Finite Group Databasebeta

← #12021374

Subgroups — #12021374

Order 1280.

1442 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#382C211yesmaximal, characteristic
2C2×#65267C212yesmaximal
3C2×C4×#683C211yesmaximal, characteristic
4C2×#64938C211yesmaximal, characteristic
5#10602361C212yesmaximal
6#10602327C211yesmaximal, characteristic
7#10600202C212yesmaximal
8#10600199C212yesmaximal
9#10600197C211yesmaximal, characteristic
10#10600195C211yesmaximal, characteristic
11#10600194C211yesmaximal, characteristic
12C22×C5×C4⋊C4C2212yes—
13C22×C42×C5C2211yescharacteristic
14C22×#683C2212yes—
15C22×#683C2212yes—
16C22×#683C2211yescharacteristic
17C22×#683C2211yescharacteristic
18C22×C4×Dic5C2212yes—
19C22×C4×Dic5C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C5×#382—24no—
22C2×C5×#95C2211yescharacteristic
23C2×C5×#95C2212yes—
24C2×C5×#95C2211yescharacteristic
25C2×#3963C2211yescharacteristic
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36#65267—28no—
37C4×#683C418yescomplemented
38#64938—24no—
39#13889—51nomaximal, Sylow
40C23×C4×C5C2312yes—
41C23×C4×C5C2311yescharacteristic
42C23×C4×C5C2312yes—
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×Dic5C2312yes—
46C23×Dic5C2312yes—
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C2×C5×C4⋊C4—24no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—42no—
54C2×C42×C5—22no—
55C2×C42×C5—22no—
56C2×C42×C5C2×C414yes—
57C2×#683—24no—
58C2×#683—24no—
59C2×#683—24no—
60C2×#683—24no—
61C2×#683—24no—
62C2×#683—24no—
63C2×#683—42no—
64C2×#683C2×C414yes—
65C2×#683C2×C414yes—
66C2×#683D414yes—
67C2×#683Q814yes—
68C2×C4×Dic5—22no—
69C2×C4×Dic5—22no—
70C2×C4×Dic5—24no—
71C2×C4×Dic5—24no—
72C2×C4×Dic5—24no—
73C2×C4×Dic5—42no—
74C2×C4×Dic5C2×C414yes—
75C2×C4×Dic5C2×C414yes—
76C5×#95—24no—
77C5×#95—22no—
78C5×#95D414yes—
79#3963—22no—
80#3963—24no—
81#3963—22no—
82#3963—24no—
83#3963—24no—
84#3963—24no—
85#3963—24no—
86#3963—24no—
87#3963—24no—
88#3963C2×C414yes—
89#3963C2×C414yes—
90C2×#387—52no—
91C2×#382D511yescharacteristic
92C2×C4×C4⋊C4—51no—
93C2×C4×C4⋊C4—51no—
94#1444—52no—
95#1441—52no—
96#1436—52no—
97C4⋊#95—51no—
98#1434—51no—
99#1434—51no—
100#1434—51no—
101C24×C5C2411yescharacteristic
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—22no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—21no—
109C22×C4×C5—22no—
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×C5C22×C412yes—
126C22×C4×C5C22×C412yes—
127C22×C4×C5C22×C412yes—
128C22×C4×C5C2×D412yes—
129C22×C4×C5C2×D414yes—
130C22×C4×C5C2×D412yes—
131C22×C4×C5C2×Q812yes—
132C22×C4×C5#4112yes—
133C22×Dic5—21no—
134C22×Dic5—21no—
135C22×Dic5—21no—
136C22×Dic5—21no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—21no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—21no—
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—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5C22×C412yes—
159C22×Dic5C22×C412yes—
160C22×Dic5C22×C412yes—
161C22×Dic5C22×C412yes—
162C22×Dic5C2×D412yes—
163C22×Dic5C2×D412yes—
164C22×Dic5C2×Q812yes—
165C22×Dic5C2×Q812yes—
166C22×Dic5#4114yes—
167C22×Dic5#4114yes—
168C22×Dic5#4114yes—
169C5×C4⋊C4—48no—
170C42×C5—28no—
171#683—216no—
172#683—28no—
173#683—48no—
174#683C4⋊C4116yescomplemented
175C4×Dic5—28no—
176C4×Dic5—28no—
177C4×Dic5—48no—
178C22×C4⋊C4—51no—
179C22×C4⋊C4—51no—
180C22×C4⋊C4—52no—
181C22×C4⋊C4—52no—
182C22×C4⋊C4C2×D512yes—
183C22×C42—51no—
184C22×C42—51no—
185C22×C42—52no—
186C22×C42C2×D511yescharacteristic
187#387—108no—
188#382—24no—
189C4×C4⋊C4—58no—
190C4×C4⋊C4—104no—
191C2×#95—51no—
192C2×#95—51no—
193C2×#95—51no—
194C2×#95—51no—
195C2×#95—52no—
196C2×#95—52no—
197C2×#95—52no—
198C2×#95—52no—
199C2×#95—52no—
200C2×#95—52no—
201C2×#95—52no—
202C2×#95C2×D511yescharacteristic
203C2×#95C2×D512yes—
204C2×#95C2×D511yescharacteristic
205C23×C5C23×C411yescharacteristic
206C23×C5C22×D411yescharacteristic
207C23×C5C22×D411yescharacteristic
208C23×C5C22×Q811yescharacteristic
209C23×C5C2×#4111yescharacteristic
210C23×C5C2×#4112yes—
211C23×C5C2×#4112yes—
212C23×C5C2×#4112yes—
213C23×C5H(5,𝔽2)11yescharacteristic
214C23×C52−1+411yescharacteristic
215C23×C52−1+412yes—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—24no—
223C2×C4×C5—22no—
224C2×C4×C5—24no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—22no—
229C2×C4×C5—24no—
230C2×C4×C5—24no—
231C2×C4×C5—24no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5C2×C4⋊C414yes—
246C2×C4×C5C4×D414yes—
247C2×Dic5—22no—
248C2×Dic5—22no—
249C2×Dic5—22no—
250C2×Dic5—22no—
251C2×Dic5—22no—
252C2×Dic5—22no—
253C2×Dic5—22no—
254C2×Dic5—22no—
255C2×Dic5—24no—
256C2×Dic5—24no—
257C2×Dic5—24no—
258C2×Dic5—24no—
259C2×Dic5—22no—
260C2×Dic5—22no—
261C2×Dic5—22no—
262C2×Dic5—24no—
263C2×Dic5—24no—
264C2×Dic5—22no—
265C2×Dic5—24no—
266C2×Dic5—24no—
267C2×Dic5—24no—
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×Dic5C2×C4⋊C414yes—
280C2×Dic5C2×C4⋊C414yes—
281C2×Dic5#11714yes—
282C2×Dic5#11714yes—
283C23×C4—51no—
284C23×C4—51no—
285C23×C4—51no—
286C23×C4—51no—
287C23×C4—52no—
288C23×C4—52no—
289C23×C4C22×D512yes—
290C23×C4C22×D511yescharacteristic
291C23×C4C22×D512yes—
292C23×C4C22×D511yescharacteristic
293C23×C4C22×D511yescharacteristic
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—54no—
298C2×C4⋊C4—54no—
299C2×C4⋊C4—54no—
300C2×C4⋊C4—54no—
301C2×C4⋊C4—104no—
302C2×C4⋊C4—104no—
303C2×C4⋊C4—104no—
304C2×C4⋊C4—104no—
305C2×C4⋊C4—104no—
306C2×C4⋊C4—104no—
307C2×C4⋊C4—202no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—54no—
311C2×C42—54no—
312C2×C42—104no—
313C2×C42—102no—
314C2×C42—102no—
315C2×C42—104no—
316C2×C42—104no—
317C2×C42—202no—
318C2×C42C4×D514yes—
319#95—24no—
320#95—22no—
321#95—54no—
322#95—54no—
323#95—104no—
324#95—104no—
325#95—104no—
326#95—104no—
327#95—104no—
328#95—104no—
329#95—102no—
330#95—104no—
331#95—102no—
332#95C22⋊D514yes—
333C22×C5C22×C4⋊C411yescharacteristic
334C22×C5C2×#11711yescharacteristic
335C22×C5C2×#11711yescharacteristic
336C22×C5C2×C4×D411yescharacteristic
337C22×C5C4×#4111yescharacteristic
338C22×C5#51911yescharacteristic
339C22×C5#52011yescharacteristic
340C22×C5#52512yes—
341C22×C5#52912yes—
342C22×C5#53212yes—
343C22×C5#53312yes—
344C22×C5#54112yes—
345C22×C5#54212yes—
346C22×C5D4211yescharacteristic
347C22×C5#54711yescharacteristic
348C22×C5#54712yes—
349C22×C5#54812yes—
350C22×C5D4×Q811yescharacteristic
351C22×C5#55112yes—
352C22×C5#55212yes—
353C22×C5#55212yes—
354C22×C5#55411yescharacteristic
355C22×C5#55712yes—
356C4×C5—24no—
357C4×C5—24no—
358C4×C5—44no—
359C4×C5—42no—
360C4×C5—82no—
361Dic5—24no—
362Dic5—24no—
363Dic5—24no—
364Dic5—24no—
365Dic5—44no—
366Dic5—82no—
367C24C23×D511yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—52no—
392C22×C4—52no—
393C22×C4—52no—
394C22×C4—52no—
395C22×C4—52no—
396C22×C4—52no—
397C22×C4—52no—
398C22×C4—52no—
399C22×C4—54no—
400C22×C4—54no—
401C22×C4—54no—
402C22×C4—101no—
403C22×C4—101no—
404C22×C4—101no—
405C22×C4—101no—
406C22×C4—101no—
407C22×C4—101no—
408C22×C4—102no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—101no—
413C22×C4—101no—
414C22×C4—102no—
415C22×C4—102no—
416C22×C4—102no—
417C22×C4—102no—
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×C4C2×C4×D512yes—
428C22×C4C2×C4×D512yes—
429C22×C4C2×C4×D512yes—
430C22×C4#70912yes—
431C22×C4D4×D512yes—
432C22×C4Q8×D512yes—
433C22×C4C2×C22⋊D514yes—
434C22×C4C2×C22⋊D512yes—
435C4⋊C4—48no—
436C4⋊C4—516no—
437C4⋊C4—108no—
438C4⋊C4—1016no—
439C4⋊C4—208no—
440C42—28no—
441C42—108no—
442C42—108no—
443C42—208no—
444C2×C5#228511yescharacteristic
445C2×C5#229011yescharacteristic
446C2×C5#232011yescharacteristic
447C2×C5#234311yescharacteristic
448C2×C5#234411yescharacteristic
449C2×C5D4×C4⋊C411yescharacteristic
450C2×C5#235111yescharacteristic
451C2×C5#246112yes—
452C2×C5#246212yes—
453C2×C5#251912yes—
454C2×C5#252012yes—
455C23C22×C4×D511yescharacteristic
456C23C2×#70911yescharacteristic
457C23C2×D4×D511yescharacteristic
458C23#414411yescharacteristic
459C23C2×Q8×D511yescharacteristic
460C23#414711yescharacteristic
461C23D5×#4112yes—
462C23D5×#4112yes—
463C23D5×#4112yes—
464C23#415012yes—
465C23C22×C22⋊D511yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—54no—
496C2×C4—54no—
497C2×C4—54no—
498C2×C4—54no—
499C2×C4—102no—
500C2×C4—102no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—102no—
505C2×C4—102no—
506C2×C4—102no—
507C2×C4—104no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—102no—
511C2×C4—102no—
512C2×C4—104no—
513C2×C4—104no—
514C2×C4—104no—
515C2×C4—104no—
516C2×C4—104no—
517C2×C4—104no—
518C2×C4—104no—
519C2×C4—104no—
520C2×C4—202no—
521C2×C4—202no—
522C2×C4—202no—
523C2×C4—202no—
524C2×C4—202no—
525C2×C4—202no—
526C2×C4—202no—
527C2×C4—202no—
528C2×C4—202no—
529C2×C4—202no—
530C2×C4—202no—
531C2×C4D5×C4⋊C414yes—
532C2×C4C4×C22⋊D514yes—
533C5#1388911yescharacteristic, complemented, Sylow
534C22C2×D5×C4⋊C411yescharacteristic
535C22#6583811yescharacteristic
536C22#6584111yescharacteristic
537C22#6584511yescharacteristic
538C22#6585011yescharacteristic
539C22D5×#11711yescharacteristic
540C22D5×#11711yescharacteristic
541C22#6585611yescharacteristic
542C22#6586212yes—
543C22#6586512yes—
544C22#6600212yes—
545C22#6600312yes—
546C22#6601112yes—
547C22#6601312yes—
548C22#6601912yes—
549C22#6602212yes—
550C22#6602712yes—
551C22#6603012yes—
552C22C2×C4×C22⋊D511yescharacteristic
553C22D4×C22⋊D511yescharacteristic
554C22Q8×C22⋊D511yescharacteristic
555C22#6615812yes—
556C22#6616212yes—
557C4—24no—
558C4—24no—
559C4—44no—
560C4—42no—
561C4—82no—
562C4—104no—
563C4—104no—
564C4—104no—
565C4—104no—
566C4—204no—
567C4—402no—
568C2#1060587911yescharacteristic
569C2#1060588211yescharacteristic
570C2#1060588811yescharacteristic
571C2#1060590612yes—
572C2#1060590712yes—
573C2#1060595811yescharacteristic
574C2C4⋊C4×C22⋊D511yescharacteristic
575C2#1061396911yescharacteristic
576C2#1061399911yescharacteristic
577C2#1061469512yes—
578C2#1061476212yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#382C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×#382D5
hypocenterC5#13889
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
37. C4×#683C4semidirect
174. #683C4⋊C4semidirect
533. C5#13889semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3822
C2×#652672
C2×C4×#6832
C2×#649382
#106023612
#106023272
#106002022
#106001992
#106001972
#106001952
#106001942
#138895