Finite Group Databasebeta

← #12021356

Subgroups — #12021356

Order 1280.

1602 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
2C2×#65500C211yesmaximal, characteristic
3C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
4#10602920C211yesmaximal, characteristic
5#10602339C212yesmaximal
6#10602338C212yesmaximal
7#10602327C211yesmaximal, characteristic, complemented
8#10602327C211yesmaximal, characteristic, complemented
9#10602327C211yesmaximal, characteristic, complemented
10#10600205C212yesmaximal, complemented
11#10600194C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2212yes—
19C22×C4⋊Dic5C2212yes—
20C22×C4×Dic5C2212yes—
21C4×C5×C22⋊C4C418yescomplemented
22C2×C5×#95C2211yescharacteristic
23C2×C5×#95C2211yescharacteristic
24#65500—24no—
25C2×#3963C2212yes—
26C2×#3963C2212yes—
27C2×#3963C2212yes—
28C2×#3963C2212yes—
29C2×#3963C2211yescharacteristic
30C2×#3963C2211yescharacteristic
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C4×C4⋊Dic5—24no—
38#13887—51nomaximal, Sylow
39C25×C5C2311yescharacteristic
40C23×C4×C5—24no—
41C23×C4×C5—22no—
42C23×C4×C5—22no—
43C23×C4×C5—42no—
44C23×C4×C5C2×C414yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×Dic5C2312yes—
52C23×Dic5C2312yes—
53C23×Dic5C2312yes—
54C23×Dic5C2312yes—
55C2×C5×C22⋊C4—22no—
56C2×C5×C22⋊C4—24no—
57C2×C5×C22⋊C4—22no—
58C2×C5×C22⋊C4C2×C414yes—
59C2×C5×C22⋊C4C2×C414yes—
60C2×C42×C5—22no—
61C2×C42×C5—22no—
62C2×C42×C5—42no—
63C2×C42×C5C2×C414yes—
64C2×C42×C5C2×C414yes—
65C2×C22⋊Dic5—24no—
66C2×C22⋊Dic5—24no—
67C2×C22⋊Dic5—24no—
68C2×C22⋊Dic5—24no—
69C2×C22⋊Dic5—42no—
70C2×C22⋊Dic5—42no—
71C2×C4⋊Dic5—24no—
72C2×C4⋊Dic5—24no—
73C2×C4⋊Dic5—24no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5—24no—
76C2×C4×Dic5—42no—
77C5×#95C2×C414yes—
78C5×#95C2×C414yes—
79#3963—22no—
80#3963—22no—
81#3963—24no—
82#3963—24no—
83#3963—22no—
84#3963—24no—
85#3963—24no—
86#3963—42no—
87#3963—42no—
88#3963—42no—
89#3963—42no—
90#3963D414yes—
91C2×#381—51no—
92C2×C4×C4⋊C4—51no—
93C2×C4×C22⋊C4D511yescharacteristic
94#1442—52no—
95#1439—52no—
96#1437—52no—
97#1434—51no—
98#1434—51no—
99#1434—51no—
100#1434—52no—
101C22⋊#95—51no—
102C24×C5—21no—
103C24×C5—22no—
104C24×C5—22no—
105C24×C5—21no—
106C24×C5—21no—
107C24×C5—21no—
108C24×C5—21no—
109C24×C5—22no—
110C24×C5—21no—
111C24×C5C22×C412yes—
112C24×C5#4114yes—
113C24×C5C2411yescharacteristic
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—28no—
124C22×C4×C5—21no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—28no—
137C22×C4×C5—44no—
138C22×C4×C5—48no—
139C22×C4×C5—48no—
140C22×C4×C5C22×C412yes—
141C22×C4×C5C22×C412yes—
142C22×C4×C5C22×C412yes—
143C22×C4×C5C22×C412yes—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C22×C412yes—
146C22×C4×C5C2×D412yes—
147C22×C4×C5#4112yes—
148C22×C4×C5#4114yes—
149C22×C4×C5#4112yes—
150C22×C4×C5#4112yes—
151C22×Dic5—22no—
152C22×Dic5—22no—
153C22×Dic5—22no—
154C22×Dic5—22no—
155C22×Dic5—22no—
156C22×Dic5—22no—
157C22×Dic5—22no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—22no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5C2×D414yes—
178C22×Dic5#4114yes—
179C5×C22⋊C4—28no—
180C5×C22⋊C4—28no—
181C42×C5—28no—
182C42×C5—44no—
183C22⋊Dic5—48no—
184C22⋊Dic5—48no—
185C4⋊Dic5—216no—
186C4×Dic5—48no—
187C24×C4C2×D511yescharacteristic
188C22×C4⋊C4—52no—
189C22×C22⋊C4—52no—
190C22×C22⋊C4—52no—
191C22×C22⋊C4C2×D511yescharacteristic
192C22×C22⋊C4C2×D511yescharacteristic
193C22×C42—52no—
194C22×C42C2×D511yescharacteristic
195C22×C42C2×D511yescharacteristic
196#381—104no—
197C4×C4⋊C4—104no—
198C4×C22⋊C4Dic518yescomplemented
199C2×#95—51no—
200C2×#95—51no—
201C2×#95—51no—
202C2×#95—52no—
203C2×#95—51no—
204C2×#95—52no—
205C2×#95—52no—
206C2×#95—52no—
207C2×#95—52no—
208C2×#95—52no—
209C2×#95—52no—
210C2×#95—52no—
211C2×#95C2×D511yescharacteristic
212C2×#95C2×D511yescharacteristic
213C23×C5—22no—
214C23×C5—22no—
215C23×C5—22no—
216C23×C5—22no—
217C23×C5—22no—
218C23×C5—22no—
219C23×C5—24no—
220C23×C5—24no—
221C23×C5—24no—
222C23×C5—24no—
223C23×C5—24no—
224C23×C5—24no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—42no—
228C23×C5—42no—
229C23×C5—41no—
230C23×C5—41no—
231C23×C5—41no—
232C23×C5—42no—
233C23×C5—41no—
234C23×C5—42no—
235C23×C5#11714yes—
236C23×C5C23×C411yescharacteristic
237C23×C5C22×D411yescharacteristic
238C23×C5C2×#4112yes—
239C23×C5C2×#4112yes—
240C23×C5C2×#4111yescharacteristic
241C23×C5C2×#4111yescharacteristic
242C23×C5C2×#4111yescharacteristic
243C23×C5C2×#4112yes—
244C23×C5H(5,𝔽2)12yes—
245C23×C5H(5,𝔽2)11yescharacteristic
246C23×C52−1+411yescharacteristic
247C2×C4×C5—22no—
248C2×C4×C5—22no—
249C2×C4×C5—22no—
250C2×C4×C5—22no—
251C2×C4×C5—22no—
252C2×C4×C5—22no—
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—22no—
256C2×C4×C5—24no—
257C2×C4×C5—22no—
258C2×C4×C5—24no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—416no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5#11714yes—
278C2×C4×C5#11714yes—
279C2×C4×C5C4×D414yes—
280C2×Dic5—24no—
281C2×Dic5—24no—
282C2×Dic5—24no—
283C2×Dic5—24no—
284C2×Dic5—24no—
285C2×Dic5—24no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—42no—
289C2×Dic5—42no—
290C2×Dic5—42no—
291C2×Dic5—42no—
292C2×Dic5—42no—
293C2×Dic5—42no—
294C2×Dic5—42no—
295C2×Dic5—42no—
296C2×Dic5—42no—
297C2×Dic5—42no—
298C2×Dic5—42no—
299C2×Dic5—42no—
300C2×Dic5—42no—
301C2×Dic5—42no—
302C2×Dic5—42no—
303C2×Dic5—42no—
304C2×Dic5—42no—
305C2×Dic5—42no—
306C2×Dic5—42no—
307C2×Dic5—42no—
308C25C22×D511yescharacteristic
309C23×C4—24no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—42no—
313C23×C4—52no—
314C23×C4—52no—
315C23×C4—52no—
316C23×C4—52no—
317C23×C4C2×Dic514yes—
318C23×C4C22×D511yescharacteristic
319C23×C4C22×D511yescharacteristic
320C23×C4C22×D511yescharacteristic
321C23×C4C22×D511yescharacteristic
322C23×C4C22×D511yescharacteristic
323C23×C4C22×D511yescharacteristic
324C2×C4⋊C4—104no—
325C2×C4⋊C4—104no—
326C2×C4⋊C4—104no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—104no—
331C2×C22⋊C4—104no—
332C2×C22⋊C4—104no—
333C2×C22⋊C4—104no—
334C2×C22⋊C4—202no—
335C2×C22⋊C4—202no—
336C2×C22⋊C4C2×Dic514yes—
337C2×C22⋊C4C2×Dic514yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—42no—
341C2×C42—104no—
342C2×C42—104no—
343C2×C42—202no—
344C2×C42C2×Dic514yes—
345C2×C42C2×Dic514yes—
346#95—54no—
347#95—104no—
348#95—104no—
349#95—104no—
350#95—104no—
351#95—102no—
352#95—102no—
353#95—102no—
354#95—202no—
355#95—202no—
356#95—202no—
357#95—202no—
358#95C2×Dic514yes—
359#95C2×Dic514yes—
360C22×C5—24no—
361C22×C5—24no—
362C22×C5—24no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—44no—
367C22×C5—44no—
368C22×C5—44no—
369C22×C5—44no—
370C22×C5—42no—
371C22×C5C2×#11711yescharacteristic
372C22×C5C2×#11711yescharacteristic
373C22×C5C2×#11711yescharacteristic
374C22×C5C2×C4×D411yescharacteristic
375C22×C5C4×#4111yescharacteristic
376C22×C5#51811yescharacteristic
377C22×C5#52011yescharacteristic
378C22×C5#52512yes—
379C22×C5#52912yes—
380C22×C5#52912yes—
381C22×C5#52912yes—
382C22×C5#54012yes—
383C22×C5#54212yes—
384C22×C5#54612yes—
385C22×C5#54611yescharacteristic
386C22×C5#54811yescharacteristic
387C22×C5#55112yes—
388C22×C5#55112yes—
389C22×C5#55212yes—
390C22×C5#55211yescharacteristic
391C22×C5#55312yes—
392C22×C5#55311yescharacteristic
393C22×C5#55912yes—
394C4×C5—24no—
395C4×C5—24no—
396C4×C5—24no—
397C4×C5—42no—
398C4×C5—42no—
399C4×C5—42no—
400Dic5—44no—
401Dic5—44no—
402Dic5—82no—
403Dic5—82no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24#70914yes—
414C24C22×Dic512yes—
415C24C23×D511yescharacteristic
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—28no—
438C22×C4—28no—
439C22×C4—44no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—54no—
443C22×C4—54no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—102no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—102no—
450C22×C4—102no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—102no—
457C22×C4—102no—
458C22×C4—102no—
459C22×C4—102no—
460C22×C4—102no—
461C22×C4—102no—
462C22×C4—102no—
463C22×C4—102no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—102no—
467C22×C4—102no—
468C22×C4—102no—
469C22×C4—102no—
470C22×C4#70912yes—
471C22×C4#70914yes—
472C22×C4#70912yes—
473C22×C4D4×D512yes—
474C22×C4#71112yes—
475C22×C4C22×Dic512yes—
476C22×C4C22×Dic512yes—
477C22×C4C22×Dic512yes—
478C22×C4C22×Dic512yes—
479C22×C4C22×Dic512yes—
480C22×C4C22×Dic512yes—
481C4⋊C4—1016no—
482C22⋊C4—28no—
483C22⋊C4—28no—
484C22⋊C4—208no—
485C22⋊C4—208no—
486C42—28no—
487C42—44no—
488C42—208no—
489C2×C5—44no—
490C2×C5#228311yescharacteristic
491C2×C5#229011yescharacteristic
492C2×C5#231911yescharacteristic
493C2×C5#234211yescharacteristic
494C2×C5#234311yescharacteristic
495C2×C5#235211yescharacteristic
496C2×C5#235711yescharacteristic
497C2×C5#245712yes—
498C2×C5#245812yes—
499C2×C5#251512yes—
500C2×C5#251612yes—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—42no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—41no—
523C23#407214yes—
524C23C2×#70912yes—
525C23C2×#70912yes—
526C23C2×#70911yescharacteristic
527C23C2×#70911yescharacteristic
528C23C2×D4×D511yescharacteristic
529C23C2×#71111yescharacteristic
530C23#414412yes—
531C23D5×#4112yes—
532C23#414911yescharacteristic
533C23#415011yescharacteristic
534C23C23×Dic511yescharacteristic
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—416no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—104no—
566C2×C4—104no—
567C2×C4—104no—
568C2×C4—104no—
569C2×C4—104no—
570C2×C4—104no—
571C2×C4—202no—
572C2×C4—202no—
573C2×C4—202no—
574C2×C4—202no—
575C2×C4—202no—
576C2×C4—202no—
577C2×C4—202no—
578C2×C4—202no—
579C2×C4—202no—
580C2×C4—202no—
581C2×C4—202no—
582C2×C4—202no—
583C2×C4—202no—
584C2×C4—202no—
585C2×C4—202no—
586C2×C4—202no—
587C2×C4—202no—
588C2×C4—202no—
589C2×C4—202no—
590C2×C4—202no—
591C2×C4—202no—
592C2×C4—202no—
593C2×C4#407214yes—
594C2×C4#407214yes—
595C2×C4D4×Dic514yes—
596C5#1388711yescharacteristic, complemented, Sylow
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22#6581312yes—
609C22#6581312yes—
610C22#6582412yes—
611C22#6582912yes—
612C22#6586112yes—
613C22#6586512yes—
614C22#6587212yes—
615C22#6587511yescharacteristic
616C22#6588112yes—
617C22#6588411yescharacteristic
618C22#6588611yescharacteristic
619C22#6589212yes—
620C22#6589312yes—
621C22#6589512yes—
622C22#6589612yes—
623C22#6589911yescharacteristic
624C22C2×#407211yescharacteristic
625C22C2×#407211yescharacteristic
626C22C2×#407211yescharacteristic
627C22C2×D4×Dic511yescharacteristic
628C22#6613211yescharacteristic
629C22#41×Dic511yescharacteristic
630C22#6616111yescharacteristic
631C4—24no—
632C4—24no—
633C4—24no—
634C4—42no—
635C4—42no—
636C4—42no—
637C4—204no—
638C4—204no—
639C4—402no—
640C4—402no—
641C2—44no—
642C2#1060522712yes—
643C2#1060525312yes—
644C2#1060525412yes—
645C2#1060532012yes—
646C2#1061379111yescharacteristic
647C2#1061382811yescharacteristic
648C2#1061396811yescharacteristic
649C2#1061404911yescharacteristic
650C2#1061405611yescharacteristic
651C2#1061406611yescharacteristic
652C2#1061406911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13887
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C4⋊Dic5C2semidirect
7. #10602327C2semidirect
8. #10602327C2semidirect
9. #10602327C2semidirect
10. #10600205C2semidirect
11. #10600194C2semidirect
21. C4×C5×C22⋊C4C4semidirect
198. C4×C22⋊C4Dic5semidirect
596. C5#13887semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C22⋊C42
C2×#655002
C2×C4×C4⋊Dic52
#106029202
#106023392
#106023382
#106023272
#106002052
#106001942
#138875