Finite Group Databasebeta

← #12030450

Subgroups — #12030450

Order 1280.

1182 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65265C211yesmaximal, characteristic
2C2×#64940C211yesmaximal, characteristic
3C2×#64940C211yesmaximal, characteristic
4C5×#1444C211yesmaximal, characteristic
5#10602361C212yesmaximal
6#10602361C212yesmaximal
7#10602360C211yesmaximal, characteristic
8#10600213C211yesmaximal, characteristic
9#10600207C212yesmaximal
10#10600206C212yesmaximal
11#10600205C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2212yes—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×#683C2212yes—
16C22×#683C2212yes—
17C22×#683C2212yes—
18C22×C4×Dic5C2211yescharacteristic
19C2×C5×#95C2211yescharacteristic
20C2×C5×#95C2212yes—
21C2×C5×#95C2211yescharacteristic
22C2×#3963C2211yescharacteristic
23C2×#3963C2211yescharacteristic
24C2×#3963C2211yescharacteristic
25C2×#3963C2211yescharacteristic
26C2×#3963C2211yescharacteristic
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35#65265—24no—
36#64940—24no—
37#64940C418yescomplemented
38#14678—51nomaximal, Sylow
39C23×C4×C5C2311yescharacteristic
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×Dic5C2312yes—
45C23×Dic5C2311yescharacteristic
46C23×Dic5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—42no—
52C2×C5×C4⋊C4—42no—
53C2×C5×C4⋊C4—42no—
54C2×C5×C4⋊C4—42no—
55C2×C4⋊Dic5—22no—
56C2×C4⋊Dic5—42no—
57C2×#683—24no—
58C2×#683—24no—
59C2×#683—42no—
60C2×#683—42no—
61C2×#683—42no—
62C2×#683—42no—
63C2×#683—42no—
64C2×#683—42no—
65C2×#683—42no—
66C2×C4×Dic5C2×C414yes—
67C2×C4×Dic5D414yes—
68C2×C4×Dic5Q814yes—
69C5×#95—22no—
70C5×#95—42no—
71C5×#95C2×C414yes—
72#3963—22no—
73#3963—22no—
74#3963—22no—
75#3963—22no—
76#3963—22no—
77#3963—42no—
78#3963—42no—
79#3963—42no—
80#3963—42no—
81#3963—42no—
82#3963C2×C414yes—
83#3963C2×C418yes—
84#3963C2×C418yes—
85C2×#384—51no—
86C2×#383—51no—
87C2×#383—51no—
88#1444—51no—
89#1444—52no—
90#1444—52no—
91#1444D511yescharacteristic
92#1442—51no—
93#1442—52no—
94#1442—52no—
95#1442—51no—
96C24×C5C2411yescharacteristic
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—22no—
105C22×C4×C5—22no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—22no—
109C22×C4×C5—21no—
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—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5C22×C414yes—
123C22×C4×C5C22×C412yes—
124C22×C4×C5C2×D412yes—
125C22×C4×C5C2×Q812yes—
126C22×Dic5—22no—
127C22×Dic5—21no—
128C22×Dic5—21no—
129C22×Dic5—22no—
130C22×Dic5—21no—
131C22×Dic5—21no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
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—22no—
151C22×Dic5—22no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—22no—
155C22×Dic5C22×C414yes—
156C22×Dic5C22×C412yes—
157C22×Dic5C22×C412yes—
158C22×Dic5C2×D412yes—
159C22×Dic5C2×D412yes—
160C22×Dic5C2×Q812yes—
161C22×Dic5C2×Q812yes—
162C5×C4⋊C4—44no—
163C5×C4⋊C4—48no—
164C4⋊Dic5—44no—
165#683—48no—
166#683—48no—
167#683—48no—
168C4×Dic5C4⋊C4116yescomplemented
169C22×C4⋊C4—52no—
170C22×C4⋊C4—52no—
171C22×C4⋊C4—51no—
172C22×C4⋊C4—52no—
173C22×C4⋊C4C2×D511yescharacteristic
174C22×C4⋊C4C2×D512yes—
175C22×C42—51no—
176#384—104no—
177#383—58no—
178#383—104no—
179C2×#95—52no—
180C2×#95—52no—
181C2×#95—51no—
182C2×#95—51no—
183C2×#95—51no—
184C2×#95—51no—
185C2×#95—51no—
186C2×#95—51no—
187C2×#95—52no—
188C2×#95—52no—
189C2×#95—52no—
190C2×#95—52no—
191C2×#95—52no—
192C2×#95C2×D511yescharacteristic
193C2×#95C2×D512yes—
194C2×#95C2×D511yescharacteristic
195C23×C5C23×C411yescharacteristic
196C23×C5C22×D411yescharacteristic
197C23×C5C22×Q811yescharacteristic
198C23×C5H(5,𝔽2)12yes—
199C23×C5H(5,𝔽2)11yescharacteristic
200C23×C5H(5,𝔽2)12yes—
201C23×C5H(5,𝔽2)11yescharacteristic
202C23×C52−1+412yes—
203C23×C52−1+411yescharacteristic
204C23×C52−1+412yes—
205C23×C52−1+411yescharacteristic
206C2×C4×C5—24no—
207C2×C4×C5—22no—
208C2×C4×C5—22no—
209C2×C4×C5—24no—
210C2×C4×C5—24no—
211C2×C4×C5—24no—
212C2×C4×C5—24no—
213C2×C4×C5—42no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5C2×C4⋊C414yes—
235C2×Dic5—24no—
236C2×Dic5—22no—
237C2×Dic5—22no—
238C2×Dic5—22no—
239C2×Dic5—22no—
240C2×Dic5—22no—
241C2×Dic5—22no—
242C2×Dic5—24no—
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—24no—
246C2×Dic5—24no—
247C2×Dic5—24no—
248C2×Dic5—42no—
249C2×Dic5—42no—
250C2×Dic5—42no—
251C2×Dic5—42no—
252C2×Dic5—42no—
253C2×Dic5—42no—
254C2×Dic5—42no—
255C2×Dic5—41no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—41no—
259C2×Dic5—41no—
260C2×Dic5—41no—
261C2×Dic5—42no—
262C2×Dic5—42no—
263C2×Dic5—42no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5C2×C4⋊C414yes—
270C2×Dic5C2×C4⋊C414yes—
271C23×C4—51no—
272C23×C4—51no—
273C23×C4—52no—
274C23×C4—52no—
275C23×C4—51no—
276C23×C4—51no—
277C23×C4C22×D511yescharacteristic
278C23×C4C22×D512yes—
279C23×C4C22×D511yescharacteristic
280C23×C4C22×D512yes—
281C23×C4C22×D511yescharacteristic
282C2×C4⋊C4—22no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—104no—
288C2×C4⋊C4—104no—
289C2×C4⋊C4—102no—
290C2×C4⋊C4—202no—
291C2×C4⋊C4—202no—
292C2×C4⋊C4—202no—
293C2×C4⋊C4—202no—
294C2×C4⋊C4—202no—
295C2×C4⋊C4—202no—
296C2×C4⋊C4—202no—
297C2×C4⋊C4—202no—
298C2×C42—54no—
299C2×C42—54no—
300C2×C42—54no—
301#95—22no—
302#95—42no—
303#95—58no—
304#95—58no—
305#95—54no—
306#95—102no—
307#95—102no—
308#95—102no—
309#95—102no—
310#95—102no—
311#95—202no—
312#95—202no—
313#95—202no—
314#95—202no—
315#95—202no—
316#95C4×D514yes—
317C22×C5C22×C4⋊C411yescharacteristic
318C22×C5#52012yes—
319C22×C5#52012yes—
320C22×C5#52011yescharacteristic
321C22×C5#52011yescharacteristic
322C22×C5#53511yescharacteristic
323C22×C5#53511yescharacteristic
324C22×C5#53511yescharacteristic
325C22×C5#53611yescharacteristic
326C22×C5#53611yescharacteristic
327C22×C5#53611yescharacteristic
328C22×C5#54412yes—
329C22×C5#54411yescharacteristic
330C22×C5#54412yes—
331C22×C5#54411yescharacteristic
332C22×C5#56012yes—
333C22×C5#56012yes—
334C22×C5#56312yes—
335C22×C5#56312yes—
336C22×C5#56312yes—
337C22×C5#56312yes—
338C22×C5#56312yes—
339C22×C5#56312yes—
340C4×C5—24no—
341C4×C5—44no—
342C4×C5—82no—
343C4×C5—81no—
344C4×C5—81no—
345Dic5—24no—
346Dic5—24no—
347Dic5—44no—
348Dic5—82no—
349Dic5—81no—
350Dic5—81no—
351C24C23×D511yescharacteristic
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—52no—
378C22×C4—52no—
379C22×C4—52no—
380C22×C4—52no—
381C22×C4—52no—
382C22×C4—52no—
383C22×C4—54no—
384C22×C4—102no—
385C22×C4—101no—
386C22×C4—102no—
387C22×C4—101no—
388C22×C4—101no—
389C22×C4—101no—
390C22×C4—102no—
391C22×C4—102no—
392C22×C4—102no—
393C22×C4—102no—
394C22×C4—102no—
395C22×C4—102no—
396C22×C4—101no—
397C22×C4—101no—
398C22×C4—102no—
399C22×C4—102no—
400C22×C4—101no—
401C22×C4—102no—
402C22×C4—102no—
403C22×C4—102no—
404C22×C4—102no—
405C22×C4—102no—
406C22×C4—102no—
407C22×C4—102no—
408C22×C4—101no—
409C22×C4—101no—
410C22×C4—102no—
411C22×C4—101no—
412C22×C4—102no—
413C22×C4C2×C4×D514yes—
414C22×C4C2×C4×D512yes—
415C22×C4D4×D512yes—
416C22×C4Q8×D512yes—
417C4⋊C4—44no—
418C4⋊C4—48no—
419C4⋊C4—204no—
420C4⋊C4—208no—
421C4⋊C4—208no—
422C4⋊C4—208no—
423C42—516no—
424C2×C5#231711yescharacteristic
425C2×C5#231711yescharacteristic
426C2×C5#231711yescharacteristic
427C2×C5#238312yes—
428C2×C5#238312yes—
429C2×C5#281811yescharacteristic
430C2×C5#282111yescharacteristic
431C2×C5#282111yescharacteristic
432C2×C5#282111yescharacteristic
433C2×C5#284312yes—
434C2×C5#284312yes—
435C23C22×C4×D511yescharacteristic
436C23C2×D4×D511yescharacteristic
437C23#414412yes—
438C23#414411yescharacteristic
439C23#414412yes—
440C23C2×Q8×D511yescharacteristic
441C23#414712yes—
442C23#414711yescharacteristic
443C23#414911yescharacteristic
444C23#415012yes—
445C23#415011yescharacteristic
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—54no—
475C2×C4—54no—
476C2×C4—102no—
477C2×C4—102no—
478C2×C4—104no—
479C2×C4—102no—
480C2×C4—104no—
481C2×C4—102no—
482C2×C4—102no—
483C2×C4—102no—
484C2×C4—102no—
485C2×C4—102no—
486C2×C4—104no—
487C2×C4—104no—
488C2×C4—104no—
489C2×C4—202no—
490C2×C4—202no—
491C2×C4—202no—
492C2×C4—202no—
493C2×C4—202no—
494C2×C4—201no—
495C2×C4—201no—
496C2×C4—202no—
497C2×C4—202no—
498C2×C4—201no—
499C2×C4—202no—
500C2×C4—202no—
501C2×C4—202no—
502C2×C4—201no—
503C2×C4—202no—
504C2×C4—202no—
505C2×C4—201no—
506C2×C4—202no—
507C2×C4—202no—
508C2×C4—201no—
509C2×C4—202no—
510C2×C4D5×C4⋊C414yes—
511C5#1467811yescharacteristic, complemented, Sylow
512C22C2×D5×C4⋊C411yescharacteristic
513C22#6583812yes—
514C22#6588012yes—
515C22#6588011yescharacteristic
516C22#6590811yescharacteristic
517C22#6592611yescharacteristic
518C22#6592912yes—
519C22#6594111yescharacteristic
520C22#6595412yes—
521C22#6595712yes—
522C22#6596211yescharacteristic
523C22#6598012yes—
524C22#6598012yes—
525C22#6598012yes—
526C22#6598211yescharacteristic
527C22#6598512yes—
528C22#6602311yescharacteristic
529C22#6603312yes—
530C22#6604911yescharacteristic
531C22#6605811yescharacteristic
532C22#6606312yes—
533C22#6606311yescharacteristic
534C22#6606912yes—
535C4—24no—
536C4—44no—
537C4—82no—
538C4—81no—
539C4—81no—
540C4—104no—
541C4—104no—
542C4—204no—
543C4—402no—
544C4—401no—
545C4—401no—
546C2#1060609011yescharacteristic
547C2#1060611311yescharacteristic
548C2#1060613412yes—
549C2#1060769911yescharacteristic
550C2#1060772512yes—
551C2#1060847511yescharacteristic
552C2#1060897712yes—
553C2#1060900711yescharacteristic
554C2#1060965611yescharacteristic
555C2#1060967412yes—
556C2#1060982311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1444C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1444D5
hypocenterC5#14678
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
37. #64940C4semidirect
168. C4×Dic5C4⋊C4semidirect
511. C5#14678semidirect

Maximal subgroups

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

subgroupindex
C2×#652652
C2×#649402
C5×#14442
#106023612
#106023602
#106002132
#106002072
#106002062
#106002052
#146785