Finite Group Databasebeta

← #12104187

Subgroups — #12104187

Order 1280.

982 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64994C211yesmaximal, characteristic
2#10605484C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic
4C5×#1776C211yesmaximal, characteristic, complemented
5#10601425C211yesmaximal, characteristic
6#10601408C211yesmaximal, characteristic, complemented
7#10601372C211yesmaximal, characteristic
8#10601356C211yesmaximal, characteristic, complemented
9#10600607C211yesmaximal, characteristic, complemented
10#10600274C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12#10599668C211yesmaximal, characteristic
13#10599667C211yesmaximal, characteristic
14#10599589C211yesmaximal, characteristic, complemented
15#10599588C211yesmaximal, characteristic, complemented
16C2×D5×C4⋊C4C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×#4018—21no—
19C2×C42×D5—21no—
20C2×C42×D5C2211yescharacteristic
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×#97C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C2×#3952C2211yescharacteristic
27C2×#3952C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3949C2211yescharacteristic
30C2×#3946C2211yescharacteristic
31C2×#3946C2211yescharacteristic
32#65276C2211yescharacteristic
33#65276C2211yescharacteristic
34#65265C2211yescharacteristic
35#65265C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C4⋊C4×Dic5C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×C4⋊Dic5C2211yescharacteristic
44C4×#683—21no—
45C4×#683—21no—
46C2×#3935C2211yescharacteristic
47#64994C418yescomplemented
48#64956—21no—
49D5×#95—21no—
50#64939—21no—
51#64938—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21365—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5D411yescharacteristic
64C22×C4×D5D411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C42×C5—21no—
73C2×C42×C5—21no—
74C2×C42×C5C2311yescharacteristic
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×#683—21no—
86C2×#683—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
96D5×C4⋊C4—22no—
97D5×C4⋊C4—22no—
98D5×C4⋊C4—22no—
99D5×C4⋊C4—22no—
100#4018—44no—
101C42×D5—44no—
102C42×D5C2×C414yes—
103C42×D5Q814yes—
104C5×#107—22no—
105C5×#106—22no—
106C5×#97C2×C414yescomplemented
107C5×#95—21no—
108C5×#95—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3952C2×C414yes—
116#3952C2×C414yes—
117#3950—22no—
118#3949—22no—
119#3946C2×C414yescomplemented
120#3946C2×C414yescomplemented
121#3940—22no—
122#3940—22no—
123#3939—22no—
124#3939—22no—
125#3935C2×C414yescomplemented
126C2×#432—51no—
127#2285—51no—
128C2×C4×C4⋊C4—51no—
129#1948—51no—
130#1948—51no—
131#1947—51no—
132#1947—51no—
133#1853—51no—
134#1853—51no—
135#1852—51no—
136#1852—51no—
137#1776—51no—
138#1776—51no—
139#1776—51no—
140#1776D511yescharacteristic, complemented
141C23×D5C2×D411yescharacteristic
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2411yescharacteristic
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5C2×D411yescharacteristic
154C22×Dic5C2×D411yescharacteristic
155C22×Dic5C2×D411yescharacteristic
156C2×C4×D5—22no—
157C2×C4×D5—22no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—21no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—24no—
165C2×C4×D5—24no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C2×C4×D5C4⋊C414yes—
171C2×C4×D5C4⋊C414yes—
172C2×C4×D5C22×C412yes—
173C2×C4×D5C2×Q812yes—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8—21no—
178C2×C5×C8C22×C412yes—
179C2×C5×C8C22×C412yes—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4#4112yes—
187C5×C4⋊C4#4112yes—
188C42×C5—42no—
189C42×C5—42no—
190C42×C5C22×C412yes—
191C42×C5C2×Q812yes—
192#685—42no—
193#685—42no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5#4112yes—
201C4⋊Dic5#4112yes—
202#683—24no—
203#683—24no—
204#683—42no—
205#683—42no—
206#683—42no—
207#683—42no—
208C4×Dic5—42no—
209C4×Dic5—42no—
210C4×Dic5—42no—
211C4×Dic5—42no—
212C4×Dic5C4⋊C414yes—
213C4×Dic5C4⋊C414yes—
214C4×Dic5C22×C412yes—
215C4×Dic5C2×Q812yes—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168C22×C412yes—
221C2×#168C22×C412yes—
222C2×#117—101no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225C22×C42—51no—
226C22×C42—101no—
227#432—58no—
228C2×#107—51no—
229C2×#107—51no—
230C2×#107—51no—
231C2×#107C2×D511yescharacteristic
232C2×#106—51no—
233C2×#106—51no—
234C2×#106—51no—
235C2×#106C2×D511yescharacteristic
236C2×C4⋊C8—51no—
237C2×C4⋊C8—51no—
238C2×C22⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×#97—51no—
241C2×#97C2×D511yescharacteristic
242#384—51no—
243#384—51no—
244#382—101no—
245#380—51no—
246#380—51no—
247#380—101no—
248C4×C4⋊C4—51no—
249C4×C4⋊C4—51no—
250C4×C4⋊C4—51no—
251C4×C4⋊C4—51no—
252C4×C4⋊C4—101no—
253C4×C4⋊C4—101no—
254C4×C4⋊C4—101no—
255C4×C4⋊C4C2×D511yescharacteristic
256C4×C4⋊C4C2×D511yescharacteristic
257C2×#95—101no—
258#340—51no—
259#340—51no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340C2×D511yescharacteristic
265#340C2×D511yescharacteristic
266C23×C5C22×D411yescharacteristic
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5—21no—
271C22×D5C2×C4⋊C412yes—
272C22×D5AGL(1,ℤ/8)12yes—
273C22×D5#13712yes—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
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×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5C2×C4⋊C412yes—
291C2×C4×C5C2×C4⋊C412yes—
292C2×C4×C5C23×C411yescharacteristic
293C2×C4×C5C22×Q811yescharacteristic
294C2×C4×C5C2×#4111yescharacteristic
295C2×C4×C5C2×#4111yescharacteristic
296C2×C4×C5C2×#4111yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5C2×C4⋊C412yes—
315C2×Dic5C2×C4⋊C412yes—
316C2×Dic5C2×C4⋊C412yes—
317C2×Dic5AGL(1,ℤ/8)12yes—
318C2×Dic5#13712yes—
319C4×D5—28no—
320C4×D5—22no—
321C4×D5—22no—
322C4×D5—22no—
323C4×D5—22no—
324C4×D5—28no—
325C4×D5—48no—
326C4×D5—48no—
327C5×C8—22no—
328C5×C8—22no—
329#168—22no—
330#168—22no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—51no—
334C23×C4—101no—
335C23×C4—101no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8C22×D511yescharacteristic
339C22×C8C22×D511yescharacteristic
340#117—204no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—102no—
346C2×C4⋊C4—102no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4—102no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—101no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C4⋊C4C22×D511yescharacteristic
359C2×C22⋊C4—101no—
360C2×C22⋊C4—101no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—54no—
367C2×C42—54no—
368C2×C42—101no—
369C2×C42—101no—
370C2×C42—101no—
371C2×C42—101no—
372C2×C42—204no—
373C2×C42C22×D511yescharacteristic
374#107—22no—
375#107—102no—
376#107—102no—
377#107—102no—
378#106—22no—
379#106—102no—
380#106—102no—
381#106—102no—
382C4⋊C8—54no—
383C4⋊C8—54no—
384C22⋊C8—54no—
385C22⋊C8—54no—
386#97—54no—
387#97C4×D514yescomplemented
388#95—21no—
389#95—21no—
390#95—101no—
391#95—101no—
392#95—101no—
393#95—101no—
394#95—101no—
395#95—101no—
396C22×C5C22×C4⋊C411yescharacteristic
397C22×C5#52511yescharacteristic
398C22×C5#52511yescharacteristic
399C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C5C2×#13711yescharacteristic
402C22×C5C2×#13711yescharacteristic
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5—22no—
407C2×D5—22no—
408C2×D5—22no—
409C2×D5#42814yes—
410C4×C5—22no—
411C4×C5—22no—
412C4×C5—42no—
413C4×C5—42no—
414C4×C5—81no—
415C4×C5—81no—
416C4×C5C4×#4111yescharacteristic
417C4×C5C4×#4111yescharacteristic
418C4×C5#53311yescharacteristic
419C4×C5#53311yescharacteristic
420Dic5—22no—
421Dic5—22no—
422Dic5—42no—
423Dic5—42no—
424Dic5—81no—
425Dic5—81no—
426Dic5#42814yes—
427C24—51no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—54no—
438C22×C4—54no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—104no—
444C22×C4—104no—
445C22×C4—101no—
446C22×C4—101no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4—202no—
454C22×C4—202no—
455C22×C4—202no—
456C22×C4—202no—
457C22×C4D4×D511yescharacteristic
458C22×C4D4×D511yescharacteristic
459C22×C4C23×D511yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—52no—
465C2×C8—52no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8C2×C4×D512yes—
471C2×C8C2×C4×D512yes—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—52no—
479C4⋊C4—52no—
480C4⋊C4—104no—
481C4⋊C4—104no—
482C4⋊C4—101no—
483C4⋊C4—101no—
484C4⋊C4—101no—
485C4⋊C4—101no—
486C4⋊C4—101no—
487C4⋊C4—101no—
488C4⋊C4—202no—
489C4⋊C4—202no—
490C4⋊C4—202no—
491C4⋊C4—202no—
492C4⋊C4#70912yes—
493C4⋊C4#70912yes—
494C22⋊C4—202no—
495C22⋊C4—202no—
496C42—42no—
497C42—42no—
498C42—52no—
499C42—52no—
500C42—54no—
501C42—54no—
502C42—202no—
503C42—202no—
504C42—202no—
505C42—202no—
506C42C2×C4×D512yes—
507C42Q8×D512yes—
508C2×C5#229611yescharacteristic
509C2×C5C2×#42811yescharacteristic
510C2×C5C2×#42811yescharacteristic
511C2×C5#310911yescharacteristic
512C2×C5#311011yescharacteristic
513C2×C5#311211yescharacteristic
514C2×C5#311311yescharacteristic
515D5—24no—
516C23—52no—
517C23—52no—
518C23—52no—
519C23—101no—
520C23—101no—
521C23—101no—
522C23—101no—
523C23C2×D4×D511yescharacteristic
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—52no—
541C2×C4—52no—
542C2×C4—52no—
543C2×C4—52no—
544C2×C4—52no—
545C2×C4—108no—
546C2×C4—108no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—101no—
550C2×C4—101no—
551C2×C4—102no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—208no—
558C2×C4—208no—
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×C4—201no—
568C2×C4—201no—
569C2×C4D5×C4⋊C412yes—
570C2×C4D5×C4⋊C412yes—
571C2×C4C22×C4×D511yescharacteristic
572C2×C4C2×#70911yescharacteristic
573C2×C4C2×#70911yescharacteristic
574C2×C4C2×Q8×D511yescharacteristic
575C2×C4D5×#4111yescharacteristic
576C2×C4D5×#4111yescharacteristic
577C8—22no—
578C8—22no—
579C8—102no—
580C8—102no—
581C5#2136511yescharacteristic, complemented, Sylow
582C22—54no—
583C22—102no—
584C22—102no—
585C22—102no—
586C22—102no—
587C22—102no—
588C22—102no—
589C22C2×D5×C4⋊C411yescharacteristic
590C22#6588111yescharacteristic
591C22#6588111yescharacteristic
592C22D5×AGL(1,ℤ/8)11yescharacteristic
593C22D5×AGL(1,ℤ/8)11yescharacteristic
594C22D5×#13711yescharacteristic
595C22D5×#13711yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—54no—
601C4—81no—
602C4—81no—
603C4—102no—
604C4—102no—
605C4—202no—
606C4—202no—
607C4—401no—
608C4—401no—
609C4C4×#70911yescharacteristic
610C4#6585611yescharacteristic
611C4#6591211yescharacteristic
612C4#6591211yescharacteristic
613C2—104no—
614C2#1060548611yescharacteristic
615C2D5×#42811yescharacteristic
616C2D5×#42811yescharacteristic
617C2#1061151011yescharacteristic
618C2#1061151211yescharacteristic
619C2#1061156411yescharacteristic
620C2#1061160011yescharacteristic
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#21365
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
106. C5×#97C2×C4semidirect
119. #3946C2×C4semidirect
120. #3946C2×C4semidirect
125. #3935C2×C4semidirect
140. #1776D5semidirect
387. #97C4×D5semidirect
581. C5#21365semidirect

Maximal subgroups

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

subgroupindex
C2×#649942
#106054842
C4×D5×C4⋊C42
C5×#17762
#106014252
#106014082
#106013722
#106013562
#106006072
#106002742
#105996682
#105996672
#105995892
#105995882
#213655