Finite Group Databasebeta

← #12021013

Subgroups — #12021013

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4018C211yesmaximal, characteristic
2C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C2×C4×#683C211yesmaximal, characteristic, complemented
4C2×C4×#685C211yesmaximal, characteristic
5C2×C4×#685C211yesmaximal, characteristic
6C4×C5×#95C211yesmaximal, characteristic, complemented
7C4×#3963C211yesmaximal, characteristic, complemented
8#10600221C212yesmaximal
9#10600220C212yesmaximal
10#10600213C212yesmaximal, complemented
11#10600206C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2212yes—
18C22×#685C2211yescharacteristic
19C22×#685C2211yescharacteristic
20C22×C4⋊Dic5C2212yes—
21C22×#683C2212yes—
22C22×#683C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C2×#4018—24no—
27C2×#4018—24no—
28C2×#4018—24no—
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C4×#685—24no—
39C4×#685C418yescomplemented
40C4×C4⋊Dic5—24no—
41C4×#683—24no—
42#13844—51nomaximal, Sylow
43C24×D5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2312yes—
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5C2×C414yes—
59C22×C4×D5D414yes—
60C22×C4×D5Q814yes—
61C2×C42×C5—22no—
62C2×C42×C5—22no—
63C2×C42×C5—22no—
64C2×C42×C5—22no—
65C2×C42×C5—22no—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5C2×C414yes—
69C2×C42×C5D414yes—
70C2×#685—24no—
71C2×#685—24no—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—24no—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685C2×C414yes—
79C2×#685C2×C414yes—
80C2×C4⋊Dic5—24no—
81C2×C4⋊Dic5—24no—
82C2×C4⋊Dic5—24no—
83C2×#683—24no—
84C2×#683—24no—
85C2×#683—24no—
86C2×#683—24no—
87C2×#683—24no—
88C2×#683—24no—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5—22no—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—22no—
95C2×C4×Dic5—22no—
96C2×C4×Dic5C2×C414yes—
97C2×C4×Dic5D414yes—
98#4018—232no—
99C5×#95—24no—
100C5×#95—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—24no—
105#3963—24no—
106#3963C2×C414yes—
107#3963C2×C414yes—
108C22×#117—51no—
109C2×C4×C4⋊C4—51no—
110C2×C4×C4⋊C4—51no—
111C2×C4×C22⋊C4—51no—
112C2×C4×C22⋊C4—51no—
113#1444—52no—
114#1442—52no—
115#1439—52no—
116#1439—52no—
117C4×#95—51no—
118C4×#95D511yescharacteristic, complemented
119C24×C5C2411yescharacteristic
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—22no—
125C23×D5—22no—
126C23×D5—22no—
127C23×D5—22no—
128C23×D5C22×C412yes—
129C23×D5C2×D412yes—
130C23×D5C2×Q812yes—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—22no—
134C22×C4×C5—21no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—21no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C22×C412yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5C2×D414yes—
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×Q812yes—
158C22×C4×C5#4114yes—
159C22×C4×C5#4114yes—
160C22×C4×C5#4112yes—
161C22×C4×C5#4112yes—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—22no—
169C22×Dic5—21no—
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—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5C22×C412yes—
186C22×Dic5C22×C412yes—
187C22×Dic5C22×C412yes—
188C22×Dic5C2×D414yes—
189C22×Dic5C2×D412yes—
190C22×Dic5C2×Q812yes—
191C22×Dic5#4114yes—
192C22×Dic5#4114yes—
193C2×C4×D5—28no—
194C2×C4×D5—28no—
195C2×C4×D5—28no—
196C2×C4×D5—28no—
197C2×C4×D5—28no—
198C2×C4×D5—28no—
199C2×C4×D5C4⋊C4116yescomplemented
200C42×C5—28no—
201C42×C5—28no—
202C42×C5—44no—
203#685—216no—
204#685—216no—
205#685—28no—
206#685—28no—
207C4⋊Dic5—216no—
208#683—216no—
209#683—216no—
210C4×Dic5—28no—
211C4×Dic5—28no—
212C4×Dic5—44no—
213C24×C4—51no—
214C2×#117—104no—
215C2×#117—104no—
216C2×#117—104no—
217C22×C4⋊C4—52no—
218C22×C4⋊C4—52no—
219C22×C4⋊C4—52no—
220C22×C22⋊C4—51no—
221C22×C22⋊C4—51no—
222C22×C22⋊C4—52no—
223C22×C22⋊C4—52no—
224C22×C42—51no—
225C22×C42—51no—
226C22×C42—51no—
227C22×C42C2×D511yescharacteristic
228C22×C42C2×D511yescharacteristic
229C22×C42C2×D511yescharacteristic
230C4×C4⋊C4—104no—
231C4×C4⋊C4—104no—
232C4×C22⋊C4—58no—
233C4×C22⋊C4—104no—
234C2×#95—51no—
235C2×#95—51no—
236C2×#95—52no—
237C2×#95—52no—
238C2×#95—52no—
239C2×#95—52no—
240C2×#95—52no—
241C2×#95C2×D512yes—
242C2×#95C2×D512yes—
243C23×C5C23×C411yescharacteristic
244C23×C5C22×D411yescharacteristic
245C23×C5C22×D411yescharacteristic
246C23×C5C22×D411yescharacteristic
247C23×C5C22×Q811yescharacteristic
248C23×C5C2×#4112yes—
249C23×C5C2×#4111yescharacteristic
250C23×C5C2×#4112yes—
251C23×C5C2×#4111yescharacteristic
252C23×C5C2×#4112yes—
253C23×C5C2×#4112yes—
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—22no—
259C22×D5—22no—
260C22×D5—22no—
261C22×D5—22no—
262C22×D5—22no—
263C22×D5—22no—
264C22×D5—24no—
265C22×D5—24no—
266C22×D5—24no—
267C22×D5—24no—
268C22×D5—42no—
269C22×D5—42no—
270C22×D5—42no—
271C22×D5—42no—
272C22×D5—42no—
273C22×D5—42no—
274C22×D5—42no—
275C22×D5—42no—
276C22×D5C2×C4⋊C414yes—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—24no—
286C2×C4×C5—24no—
287C2×C4×C5—24no—
288C2×C4×C5—24no—
289C2×C4×C5—24no—
290C2×C4×C5—42no—
291C2×C4×C5—42no—
292C2×C4×C5—42no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—42no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5C2×C4⋊C414yes—
301C2×C4×C5#11714yescomplemented
302C2×C4×C5C4×D414yes—
303C2×C4×C5C4×D414yes—
304C2×C4×C5#12014yes—
305C2×C4×C5C22⋊Q814yes—
306C2×C4×C5C22⋊Q814yes—
307C2×C4×C5#12314yes—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—24no—
317C2×Dic5—24no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—24no—
322C2×Dic5—24no—
323C2×Dic5—24no—
324C2×Dic5—24no—
325C2×Dic5—24no—
326C2×Dic5—24no—
327C2×Dic5—42no—
328C2×Dic5—42no—
329C2×Dic5—42no—
330C2×Dic5—42no—
331C2×Dic5—42no—
332C2×Dic5—42no—
333C2×Dic5—42no—
334C2×Dic5—42no—
335C2×Dic5—42no—
336C2×Dic5—42no—
337C2×Dic5C2×C4⋊C414yes—
338C2×Dic5#11714yescomplemented
339C4×D5—232no—
340C25—51no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—54no—
344C23×C4—54no—
345C23×C4—54no—
346C23×C4—52no—
347C23×C4—52no—
348C23×C4—51no—
349C23×C4—102no—
350C23×C4—102no—
351C23×C4—102no—
352C23×C4—102no—
353C23×C4C22×D511yescharacteristic
354C23×C4C22×D512yes—
355C23×C4C22×D512yes—
356C23×C4C22×D511yescharacteristic
357C23×C4C22×D511yescharacteristic
358#117—1032no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—104no—
361C2×C4⋊C4—104no—
362C2×C4⋊C4—104no—
363C2×C4⋊C4—104no—
364C2×C4⋊C4—104no—
365C2×C4⋊C4—104no—
366C2×C4⋊C4—104no—
367C2×C4⋊C4—104no—
368C2×C22⋊C4—54no—
369C2×C22⋊C4—54no—
370C2×C22⋊C4—104no—
371C2×C22⋊C4—104no—
372C2×C22⋊C4—104no—
373C2×C22⋊C4—104no—
374C2×C22⋊C4—104no—
375C2×C22⋊C4—104no—
376C2×C22⋊C4—104no—
377C2×C22⋊C4—104no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—54no—
386C2×C42—54no—
387C2×C42—102no—
388C2×C42—102no—
389C2×C42—102no—
390C2×C42—102no—
391C2×C42—102no—
392C2×C42—102no—
393C2×C42—102no—
394C2×C42C4×D514yes—
395C2×C42D2014yes—
396#95—24no—
397#95—24no—
398#95—54no—
399#95—54no—
400#95—104no—
401#95—104no—
402#95—104no—
403#95—104no—
404#95—104no—
405C22×C5C22×C4⋊C411yescharacteristic
406C22×C5C2×#11711yescharacteristic
407C22×C5C2×#11711yescharacteristic
408C22×C5C2×C4×D411yescharacteristic
409C22×C5C2×C4×D411yescharacteristic
410C22×C5C4×#4111yescharacteristic
411C22×C5C4×#4111yescharacteristic
412C22×C5C2×#12011yescharacteristic
413C22×C5C2×C22⋊Q811yescharacteristic
414C22×C5C2×C22⋊Q811yescharacteristic
415C22×C5C2×#12311yescharacteristic
416C22×C5#52512yes—
417C22×C5#52512yes—
418C22×C5#52512yes—
419C22×C5#52912yes—
420C22×C5#52912yes—
421C22×C5#52912yes—
422C22×C5#52912yes—
423C22×C5#53212yes—
424C22×C5#53212yes—
425C22×C5#53212yes—
426C22×C5#53312yes—
427C22×C5#53312yes—
428C2×D5—24no—
429C2×D5—24no—
430C2×D5—24no—
431C2×D5—44no—
432C2×D5—44no—
433C2×D5—44no—
434C2×D5—44no—
435C2×D5—42no—
436C2×D5—42no—
437C2×D5—42no—
438C2×D5—42no—
439C4×C5—24no—
440C4×C5—44no—
441C4×C5—44no—
442C4×C5—42no—
443C4×C5#38518yes—
444Dic5—24no—
445Dic5—24no—
446Dic5—44no—
447Dic5—44no—
448Dic5—42no—
449C24—52no—
450C24—52no—
451C24—52no—
452C24—101no—
453C24—102no—
454C24—102no—
455C24—101no—
456C24—101no—
457C24—101no—
458C24—102no—
459C24—102no—
460C24C23×D511yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—52no—
481C22×C4—52no—
482C22×C4—52no—
483C22×C4—52no—
484C22×C4—54no—
485C22×C4—516no—
486C22×C4—52no—
487C22×C4—54no—
488C22×C4—54no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—101no—
492C22×C4—101no—
493C22×C4—101no—
494C22×C4—101no—
495C22×C4—102no—
496C22×C4—108no—
497C22×C4—108no—
498C22×C4—108no—
499C22×C4—108no—
500C22×C4—108no—
501C22×C4—108no—
502C22×C4—101no—
503C22×C4—102no—
504C22×C4—102no—
505C22×C4—102no—
506C22×C4—102no—
507C22×C4—101no—
508C22×C4—102no—
509C22×C4—102no—
510C22×C4—102no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4C2×C4×D512yes—
519C22×C4C2×C4×D512yes—
520C22×C4C2×C4×D512yes—
521C22×C4C2×D2014yes—
522C22×C4C2×D2012yes—
523C22×C4#70914yes—
524C22×C4#70914yes—
525C22×C4#70912yes—
526C22×C4D4×D512yes—
527C22×C4D4×D512yes—
528C22×C4#71112yes—
529C22×C4Q8×D512yes—
530C4⋊C4—1016no—
531C4⋊C4—1016no—
532C4⋊C4—1016no—
533C22⋊C4—108no—
534C22⋊C4—1016no—
535C22⋊C4—1016no—
536C22⋊C4—108no—
537C42—28no—
538C42—28no—
539C42—44no—
540C42—108no—
541C42—108no—
542C42—204no—
543C2×C5#228511yescharacteristic
544C2×C5C2×#38511yescharacteristic
545C2×C5#229011yescharacteristic
546C2×C5#229011yescharacteristic
547C2×C5#229311yescharacteristic
548C2×C5#229311yescharacteristic
549C2×C5#229611yescharacteristic
550C2×C5#238812yes—
551C2×C5#239512yes—
552C2×C5#239612yes—
553C2×C5#239612yes—
554D5—44no—
555C23—54no—
556C23—102no—
557C23—102no—
558C23—102no—
559C23—102no—
560C23—102no—
561C23—102no—
562C23—102no—
563C23—102no—
564C23—102no—
565C23—102no—
566C23—104no—
567C23—104no—
568C23—104no—
569C23—104no—
570C23—202no—
571C23—202no—
572C23—202no—
573C23—202no—
574C23—202no—
575C23—202no—
576C23—202no—
577C23—202no—
578C23C22×C4×D511yescharacteristic
579C23C22×D2011yescharacteristic
580C23C2×#70912yes—
581C23C2×#70911yescharacteristic
582C23C2×#70912yes—
583C23C2×D4×D511yescharacteristic
584C23C2×D4×D511yescharacteristic
585C23C2×#71111yescharacteristic
586C23C2×Q8×D511yescharacteristic
587C23D5×#4112yes—
588C23D5×#4112yes—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—54no—
613C2×C4—54no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—104no—
623C2×C4—104no—
624C2×C4—1032no—
625C2×C4—102no—
626C2×C4—102no—
627C2×C4—102no—
628C2×C4—104no—
629C2×C4—104no—
630C2×C4—104no—
631C2×C4—104no—
632C2×C4—104no—
633C2×C4—104no—
634C2×C4—202no—
635C2×C4—202no—
636C2×C4—202no—
637C2×C4—202no—
638C2×C4—202no—
639C2×C4—202no—
640C2×C4—202no—
641C2×C4—202no—
642C2×C4—202no—
643C2×C4—202no—
644C2×C4#401814yescomplemented
645C2×C4C4×D2014yes—
646C2×C4#402714yes—
647C2×C4#402814yes—
648C2×C4#402914yes—
649C2×C4D5×C4⋊C414yes—
650C2×C4#404214yes—
651C2×C4#404314yes—
652C5#1384411yescharacteristic, complemented, Sylow
653C22—104no—
654C22—104no—
655C22—104no—
656C22—204no—
657C22—204no—
658C22—202no—
659C22—202no—
660C22—202no—
661C22—204no—
662C22—202no—
663C22—204no—
664C22C2×#401811yescharacteristic
665C22C2×C4×D2011yescharacteristic
666C22C4×#70911yescharacteristic
667C22#6581112yes—
668C22#6581312yes—
669C22C2×#402711yescharacteristic
670C22C2×#402811yescharacteristic
671C22C2×#402911yescharacteristic
672C22C2×D5×C4⋊C411yescharacteristic
673C22C2×#404211yescharacteristic
674C22C2×#404311yescharacteristic
675C22D5×#11711yescharacteristic
676C22#6585611yescharacteristic
677C22#6585812yes—
678C22#6586212yes—
679C22#6587212yes—
680C22#6587212yes—
681C22#6588112yes—
682C22#6588112yes—
683C22#6588212yes—
684C22#6588212yes—
685C22#6591212yes—
686C22#6591212yes—
687C4—24no—
688C4—44no—
689C4—42no—
690C4—44no—
691C4—104no—
692C4—104no—
693C4—202no—
694C4—204no—
695C4—204no—
696C4#6495718yes—
697C2—204no—
698C2#1060503011yescharacteristic
699C2C2×#6495711yescharacteristic
700C2#1060514511yescharacteristic
701C2#1060516911yescharacteristic
702C2#1060517011yescharacteristic
703C2#1060531112yes—
704C2#1060531312yes—
705C2#1060539912yes—
706C2#1060548411yescharacteristic
707C2#1060548611yescharacteristic
708C2#1060550912yes—
subgroupG/H
centerC23×C4C22×D5
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC4×C5×#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4×#95D5
hypocenterC5#13844
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊Dic5C2semidirect
3. C2×C4×#683C2semidirect
6. C4×C5×#95C2semidirect
7. C4×#3963C2semidirect
10. #10600213C2semidirect
11. #10600206C2semidirect
39. C4×#685C4semidirect
118. C4×#95D5semidirect
199. C2×C4×D5C4⋊C4semidirect
301. C2×C4×C5#117semidirect
338. C2×Dic5#117semidirect
644. C2×C4#4018semidirect
652. C5#13844semidirect

Maximal subgroups

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

subgroupindex
C22×#40182
C2×C4×C4⋊Dic52
C2×C4×#6832
C2×C4×#6852
C4×C5×#952
C4×#39632
#106002212
#106002202
#106002132
#106002062
#138445