Finite Group Databasebeta

← #12028024

Subgroups — #12028024

Order 1280.

1398 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×#65218C211yesmaximal, characteristic
2C2×#64935C212yesmaximal
3C5×C4⋊#95C211yesmaximal, characteristic
4#10602361C212yesmaximal
5#10602357C212yesmaximal
6#10602328C211yesmaximal, characteristic
7#10600213C212yesmaximal
8#10600204C212yesmaximal
9#10600200C212yesmaximal
10C23×Dic10C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×C4⋊Dic5C2211yescharacteristic
17C22×#683C2212yes—
18C22×#683C2212yes—
19C22×C4×Dic5C2212yes—
20C2×C5×#95C2212yes—
21C2×C5×#95C2212yes—
22C2×#3963C2212yes—
23C2×#3963C2212yes—
24C2×#3963C2212yes—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31#65218C418yescomplemented
32#64935—28no—
33#14467—51nomaximal, Sylow
34C23×C4×C5C2312yes—
35C23×C4×C5C2312yes—
36C23×C4×C5C2311yescharacteristic
37C23×C4×C5C2311yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C23×Dic5C2312yes—
40C23×Dic5C2312yes—
41C23×Dic5C2312yes—
42C23×Dic5C2312yes—
43C22×Dic10—41no—
44C22×Dic10—41no—
45C22×Dic10—41no—
46C22×Dic10—41no—
47C22×Dic10C2×C414yes—
48C22×Dic10D414yes—
49C22×Dic10Q814yes—
50C2×C5×C4⋊C4—22no—
51C2×C5×C4⋊C4—41no—
52C2×C5×C4⋊C4—41no—
53C2×C5×C4⋊C4—41no—
54C2×C5×C4⋊C4—41no—
55C2×C5×C4⋊C4Q814yescomplemented
56C2×C42×C5—41no—
57C2×C42×C5—41no—
58C2×C42×C5C2×C414yes—
59C2×C4⋊Dic5—22no—
60C2×C4⋊Dic5—41no—
61C2×C4⋊Dic5—41no—
62C2×C4⋊Dic5—41no—
63C2×C4⋊Dic5—41no—
64C2×C4⋊Dic5—41no—
65C2×C4⋊Dic5—41no—
66C2×C4⋊Dic5C2×C414yes—
67C2×C4⋊Dic5Q814yescomplemented
68C2×#683—24no—
69C2×#683—42no—
70C2×#683—42no—
71C2×#683—42no—
72C2×#683—42no—
73C2×#683—42no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5—42no—
76C2×C4×Dic5—42no—
77C5×#95—24no—
78C5×#95—24no—
79#3963—24no—
80#3963—24no—
81#3963—24no—
82#3963—24no—
83#3963—42no—
84#3963—42no—
85#3963—42no—
86#3963C2×C418yes—
87#3963C2×C418yes—
88C2×#391—51no—
89C2×#391—52no—
90#1444—52no—
91#1444—52no—
92#1441—52no—
93#1436—52no—
94#1436—52no—
95C4⋊#95—51no—
96C4⋊#95D511yescharacteristic
97C24×C5C2411yescharacteristic
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—22no—
111C22×C4×C5—22no—
112C22×C4×C5—22no—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5—22no—
116C22×C4×C5—22no—
117C22×C4×C5—22no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—22no—
123C22×C4×C5C22×C412yes—
124C22×C4×C5C22×C412yes—
125C22×C4×C5C22×C412yes—
126C22×C4×C5C2×D412yes—
127C22×C4×C5C2×Q814yes—
128C22×C4×C5C2×Q812yes—
129C22×C4×C5C2×Q812yes—
130C22×C4×C5C2×Q812yes—
131C22×C4×C5#4112yes—
132C22×C4×C5#4112yes—
133C22×Dic5—22no—
134C22×Dic5—22no—
135C22×Dic5—22no—
136C22×Dic5—22no—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5—22no—
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—22no—
143C22×Dic5—22no—
144C22×Dic5—22no—
145C22×Dic5—22no—
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—22no—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5C22×C414yes—
157C22×Dic5C22×C414yes—
158C22×Dic5C2×D414yes—
159C22×Dic5C2×Q814yes—
160C22×Dic5C2×Q814yes—
161C2×Dic10—44no—
162C2×Dic10—44no—
163C2×Dic10—44no—
164C2×Dic10—44no—
165C2×Dic10—44no—
166C2×Dic10—44no—
167C2×Dic10C4⋊C4116yescomplemented
168C5×C4⋊C4—44no—
169C5×C4⋊C4—44no—
170C42×C5—44no—
171C4⋊Dic5—44no—
172C4⋊Dic5—44no—
173C4⋊Dic5—44no—
174#683—48no—
175#683—48no—
176C4×Dic5—48no—
177C23×Q8—51no—
178C22×C4⋊C4—51no—
179C22×C4⋊C4—51no—
180C22×C4⋊C4—52no—
181C22×C4⋊C4—51no—
182C22×C4⋊C4—52no—
183C22×C4⋊C4C2×D511yescharacteristic
184C22×C4⋊C4C2×D511yescharacteristic
185C22×C42—52no—
186C22×C42C2×D511yescharacteristic
187#391—58no—
188#391—108no—
189C2×#95—52no—
190C2×#95—52no—
191C2×#95—52no—
192C2×#95—52no—
193C2×#95—52no—
194C2×#95—52no—
195C2×#95—52no—
196C2×#95—52no—
197C2×#95—52no—
198C2×#95C2×D512yes—
199C2×#95C2×D512yes—
200C23×C5C23×C411yescharacteristic
201C23×C5C22×D411yescharacteristic
202C23×C5C22×Q811yescharacteristic
203C23×C5C22×Q811yescharacteristic
204C23×C5C22×Q811yescharacteristic
205C23×C5C2×#4111yescharacteristic
206C23×C5C2×#4111yescharacteristic
207C23×C5H(5,𝔽2)11yescharacteristic
208C23×C5H(5,𝔽2)11yescharacteristic
209C23×C5H(5,𝔽2)11yescharacteristic
210C23×C5H(5,𝔽2)11yescharacteristic
211C23×C5H(5,𝔽2)11yescharacteristic
212C23×C5H(5,𝔽2)11yescharacteristic
213C23×C52−1+411yescharacteristic
214C23×C52−1+411yescharacteristic
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—22no—
224C2×C4×C5—22no—
225C2×C4×C5—22no—
226C2×C4×C5—22no—
227C2×C4×C5—22no—
228C2×C4×C5—22no—
229C2×C4×C5—22no—
230C2×C4×C5—22no—
231C2×C4×C5—22no—
232C2×C4×C5—22no—
233C2×C4×C5—24no—
234C2×C4×C5—24no—
235C2×C4×C5—24no—
236C2×C4×C5—42no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5—42no—
241C2×C4×C5—42no—
242C2×C4×C5—42no—
243C2×C4×C5—42no—
244C2×C4×C5—42no—
245C2×C4×C5—42no—
246C2×C4×C5—42no—
247C2×C4×C5C2×C4⋊C414yes—
248C2×C4×C5C4×Q814yes—
249C2×C4×C5C4×Q814yes—
250C2×Dic5—24no—
251C2×Dic5—24no—
252C2×Dic5—24no—
253C2×Dic5—24no—
254C2×Dic5—24no—
255C2×Dic5—24no—
256C2×Dic5—24no—
257C2×Dic5—24no—
258C2×Dic5—24no—
259C2×Dic5—24no—
260C2×Dic5—24no—
261C2×Dic5—24no—
262C2×Dic5—42no—
263C2×Dic5—42no—
264C2×Dic5—42no—
265C2×Dic5—42no—
266C2×Dic5—42no—
267C2×Dic5—42no—
268C2×Dic5—42no—
269C2×Dic5—42no—
270C2×Dic5—42no—
271C2×Dic5—42no—
272C2×Dic5—42no—
273C2×Dic5—42no—
274C2×Dic5—42no—
275C2×Dic5—42no—
276C2×Dic5—42no—
277C2×Dic5C2×C4⋊C418yes—
278Dic10—416no—
279C22×Q8—54no—
280C22×Q8—54no—
281C22×Q8—54no—
282C22×Q8—201no—
283C22×Q8—201no—
284C22×Q8—201no—
285C22×Q8—201no—
286C23×C4—52no—
287C23×C4—52no—
288C23×C4—52no—
289C23×C4—52no—
290C23×C4C22×D512yes—
291C23×C4C22×D512yes—
292C23×C4C22×D511yescharacteristic
293C23×C4C22×D511yescharacteristic
294C23×C4C22×D511yescharacteristic
295C2×C4⋊C4—22no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—54no—
301C2×C4⋊C4—54no—
302C2×C4⋊C4—104no—
303C2×C4⋊C4—102no—
304C2×C4⋊C4—202no—
305C2×C4⋊C4—202no—
306C2×C4⋊C4—202no—
307C2×C4⋊C4—202no—
308C2×C4⋊C4—202no—
309C2×C4⋊C4—201no—
310C2×C4⋊C4—201no—
311C2×C4⋊C4—201no—
312C2×C4⋊C4—201no—
313C2×C4⋊C4—201no—
314C2×C4⋊C4—201no—
315C2×C4⋊C4Dic1014yescomplemented
316C2×C42—41no—
317C2×C42—41no—
318C2×C42—104no—
319C2×C42—202no—
320C2×C42—202no—
321C2×C42C4×D514yes—
322#95—24no—
323#95—24no—
324#95—58no—
325#95—58no—
326#95—104no—
327#95—104no—
328#95—104no—
329#95—104no—
330#95—202no—
331#95—202no—
332#95—202no—
333C22×C5C22×C4⋊C411yescharacteristic
334C22×C5C2×C4×Q811yescharacteristic
335C22×C5C2×C4×Q811yescharacteristic
336C22×C5#51811yescharacteristic
337C22×C5#51811yescharacteristic
338C22×C5#52011yescharacteristic
339C22×C5#52011yescharacteristic
340C22×C5#53411yescharacteristic
341C22×C5#53411yescharacteristic
342C22×C5#53811yescharacteristic
343C22×C5#53811yescharacteristic
344C22×C5#53911yescharacteristic
345C22×C5#53911yescharacteristic
346C22×C5#54311yescharacteristic
347C22×C5#54311yescharacteristic
348C22×C5#54311yescharacteristic
349C22×C5#54311yescharacteristic
350C22×C5#54411yescharacteristic
351C22×C5#54411yescharacteristic
352C22×C5D4×Q811yescharacteristic
353C22×C5D4×Q811yescharacteristic
354C22×C5#55011yescharacteristic
355C22×C5#55011yescharacteristic
356C22×C5#55411yescharacteristic
357C22×C5#55411yescharacteristic
358C22×C5#55511yescharacteristic
359C22×C5#55711yescharacteristic
360C22×C5#55711yescharacteristic
361C22×C5Q8211yescharacteristic
362C22×C5Q8211yescharacteristic
363C22×C5Q8211yescharacteristic
364C22×C5H(3,𝔽4)11yescharacteristic
365C22×C5#56211yescharacteristic
366C22×C5#56211yescharacteristic
367C22×C5#56311yescharacteristic
368C4×C5—24no—
369C4×C5—24no—
370C4×C5—24no—
371C4×C5—44no—
372C4×C5—82no—
373Dic5—28no—
374Dic5—44no—
375Dic5—44no—
376Dic5—82no—
377C24C23×D511yescharacteristic
378C2×Q8—516no—
379C2×Q8—204no—
380C2×Q8—204no—
381C2×Q8—204no—
382C2×Q8—204no—
383C2×Q8—204no—
384C2×Q8—204no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—54no—
411C22×C4—54no—
412C22×C4—54no—
413C22×C4—54no—
414C22×C4—54no—
415C22×C4—102no—
416C22×C4—102no—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—102no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—102no—
423C22×C4—102no—
424C22×C4—102no—
425C22×C4—102no—
426C22×C4—102no—
427C22×C4—102no—
428C22×C4—102no—
429C22×C4—102no—
430C22×C4—102no—
431C22×C4—102no—
432C22×C4—102no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—102no—
436C22×C4—102no—
437C22×C4—102no—
438C22×C4C2×Dic1014yes—
439C22×C4C2×Dic1012yes—
440C22×C4C2×C4×D512yes—
441C22×C4C2×C4×D512yes—
442C22×C4C2×C4×D512yes—
443C22×C4#70912yes—
444C22×C4D4×D512yes—
445C22×C4#71112yes—
446C22×C4Q8×D512yes—
447C22×C4Q8×D512yes—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—204no—
451C4⋊C4—204no—
452C4⋊C4—204no—
453C4⋊C4—208no—
454C4⋊C4—208no—
455C42—44no—
456C42—208no—
457C2×C5#231511yescharacteristic
458C2×C5#232911yescharacteristic
459C2×C5#232911yescharacteristic
460C2×C5Q8×C4⋊C411yescharacteristic
461C2×C5Q8×C4⋊C411yescharacteristic
462C2×C5#236911yescharacteristic
463C2×C5#237911yescharacteristic
464C2×C5#273211yescharacteristic
465C2×C5#273211yescharacteristic
466C2×C5#273311yescharacteristic
467C2×C5#273411yescharacteristic
468C2×C5#280611yescharacteristic
469C2×C5#280611yescharacteristic
470C2×C5#280911yescharacteristic
471C2×C5#281111yescharacteristic
472C23C22×Dic1011yescharacteristic
473C23C22×C4×D511yescharacteristic
474C23C2×#70911yescharacteristic
475C23C2×D4×D511yescharacteristic
476C23C2×#71111yescharacteristic
477C23#414411yescharacteristic
478C23#414411yescharacteristic
479C23#414411yescharacteristic
480C23C2×Q8×D511yescharacteristic
481C23C2×Q8×D511yescharacteristic
482C23#414711yescharacteristic
483C23#414911yescharacteristic
484C23#414911yescharacteristic
485C23#414911yescharacteristic
486C23#415011yescharacteristic
487Q8—2016no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—58no—
521C2×C4—104no—
522C2×C4—104no—
523C2×C4—104no—
524C2×C4—104no—
525C2×C4—104no—
526C2×C4—104no—
527C2×C4—104no—
528C2×C4—104no—
529C2×C4—104no—
530C2×C4—104no—
531C2×C4—104no—
532C2×C4—104no—
533C2×C4—202no—
534C2×C4—202no—
535C2×C4—202no—
536C2×C4—202no—
537C2×C4—202no—
538C2×C4—202no—
539C2×C4—202no—
540C2×C4—202no—
541C2×C4—202no—
542C2×C4—202no—
543C2×C4—202no—
544C2×C4—202no—
545C2×C4—202no—
546C2×C4—202no—
547C2×C4—202no—
548C2×C4C4×Dic1014yes—
549C2×C4#403314yes—
550C2×C4D5×C4⋊C414yes—
551C5#1446711yescharacteristic, complemented, Sylow
552C22C2×C4×Dic1011yescharacteristic
553C22#6581711yescharacteristic
554C22#6582011yescharacteristic
555C22#6582811yescharacteristic
556C22C2×#403311yescharacteristic
557C22#6583411yescharacteristic
558C22C2×D5×C4⋊C411yescharacteristic
559C22#6583811yescharacteristic
560C22#6584911yescharacteristic
561C22#6585511yescharacteristic
562C22#6585711yescharacteristic
563C22D4×Dic1011yescharacteristic
564C22#6587711yescharacteristic
565C22#6588711yescharacteristic
566C22#6589711yescharacteristic
567C22Q8×Dic1011yescharacteristic
568C22Q8×Dic1011yescharacteristic
569C22#6590111yescharacteristic
570C22#6591311yescharacteristic
571C22#6593611yescharacteristic
572C22#6593911yescharacteristic
573C22#6593911yescharacteristic
574C22#6595111yescharacteristic
575C22#6595711yescharacteristic
576C22#6596811yescharacteristic
577C22#6596811yescharacteristic
578C22#6596811yescharacteristic
579C22#6601711yescharacteristic
580C22#6601811yescharacteristic
581C22#6603311yescharacteristic
582C22#6603411yescharacteristic
583C22#6605211yescharacteristic
584C22#6605511yescharacteristic
585C22#6605611yescharacteristic
586C22#6606111yescharacteristic
587C4—24no—
588C4—24no—
589C4—24no—
590C4—44no—
591C4—82no—
592C4—108no—
593C4—204no—
594C4—204no—
595C4—402no—
596C2#1060506511yescharacteristic
597C2C4⋊C4×Dic1011yescharacteristic
598C2#1060538711yescharacteristic
599C2#1060560511yescharacteristic
600C2#1060573611yescharacteristic
601C2#1060596111yescharacteristic
602C2#1060605411yescharacteristic
603C2#1060786511yescharacteristic
604C2#1060786611yescharacteristic
605C2#1060791411yescharacteristic
606C2#1060791711yescharacteristic
607C2#1060813211yescharacteristic
608C2#1060813311yescharacteristic
609C2#1060832911yescharacteristic
610C2#1060833511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, prime radical, cosocleC24×C5C24
hypercenterC4⋊#95D5
hypocenterC5#14467
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
31. #65218C4semidirect
55. C2×C5×C4⋊C4Q8semidirect
67. C2×C4⋊Dic5Q8semidirect
167. C2×Dic10C4⋊C4semidirect
315. C2×C4⋊C4Dic10semidirect
551. C5#14467semidirect

Maximal subgroups

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

subgroupindex
C2×#652182
C2×#649352
C5×C4⋊#952
#106023612
#106023572
#106023282
#106002132
#106002042
#106002002
#144675