Finite Group Databasebeta

← #12030434

Subgroups — #12030434

Order 1280.

1486 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65232C211yesmaximal, characteristic
2C2×#65231C212yesmaximal
3C5×#1439C211yesmaximal, characteristic
4#10602361C212yesmaximal, complemented
5#10602340C212yesmaximal
6#10602339C211yesmaximal, characteristic
7#10600213C212yesmaximal, complemented
8#10600207C212yesmaximal, complemented
9#10600206C212yesmaximal, complemented
10C24×Dic5C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C22⋊C4C2212yes—
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic5C2212yes—
15C22×C22⋊Dic5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C22×#683C2212yes—
18C22×#683C2212yes—
19C22×#683C2212yes—
20C2×C5×#95C2212yes—
21C2×C5×#95C2211yescharacteristic
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2211yescharacteristic
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31#65232C418yescomplemented
32#65231—28no—
33#14674—51nomaximal, Sylow
34C25×C5C2311yescharacteristic
35C23×C4×C5C2312yes—
36C23×C4×C5C2312yes—
37C23×C4×C5C2311yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C23×Dic5—41no—
40C23×Dic5—41no—
41C23×Dic5—41no—
42C23×Dic5—41no—
43C23×Dic5C2×C414yes—
44C23×Dic5D414yes—
45C23×Dic5Q814yes—
46C23×Dic5C2312yes—
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2312yes—
50C2×C5×C4⋊C4—41no—
51C2×C5×C4⋊C4—42no—
52C2×C5×C22⋊C4—24no—
53C2×C5×C22⋊C4—41no—
54C2×C5×C22⋊C4—41no—
55C2×C5×C22⋊C4—42no—
56C2×C5×C22⋊C4—42no—
57C2×C5×C22⋊C4C2×C414yes—
58C2×C22⋊Dic5—24no—
59C2×C22⋊Dic5—41no—
60C2×C22⋊Dic5—41no—
61C2×C22⋊Dic5—42no—
62C2×C22⋊Dic5—42no—
63C2×C22⋊Dic5C2×C414yes—
64C2×C4⋊Dic5—42no—
65C2×C4⋊Dic5—41no—
66C2×#683—24no—
67C2×#683—24no—
68C2×#683—42no—
69C2×#683—42no—
70C2×#683—42no—
71C2×#683—42no—
72C2×#683—42no—
73C2×#683—42no—
74C2×#683—42no—
75C5×#95—41no—
76C5×#95—42no—
77#3963—24no—
78#3963—24no—
79#3963—42no—
80#3963—42no—
81#3963—42no—
82#3963—42no—
83#3963—41no—
84#3963C2×C418yes—
85#3963C2×C418yes—
86C2×#381—51no—
87C2×#380—52no—
88#1444—52no—
89#1444—52no—
90#1442—52no—
91#1442—52no—
92#1439—51no—
93#1439—52no—
94#1439D511yescharacteristic
95C24×C5—22no—
96C24×C5—22no—
97C24×C5—21no—
98C24×C5—21no—
99C24×C5—21no—
100C24×C5—21no—
101C24×C5—22no—
102C24×C5—22no—
103C24×C5C22×C412yes—
104C24×C5C2×D412yes—
105C24×C5C2×Q812yes—
106C24×C5C2411yescharacteristic
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
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—22no—
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×C5C22×C412yes—
130C22×C4×C5C22×C412yes—
131C22×Dic5—22no—
132C22×Dic5—22no—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
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—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—44no—
156C22×Dic5—44no—
157C22×Dic5—44no—
158C22×Dic5—44no—
159C22×Dic5—44no—
160C22×Dic5—44no—
161C22×Dic5C4⋊C4116yescomplemented
162C22×Dic5C22×C414yes—
163C22×Dic5C22×C414yes—
164C22×Dic5C2×D414yes—
165C22×Dic5C2×Q814yes—
166C5×C4⋊C4—44no—
167C5×C22⋊C4—44no—
168C5×C22⋊C4—48no—
169C22⋊Dic5—44no—
170C22⋊Dic5—48no—
171C4⋊Dic5—44no—
172#683—48no—
173#683—48no—
174#683—48no—
175C24×C4—51no—
176C22×C4⋊C4—52no—
177C22×C4⋊C4—52no—
178C22×C4⋊C4—52no—
179C22×C4⋊C4—51no—
180C22×C4⋊C4C2×D511yescharacteristic
181C22×C22⋊C4—51no—
182C22×C22⋊C4—52no—
183C22×C22⋊C4C2×D512yes—
184C22×C22⋊C4C2×D511yescharacteristic
185#381—58no—
186#380—108no—
187C2×#95—52no—
188C2×#95—52no—
189C2×#95—52no—
190C2×#95—52no—
191C2×#95—52no—
192C2×#95—51no—
193C2×#95—52no—
194C2×#95—52no—
195C2×#95—52no—
196C2×#95C2×D511yescharacteristic
197C2×#95C2×D512yes—
198C23×C5—22no—
199C23×C5—22no—
200C23×C5—24no—
201C23×C5—24no—
202C23×C5—22no—
203C23×C5—22no—
204C23×C5—24no—
205C23×C5—24no—
206C23×C5—22no—
207C23×C5—22no—
208C23×C5—24no—
209C23×C5—24no—
210C23×C5—41no—
211C23×C5—41no—
212C23×C5—42no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5—42no—
217C23×C5—41no—
218C23×C5—41no—
219C23×C5—42no—
220C23×C5C2×C4⋊C414yes—
221C23×C5C23×C411yescharacteristic
222C23×C5C22×D411yescharacteristic
223C23×C5C22×Q811yescharacteristic
224C23×C5H(5,𝔽2)11yescharacteristic
225C23×C5H(5,𝔽2)11yescharacteristic
226C23×C5H(5,𝔽2)12yes—
227C23×C5H(5,𝔽2)12yes—
228C23×C5H(5,𝔽2)11yescharacteristic
229C23×C5H(5,𝔽2)11yescharacteristic
230C23×C52−1+412yes—
231C23×C52−1+412yes—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—41no—
237C2×C4×C5—41no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5—42no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×Dic5—24no—
257C2×Dic5—24no—
258C2×Dic5—24no—
259C2×Dic5—24no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—24no—
263C2×Dic5—24no—
264C2×Dic5—24no—
265C2×Dic5—416no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—42no—
274C2×Dic5—42no—
275C2×Dic5—42no—
276C2×Dic5—42no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5C2×C4⋊C418yes—
285C25C22×D511yescharacteristic
286C23×C4—52no—
287C23×C4—54no—
288C23×C4—54no—
289C23×C4—54no—
290C23×C4—52no—
291C23×C4—52no—
292C23×C4—52no—
293C23×C4—201no—
294C23×C4—201no—
295C23×C4—201no—
296C23×C4—201no—
297C23×C4C22×D512yes—
298C23×C4C22×D512yes—
299C23×C4C22×D511yescharacteristic
300C23×C4C22×D511yescharacteristic
301C2×C4⋊C4—42no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—104no—
304C2×C4⋊C4—104no—
305C2×C4⋊C4—202no—
306C2×C4⋊C4—202no—
307C2×C4⋊C4—202no—
308C2×C4⋊C4—202no—
309C2×C4⋊C4—202no—
310C2×C4⋊C4—202no—
311C2×C4⋊C4—202no—
312C2×C4⋊C4—202no—
313C2×C4⋊C4—201no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—54no—
320C2×C22⋊C4—104no—
321C2×C22⋊C4—201no—
322C2×C22⋊C4—201no—
323C2×C22⋊C4—202no—
324C2×C22⋊C4—202no—
325C2×C22⋊C4C4×D514yes—
326#95—41no—
327#95—42no—
328#95—58no—
329#95—58no—
330#95—104no—
331#95—104no—
332#95—201no—
333#95—202no—
334#95—202no—
335#95—202no—
336#95—202no—
337C22×C5—24no—
338C22×C5—28no—
339C22×C5—44no—
340C22×C5—42no—
341C22×C5—42no—
342C22×C5—42no—
343C22×C5—44no—
344C22×C5—42no—
345C22×C5—44no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5C22×C4⋊C411yescharacteristic
349C22×C5#51811yescharacteristic
350C22×C5#51811yescharacteristic
351C22×C5#52012yes—
352C22×C5#52012yes—
353C22×C5#53411yescharacteristic
354C22×C5#53411yescharacteristic
355C22×C5#53512yes—
356C22×C5#53612yes—
357C22×C5#54311yescharacteristic
358C22×C5#54311yescharacteristic
359C22×C5#54412yes—
360C22×C5#54412yes—
361C22×C5#56011yescharacteristic
362C22×C5#56011yescharacteristic
363C22×C5#56012yes—
364C22×C5#56212yes—
365C22×C5#56212yes—
366C22×C5#56212yes—
367C22×C5#56212yes—
368C22×C5#56311yescharacteristic
369C22×C5#56311yescharacteristic
370C22×C5#56312yes—
371C4×C5—42no—
372C4×C5—42no—
373C4×C5—82no—
374C4×C5—82no—
375Dic5—28no—
376Dic5—44no—
377Dic5—82no—
378Dic5—82no—
379C24—22no—
380C24—22no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24C2×C4×D512yes—
388C24D4×D512yes—
389C24Q8×D512yes—
390C24C23×D511yescharacteristic
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—54no—
414C22×C4—54no—
415C22×C4—54no—
416C22×C4—516no—
417C22×C4—54no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—204no—
443C22×C4—204no—
444C22×C4—204no—
445C22×C4—204no—
446C22×C4—204no—
447C22×C4—204no—
448C22×C4C2×C4×D512yes—
449C22×C4C2×C4×D512yes—
450C4⋊C4—44no—
451C4⋊C4—208no—
452C4⋊C4—208no—
453C4⋊C4—208no—
454C4⋊C4—204no—
455C22⋊C4—44no—
456C22⋊C4—48no—
457C22⋊C4—204no—
458C22⋊C4—208no—
459C2×C5—44no—
460C2×C5#231511yescharacteristic
461C2×C5#231712yes—
462C2×C5#237611yescharacteristic
463C2×C5#237612yes—
464C2×C5#237611yescharacteristic
465C2×C5#281511yescharacteristic
466C2×C5#281612yes—
467C2×C5#281711yescharacteristic
468C2×C5#284111yescharacteristic
469C2×C5#284111yescharacteristic
470C2×C5#284112yes—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—22no—
477C23—22no—
478C23—24no—
479C23—24no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—41no—
489C23—42no—
490C23—41no—
491C23—42no—
492C23—42no—
493C23D5×C4⋊C414yes—
494C23C22×C4×D511yescharacteristic
495C23C2×D4×D511yescharacteristic
496C23#414411yescharacteristic
497C23#414412yes—
498C23#414411yescharacteristic
499C23#414412yes—
500C23C2×Q8×D511yescharacteristic
501C23#414911yescharacteristic
502C23#414911yescharacteristic
503C23#415012yes—
504C23#415012yes—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
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—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—58no—
530C2×C4—104no—
531C2×C4—104no—
532C2×C4—104no—
533C2×C4—104no—
534C2×C4—104no—
535C2×C4—104no—
536C2×C4—104no—
537C2×C4—104no—
538C2×C4—104no—
539C2×C4—2016no—
540C2×C4—202no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4—202no—
544C2×C4—202no—
545C2×C4—202no—
546C2×C4—202no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—202no—
550C2×C4—202no—
551C2×C4—202no—
552C2×C4—202no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—202no—
556C2×C4—202no—
557C2×C4—202no—
558C5#1467411yescharacteristic, complemented, Sylow
559C22—28no—
560C22—24no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—42no—
565C22—42no—
566C22—44no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22#6582011yescharacteristic
571C22C2×D5×C4⋊C411yescharacteristic
572C22#6585511yescharacteristic
573C22#6588012yes—
574C22#6588012yes—
575C22#6592612yes—
576C22#6592911yescharacteristic
577C22#6593911yescharacteristic
578C22#6593911yescharacteristic
579C22#6595412yes—
580C22#6595512yes—
581C22#6595512yes—
582C22#6595712yes—
583C22#6595712yes—
584C22#6596811yescharacteristic
585C22#6596811yescharacteristic
586C22#6598212yes—
587C22#6598511yescharacteristic
588C22#6600112yes—
589C22#6600611yescharacteristic
590C22#6601812yes—
591C22#6604612yes—
592C22#6605411yescharacteristic
593C4—42no—
594C4—42no—
595C4—82no—
596C4—82no—
597C4—108no—
598C4—204no—
599C4—402no—
600C4—402no—
601C2—44no—
602C2#1060573611yescharacteristic
603C2#1060611312yes—
604C2#1060641311yescharacteristic
605C2#1060722012yes—
606C2#1060804011yescharacteristic
607C2#1060847411yescharacteristic
608C2#1060859211yescharacteristic
609C2#1060881712yes—
610C2#1060914312yes—
611C2#1060937711yescharacteristic
612C2#1060983011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1439C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenter#1439D5
hypocenterC5#14674
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. #10602361C2semidirect
7. #10600213C2semidirect
8. #10600207C2semidirect
9. #10600206C2semidirect
31. #65232C4semidirect
161. C22×Dic5C4⋊C4semidirect
558. C5#14674semidirect

Maximal subgroups

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

subgroupindex
C2×#652322
C2×#652312
C5×#14392
#106023612
#106023402
#106023392
#106002132
#106002072
#106002062
#146745