Finite Group Databasebeta

← #12020997

Subgroups — #12020997

Order 1280.

1814 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
2C2×C4×C22⋊Dic5C211yesmaximal, characteristic
3C2×C4×C22⋊Dic5C211yesmaximal, characteristic
4C2×C4×#683C211yesmaximal, characteristic, complemented
5C2×#65221C211yesmaximal, characteristic, complemented
6#10602342C212yesmaximal
7#10602340C212yesmaximal
8C4×#3963C211yesmaximal, characteristic, complemented
9C4×#3963C211yesmaximal, characteristic, complemented
10#10600210C212yesmaximal, complemented
11#10600206C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C22⋊C4C2212yes—
14C22×C42×C5C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C22⋊Dic5C2212yes—
17C22×C22⋊Dic5C2211yescharacteristic
18C22×C22⋊Dic5C2211yescharacteristic
19C22×#683C2212yes—
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C22×C4×Dic5C2211yescharacteristic
24C4×C5×C22⋊C4—24no—
25C2×C5×#95C2212yes—
26C4×C22⋊Dic5—24no—
27C4×C22⋊Dic5C418yescomplemented
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38#65221—24no—
39C4×#683—24no—
40#13842—51nomaximal, Sylow
41C25×C5C2311yescharacteristic
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5C2×C414yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2312yes—
51C23×C4×C5C2312yes—
52C23×C4×C5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C23×Dic5C2311yescharacteristic
55C23×Dic5C2311yescharacteristic
56C23×Dic5C2312yes—
57C23×Dic5C2312yes—
58C23×Dic5C2311yescharacteristic
59C2×C5×C22⋊C4—24no—
60C2×C5×C22⋊C4—24no—
61C2×C5×C22⋊C4—24no—
62C2×C42×C5—22no—
63C2×C42×C5—22no—
64C2×C42×C5—22no—
65C2×C42×C5—22no—
66C2×C42×C5—22no—
67C2×C42×C5D414yes—
68C2×C22⋊Dic5—24no—
69C2×C22⋊Dic5—24no—
70C2×C22⋊Dic5—24no—
71C2×C22⋊Dic5—24no—
72C2×C22⋊Dic5—24no—
73C2×C22⋊Dic5C2×C414yes—
74C2×C22⋊Dic5C2×C414yes—
75C2×#683—24no—
76C2×#683—24no—
77C2×#683—24no—
78C2×C4×Dic5—22no—
79C2×C4×Dic5—22no—
80C2×C4×Dic5—22no—
81C2×C4×Dic5—22no—
82C2×C4×Dic5—22no—
83C2×C4×Dic5—22no—
84C2×C4×Dic5—22no—
85C2×C4×Dic5—22no—
86C2×C4×Dic5—22no—
87C2×C4×Dic5C2×C414yes—
88C2×C4×Dic5C2×C414yes—
89C2×C4×Dic5D414yes—
90C5×#95—24no—
91#3963—24no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963—24no—
96#3963—24no—
97#3963—24no—
98#3963—24no—
99#3963C2×C414yes—
100#3963C2×C414yes—
101C2×C4×C4⋊C4—51no—
102C2×C4×C22⋊C4—51no—
103C2×C4×C22⋊C4—51no—
104C2×C4×C22⋊C4D511yescharacteristic
105C2×#376—51no—
106#1443—52no—
107#1442—52no—
108#1440—52no—
109#1439—52no—
110C4×#95—51no—
111C4×#95—51no—
112C24×C5—21no—
113C24×C5—21no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—22no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5C22×C412yes—
122C24×C5#4114yes—
123C24×C5C2411yescharacteristic
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
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—21no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—28no—
143C22×C4×C5—28no—
144C22×C4×C5—28no—
145C22×C4×C5—44no—
146C22×C4×C5—44no—
147C22×C4×C5—44no—
148C22×C4×C5—44no—
149C22×C4×C5C22×C412yes—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C2×D412yes—
152C22×C4×C5C2×D414yes—
153C22×C4×C5C2×D412yes—
154C22×C4×C5#4114yes—
155C22×C4×C5#4112yes—
156C22×C4×C5#4112yes—
157C22×C4×C5#4112yes—
158C22×C4×C5#4112yes—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—22no—
162C22×Dic5—22no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
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×Dic5—22no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—22no—
181C22×Dic5—21no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5C22×C412yes—
187C22×Dic5C22×C412yes—
188C22×Dic5C22×C412yes—
189C22×Dic5C22×C412yes—
190C22×Dic5C2×D414yes—
191C22×Dic5#4114yes—
192C22×Dic5#4114yes—
193C5×C22⋊C4—216no—
194C42×C5—28no—
195C42×C5—44no—
196C22⋊Dic5—216no—
197C22⋊Dic5—28no—
198C22⋊Dic5—28no—
199#683—216no—
200C4×Dic5—28no—
201C4×Dic5—28no—
202C4×Dic5—28no—
203C4×Dic5—44no—
204C24×C4C2×D511yescharacteristic
205C22×C4⋊C4—52no—
206C22×C22⋊C4—51no—
207C22×C22⋊C4—51no—
208C22×C22⋊C4—52no—
209C22×C22⋊C4C2×D512yes—
210C22×C42—51no—
211C22×C42—51no—
212C22×C42—51no—
213C22×C42—51no—
214C22×C42C2×D511yescharacteristic
215C22×C42C2×D511yescharacteristic
216C4×C4⋊C4—104no—
217C4×C22⋊C4—24no—
218C4×C22⋊C4—58no—
219C4×C22⋊C4—104no—
220#376—104no—
221C2×#95—51no—
222C2×#95—51no—
223C2×#95—52no—
224C2×#95—52no—
225C2×#95—52no—
226C2×#95—52no—
227C2×#95—52no—
228C2×#95—52no—
229C2×#95—52no—
230C2×#95—52no—
231C2×#95C2×D512yes—
232C23×C5—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—24no—
239C23×C5—24no—
240C23×C5—24no—
241C23×C5—24no—
242C23×C5—24no—
243C23×C5—24no—
244C23×C5—41no—
245C23×C5—41no—
246C23×C5—42no—
247C23×C5—41no—
248C23×C5—41no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—42no—
254C23×C5#11714yes—
255C23×C5C23×C411yescharacteristic
256C23×C5C22×D411yescharacteristic
257C23×C5C22×D411yescharacteristic
258C23×C5C2×#4112yes—
259C23×C5C2×#4111yescharacteristic
260C23×C5C2×#4112yes—
261C23×C5C2×#4111yescharacteristic
262C23×C5C2×#4111yescharacteristic
263C23×C5C2×#4111yescharacteristic
264C23×C5C2×#4112yes—
265C23×C5C2×#4112yes—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—24no—
271C2×C4×C5—24no—
272C2×C4×C5—24no—
273C2×C4×C5—24no—
274C2×C4×C5—24no—
275C2×C4×C5—42no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—42no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—42no—
282C2×C4×C5—42no—
283C2×C4×C5—42no—
284C2×C4×C5—42no—
285C2×C4×C5—42no—
286C2×C4×C5—42no—
287C2×C4×C5—416no—
288C2×C4×C5#11714yes—
289C2×C4×C5C4×D414yes—
290C2×C4×C5C4×D414yes—
291C2×C4×C5#12114yes—
292C2×C4×C5#12314yes—
293C2×C4×C5#12414yes—
294C2×C4×C5#12614yes—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—24no—
298C2×Dic5—24no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—24no—
309C2×Dic5—24no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—24no—
313C2×Dic5—24no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—42no—
318C2×Dic5—42no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5—42no—
325C2×Dic5—42no—
326C2×Dic5—42no—
327C2×Dic5—42no—
328C2×Dic5#11714yes—
329C25C22×D511yescharacteristic
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—51no—
337C23×C4—52no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4—52no—
342C23×C4C4×D514yes—
343C23×C4C22×D511yescharacteristic
344C23×C4C22×D512yes—
345C23×C4C22×D512yes—
346C23×C4C22×D511yescharacteristic
347C2×C4⋊C4—104no—
348C2×C4⋊C4—104no—
349C2×C4⋊C4—104no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—54no—
354C2×C22⋊C4—54no—
355C2×C22⋊C4—104no—
356C2×C22⋊C4—104no—
357C2×C22⋊C4—104no—
358C2×C22⋊C4—104no—
359C2×C22⋊C4—104no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—54no—
366C2×C42—54no—
367C2×C42—54no—
368C2×C42—102no—
369C2×C42—102no—
370C2×C42—102no—
371C2×C42—102no—
372C2×C42—102no—
373C2×C42—102no—
374C2×C42—102no—
375C2×C42—102no—
376C2×C42—102no—
377C2×C42C22⋊D514yes—
378#95—24no—
379#95—54no—
380#95—54no—
381#95—104no—
382#95—104no—
383#95—104no—
384#95—104no—
385#95—104no—
386#95—104no—
387#95—104no—
388#95—104no—
389C22×C5—24no—
390C22×C5—24no—
391C22×C5—24no—
392C22×C5—44no—
393C22×C5—44no—
394C22×C5—44no—
395C22×C5—44no—
396C22×C5—42no—
397C22×C5—42no—
398C22×C5—42no—
399C22×C5—42no—
400C22×C5C2×#11711yescharacteristic
401C22×C5C2×#11711yescharacteristic
402C22×C5C2×#11711yescharacteristic
403C22×C5C2×C4×D411yescharacteristic
404C22×C5C2×C4×D411yescharacteristic
405C22×C5C4×#4111yescharacteristic
406C22×C5C4×#4111yescharacteristic
407C22×C5C2×#12111yescharacteristic
408C22×C5C2×#12311yescharacteristic
409C22×C5#52512yes—
410C22×C5#52512yes—
411C22×C5#52512yes—
412C22×C5C2×#12411yescharacteristic
413C22×C5C2×#12611yescharacteristic
414C22×C5#52912yes—
415C22×C5#52912yes—
416C22×C5#52912yes—
417C22×C5#52912yes—
418C22×C5#52912yes—
419C22×C5#52912yes—
420C22×C5#52912yes—
421C22×C5#52912yes—
422C22×C5#53212yes—
423C4×C5—44no—
424C4×C5—44no—
425C4×C5—42no—
426C4×C5#38818yes—
427Dic5—24no—
428Dic5—44no—
429Dic5—44no—
430Dic5—42no—
431Dic5—42no—
432Dic5—42no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24C2×C4×D512yes—
443C24#70914yes—
444C24C23×D511yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—52no—
471C22×C4—54no—
472C22×C4—52no—
473C22×C4—52no—
474C22×C4—52no—
475C22×C4—54no—
476C22×C4—54no—
477C22×C4—102no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—102no—
488C22×C4—102no—
489C22×C4—102no—
490C22×C4—101no—
491C22×C4—102no—
492C22×C4—101no—
493C22×C4—102no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—102no—
499C22×C4—102no—
500C22×C4—102no—
501C22×C4—101no—
502C22×C4—101no—
503C22×C4—102no—
504C22×C4C2×C4×D512yes—
505C22×C4C2×C4×D512yes—
506C22×C4#70914yes—
507C22×C4#70912yes—
508C22×C4D4×D512yes—
509C22×C4#71112yes—
510C22×C4#71112yes—
511C22×C4#71112yes—
512C22×C4C2×C22⋊D514yes—
513C22×C4C2×C22⋊D512yes—
514C4⋊C4—1016no—
515C22⋊C4—216no—
516C22⋊C4—108no—
517C22⋊C4—1016no—
518C22⋊C4—108no—
519C42—28no—
520C42—44no—
521C42—108no—
522C42—108no—
523C42—108no—
524C42—204no—
525C2×C5—44no—
526C2×C5#228311yescharacteristic
527C2×C5C2×#38811yescharacteristic
528C2×C5#229011yescharacteristic
529C2×C5#229011yescharacteristic
530C2×C5#229011yescharacteristic
531C2×C5#229311yescharacteristic
532C2×C5#229811yescharacteristic
533C2×C5#239212yes—
534C2×C5#239512yes—
535C2×C5#239812yes—
536C2×C5#240112yes—
537C23—22no—
538C23—24no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—41no—
550C23—41no—
551C23—42no—
552C23—42no—
553C23—41no—
554C23—41no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23#401814yes—
560C23C22×C4×D511yescharacteristic
561C23C2×#70912yes—
562C23C2×#70912yes—
563C23C2×#70911yescharacteristic
564C23C2×D4×D511yescharacteristic
565C23C2×#71111yescharacteristic
566C23C2×#71111yescharacteristic
567C23C2×#71111yescharacteristic
568C23D5×#4112yes—
569C23D5×#4112yes—
570C23C22×C22⋊D511yescharacteristic
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—416no—
593C2×C4—54no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—104no—
597C2×C4—104no—
598C2×C4—102no—
599C2×C4—102no—
600C2×C4—102no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—104no—
606C2×C4—102no—
607C2×C4—102no—
608C2×C4—104no—
609C2×C4—104no—
610C2×C4—104no—
611C2×C4—104no—
612C2×C4—104no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—202no—
616C2×C4—202no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4—202no—
621C2×C4—202no—
622C2×C4—202no—
623C2×C4—202no—
624C2×C4—202no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4#402314yes—
628C2×C4#402514yes—
629C2×C4#402714yes—
630C2×C4#403114yes—
631C2×C4C4×C22⋊D514yes—
632C2×C4#408114yes—
633C2×C4#408414yes—
634C5#1384211yescharacteristic, complemented, Sylow
635C22—24no—
636C22—24no—
637C22—24no—
638C22—42no—
639C22—44no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—42no—
645C22—42no—
646C22C2×#401811yescharacteristic
647C22C4×#70911yescharacteristic
648C22#6581312yes—
649C22C2×#402311yescharacteristic
650C22C2×#402511yescharacteristic
651C22C2×#402711yescharacteristic
652C22C2×#403111yescharacteristic
653C22D5×#11711yescharacteristic
654C22#6585611yescharacteristic
655C22#6586212yes—
656C22#6587212yes—
657C22#6587212yes—
658C22#6587212yes—
659C22#6587212yes—
660C22#6588112yes—
661C22#6588112yes—
662C22#6589112yes—
663C22#6589112yes—
664C22C2×C4×C22⋊D511yescharacteristic
665C22#6612512yes—
666C22C2×#408111yescharacteristic
667C22C2×#408411yescharacteristic
668C22#6616612yes—
669C4—42no—
670C4—44no—
671C4—44no—
672C4—104no—
673C4—202no—
674C4—202no—
675C4—204no—
676C4—204no—
677C4—202no—
678C4#6523318yes—
679C2—44no—
680C2#1060516811yescharacteristic
681C2#1060516911yescharacteristic
682C2#1060517111yescharacteristic
683C2#1060521212yes—
684C2#1060521312yes—
685C2#1060529311yescharacteristic
686C2#1061379611yescharacteristic
687C2C2×#6523311yescharacteristic
688C2#1061395611yescharacteristic
689C2#1061407712yes—
690C2#1061413212yes—
subgroupG/H
centerC23×C4C22×D5
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13842
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×#683C2semidirect
5. C2×#65221C2semidirect
8. C4×#3963C2semidirect
9. C4×#3963C2semidirect
10. #10600210C2semidirect
11. #10600206C2semidirect
27. C4×C22⋊Dic5C4semidirect
634. C5#13842semidirect

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×C4×C22⋊Dic52
C2×C4×#6832
C2×#652212
#106023422
#106023402
C4×#39632
#106002102
#106002062
#138425