5—81no—
374Dic5—81no—
375Dic5#38418yes—
376C24C23×D511yescharacteristic
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—52no—
400C22×C4—52no—
401C22×C4—54no—
402C22×C4—52no—
403C22×C4—54no—
404C22×C4—54no—
405C22×C4—52no—
406C22×C4—52no—
407C22×C4—54no—
408C22×C4—52no—
409C22×C4—54no—
410C22×C4—54no—
411C22×C4—102no—
412C22×C4—101no—
413C22×C4—102no—
414C22×C4—101no—
415C22×C4—102no—
416C22×C4—101no—
417C22×C4—102no—
418C22×C4—101no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—101no—
426C22×C4—101no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—101no—
431C22×C4—101no—
432C22×C4—102no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4C2×C4×D512yes—
436C22×C4C2×C4×D514yes—
437C22×C4D4×D512yes—
438C22×C4D4×D514yes—
439C22×C4#71114yes—
440C22×C4Q8×D512yes—
441C22×C4Q8×D514yes—
442C4⋊C4—28no—
443C4⋊C4—48no—
444C4⋊C4—532no—
445C4⋊C4—108no—
446C4⋊C4—208no—
447C4⋊C4—208no—
448C4⋊C4—204no—
449C4⋊C4—204no—
450C4⋊C4—208no—
451C42—516no—
452C42—208no—
453C42—208no—
454C2×C5C2×#38411yescharacteristic
455C2×C5#229611yescharacteristic
456C2×C5#231611yescharacteristic
457C2×C5#234912yes—
458C2×C5#235112yes—
459C2×C5#254011yescharacteristic
460C2×C5#254011yescharacteristic
461C2×C5#255012yes—
462C2×C5#255012yes—
463C2×C5#258411yescharacteristic
464C2×C5#258411yescharacteristic
465C23C22×C4×D511yescharacteristic
466C23C2×D4×D511yescharacteristic
467C23C2×D4×D512yes—
468C23C2×#71112yes—
469C23#414411yescharacteristic
470C23C2×Q8×D512yes—
471C23C2×Q8×D511yescharacteristic
472C23#414711yescharacteristic
473C23D5×#4112yes—
474C23#414911yescharacteristic
475C23#415011yescharacteristic
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—54no—
504C2×C4—58no—
505C2×C4—54no—
506C2×C4—54no—
507C2×C4—58no—
508C2×C4—54no—
509C2×C4—58no—
510C2×C4—102no—
511C2×C4—104no—
512C2×C4—102no—
513C2×C4—104no—
514C2×C4—102no—
515C2×C4—104no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—104no—
519C2×C4—104no—
520C2×C4—104no—
521C2×C4—102no—
522C2×C4—104no—
523C2×C4—104no—
524C2×C4—104no—
525C2×C4—202no—
526C2×C4—202no—
527C2×C4—202no—
528C2×C4—202no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—202no—
533C2×C4—202no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—202no—
537C2×C4—202no—
538C2×C4—201no—
539C2×C4D5×C4⋊C414yes—
540C2×C4D5×C4⋊C418yes—
541C5#1395411yescharacteristic, complemented, Sylow
542C22C2×D5×C4⋊C411yescharacteristic
543C22C2×D5×C4⋊C412yes—
544C22C4×#71112yes—
545C22#6587911yescharacteristic
546C22#6590611yescharacteristic
547C22#6592011yescharacteristic
548C22#6592512yes—
549C22#6593212yes—
550C22#6594211yescharacteristic
551C22#6595612yes—
552C22#6596311yescharacteristic
553C22#6596712yes—
554C22#6596912yes—
555C22#6597012yes—
556C22#6598812yes—
557C22#6599011yescharacteristic
558C22#6601912yes—
559C22#6602311yescharacteristic
560C22D5×#12711yescharacteristic
561C22#6605512yes—
562C22D5×C4⋊Q812yes—
563C22D5×C4⋊Q811yescharacteristic
564C22#6606311yescharacteristic
565C4—24no—
566C4—28no—
567C4—44no—
568C4—58no—
569C4—81no—
570C4—81no—
571C4—108no—
572C4—104no—
573C4—204no—
574C4—401no—
575C4—401no—
576C2D5×#38411yescharacteristic
577C2#1060610911yescharacteristic
578C2#1060612512yes—
579C2#1060771312yes—
580C2#1060792611yescharacteristic
581C2#1060841811yescharacteristic
582C2#1060891612yes—
583C2#1060892311yescharacteristic
584C2#1060951712yes—
585C2#1060952811yescharacteristic
586C2#1060976711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1444C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1444D5
hypocenterC5#13954
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
38. #64938C4semidirect
180. #683C4⋊C4semidirect
183. C4×Dic5C4⋊C4semidirect
541. C5#13954semidirect

Maximal subgroups

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

subgroupindex
C2×#652612
C2×C4⋊C4×Dic52
C2×#649362
C2×#649392
C2×#649382
C5×#14442
#106023612
#106023562
#106002132
#106002122
#106001972
#139545