Finite Group Databasebeta

← #12104180

Subgroups — #12104180

Order 1280.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64994C211yesmaximal, characteristic
2#10605484C211yesmaximal, characteristic
3C4×#4038C211yesmaximal, characteristic
4C5×#1776C211yesmaximal, characteristic, complemented
5#10601426C211yesmaximal, characteristic
6#10601408C211yesmaximal, characteristic, complemented
7#10601373C211yesmaximal, characteristic
8#10601356C211yesmaximal, characteristic, complemented
9#10600607C211yesmaximal, characteristic, complemented
10#10600274C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12#10599670C211yesmaximal, characteristic
13#10599669C211yesmaximal, characteristic
14#10599589C211yesmaximal, characteristic, complemented
15#10599588C211yesmaximal, characteristic, complemented
16C2×#4038C2211yescharacteristic
17C2×#4038C2211yescharacteristic
18C2×#4018—21no—
19C2×C42×D5C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×#97C2211yescharacteristic
23C4×C5×C4⋊C4C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3952C2211yescharacteristic
27C2×#3950C2211yescharacteristic
28C2×#3949C2211yescharacteristic
29C2×#3946C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31#65276C2211yescharacteristic
32#65276C2211yescharacteristic
33#65265C2211yescharacteristic
34#65265C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C4×#685—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C4×#683—21no—
45C42×Dic5—21no—
46C2×#3935C2211yescharacteristic
47#64994C418yescomplemented
48#64956—21no—
49#64955—21no—
50#64939—21no—
51#64937—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21364—51nomaximal, Sylow
61C22×C4×D5D411yescharacteristic
62C22×C4×D5D411yescharacteristic
63C22×C4×D5C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C2×C5×C4⋊C4C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C42×C5—21no—
71C2×C42×C5—21no—
72C2×C42×C5C2311yescharacteristic
73C2×#685—21no—
74C2×#685—21no—
75C2×#685—21no—
76C2×#685—21no—
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×C4⋊Dic5C2311yescharacteristic
81C2×#683—21no—
82C2×#683—21no—
83C2×#683—21no—
84C2×#683—21no—
85C2×C4×Dic5—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5—21no—
88C2×C4×Dic5—21no—
89C2×C4×Dic5—21no—
90C2×C4×Dic5—21no—
91C2×C4×Dic5D411yescharacteristic
92C2×C4×Dic5D411yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96#4038—22no—
97#4038—22no—
98#4038—22no—
99#4038—22no—
100#4018—44no—
101C42×D5C2×C414yes—
102C42×D5Q814yes—
103C5×#107—22no—
104C5×#106—22no—
105C5×#97C2×C414yes—
106C5×#95—21no—
107C5×#95—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3952C2×C414yes—
115#3952C2×C414yes—
116#3950—22no—
117#3949—22no—
118#3946C2×C414yes—
119#3946C2×C414yes—
120#3940—22no—
121#3940—22no—
122#3939—22no—
123#3939—22no—
124#3935C2×C414yes—
125C2×#432—51no—
126#2285—51no—
127C4×#117—51no—
128#1948—51no—
129#1948—51no—
130#1947—51no—
131#1947—51no—
132#1854—51no—
133#1854—51no—
134#1854—51no—
135#1854—51no—
136#1776—51no—
137#1776—51no—
138#1776—51no—
139#1776D511yescharacteristic, complemented
140C23×D5C2×D411yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C22×Dic5C2×D411yescharacteristic
155C2×C4×D5—21no—
156C2×C4×D5—21no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—22no—
160C2×C4×D5—22no—
161C2×C4×D5—41no—
162C2×C4×D5—41no—
163C2×C4×D5C4⋊C414yes—
164C2×C4×D5C4⋊C414yes—
165C2×C4×D5C22×C412yes—
166C2×C4×D5C2×Q812yes—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8C22×C412yes—
172C2×C5×C8C22×C412yes—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4#4112yes—
180C5×C4⋊C4#4112yes—
181C42×C5—42no—
182C42×C5—42no—
183C42×C5C22×C412yes—
184C42×C5C2×Q812yes—
185#685—24no—
186#685—24no—
187#685—42no—
188#685—42no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5#4112yes—
196C4⋊Dic5#4112yes—
197#683—42no—
198#683—42no—
199#683—42no—
200#683—42no—
201C4×Dic5—24no—
202C4×Dic5—24no—
203C4×Dic5—42no—
204C4×Dic5—42no—
205C4×Dic5—42no—
206C4×Dic5—42no—
207C4×Dic5C4⋊C414yes—
208C4×Dic5C4⋊C414yes—
209C4×Dic5C22×C412yes—
210C4×Dic5C2×Q812yes—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168C22×C412yes—
216C2×#168C22×C412yes—
217C2×#117—51no—
218C2×#117—51no—
219C2×#117—101no—
220C22×C42—51no—
221#432—58no—
222C2×#107—51no—
223C2×#107—51no—
224C2×#107—51no—
225C2×#107C2×D511yescharacteristic
226C2×#106—51no—
227C2×#106—51no—
228C2×#106—51no—
229C2×#106C2×D511yescharacteristic
230C2×C4⋊C8—51no—
231C2×C4⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×#97—51no—
235C2×#97C2×D511yescharacteristic
236#384—51no—
237#384—51no—
238#382—101no—
239#380—51no—
240#380—51no—
241#380—101no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—101no—
247C4×C4⋊C4C2×D511yescharacteristic
248C4×C4⋊C4C2×D511yescharacteristic
249C4×C22⋊C4—101no—
250C4×C22⋊C4—101no—
251#376—101no—
252C43—101no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340C2×D511yescharacteristic
260#340C2×D511yescharacteristic
261C23×C5C22×D411yescharacteristic
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5C2×C4⋊C412yes—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5C2×C4⋊C412yes—
286C2×C4×C5C2×C4⋊C412yes—
287C2×C4×C5C23×C411yescharacteristic
288C2×C4×C5C22×Q811yescharacteristic
289C2×C4×C5C2×#4111yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5C2×C4⋊C412yes—
310C2×Dic5C2×C4⋊C412yes—
311C2×Dic5C2×C4⋊C412yes—
312C2×Dic5AGL(1,ℤ/8)12yes—
313C2×Dic5#13712yes—
314C4×D5—22no—
315C4×D5—22no—
316C4×D5—22no—
317C4×D5—22no—
318C4×D5—28no—
319C4×D5—44no—
320C5×C8—22no—
321C5×C8—22no—
322#168—22no—
323#168—22no—
324C23×C4—51no—
325C23×C4—51no—
326C23×C4—51no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8C22×D511yescharacteristic
330C22×C8C22×D511yescharacteristic
331#117—102no—
332#117—102no—
333#117—102no—
334#117—102no—
335#117—204no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—101no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—101no—
344C2×C4⋊C4C22×D511yescharacteristic
345C2×C4⋊C4C22×D511yescharacteristic
346C2×C4⋊C4C22×D511yescharacteristic
347C2×C4⋊C4C22×D511yescharacteristic
348C2×C22⋊C4—101no—
349C2×C22⋊C4—101no—
350C2×C22⋊C4—101no—
351C2×C22⋊C4—101no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—54no—
358C2×C42—54no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—101no—
362C2×C42—101no—
363C2×C42—101no—
364C2×C42—101no—
365C2×C42C22×D511yescharacteristic
366#107—22no—
367#107—102no—
368#107—102no—
369#107—102no—
370#106—22no—
371#106—102no—
372#106—102no—
373#106—102no—
374C4⋊C8—54no—
375C4⋊C8—54no—
376C22⋊C8—54no—
377C22⋊C8—54no—
378#97—54no—
379#97C4×D514yes—
380#95—21no—
381#95—21no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388C22×C5C22×C4⋊C411yescharacteristic
389C22×C5#52511yescharacteristic
390C22×C5#52511yescharacteristic
391C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C5C2×#13711yescharacteristic
393C22×C5#57511yescharacteristic
394C22×C5#57511yescharacteristic
395C2×D5—22no—
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—41no—
399C2×D5—41no—
400C2×D5—41no—
401C2×D5—41no—
402C4×C5—22no—
403C4×C5—22no—
404C4×C5—42no—
405C4×C5—42no—
406C4×C5—81no—
407C4×C5—81no—
408C4×C5C4×#4111yescharacteristic
409C4×C5C4×#4111yescharacteristic
410C4×C5#53311yescharacteristic
411C4×C5#53311yescharacteristic
412Dic5—22no—
413Dic5—22no—
414Dic5—42no—
415Dic5—42no—
416Dic5—81no—
417Dic5—81no—
418Dic5#42814yes—
419C24—51no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—51no—
427C22×C4—52no—
428C22×C4—52no—
429C22×C4—54no—
430C22×C4—54no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—201no—
442C22×C4—201no—
443C22×C4D4×D511yescharacteristic
444C22×C4D4×D511yescharacteristic
445C22×C4C23×D511yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—52no—
451C2×C8—52no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8C2×C4×D512yes—
457C2×C8C2×C4×D512yes—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—52no—
465C4⋊C4—52no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—202no—
473C4⋊C4—202no—
474C4⋊C4—202no—
475C4⋊C4—202no—
476C4⋊C4#70912yes—
477C4⋊C4#70912yes—
478C22⋊C4—104no—
479C22⋊C4—104no—
480C22⋊C4—202no—
481C22⋊C4—202no—
482C42—42no—
483C42—42no—
484C42—52no—
485C42—52no—
486C42—54no—
487C42—54no—
488C42—104no—
489C42—104no—
490C42—202no—
491C42—202no—
492C42—202no—
493C42—202no—
494C42C2×C4×D512yes—
495C42Q8×D512yes—
496C2×C5#229611yescharacteristic
497C2×C5C2×#42811yescharacteristic
498C2×C5#291111yescharacteristic
499C2×C5#311511yescharacteristic
500C2×C5#311511yescharacteristic
501C2×C5#311611yescharacteristic
502C2×C5#311611yescharacteristic
503D5—42no—
504C23—52no—
505C23—101no—
506C23—101no—
507C23—101no—
508C23—101no—
509C23—101no—
510C23—101no—
511C23C2×D4×D511yescharacteristic
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—52no—
529C2×C4—52no—
530C2×C4—52no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—108no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—204no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4D5×C4⋊C412yes—
556C2×C4D5×C4⋊C412yes—
557C2×C4C22×C4×D511yescharacteristic
558C2×C4C2×#70911yescharacteristic
559C2×C4C2×#70911yescharacteristic
560C2×C4C2×Q8×D511yescharacteristic
561C2×C4D5×#4111yescharacteristic
562C2×C4D5×#4111yescharacteristic
563C8—22no—
564C8—22no—
565C8—102no—
566C8—102no—
567C5#2136411yescharacteristic, complemented, Sylow
568C22—102no—
569C22—102no—
570C22—102no—
571C22—201no—
572C22—201no—
573C22—201no—
574C22—201no—
575C22C2×D5×C4⋊C411yescharacteristic
576C22#6588111yescharacteristic
577C22#6588111yescharacteristic
578C22D5×AGL(1,ℤ/8)11yescharacteristic
579C22#6610711yescharacteristic
580C22D5×#13711yescharacteristic
581C22#6611111yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—42no—
586C4—54no—
587C4—81no—
588C4—81no—
589C4—102no—
590C4—102no—
591C4—202no—
592C4—202no—
593C4—401no—
594C4—401no—
595C4C4×#70911yescharacteristic
596C4#6585611yescharacteristic
597C4#6591211yescharacteristic
598C4#6591211yescharacteristic
599C2—202no—
600C2#1060548611yescharacteristic
601C2D5×#42811yescharacteristic
602C2#1061093911yescharacteristic
603C2#1061151411yescharacteristic
604C2#1061154211yescharacteristic
605C2#1061157911yescharacteristic
606C2#1061160311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1776C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1776D5
hypocenterC5#21364
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
4. C5×#1776C2semidirect
6. #10601408C2semidirect
8. #10601356C2semidirect
9. #10600607C2semidirect
10. #10600274C2semidirect
11. #10600274C2semidirect
14. #10599589C2semidirect
15. #10599588C2semidirect
47. #64994C4semidirect
139. #1776D5semidirect
567. C5#21364semidirect

Maximal subgroups

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

subgroupindex
C2×#649942
#106054842
C4×#40382
C5×#17762
#106014262
#106014082
#106013732
#106013562
#106006072
#106002742
#105996702
#105996692
#105995892
#105995882
#213645