Finite Group Databasebeta

← #12106901

Subgroups — #12106901

Order 1280.

948 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
1C2×#65136C211yesmaximal, characteristic
2#10605881C211yesmaximal, characteristic, complemented
3C4×#4039C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5#10601431C211yesmaximal, characteristic
6Dic5×#107C211yesmaximal, characteristic, complemented
7#10601377C211yesmaximal, characteristic
8Dic5×#106C211yesmaximal, characteristic, complemented
9Dic5×C4⋊C8C211yesmaximal, characteristic, complemented
10#10600349C211yesmaximal, characteristic
11#10600284C211yesmaximal, characteristic, complemented
12#10599613C211yesmaximal, characteristic, complemented
13#10599609C211yesmaximal, characteristic, complemented
14#10599573C211yesmaximal, characteristic
15#10599573C211yesmaximal, characteristic
16C2×#4039C2211yescharacteristic
17C2×#4039C2211yescharacteristic
18C2×C4×D20C2211yescharacteristic
19C2×C42×D5—21no—
20C2×#4016C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C5×#382C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C2×#3953C2211yescharacteristic
27C2×#3953C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×C8×Dic5C2211yescharacteristic
31C2×C8×Dic5C2211yescharacteristic
32C4⋊C4×Dic5C2211yescharacteristic
33C4⋊C4×Dic5C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36#65262C2211yescharacteristic
37#65262C2211yescharacteristic
38C2×#3941C2211yescharacteristic
39C2×#3941C2211yescharacteristic
40C4×#685—21no—
41C42×Dic5C2211yescharacteristic
42C2×C4⋊#168C2211yescharacteristic
43#65136C418yescomplemented
44#64955—21no—
45#64955—21no—
46#64941—21no—
47#64941—21no—
48#64938—21no—
49#64938—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60C4×#478—51nomaximal, Sylow
61C22×D20C2311yescharacteristic
62C22×C4×D5—21no—
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C42×C5—21no—
72C2×C42×C5C2311yescharacteristic
73C2×#685—21no—
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C2311yescharacteristic
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×#683—21no—
80C2×#683—21no—
81C2×#683—21no—
82C2×#683—21no—
83C2×C4×Dic5—21no—
84C2×C4×Dic5—21no—
85C2×C4×Dic5—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5D411yescharacteristic
88C2×C4×Dic5D411yescharacteristic
89C2×C4×Dic5D411yescharacteristic
90C2×C4×Dic5D411yescharacteristic
91C2×C4×Dic5C2311yescharacteristic
92C2×C4×Dic5C2311yescharacteristic
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95#4039—22no—
96#4039—22no—
97#4039—22no—
98#4039Q814yes—
99C4×D20—22no—
100C4×D20C2×C414yes—
101C42×D5—44no—
102#4016—22no—
103#4016C2×C414yescomplemented
104C5×#107—22no—
105C5×#106—22no—
106C5×C4⋊C8C2×C414yescomplemented
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3953C2×C414yes—
117#3953C2×C414yes—
118#3950C2×C414yescomplemented
119#3949C2×C414yescomplemented
120C8×Dic5—22no—
121C8×Dic5—22no—
122#3941—22no—
123#3941—22no—
124C4⋊#168—22no—
125C2×#478—51no—
126C4×#125—51no—
127C42×D4—51no—
128#1989—51no—
129#1949D511yescharacteristic, complemented
130#1921—51no—
131#1919—51no—
132#1864—51no—
133#1862—51no—
134#1804—51no—
135C4×#107—51no—
136C4×#106—51no—
137C4×C4⋊C8—51no—
138C4×#102—51no—
139C4×#102—51no—
140C23×D5—21no—
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×Dic5C2×D411yescharacteristic
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C22×Dic5C2×D411yescharacteristic
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20C22×C412yes—
159C2×D20C2×Q812yes—
160C2×D20#4112yes—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—24no—
164C2×C4×D5—42no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8—21no—
174C2×C5×C8C22×C412yes—
175C2×C5×C8C22×C412yes—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4C2×Q812yes—
183C5×C4⋊C4#4112yes—
184C42×C5—42no—
185C42×C5C22×C412yes—
186C42×C5#4112yes—
187#685—24no—
188#685—24no—
189#685—24no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5C22×C412yes—
194C4⋊Dic5C22×C412yes—
195C4⋊Dic5C22×C412yes—
196#683—24no—
197#683—24no—
198#683—42no—
199#683—42no—
200C4×Dic5—21no—
201C4×Dic5—21no—
202C4×Dic5—22no—
203C4×Dic5—22no—
204C4×Dic5—22no—
205C4×Dic5—41no—
206C4×Dic5—42no—
207C4×Dic5—42no—
208C4×Dic5—42no—
209C4×Dic5—42no—
210C4×Dic5C2×Q812yes—
211C4×Dic5#4112yes—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#125—51no—
219C2×C4×D4—51no—
220C2×C4×D4—51no—
221C2×C4×D4—51no—
222C22×C42—101no—
223#478—58no—
224C2×#107—51no—
225C2×#107C2×D511yescharacteristic
226C2×#106—51no—
227C2×#106C2×D511yescharacteristic
228C2×C4⋊C8—51no—
229C2×C4⋊C8C2×D511yescharacteristic
230C2×#102—51no—
231C2×#102—51no—
232C2×#102—51no—
233C2×#102—51no—
234C2×C4×C8—51no—
235C2×C4×C8—51no—
236#389—51no—
237#389—51no—
238#387—101no—
239#387—101no—
240#382C2×D511yescharacteristic
241C4×C4⋊C4—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—101no—
246C4×C4⋊C4—101no—
247C4×C4⋊C4C2×D511yescharacteristic
248C4×C22⋊C4—101no—
249C4×C22⋊C4—101no—
250C4×C22⋊C4—101no—
251C43—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340C2×D511yescharacteristic
259#340C2×D511yescharacteristic
260#336—51no—
261#336—51no—
262C23×C5C22×D411yescharacteristic
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—41no—
267C22×D5—41no—
268C22×D5—41no—
269C22×D5—41no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
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×C5—41no—
286C2×C4×C5C4×D412yes—
287C2×C4×C5C4×D412yes—
288C2×C4×C5C23×C411yescharacteristic
289C2×C4×C5C22×Q811yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×C4×C5C2×#4111yescharacteristic
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5C22⋊Q812yes—
311C2×Dic5C22⋊Q812yes—
312C2×Dic5#13512yes—
313C2×Dic5#13512yes—
314C2×Dic5AGL(1,ℤ/8)12yes—
315D20—22no—
316D20—22no—
317D20—22no—
318D20C4×Q814yes—
319C4×D5—48no—
320C4×D5—48no—
321C4×D5—48no—
322C5×C8—22no—
323C5×C8—22no—
324#168—41no—
325#168—41no—
326C22×D4—51no—
327C23×C4—101no—
328C23×C4—101no—
329C23×C4—101no—
330C22×C8—51no—
331C22×C8—51no—
332C22×C8C22×D511yescharacteristic
333C22×C8C22×D511yescharacteristic
334#125—54no—
335#125—102no—
336C4×D4—54no—
337C4×D4—54no—
338C4×D4—102no—
339C4×D4—102no—
340C4×D4—102no—
341C4×D4—102no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C4⋊C4C22×D511yescharacteristic
352C2×C4⋊C4C22×D511yescharacteristic
353C2×C22⋊C4—101no—
354C2×C22⋊C4—101no—
355C2×C22⋊C4—101no—
356C2×C42—21no—
357C2×C42—51no—
358C2×C42—51no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—101no—
364C2×C42—101no—
365C2×C42—101no—
366C2×C42—101no—
367C2×C42—204no—
368C2×C42C22×D511yescharacteristic
369#107—22no—
370#107—54no—
371#106—22no—
372#106—54no—
373C4⋊C8—102no—
374C4⋊C8C4×D514yescomplemented
375#102—54no—
376#102—54no—
377#102—102no—
378#102—102no—
379C4×C8—102no—
380C4×C8—102no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390C22×C5C2×C4×D411yescharacteristic
391C22×C5C2×C22⋊Q811yescharacteristic
392C22×C5#52511yescharacteristic
393C22×C5C2×#13511yescharacteristic
394C22×C5C2×#13511yescharacteristic
395C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C5#57511yescharacteristic
397C2×D5—24no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C4×C5—22no—
405C4×C5—22no—
406C4×C5—42no—
407C4×C5—42no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5C2×C4×Q811yescharacteristic
411C4×C5C4×#4111yescharacteristic
412C4×C5#52911yescharacteristic
413C4×C5#53311yescharacteristic
414Dic5—22no—
415Dic5—22no—
416Dic5—41no—
417Dic5—42no—
418Dic5—42no—
419Dic5—42no—
420Dic5#47814yescomplemented
421C24—101no—
422C2×D4—52no—
423C2×D4—52no—
424C2×D4—52no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—104no—
437C22×C4—104no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—104no—
442C22×C4—202no—
443C22×C4—202no—
444C22×C4—202no—
445C22×C4—202no—
446C22×C4—202no—
447C22×C4—202no—
448C22×C4D4×D511yescharacteristic
449C22×C4D4×D511yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8C2×C4×D512yes—
462C2×C8C2×C4×D512yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—52no—
470C4⋊C4—52no—
471C4⋊C4—52no—
472C4⋊C4—101no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—104no—
476C4⋊C4—104no—
477C4⋊C4—202no—
478C4⋊C4—202no—
479C4⋊C4#71112yes—
480C4⋊C4Q8×D512yes—
481C22⋊C4—104no—
482C22⋊C4—104no—
483C22⋊C4—104no—
484C42—42no—
485C42—52no—
486C42—52no—
487C42—102no—
488C42—102no—
489C42—102no—
490C42—101no—
491C42—101no—
492C42—201no—
493C42—202no—
494C42—202no—
495C42—202no—
496C42—202no—
497C42C2×C4×D512yes—
498C42#71312yes—
499C2×C5C4×C22⋊Q811yescharacteristic
500C2×C5C4×#13511yescharacteristic
501C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
502C2×C5C2×#47811yescharacteristic
503C2×C5#307611yescharacteristic
504C2×C5#310211yescharacteristic
505C2×C5#310511yescharacteristic
506D5—44no—
507C23—102no—
508C23—102no—
509C23—102no—
510C23—201no—
511C23—201no—
512C23—201no—
513C23—201no—
514C23C2×D4×D511yescharacteristic
515D4—54no—
516D4—102no—
517D4—102no—
518D4—102no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—52no—
536C2×C4—52no—
537C2×C4—52no—
538C2×C4—52no—
539C2×C4—52no—
540C2×C4—101no—
541C2×C4—101no—
542C2×C4—101no—
543C2×C4—101no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—208no—
551C2×C4—208no—
552C2×C4—208no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4#403912yes—
560C2×C4#403912yes—
561C2×C4C22×C4×D511yescharacteristic
562C2×C4C2×#71111yescharacteristic
563C2×C4C2×Q8×D511yescharacteristic
564C2×C4C2×#71311yescharacteristic
565C2×C4D5×#4111yescharacteristic
566C2×C4D5×#4111yescharacteristic
567C8—22no—
568C8—22no—
569C8—201no—
570C8—201no—
571C5C4×#47811yescharacteristic, complemented, Sylow
572C22—104no—
573C22—202no—
574C22—202no—
575C22—202no—
576C22—202no—
577C22—202no—
578C22—202no—
579C22C2×#403911yescharacteristic
580C22#6594011yescharacteristic
581C22D5×C22⋊Q811yescharacteristic
582C22D5×#13511yescharacteristic
583C22D5×#13511yescharacteristic
584C22D5×AGL(1,ℤ/8)11yescharacteristic
585C22#6611111yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—54no—
591C4—81no—
592C4—81no—
593C4—102no—
594C4—102no—
595C4—201no—
596C4—202no—
597C4—202no—
598C4—202no—
599C4C4×#71111yescharacteristic
600C4C4×Q8×D511yescharacteristic
601C4#6602511yescharacteristic
602C4#6606211yescharacteristic
603C2—204no—
604C2#1060769611yescharacteristic
605C2#1061089611yescharacteristic
606C2#1061093011yescharacteristic
607C2#1061223611yescharacteristic
608C2#1061229911yescharacteristic
609C2D5×#47811yescharacteristic
610C2#1061296011yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1949C2
socleC23×C5C22×D4
prime radicalC22×D20C23
cosocleC22×C4×C5C24
hypercenter#1949D5
hypocenterC5C4×#478
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
2. #10605881C2semidirect
4. C5×#1949C2semidirect
6. Dic5×#107C2semidirect
8. Dic5×#106C2semidirect
9. Dic5×C4⋊C8C2semidirect
11. #10600284C2semidirect
12. #10599613C2semidirect
13. #10599609C2semidirect
43. #65136C4semidirect
103. #4016C2×C4semidirect
106. C5×C4⋊C8C2×C4semidirect
118. #3950C2×C4semidirect
119. #3949C2×C4semidirect
129. #1949D5semidirect
374. C4⋊C8C4×D5semidirect
420. Dic5#478semidirect
571. C5C4×#478semidirect

Maximal subgroups

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

subgroupindex
C2×#651362
#106058812
C4×#40392
C5×#19492
#106014312
Dic5×#1072
#106013772
Dic5×#1062
Dic5×C4⋊C82
#106003492
#106002842
#105996132
#105996092
#105995732
C4×#4785