Finite Group Databasebeta

← #12103643

Subgroups — #12103643

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#440C211yesmaximal, characteristic
2#10614182C211yesmaximal, characteristic, complemented
3#10614050C211yesmaximal, characteristic
4#10602843C211yesmaximal, characteristic
5#10602842C211yesmaximal, characteristic
6#10602424C211yesmaximal, characteristic, complemented
7#10602402C211yesmaximal, characteristic
8#10601406C211yesmaximal, characteristic, complemented
9#10601405C211yesmaximal, characteristic, complemented
10#10601048C211yesmaximal, characteristic, complemented
11#10601046C211yesmaximal, characteristic, complemented
12#10600980C211yesmaximal, characteristic
13#10600978C211yesmaximal, characteristic
14#10600607C211yesmaximal, characteristic, complemented
15Dic5×#97C211yesmaximal, characteristic, complemented
16C22×C5×SD16C2211yescharacteristic
17C2×C4×C5×Q8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×#4072—21no—
20C5×#440C418yescomplemented
21C2×C5×#107C2211yescharacteristic
22C2×C5×#103C2211yescharacteristic
23C2×C5×#102C2211yescharacteristic
24C2×C5×#97C2211yescharacteristic
25#65519C2211yescharacteristic
26#65519C2211yescharacteristic
27C2×#3967C2211yescharacteristic
28C2×#3967C2211yescharacteristic
29#65510C2211yescharacteristic
30#65510C2211yescharacteristic
31C2×#3964C2211yescharacteristic
32C2×#3964C2211yescharacteristic
33C4×C22⋊Dic5—21no—
34C2×#3950C2211yescharacteristic
35C2×#3949C2211yescharacteristic
36C2×#3947C2211yescharacteristic
37C2×#3947C2211yescharacteristic
38C2×C8×Dic5C2211yescharacteristic
39C2×C8×Dic5C2211yescharacteristic
40#65274C2211yescharacteristic
41#65274C2211yescharacteristic
42#65274C2211yescharacteristic
43#65274C2211yescharacteristic
44#65270—21no—
45#65270—21no—
46#65240—21no—
47#65240—21no—
48C4×C4⋊Dic5—21no—
49C4×C4⋊Dic5C2211yescharacteristic
50C4×C4⋊Dic5C2211yescharacteristic
51#65221—21no—
52C42×Dic5C2211yescharacteristic
53C2×#3935C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21288—51nomaximal, Sylow
61C22×C5×Q8C2311yescharacteristic
62C22×C5×D4C2311yescharacteristic
63C23×C4×C5—21no—
64C2×C5×SD16—22no—
65C2×C5×SD16—22no—
66C2×C5×SD16C2×C414yes—
67C22×C5×C8C2311yescharacteristic
68C22×C5×C8C2311yescharacteristic
69C4×C5×Q8—22no—
70C4×C5×Q8C2×C414yes—
71C4×C5×D4—22no—
72C4×C5×D4C2×C414yes—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C22⋊C4—21no—
77C2×C42×C5—21no—
78C2×C42×C5C2311yescharacteristic
79C2×C22⋊Dic5—21no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—21no—
82C2×C22⋊Dic5—21no—
83#4072—44no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5D411yescharacteristic
95C2×C4×Dic5D411yescharacteristic
96C2×C4×Dic5D411yescharacteristic
97C2×C4×Dic5D411yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99C2×C4×Dic5C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102C5×#107C2×C414yes—
103C5×#103C2×C414yes—
104C5×#102C2×C414yes—
105C5×#97C2×C414yes—
106#3967—22no—
107#3967—22no—
108#3964—22no—
109#3964—22no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119#3963—21no—
120#3950—22no—
121#3949—22no—
122#3947—22no—
123#3947—22no—
124C8×Dic5—22no—
125C8×Dic5—22no—
126#3935—22no—
127C2×#440D511yescharacteristic
128#2295—51no—
129#2293—51no—
130#1973—51no—
131#1968—51no—
132#1943—51no—
133#1942—51no—
134#1936—51no—
135#1935—51no—
136#1934—51no—
137#1933—51no—
138#1776—51no—
139#1763—51no—
140#1762—51no—
141C4×#97—51no—
142C24×C5—21no—
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8C22×C412yes—
149C2×C5×D4—21no—
150C2×C5×D4—21no—
151C2×C5×D4—21no—
152C2×C5×D4—21no—
153C2×C5×D4—21no—
154C2×C5×D4C22×C412yes—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—24no—
159C22×C4×C5—42no—
160C22×C4×C5—42no—
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2411yescharacteristic
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5C2×D411yescharacteristic
169C22×Dic5C2×D411yescharacteristic
170C22×Dic5C2×D411yescharacteristic
171C22×Dic5C2×D411yescharacteristic
172C5×SD16—28no—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8C22×C412yes—
176C2×C5×C8C22×C412yes—
177C2×C5×C8#4112yes—
178C2×C5×C8#4112yes—
179C5×C4⋊C4—24no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4C22×C412yes—
183C5×C4⋊C4C22×C412yes—
184C5×C22⋊C4—24no—
185C42×C5—24no—
186C42×C5C22×C412yes—
187C42×C5#4112yes—
188C22⋊Dic5—42no—
189C22⋊Dic5—42no—
190C22⋊Dic5—42no—
191C22⋊Dic5—42no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—42no—
201C4⋊Dic5—42no—
202C4⋊Dic5—42no—
203C4⋊Dic5—42no—
204C4×Dic5—21no—
205C4×Dic5—21no—
206C4×Dic5—21no—
207C4×Dic5—21no—
208C4×Dic5—22no—
209C4×Dic5—22no—
210C4×Dic5—41no—
211C4×Dic5—41no—
212C4×Dic5—42no—
213C4×Dic5—42no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168#4112yes—
219C2×#168#4112yes—
220C22×SD16C2×D511yescharacteristic
221C2×C4×Q8C2×D511yescharacteristic
222C2×C4×D4C2×D511yescharacteristic
223C2×#117—101no—
224#440Dic518yescomplemented
225C2×#107—51no—
226C2×#107C2×D511yescharacteristic
227C2×#106—51no—
228C2×#103—51no—
229C2×#103—51no—
230C2×#103C2×D511yescharacteristic
231C2×#102—51no—
232C2×#102—51no—
233C2×#102C2×D511yescharacteristic
234C2×#97—51no—
235C2×#97—51no—
236C2×#97—51no—
237C2×#97C2×D511yescharacteristic
238C2×C4×C8—51no—
239C2×C4×C8—51no—
240#391—51no—
241#391—51no—
242#390—51no—
243#390—51no—
244#389—51no—
245#389—51no—
246#389—51no—
247#389—51no—
248#388—101no—
249#388—101no—
250#387—101no—
251#387—101no—
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C4⋊C4—101no—
255C4×C22⋊C4—101no—
256#376—101no—
257C43—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264C23×C5—22no—
265C23×C5—41no—
266C23×C5—41no—
267C23×C5—41no—
268C23×C5—41no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5C22×D411yescharacteristic
272C5×Q8—22no—
273C5×Q8—22no—
274C5×Q8—41no—
275C5×Q8—41no—
276C5×D4—22no—
277C5×D4—22no—
278C5×D4—41no—
279C5×D4—41no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—48no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5C4×D412yes—
295C2×C4×C5C4×D412yes—
296C2×C4×C5C23×C411yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C2×C4×C5C2×#4111yescharacteristic
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315C2×Dic5—41no—
316C2×Dic5—41no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5AGL(1,ℤ/8)12yes—
325C2×Dic5#13712yes—
326C5×C8—22no—
327C5×C8#11714yescomplemented
328#168—22no—
329#168—22no—
330C22×Q8C22×D511yescharacteristic
331C22×D4C22×D511yescharacteristic
332C23×C4—21no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16C2×Dic514yes—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8C22×D511yescharacteristic
339C22×C8C22×D511yescharacteristic
340C4×Q8—22no—
341C4×Q8C2×Dic514yes—
342C4×D4—22no—
343C4×D4C2×Dic514yes—
344#117—204no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—101no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4C22×D511yescharacteristic
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C22⋊C4—21no—
357C2×C22⋊C4—101no—
358C2×C22⋊C4—101no—
359C2×C22⋊C4—101no—
360C2×C22⋊C4—101no—
361C2×C42—21no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—101no—
369C2×C42—101no—
370C2×C42C22×D511yescharacteristic
371#107—102no—
372#107C2×Dic514yes—
373#106—102no—
374#103—102no—
375#103—102no—
376#103C2×Dic514yes—
377#102—102no—
378#102—102no—
379#102C2×Dic514yes—
380#97—102no—
381#97—102no—
382#97—102no—
383#97C2×Dic514yes—
384C4×C8—102no—
385C4×C8—102no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390#95—101no—
391#95—101no—
392#95—101no—
393#95—101no—
394#95—101no—
395#95—101no—
396C22×C5—42no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—81no—
400C22×C5—81no—
401C22×C5—81no—
402C22×C5—81no—
403C22×C5C2×C4×D411yescharacteristic
404C22×C5#53211yescharacteristic
405C22×C5#53211yescharacteristic
406C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C5C2×#13711yescharacteristic
408C22×C5#57511yescharacteristic
409C22×C5#57511yescharacteristic
410C4×C5—22no—
411C4×C5—22no—
412C4×C5—42no—
413C4×C5—42no—
414C4×C5—42no—
415C4×C5C2×#11711yescharacteristic
416C4×C5C4×#4111yescharacteristic
417C4×C5#52911yescharacteristic
418C4×C5#52911yescharacteristic
419Dic5—22no—
420Dic5—22no—
421Dic5—41no—
422Dic5—41no—
423Dic5—81no—
424Dic5—81no—
425Dic5—81no—
426Dic5—81no—
427C24—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C22×Dic512yes—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C22×Dic512yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—24no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—101no—
454C22×C4D4×D511yescharacteristic
455C22×C4D4×D511yescharacteristic
456C22×C4C23×D511yescharacteristic
457SD16—28no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—52no—
461C2×C8—52no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8#70912yes—
467C2×C8#70912yes—
468C2×C8C22×Dic512yes—
469C2×C8C22×Dic512yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—24no—
473C4⋊C4—101no—
474C4⋊C4—101no—
475C4⋊C4—101no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4—101no—
481C4⋊C4—202no—
482C4⋊C4—202no—
483C4⋊C4—202no—
484C4⋊C4—202no—
485C4⋊C4C22×Dic512yes—
486C4⋊C4C22×Dic512yes—
487C22⋊C4—24no—
488C22⋊C4—202no—
489C22⋊C4—202no—
490C22⋊C4—202no—
491C22⋊C4—202no—
492C42—24no—
493C42—102no—
494C42—102no—
495C42—101no—
496C42—101no—
497C42—101no—
498C42—101no—
499C42—201no—
500C42—201no—
501C42—202no—
502C42—202no—
503C42#71112yes—
504C42C22×Dic512yes—
505C2×C5—82no—
506C2×C5#229311yescharacteristic
507C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
508C2×C5C4×#13711yescharacteristic
509C2×C5#318011yescharacteristic
510C2×C5#318111yescharacteristic
511C2×C5#318211yescharacteristic
512C2×C5#318311yescharacteristic
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C2×D4×D511yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525D4—22no—
526D4—22no—
527D4—41no—
528D4—41no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—48no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—52no—
544C2×C4—52no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—101no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—201no—
562C2×C4—201no—
563C2×C4—201no—
564C2×C4—201no—
565C2×C4—201no—
566C2×C4—201no—
567C2×C4D4×Dic512yes—
568C2×C4D4×Dic512yes—
569C2×C4C2×#70911yescharacteristic
570C2×C4C2×#70911yescharacteristic
571C2×C4C2×#71111yescharacteristic
572C2×C4D5×#4111yescharacteristic
573C2×C4D5×#4111yescharacteristic
574C2×C4C23×Dic511yescharacteristic
575C8—22no—
576C8—102no—
577C8—102no—
578C8#407214yescomplemented
579C5#2128811yescharacteristic, complemented, Sylow
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22#6588211yescharacteristic
588C22#6588211yescharacteristic
589C22D5×AGL(1,ℤ/8)11yescharacteristic
590C22#6610711yescharacteristic
591C22D5×#13711yescharacteristic
592C22#6611111yescharacteristic
593C22C2×D4×Dic511yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—102no—
600C4—102no—
601C4—201no—
602C4—201no—
603C4—401no—
604C4—401no—
605C4—401no—
606C4—401no—
607C4#6589111yescharacteristic
608C4#6589111yescharacteristic
609C4C2×#407211yescharacteristic
610C4#41×Dic511yescharacteristic
611C2—82no—
612C2#1061152111yescharacteristic
613C2#1061152211yescharacteristic
614C2#1061152311yescharacteristic
615C2#1061152411yescharacteristic
616C2#1061405011yescharacteristic
617C2Dic5×AGL(1,ℤ/8)11yescharacteristic
618C2Dic5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenterC2×#440D5
hypocenterC5#21288
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. #10614182C2semidirect
6. #10602424C2semidirect
8. #10601406C2semidirect
9. #10601405C2semidirect
10. #10601048C2semidirect
11. #10601046C2semidirect
14. #10600607C2semidirect
15. Dic5×#97C2semidirect
20. C5×#440C4semidirect
224. #440Dic5semidirect
327. C5×C8#117semidirect
578. C8#4072semidirect
579. C5#21288semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4402
#106141822
#106140502
#106028432
#106028422
#106024242
#106024022
#106014062
#106014052
#106010482
#106010462
#106009802
#106009782
#106006072
Dic5×#972
#212885