Finite Group Databasebeta

← #12970862

Subgroups — #12970862

Order 1280.

2098 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3449C211yesmaximal, characteristic, complemented
2C2×#65868C211yesmaximal, characteristic, complemented
3#10615815C212yesmaximal, complemented
4#10615813C212yesmaximal, complemented
5#10615141C218yesmaximal, complemented
6#10615120C218yesmaximal, complemented
7#10615045C212yesmaximal, complemented
8#10615028C212yesmaximal, complemented
9#10615020C212yesmaximal, complemented
10#10615014C212yesmaximal, complemented
11#10613940C211yesmaximal, characteristic, complemented
12C22×C5×#41C2212yes—
13C5×#537—21no—
14C5×#537—21no—
15C5×#536C2214yescomplemented
16C5×#535C2214yescomplemented
17C5×#534—21no—
18C5×#534—21no—
19C5×#532C2212yes—
20C5×#532C2212yes—
21C5×#525—24no—
22C2×C5×#117C2211yescharacteristic
23C2×#4097C2214yescomplemented
24C2×#4095C2214yescomplemented
25C2×#4076C2211yescharacteristic
26C2×#4070C2211yescharacteristic
27#65868—24no—
28#65868C2218yescomplemented
29C2×#4044—21no—
30C2×#4042—21no—
31C2×#4031—21no—
32C2×#4029—21no—
33C2×#4021C2211yescharacteristic, complemented
34C2×C4×D20C2211yescharacteristic, complemented
35C2×#4015C2211yescharacteristic, complemented
36C2×C4×Dic10C2211yescharacteristic, complemented
37#65528C2218yescomplemented
38#65527C2218yes—
39#65521C2214yescomplemented
40#65521C2214yescomplemented
41#65517C2214yescomplemented
42#65516C2214yescomplemented
43#65507C2214yescomplemented
44#65506C2214yescomplemented
45#65496C2212yes—
46#65379C2214yescomplemented
47#65375C2214yescomplemented
48#65372C2214yescomplemented
49#65370C2214yescomplemented
50#65364C2214yescomplemented
51#65363C2214yescomplemented
52#65361C2214yescomplemented
53#65359C2214yescomplemented
54#65348C2218yescomplemented
55#65346C2218yescomplemented
56#65344C2218yescomplemented
57#65343C2218yescomplemented
58#65289C2218yescomplemented
59#65213C2212yescomplemented
60C4×#681C2212yescomplemented
61#60810—51nomaximal, Sylow
62C2×C5×#41—22no—
63C2×C5×#41—22no—
64C2×C5×#41—48no—
65C2×C5×#41C2314yes—
66C2×C5×#41C2314yes—
67C22×C5×Q8C2312yes—
68C22×C5×D4—22no—
69C22×C5×D4C2312yes—
70C23×C4×C5—22no—
71C23×C4×C5C2311yescharacteristic
72C22×C22⋊D5—21no—
73C22×D20C2311yescharacteristic
74C22×C4×D5—21no—
75C22×Dic10—21no—
76C22×Dic10C2311yescharacteristic
77C5×C4⋊Q8C2312yes—
78C5×C4⋊Q8C2312yes—
79C5×#127C2312yes—
80C5×#127C2312yes—
81C5×#124C2314yes—
82C5×#124C2314yes—
83C5×#123—24no—
84C5×#123—24no—
85C5×C22⋊Q8—24no—
86C5×C22⋊Q8—24no—
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—22no—
90C5×#121—22no—
91C5×#121—24no—
92C5×#121—24no—
93C5×#120—24no—
94C5×#120—24no—
95C4×C5×D4—22no—
96C4×C5×D4—22no—
97C4×C5×D4—22no—
98C4×C5×D4—22no—
99C5×#117D414yes—
100C5×#117C2314yes—
101C2×C5×C4⋊C4D411yescharacteristic
102C2×C5×C4⋊C4D411yescharacteristic
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C42×C5C2311yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C2×C22⋊Dic5—21no—
108#4097—48no—
109#4095—48no—
110C2×#689C2318yes—
111C2×#688C2318yes—
112C2×#687C2318yes—
113C2×#686C2318yes—
114#4076—22no—
115#4076C2314yes—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119C2×#685—21no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5C2311yescharacteristic
122C2×C4⋊Dic5C2311yescharacteristic
123#4070—22no—
124#4070C2314yes—
125C2×#683—21no—
126C2×#683—21no—
127C2×C4×Dic5—21no—
128C2×#681C2314yes—
129#4044—28no—
130#4042—28no—
131#4031—28no—
132#4029—28no—
133#4021—22no—
134#4021C2314yes—
135C4×D20—22no—
136C4×D20C2314yes—
137#4015—22no—
138#4015C2314yes—
139C4×Dic10—22no—
140C4×Dic10C2314yes—
141#3967C2318yes—
142#3967C2318yes—
143#3964C2318yes—
144#3964C2318yes—
145C22⋊#168C2314yes—
146C22⋊#168C2314yes—
147C4⋊#168C2314yes—
148C4⋊#168C2314yes—
149#3935C2314yes—
150C4×#168C2314yes—
151C2×#542—51no—
152#3449D511yescharacteristic, complemented
153#3225—58no—
154#3224—58no—
155#3153—52no—
156#3141—52no—
157#3037—52no—
158#3036—52no—
159#3007—52no—
160#3006—52no—
161#2921—51no—
162C24×C5—22no—
163C24×C5C2×D411yescharacteristic
164C23×D5—21no—
165C5×#41—28no—
166C5×#41—28no—
167C5×#41—44no—
168C5×#41—44no—
169C5×#41—48no—
170C5×#41—48no—
171C2×C5×Q8—22no—
172C2×C5×Q8—44no—
173C2×C5×Q8C2414yes—
174C2×C5×D4—24no—
175C2×C5×D4—24no—
176C2×C5×D4—22no—
177C2×C5×D4—22no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—22no—
181C2×C5×D4—44no—
182C2×C5×D4—48no—
183C2×C5×D4C2414yes—
184C22×C4×C5—24no—
185C22×C4×C5—22no—
186C22×C4×C5—24no—
187C22×C4×C5—24no—
188C22×C4×C5—48no—
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2412yes—
196C22×C4×C5C2411yescharacteristic
197C2×C22⋊D5—24no—
198C2×C22⋊D5—82no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C2×D20—24no—
203C2×D20—21no—
204C2×D20C2412yes—
205C2×C4×D5—24no—
206C2×C4×D5—82no—
207C2×Dic10—24no—
208C2×Dic10—21no—
209C2×Dic10—24no—
210C2×Dic10—82no—
211C2×Dic10C2412yes—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4C2×D414yes—
217C5×C4⋊C4C2×D414yes—
218C5×C22⋊C4—24no—
219C5×C22⋊C4—24no—
220C5×C22⋊C4—24no—
221C5×C22⋊C4—24no—
222C5×C22⋊C4C2×D414yes—
223C5×C22⋊C4C2×D414yes—
224C42×C5C2×D412yes—
225C42×C5C2×D412yes—
226C42×C5C2412yes—
227C42×C5C2412yes—
228C22⋊Dic5—24no—
229#689—48no—
230#688—48no—
231#687—48no—
232#686—48no—
233#685—24no—
234#685—24no—
235#685—24no—
236#685—24no—
237C4⋊Dic5—21no—
238C4⋊Dic5—21no—
239C4⋊Dic5—24no—
240C4⋊Dic5C2412yes—
241C4⋊Dic5C2412yes—
242#683—24no—
243#683—24no—
244C4×Dic5—24no—
245#681—28no—
246C2×#168C2418yes—
247C22×#41C2×D512yes—
248C2×#137—54no—
249C2×AGL(1,ℤ/8)—54no—
250#542—58no—
251#542—104no—
252#537—21no—
253#537—21no—
254#536C2×D514yescomplemented
255#535C2×D514yescomplemented
256#534—21no—
257#534—21no—
258#532C2×D512yes—
259#532C2×D512yes—
260C2×C4⋊Q8—51no—
261C2×#126—101no—
262C2×#124—51no—
263C2×#124—101no—
264#525—24no—
265C2×#123—101no—
266C2×C22⋊Q8—51no—
267C2×C22⋊Q8—101no—
268C2×#121—51no—
269C2×C4×Q8—51no—
270C2×C4×D4—51no—
271C2×#117C2×D511yescharacteristic
272#497—54no—
273#496—54no—
274#495—58no—
275#489—58no—
276#487—54no—
277#486—54no—
278#464—58no—
279#463—58no—
280#462—54no—
281#461—54no—
282#460—54no—
283#459—54no—
284#452—58no—
285#451—54no—
286#450—54no—
287#449—58no—
288#448—54no—
289#447—54no—
290#433—58no—
291#423—52no—
292#417—54no—
293#417—54no—
294#407—52no—
295C4×M16—52no—
296C23×C5—22no—
297C23×C5—24no—
298C23×C5—41no—
299C23×C5—41no—
300C23×C5—44no—
301C23×C5—82no—
302C23×C5—82no—
303C23×C5C22×D412yes—
304C23×C5C22×D411yescharacteristic
305C22×D5—22no—
306C22×D5—42no—
307C22×D5—42no—
308C22×D5—42no—
309C5×Q8—24no—
310C5×Q8—24no—
311C5×Q8—44no—
312C5×D4—24no—
313C5×D4—24no—
314C5×D4—44no—
315C5×D4—48no—
316C5×D4—48no—
317C5×D4—82no—
318C5×D4—82no—
319C5×D4—82no—
320C5×D4—82no—
321C2×C4×C5—22no—
322C2×C4×C5—24no—
323C2×C4×C5—24no—
324C2×C4×C5—24no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—48no—
330C2×C4×C5—44no—
331C2×C4×C5—48no—
332C2×C4×C5C22×D412yes—
333C2×C4×C5C22×D412yes—
334C2×C4×C5C22×D412yes—
335C2×C4×C5C22×D412yes—
336C2×C4×C5C22×D412yes—
337C2×C4×C5C22×D411yescharacteristic
338C2×C4×C5H(5,𝔽2)14yes—
339C2×C4×C5C2511yescharacteristic
340C22⋊D5—84no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—42no—
345C2×Dic5—42no—
346C2×Dic5—42no—
347D20—24no—
348D20—42no—
349C4×D5—84no—
350Dic10—24no—
351Dic10—42no—
352Dic10—84no—
353#168—28no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—48no—
357C2×#41C22×D514yes—
358C2×#41C22×D514yes—
359C22×Q8—51no—
360C22×Q8—101no—
361C22×Q8C22×D512yes—
362C22×D4—22no—
363C22×D4—51no—
364C22×D4—101no—
365C22×D4C22×D512yes—
366C23×C4—22no—
367C23×C4—101no—
368C23×C4C22×D511yescharacteristic
369#137—208no—
370AGL(1,ℤ/8)—208no—
371C2×Q16—58no—
372C2×SD16—58no—
373C2×SD16—58no—
374C2×D8—58no—
375C2×M16—54no—
376C4⋊Q8—54no—
377C4⋊Q8—102no—
378C4⋊Q8C22×D512yes—
379C4⋊Q8C22×D512yes—
380#127C22×D512yes—
381#127C22×D512yes—
382#126—108no—
383#124—54no—
384#124—108no—
385#124—102no—
386#124C22×D514yes—
387#124C22×D514yes—
388#123—24no—
389#123—24no—
390#123—108no—
391C22⋊Q8—24no—
392C22⋊Q8—24no—
393C22⋊Q8—54no—
394C22⋊Q8—102no—
395C22⋊Q8—108no—
396#121—22no—
397#121—22no—
398#121—22no—
399#121—22no—
400#121—24no—
401#121—24no—
402#121—54no—
403#121—102no—
404#120—24no—
405#120—24no—
406C4×Q8—54no—
407C4×Q8—102no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—54no—
413C4×D4—102no—
414#117C22⋊D514yes—
415#117C22×D514yes—
416C2×C4⋊C4—51no—
417C2×C4⋊C4—51no—
418C2×C4⋊C4—101no—
419C2×C4⋊C4—101no—
420C2×C4⋊C4—101no—
421C2×C4⋊C4C22⋊D511yescharacteristic
422C2×C4⋊C4C22⋊D511yescharacteristic
423C2×C22⋊C4—101no—
424C2×C22⋊C4—101no—
425C2×C22⋊C4—101no—
426C2×C22⋊C4—101no—
427C2×C22⋊C4—101no—
428C2×C22⋊C4C22⋊D511yescharacteristic
429C2×C22⋊C4C22⋊D511yescharacteristic
430C2×C42—101no—
431C2×C42C22×D511yescharacteristic
432C2×C42C22×D511yescharacteristic
433C4⋊C8—54no—
434C4⋊C8—54no—
435#103—58no—
436#103—58no—
437#102—58no—
438#102—58no—
439C22⋊C8—54no—
440C22⋊C8—54no—
441#97—54no—
442C4×C8—54no—
443C22×C5—21no—
444C22×C5—21no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—44no—
449C22×C5—44no—
450C22×C5—44no—
451C22×C5—82no—
452C22×C5—88no—
453C22×C5#53512yes—
454C22×C5C23×D411yescharacteristic
455C2×D5—42no—
456C2×D5—42no—
457C2×D5—42no—
458C2×D5—84no—
459C4×C5—22no—
460C4×C5—22no—
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—22no—
464C4×C5—44no—
465C4×C5#53512yes—
466C4×C5C2×H(5,𝔽2)12yes—
467Dic5—42no—
468Dic5—42no—
469Dic5—42no—
470C24—22no—
471C24—101no—
472C24C2×C22⋊D511yescharacteristic
473#41—28no—
474#41—28no—
475#41—44no—
476#41—44no—
477#41—48no—
478#41—48no—
479C2×Q8—22no—
480C2×Q8—44no—
481C2×Q8—52no—
482C2×Q8—101no—
483C2×Q8—104no—
484C2×Q8—104no—
485C2×Q8—402no—
486C2×Q8C23×D514yes—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—44no—
495C2×D4—48no—
496C2×D4—52no—
497C2×D4—104no—
498C2×D4—104no—
499C2×D4—101no—
500C2×D4—402no—
501C2×D4C23×D514yes—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—48no—
507C22×C4—101no—
508C22×C4—101no—
509C22×C4—101no—
510C22×C4—104no—
511C22×C4—402no—
512C22×C4C2×C22⋊D511yescharacteristic
513C22×C4C2×C22⋊D512yes—
514C22×C4C2×C22⋊D511yescharacteristic
515C22×C4C2×C22⋊D511yescharacteristic
516C22×C4C2×C22⋊D511yescharacteristic
517C22×C4C2×C22⋊D511yescharacteristic
518C22×C4C23×D512yes—
519C22×C4C23×D511yescharacteristic
520Q16—208no—
521SD16—208no—
522SD16—208no—
523D8—208no—
524M16—108no—
525C2×C8—58no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—52no—
531C4⋊C4—52no—
532C4⋊C4—101no—
533C4⋊C4—101no—
534C4⋊C4—104no—
535C4⋊C4—104no—
536C4⋊C4—104no—
537C4⋊C4C2×C22⋊D514yes—
538C4⋊C4C2×C22⋊D514yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—104no—
544C22⋊C4—104no—
545C22⋊C4—104no—
546C22⋊C4—104no—
547C22⋊C4—104no—
548C22⋊C4C2×C22⋊D514yes—
549C22⋊C4C2×C22⋊D514yes—
550C42—104no—
551C42C2×C22⋊D512yes—
552C42C2×C22⋊D512yes—
553C42C23×D512yes—
554C42C23×D512yes—
555C2×C5—22no—
556C2×C5—42no—
557C2×C5—84no—
558C2×C5C2×#53511yescharacteristic
559C2×C5#358511yescharacteristic
560C2×C5#358611yescharacteristic
561D5—82no—
562C23—22no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—44no—
567C23—82no—
568C23—82no—
569C23—102no—
570C23—202no—
571C23—202no—
572C23—202no—
573C23C22×C22⋊D512yes—
574C23C22×C22⋊D511yescharacteristic
575Q8—24no—
576Q8—24no—
577Q8—44no—
578Q8—104no—
579Q8—202no—
580Q8—404no—
581D4—24no—
582D4—24no—
583D4—44no—
584D4—48no—
585D4—48no—
586D4—82no—
587D4—82no—
588D4—82no—
589D4—82no—
590D4—104no—
591D4—202no—
592D4—404no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—48no—
602C2×C4—44no—
603C2×C4—48no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—102no—
607C2×C4—202no—
608C2×C4—202no—
609C2×C4—202no—
610C2×C4—404no—
611C2×C4#414414yes—
612C2×C4C22×C22⋊D512yes—
613C2×C4C22×C22⋊D512yes—
614C2×C4C22×C22⋊D512yes—
615C2×C4C22×C22⋊D512yes—
616C2×C4C22×C22⋊D512yes—
617C2×C4C22×C22⋊D511yescharacteristic
618C2×C4C24×D511yescharacteristic
619C8—108no—
620C5#6081011yescharacteristic, complemented, Sylow
621C22—21no—
622C22—21no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—82no—
630C22—88no—
631C22—202no—
632C22—202no—
633C22—202no—
634C22—404no—
635C22#6613912yes—
636C22C23×C22⋊D511yescharacteristic
637C4—22no—
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—44no—
643C4—202no—
644C4—202no—
645C4—202no—
646C4#6613912yes—
647C4C2×#414412yes—
648C2—22no—
649C2—42no—
650C2—84no—
651C2—402no—
652C2C2×#6613911yescharacteristic
653C2#1061919911yescharacteristic
654C2#1061920011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3449C2
socleC22×C5C23×D4
hypercenter#3449D5
hypocenterC5#60810
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C5×#3449C2semidirect
2. C2×#65868C2semidirect
3. #10615815C2semidirect
4. #10615813C2semidirect
5. #10615141C2semidirect
6. #10615120C2semidirect
7. #10615045C2semidirect
8. #10615028C2semidirect
9. #10615020C2semidirect
10. #10615014C2semidirect
11. #10613940C2semidirect
15. C5×#536C22semidirect
16. C5×#535C22semidirect
23. C2×#4097C22semidirect
24. C2×#4095C22semidirect
28. #65868C22semidirect
33. C2×#4021C22semidirect
34. C2×C4×D20C22semidirect
35. C2×#4015C22semidirect
36. C2×C4×Dic10C22semidirect
37. #65528C22semidirect
39. #65521C22semidirect
40. #65521C22semidirect
41. #65517C22semidirect
42. #65516C22semidirect
43. #65507C22semidirect
44. #65506C22semidirect
46. #65379C22semidirect
47. #65375C22semidirect
48. #65372C22semidirect
49. #65370C22semidirect
50. #65364C22semidirect
51. #65363C22semidirect
52. #65361C22semidirect
53. #65359C22semidirect
54. #65348C22semidirect
55. #65346C22semidirect
56. #65344C22semidirect
57. #65343C22semidirect
58. #65289C22semidirect
59. #65213C22semidirect
60. C4×#681C22semidirect
152. #3449D5semidirect
254. #536C2×D5semidirect
255. #535C2×D5semidirect
620. C5#60810semidirect

Maximal subgroups

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

subgroupindex
C5×#34492
C2×#658682
#106158152
#106158132
#106151412
#106151202
#106150452
#106150282
#106150202
#106150142
#106139402
#608105