Finite Group Databasebeta

← #12109528

Subgroups — #12109528

Order 1280.

1258 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#685C211yesmaximal, characteristic
2C2×#65015C211yesmaximal, characteristic
3C2×D5×C22⋊C8C211yesmaximal, characteristic
4C5×#1797C211yesmaximal, characteristic, complemented
5#10602323C211yesmaximal, characteristic, complemented
6#10601271C212yesmaximal, complemented
7#10601270C212yesmaximal, complemented
8#10600701C211yesmaximal, characteristic, complemented
9#10600701C211yesmaximal, characteristic, complemented
10#10599460C212yesmaximal, complemented
11#10599459C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C42×C5C2211yescharacteristic
14C22×#685C411yescharacteristic
15C22×#685C411yescharacteristic
16C22×C4×Dic5C2211yescharacteristic
17C22×#676C2212yes—
18C22×C8×D5C2212yes—
19C2×C5×C4⋊C8C2212yescomplemented
20C2×C5×C22⋊C8C2211yescharacteristic
21C2×C5×C22⋊C8C2211yescharacteristic
22C2×#3963C411yescharacteristic
23C2×#3963C411yescharacteristic
24C2×C22⋊#168C2211yescharacteristic
25C2×C22⋊#168C2211yescharacteristic
26C2×#3952C2212yes—
27C2×#3952C2212yes—
28C2×#3946C2212yescomplemented
29C2×#3946C2212yescomplemented
30C4×#685C411yescharacteristic
31C4×#685C411yescharacteristic
32C4×#685C411yescharacteristic
33C4×#685C411yescharacteristic
34C4×#685C2211yescharacteristic
35C4×#685C2211yescharacteristic
36C4×#685C2211yescharacteristic
37C4×#685C2211yescharacteristic
38C2×C4⋊#168C2212yescomplemented
39#65015—24no—
40D5×C22⋊C8—24no—
41C5×#336C2212yescomplemented
42#64770C2212yescomplemented
43#64770C2212yescomplemented
44#64744C2212yescomplemented
45#21932—51nomaximal, Sylow
46C24×D5C2×C411yescharacteristic
47C23×C4×C5C2×C411yescharacteristic
48C23×C4×C5C2×C411yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2×C411yescharacteristic
51C23×Dic5C2×C411yescharacteristic
52C23×Dic5C2×C411yescharacteristic
53C22×C4×D5—42no—
54C22×C4×D5—42no—
55C22×C4×D5C2×C411yescharacteristic
56C22×C4×D5C2×C411yescharacteristic
57C22×C4×D5D414yes—
58C22×C4×D5Q814yes—
59C22×C4×D5C2311yescharacteristic
60C22×C4×D5C2311yescharacteristic
61C22×C5×C8C2312yes—
62C22×C5×C8C2312yes—
63C2×C42×C5—42no—
64C2×C42×C5C2×C411yescharacteristic
65C2×C42×C5C2×C411yescharacteristic
66C2×C42×C5C2311yescharacteristic
67C2×C42×C5C2311yescharacteristic
68C2×#685—24no—
69C2×#685—24no—
70C2×#685C2×C411yescharacteristic
71C2×#685C2×C411yescharacteristic
72C2×#685C2×C411yescharacteristic
73C2×#685C2×C411yescharacteristic
74C2×#685C2×C411yescharacteristic
75C2×#685C2×C411yescharacteristic
76C2×#685C2×C411yescharacteristic
77C2×#685C2×C411yescharacteristic
78C2×C4×Dic5—42no—
79C2×C4×Dic5C2×C411yescharacteristic
80C2×C4×Dic5C2×C411yescharacteristic
81C2×C4×Dic5C2311yescharacteristic
82C2×C4×Dic5C2311yescharacteristic
83C22×#168C2312yes—
84C22×#168C2312yes—
85C2×#676—24no—
86C2×#676—42no—
87C2×#676—42no—
88C2×C8×D5—24no—
89C2×C8×D5—42no—
90C2×C8×D5—42no—
91C5×C4⋊C8—42no—
92C5×C22⋊C8—22no—
93C5×C22⋊C8—22no—
94#3963C2×C411yescharacteristic
95#3963C2×C411yescharacteristic
96#3963C2×C411yescharacteristic
97#3963C2×C411yescharacteristic
98#3963C2×C411yescharacteristic
99#3963C2×C411yescharacteristic
100#3963C2×C411yescharacteristic
101#3963C2×C411yescharacteristic
102C22⋊#168—22no—
103C22⋊#168—22no—
104#3952—24no—
105#3952—24no—
106#3946—42no—
107#3946—42no—
108C4⋊#168—42no—
109C2×#407—51no—
110C22×C22⋊C8—51no—
111C2×C4×C22⋊C4—51no—
112#1851—52no—
113#1851—52no—
114#1850—52no—
115#1850—52no—
116#1797—51no—
117#1797—51no—
118#1797—51no—
119#1797D511yescharacteristic, complemented
120C24×C5C22×C411yescharacteristic
121C23×D5—22no—
122C23×D5—22no—
123C23×D5—22no—
124C23×D5—22no—
125C23×D5—41no—
126C23×D5—41no—
127C23×D5C4⋊C414yes—
128C23×D5C22×C411yescharacteristic
129C23×D5C22×C411yescharacteristic
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—41no—
137C22×C4×C5—41no—
138C22×C4×C5C22×C411yescharacteristic
139C22×C4×C5C22×C411yescharacteristic
140C22×C4×C5C22×C411yescharacteristic
141C22×C4×C5C22×C411yescharacteristic
142C22×C4×C5C22×C411yescharacteristic
143C22×C4×C5C2×D412yes—
144C22×C4×C5C2×Q812yes—
145C22×C4×C5C2411yescharacteristic
146C22×Dic5—22no—
147C22×Dic5—22no—
148C22×Dic5—22no—
149C22×Dic5—22no—
150C22×Dic5—41no—
151C22×Dic5—41no—
152C22×Dic5—41no—
153C22×Dic5—41no—
154C22×Dic5C4⋊C414yes—
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C22×C411yescharacteristic
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5—22no—
164C2×C4×D5—22no—
165C2×C4×D5—48no—
166C2×C4×D5—48no—
167C2×C4×D5—41no—
168C2×C4×D5—41no—
169C2×C4×D5—41no—
170C2×C4×D5—41no—
171C2×C4×D5C4⋊C414yes—
172C2×C4×D5C4⋊C414yes—
173C2×C4×D5C2×D412yes—
174C2×C4×D5C2×D412yes—
175C2×C4×D5C2×Q812yes—
176C2×C4×D5C2×Q812yes—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—22no—
181C2×C5×C8—22no—
182C2×C5×C8—22no—
183C42×C5—22no—
184C42×C5—22no—
185C42×C5—41no—
186C42×C5—41no—
187#685—22no—
188#685—22no—
189#685—22no—
190#685—22no—
191#685—22no—
192#685—22no—
193#685M1614yescomplemented
194#685M1614yescomplemented
195C4×Dic5—22no—
196C4×Dic5—22no—
197C4×Dic5—41no—
198C4×Dic5—41no—
199C2×#168—22no—
200C2×#168—22no—
201C2×#168—22no—
202C2×#168—22no—
203C2×#168—22no—
204C2×#168—22no—
205#676—48no—
206C8×D5—48no—
207C24×C4—51no—
208C22×M16—52no—
209C23×C8—52no—
210C22×C22⋊C4—51no—
211C22×C22⋊C4—51no—
212C22×C42—51no—
213C22×C42C2×D511yescharacteristic
214C2×C4⋊C8—52no—
215C2×C4⋊C8—52no—
216C2×C4⋊C8—52no—
217C2×C4⋊C8C2×D512yescomplemented
218#407—104no—
219C2×C22⋊C8—51no—
220C2×C22⋊C8—51no—
221C2×C22⋊C8—52no—
222C2×C22⋊C8—52no—
223C2×C22⋊C8—104no—
224C2×C22⋊C8C2×D511yescharacteristic
225C2×C22⋊C8C2×D511yescharacteristic
226C4×C22⋊C4—51no—
227C4×C22⋊C4—51no—
228C4×C22⋊C4—51no—
229C4×C22⋊C4—51no—
230C4×C22⋊C4—51no—
231C4×C22⋊C4—51no—
232C4×C22⋊C4—51no—
233C4×C22⋊C4—51no—
234C2×#95—51no—
235C2×#95—51no—
236#336—52no—
237#336—52no—
238#336—52no—
239#336C2×D512yescomplemented
240C23×C5—21no—
241C23×C5—21no—
242C23×C5—21no—
243C23×C5—21no—
244C23×C5C2×C4⋊C412yes—
245C23×C5#13112yes—
246C23×C5#13112yes—
247C23×C5C23×C411yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—21no—
251C22×D5—21no—
252C22×D5—21no—
253C22×D5—21no—
254C22×D5—21no—
255C22×D5—21no—
256C22×D5—21no—
257C22×D5—21no—
258C22×D5—28no—
259C22×D5—28no—
260C22×D5—44no—
261C22×D5—44no—
262C22×D5—44no—
263C22×D5—44no—
264C22×D5—44no—
265C22×D5C2×C4⋊C412yes—
266C22×D5C2×C4⋊C412yes—
267C22×D5C2×M1612yes—
268C22×D5C2×M1612yes—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—24no—
276C2×C4×C5—24no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—21no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—44no—
284C2×C4×C5—44no—
285C2×C4×C5C2×C4⋊C412yes—
286C2×C4×C5C2×M1612yes—
287C2×C4×C5C2×M1612yes—
288C2×C4×C5C22×D411yescharacteristic
289C2×C4×C5C22×Q811yescharacteristic
290C2×C4×C5H(5,𝔽2)12yes—
291C2×C4×C5H(5,𝔽2)12yes—
292C2×Dic5—21no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—44no—
307C2×Dic5—44no—
308C2×Dic5—44no—
309C2×Dic5C2×C4⋊C412yes—
310C2×Dic5C2×C4⋊C412yes—
311C2×Dic5C2×M1612yes—
312C2×Dic5C2×M1612yes—
313C4×D5—24no—
314C4×D5—24no—
315C4×D5—24no—
316C4×D5—24no—
317C4×D5—44no—
318C4×D5—44no—
319C5×C8—42no—
320C5×C8—42no—
321#168—42no—
322#168—42no—
323C25—51no—
324C23×C4—51no—
325C23×C4—51no—
326C23×C4—51no—
327C23×C4—51no—
328C23×C4—51no—
329C23×C4—54no—
330C23×C4—54no—
331C23×C4—51no—
332C23×C4—51no—
333C23×C4—202no—
334C23×C4—202no—
335C23×C4C4×D511yescharacteristic
336C23×C4C4×D511yescharacteristic
337C23×C4C22×D511yescharacteristic
338C2×M16—104no—
339C2×M16—202no—
340C2×M16—202no—
341C22×C8—52no—
342C22×C8—52no—
343C22×C8—104no—
344C22×C8—202no—
345C22×C8—202no—
346C22×C8C22×D512yes—
347C22×C8C22×D512yes—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—51no—
353C2×C22⋊C4—51no—
354C2×C22⋊C4—51no—
355C2×C22⋊C4—51no—
356C2×C22⋊C4—104no—
357C2×C22⋊C4—104no—
358C2×C42—42no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—202no—
364C2×C42C4×D511yescharacteristic
365C2×C42C4×D511yescharacteristic
366C2×C42C22×D511yescharacteristic
367C2×C42C22×D511yescharacteristic
368C4⋊C8—42no—
369C4⋊C8—202no—
370C4⋊C8—202no—
371C4⋊C8—202no—
372C22⋊C8—22no—
373C22⋊C8—22no—
374C22⋊C8—104no—
375C22⋊C8—104no—
376C22⋊C8—102no—
377C22⋊C8—102no—
378#95—51no—
379#95—51no—
380#95—51no—
381#95—51no—
382#95—51no—
383#95—51no—
384#95—51no—
385#95—51no—
386C22×C5—22no—
387C22×C5—22no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—22no—
391C22×C5—22no—
392C22×C5#42414yes—
393C22×C5C22×C4⋊C411yescharacteristic
394C22×C5#51811yescharacteristic
395C22×C5#51811yescharacteristic
396C22×C5C22×M1611yescharacteristic
397C22×C5C22×M1611yescharacteristic
398C22×C5C2×#13111yescharacteristic
399C22×C5C2×#13111yescharacteristic
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—22no—
403C2×D5—22no—
404C2×D5—22no—
405C2×D5—22no—
406C2×D5—22no—
407C2×D5—22no—
408C2×D5—22no—
409C2×D5—416no—
410C2×D5—41no—
411C2×D5—41no—
412C2×D5—41no—
413C2×D5—41no—
414C2×D5#42314yes—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—41no—
419C4×C5—41no—
420C4×C5#53412yes—
421C4×C5#54312yes—
422Dic5—22no—
423Dic5—22no—
424Dic5—22no—
425Dic5—22no—
426Dic5—41no—
427Dic5—41no—
428C24—51no—
429C24—51no—
430C24—54no—
431C24—102no—
432C24—102no—
433C24—102no—
434C24—102no—
435C24—201no—
436C24—201no—
437C24C2×C4×D511yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—54no—
451C22×C4—52no—
452C22×C4—52no—
453C22×C4—52no—
454C22×C4—52no—
455C22×C4—54no—
456C22×C4—54no—
457C22×C4—51no—
458C22×C4—51no—
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—208no—
468C22×C4—208no—
469C22×C4—201no—
470C22×C4—201no—
471C22×C4—201no—
472C22×C4—201no—
473C22×C4—201no—
474C22×C4—201no—
475C22×C4—201no—
476C22×C4—201no—
477C22×C4C2×C4×D511yescharacteristic
478C22×C4C2×C4×D511yescharacteristic
479C22×C4C2×C4×D511yescharacteristic
480C22×C4C2×C4×D511yescharacteristic
481C22×C4C2×C4×D511yescharacteristic
482C22×C4D4×D512yes—
483C22×C4Q8×D512yes—
484C22×C4C23×D511yescharacteristic
485M16—208no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—102no—
493C2×C8—102no—
494C2×C8—102no—
495C2×C8—102no—
496C2×C8—102no—
497C2×C8—102no—
498C2×C8—208no—
499C22⋊C4—54no—
500C22⋊C4—54no—
501C22⋊C4—102no—
502C22⋊C4—102no—
503C22⋊C4—102no—
504C22⋊C4—102no—
505C22⋊C4—102no—
506C22⋊C4—102no—
507C42—22no—
508C42—22no—
509C42—41no—
510C42—41no—
511C42—102no—
512C42—102no—
513C42—201no—
514C42—201no—
515C2×C5—24no—
516C2×C5#231511yescharacteristic
517C2×C5C2×#42311yescharacteristic
518C2×C5C2×#42411yescharacteristic
519C2×C5#297411yescharacteristic
520C2×C5#297411yescharacteristic
521C2×C5#297411yescharacteristic
522C2×C5#297411yescharacteristic
523D5—24no—
524D5—42no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—52no—
530C23—52no—
531C23—52no—
532C23—52no—
533C23—108no—
534C23—101no—
535C23—101no—
536C23—101no—
537C23—101no—
538C23—101no—
539C23—101no—
540C23—101no—
541C23—101no—
542C23—101no—
543C23—101no—
544C23—108no—
545C23—204no—
546C23—204no—
547C23—204no—
548C23—204no—
549C23—204no—
550C23D5×C4⋊C412yes—
551C23#404712yes—
552C23#405312yes—
553C23C22×C4×D511yescharacteristic
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—52no—
571C2×C4—52no—
572C2×C4—52no—
573C2×C4—52no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—101no—
580C2×C4—101no—
581C2×C4—101no—
582C2×C4—104no—
583C2×C4—104no—
584C2×C4—104no—
585C2×C4—104no—
586C2×C4—101no—
587C2×C4—101no—
588C2×C4—101no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—101no—
592C2×C4—204no—
593C2×C4—204no—
594C2×C4—204no—
595C2×C4—204no—
596C2×C4—204no—
597C2×C4D5×C4⋊C412yes—
598C2×C4D5×M1612yes—
599C2×C4D5×M1612yes—
600C2×C4C2×D4×D511yescharacteristic
601C2×C4#414412yes—
602C2×C4C2×Q8×D511yescharacteristic
603C2×C4#414912yes—
604C8—42no—
605C8—42no—
606C8—202no—
607C8—202no—
608C5#2193211yescharacteristic, complemented, Sylow
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—54no—
616C22—102no—
617C22—102no—
618C22—102no—
619C22—102no—
620C22—102no—
621C22—102no—
622C22—102no—
623C22—102no—
624C22—102no—
625C22—2016no—
626C22—201no—
627C22—201no—
628C22—201no—
629C22—201no—
630C22#6512814yes—
631C22#6582011yescharacteristic
632C22C2×D5×C4⋊C411yescharacteristic
633C22#6585511yescharacteristic
634C22C2×#404711yescharacteristic
635C22C2×D5×M1611yescharacteristic
636C22C2×D5×M1611yescharacteristic
637C22C2×#405311yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—102no—
644C4—102no—
645C4—102no—
646C4—102no—
647C4—201no—
648C4—201no—
649C4#6593912yes—
650C4#6596812yes—
651C2—24no—
652C2—104no—
653C2—202no—
654C2#1060573611yescharacteristic
655C2#1061033411yescharacteristic
656C2#1061036411yescharacteristic
657C2C2×#6512811yescharacteristic
658C2D5×#42311yescharacteristic
659C2#1061101811yescharacteristic
660C2#1061106711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1797C2
prime radicalC24×D5C2×C4
cosocleC22×C4×C5C24
hypercenter#1797D5
hypocenterC5#21932
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
4. C5×#1797C2semidirect
5. #10602323C2semidirect
6. #10601271C2semidirect
7. #10601270C2semidirect
8. #10600701C2semidirect
9. #10600701C2semidirect
10. #10599460C2semidirect
11. #10599459C2semidirect
19. C2×C5×C4⋊C8C22semidirect
28. C2×#3946C22semidirect
29. C2×#3946C22semidirect
38. C2×C4⋊#168C22semidirect
41. C5×#336C22semidirect
42. #64770C22semidirect
43. #64770C22semidirect
44. #64744C22semidirect
119. #1797D5semidirect
193. #685M16semidirect
194. #685M16semidirect
217. C2×C4⋊C8C2×D5semidirect
239. #336C2×D5semidirect
608. C5#21932semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6852
C2×#650152
C2×D5×C22⋊C82
C5×#17972
#106023232
#106012712
#106012702
#106007012
#105994602
#105994592
#219325