Finite Group Databasebeta

← #12022026

Subgroups — #12022026

Order 1280.

1622 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic10C211yesmaximal, characteristic
2C2×#64940C211yesmaximal, characteristic
3C2×#64937C211yesmaximal, characteristic
4C5×#1434C211yesmaximal, characteristic
5#10602327C211yesmaximal, characteristic
6#10600217C212yesmaximal
7#10600214C212yesmaximal
8#10600200C212yesmaximal
9#10600199C212yesmaximal
10#10600195C211yesmaximal, characteristic
11#10600195C211yesmaximal, characteristic
12C23×Dic10C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×#683C2211yescharacteristic
16C22×#683C2211yescharacteristic
17C22×C4×Dic5C2212yes—
18C22×C4×Dic5C2211yescharacteristic
19C22×C4×Dic5C2211yescharacteristic
20C2×C4×Dic10—24no—
21C2×C4×Dic10—24no—
22C2×C4×Dic10C418yescomplemented
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
25C2×C5×#95C2212yes—
26C2×C5×#95C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#64940—24no—
39#64937—24no—
40#13961—51nomaximal, Sylow
41C23×C4×C5C2312yes—
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×Dic5C2312yes—
47C23×Dic5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C22×Dic10—22no—
53C22×Dic10—22no—
54C22×Dic10—22no—
55C22×Dic10—22no—
56C22×Dic10—22no—
57C22×Dic10—22no—
58C22×Dic10C2×C414yes—
59C2×C42×C5—22no—
60C2×C42×C5—22no—
61C2×C42×C5C2×C414yes—
62C2×C4⋊Dic5—22no—
63C2×C4⋊Dic5—22no—
64C2×C4⋊Dic5C2×C414yes—
65C2×#683—22no—
66C2×#683—22no—
67C2×#683—22no—
68C2×#683—22no—
69C2×#683C2×C414yes—
70C2×#683C2×C414yes—
71C2×C4×Dic5—22no—
72C2×C4×Dic5—22no—
73C2×C4×Dic5—24no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5—24no—
76C2×C4×Dic5C2×C414yes—
77C2×C4×Dic5C2×C414yes—
78C2×C4×Dic5D414yes—
79C2×C4×Dic5D414yes—
80C4×Dic10—232no—
81C5×#95—22no—
82C5×#95—22no—
83C5×#95—24no—
84C5×#95—24no—
85#3963—22no—
86#3963—22no—
87#3963—24no—
88#3963—24no—
89#3963—24no—
90#3963—24no—
91#3963—24no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963—24no—
96C22×C4×Q8—51no—
97C2×#383—51no—
98C2×#376—51no—
99#1446—52no—
100#1445—52no—
101#1436—52no—
102#1436—52no—
103#1434—51no—
104#1434—51no—
105#1434—51no—
106#1434D511yescharacteristic
107C24×C5C2411yescharacteristic
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
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×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5C22×C412yes—
132C22×C4×C5C22×C412yes—
133C22×C4×C5C22×C412yes—
134C22×C4×C5C2×D412yes—
135C22×C4×C5C2×D412yes—
136C22×C4×C5#4114yes—
137C22×C4×C5#4112yes—
138C22×C4×C5#4112yes—
139C22×Dic5—21no—
140C22×Dic5—21no—
141C22×Dic5—21no—
142C22×Dic5—21no—
143C22×Dic5—21no—
144C22×Dic5—21no—
145C22×Dic5—21no—
146C22×Dic5—21no—
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—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5C22×C412yes—
167C22×Dic5C22×C412yes—
168C22×Dic5C22×C412yes—
169C22×Dic5C22×C412yes—
170C22×Dic5C2×D412yes—
171C22×Dic5C2×D412yes—
172C22×Dic5C2×D412yes—
173C22×Dic5C2×D412yes—
174C22×Dic5#4114yes—
175C22×Dic5#4112yes—
176C22×Dic5#4112yes—
177C2×Dic10—28no—
178C2×Dic10—28no—
179C2×Dic10—28no—
180C2×Dic10—28no—
181C2×Dic10—28no—
182C2×Dic10—28no—
183C2×Dic10—28no—
184C42×C5—28no—
185C4⋊Dic5—28no—
186#683—28no—
187#683—28no—
188C4×Dic5—216no—
189C4×Dic5—28no—
190C4×Dic5C22⋊C4116yes—
191C23×Q8—51no—
192C2×C4×Q8—58no—
193C2×C4×Q8—104no—
194C2×C4×Q8—104no—
195C22×C4⋊C4—51no—
196C22×C4⋊C4—51no—
197C22×C4⋊C4—51no—
198C22×C42—51no—
199C22×C42—51no—
200C22×C42—52no—
201C22×C42C2×D511yescharacteristic
202#383—104no—
203#376—104no—
204C2×#95—51no—
205C2×#95—51no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95—52no—
211C2×#95—52no—
212C2×#95—52no—
213C2×#95—52no—
214C2×#95—52no—
215C2×#95C2×D511yescharacteristic
216C2×#95C2×D511yescharacteristic
217C2×#95C2×D512yes—
218C2×#95C2×D512yes—
219C23×C5C23×C411yescharacteristic
220C23×C5C22×D411yescharacteristic
221C23×C5C22×D411yescharacteristic
222C23×C5C2×#4112yes—
223C23×C5C2×#4111yescharacteristic
224C23×C5C2×#4111yescharacteristic
225C23×C5C2×#4111yescharacteristic
226C23×C5C2×#4111yescharacteristic
227C23×C5C2×#4112yes—
228C23×C52−1+412yes—
229C23×C52−1+412yes—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—24no—
239C2×C4×C5—24no—
240C2×C4×C5—22no—
241C2×C4×C5—22no—
242C2×C4×C5—22no—
243C2×C4×C5—24no—
244C2×C4×C5—24no—
245C2×C4×C5—24no—
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×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5C2×C22⋊C414yes—
260C2×C4×C5#11714yes—
261C2×Dic5—22no—
262C2×Dic5—22no—
263C2×Dic5—22no—
264C2×Dic5—22no—
265C2×Dic5—22no—
266C2×Dic5—22no—
267C2×Dic5—24no—
268C2×Dic5—22no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—22no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—22no—
276C2×Dic5—24no—
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—24no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—42no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5C2×C22⋊C414yes—
297C2×Dic5C2×C22⋊C414yes—
298C2×Dic5#11714yes—
299Dic10—232no—
300C22×Q8—54no—
301C22×Q8—102no—
302C22×Q8—102no—
303C22×Q8—102no—
304C22×Q8—102no—
305C22×Q8—102no—
306C22×Q8—102no—
307C23×C4—51no—
308C23×C4—51no—
309C23×C4—51no—
310C23×C4—51no—
311C23×C4—52no—
312C23×C4—52no—
313C23×C4C22×D512yes—
314C23×C4C22×D511yescharacteristic
315C23×C4C22×D512yes—
316C23×C4C22×D511yescharacteristic
317C23×C4C22×D511yescharacteristic
318C4×Q8—1032no—
319C2×C4⋊C4—54no—
320C2×C4⋊C4—54no—
321C2×C4⋊C4—54no—
322C2×C4⋊C4—102no—
323C2×C4⋊C4—102no—
324C2×C4⋊C4—102no—
325C2×C4⋊C4—102no—
326C2×C4⋊C4—102no—
327C2×C4⋊C4—102no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—54no—
331C2×C42—54no—
332C2×C42—54no—
333C2×C42—54no—
334C2×C42—104no—
335C2×C42—104no—
336C2×C42—104no—
337C2×C42—102no—
338C2×C42—102no—
339C2×C42C4×D514yes—
340#95—24no—
341#95—22no—
342#95—22no—
343#95—24no—
344#95—104no—
345#95—104no—
346#95—104no—
347#95—104no—
348#95—104no—
349#95—104no—
350#95—104no—
351#95—104no—
352#95—102no—
353#95—102no—
354#95—104no—
355C22×C5C22×C22⋊C411yescharacteristic
356C22×C5C2×#11711yescharacteristic
357C22×C5C2×#11711yescharacteristic
358C22×C5C4×#4111yescharacteristic
359C22×C5C4×#4111yescharacteristic
360C22×C5#51911yescharacteristic
361C22×C5#51911yescharacteristic
362C22×C5#52512yes—
363C22×C5#52511yescharacteristic
364C22×C5#52511yescharacteristic
365C22×C5#52511yescharacteristic
366C22×C5#52511yescharacteristic
367C22×C5#53212yes—
368C22×C5#53612yes—
369C22×C5#53612yes—
370C22×C5#55212yes—
371C22×C5#55212yes—
372C22×C5#55212yes—
373C22×C5#55212yes—
374C22×C5#55612yes—
375C22×C5#55612yes—
376C22×C5#55612yes—
377C22×C5#55612yes—
378C4×C5—24no—
379C4×C5—24no—
380C4×C5—44no—
381C4×C5—42no—
382C4×C5—82no—
383Dic5—24no—
384Dic5—24no—
385Dic5—24no—
386Dic5—44no—
387Dic5—42no—
388Dic5—82no—
389C24C23×D511yescharacteristic
390C2×Q8—108no—
391C2×Q8—108no—
392C2×Q8—108no—
393C2×Q8—108no—
394C2×Q8—108no—
395C2×Q8—108no—
396C2×Q8—108no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
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—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—52no—
421C22×C4—52no—
422C22×C4—52no—
423C22×C4—52no—
424C22×C4—52no—
425C22×C4—52no—
426C22×C4—52no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—52no—
430C22×C4—54no—
431C22×C4—102no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—102no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—101no—
445C22×C4—101no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4C2×C4×D512yes—
459C22×C4C2×C4×D512yes—
460C22×C4C2×C4×D512yes—
461C22×C4#70914yes—
462C22×C4D4×D512yes—
463C22×C4D4×D512yes—
464C22×C4#71112yes—
465C22×C4#71312yes—
466C4⋊C4—108no—
467C4⋊C4—108no—
468C4⋊C4—108no—
469C42—28no—
470C42—516no—
471C42—1016no—
472C42—108no—
473C2×C5#228011yescharacteristic
474C2×C5#229711yescharacteristic
475C2×C5#231011yescharacteristic
476C2×C5#235611yescharacteristic
477C2×C5#235611yescharacteristic
478C2×C5#235611yescharacteristic
479C2×C5#235611yescharacteristic
480C2×C5#259912yes—
481C2×C5#259912yes—
482C2×C5#260412yes—
483C2×C5#260412yes—
484C23C22×C4×D511yescharacteristic
485C23C2×#70912yes—
486C23C2×D4×D511yescharacteristic
487C23C2×D4×D511yescharacteristic
488C23C2×#71111yescharacteristic
489C23C2×#71311yescharacteristic
490C23D5×#4111yescharacteristic
491C23D5×#4111yescharacteristic
492C23D5×#4112yes—
493C23#415012yes—
494C23#415012yes—
495Q8—1032no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
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—54no—
526C2×C4—54no—
527C2×C4—54no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—104no—
535C2×C4—104no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—104no—
548C2×C4—104no—
549C2×C4—104no—
550C2×C4—202no—
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×C4—202no—
560C2×C4—202no—
561C2×C4—202no—
562C2×C4—202no—
563C2×C4D5×C22⋊C414yes—
564C2×C4#403814yes—
565C5#1396111yescharacteristic, complemented, Sylow
566C22C4×#70911yescharacteristic
567C22C2×D5×C22⋊C411yescharacteristic
568C22C2×#403811yescharacteristic
569C22#6585011yescharacteristic
570C22#6585011yescharacteristic
571C22D5×#11711yescharacteristic
572C22#6585611yescharacteristic
573C22#6586512yes—
574C22#6586712yes—
575C22#6587512yes—
576C22#6588112yes—
577C22#6588212yes—
578C22#6591812yes—
579C22#6594011yescharacteristic
580C22#6594011yescharacteristic
581C22#6596111yescharacteristic
582C22#6596111yescharacteristic
583C22#6598212yes—
584C22#6598212yes—
585C22#6600512yes—
586C22#6602812yes—
587C22#6603612yes—
588C22#6604212yes—
589C4—24no—
590C4—24no—
591C4—44no—
592C4—42no—
593C4—82no—
594C4—104no—
595C4—104no—
596C4—104no—
597C4—204no—
598C4—202no—
599C4—402no—
600C2#1060512411yescharacteristic
601C2#1060529411yescharacteristic
602C2#1060537411yescharacteristic
603C2#1060559311yescharacteristic
604C2#1060578411yescharacteristic
605C2#1060589011yescharacteristic
606C2#1060599511yescharacteristic
607C2#1060685612yes—
608C2#1060685712yes—
609C2#1060737312yes—
610C2#1060738012yes—
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1434C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1434D5
hypocenterC5#13961
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
22. C2×C4×Dic10C4semidirect
565. C5#13961semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic102
C2×#649402
C2×#649372
C5×#14342
#106023272
#106002172
#106002142
#106002002
#106001992
#106001952
#139615