Finite Group Databasebeta

← #12110431

Subgroups — #12110431

Order 1280.

1308 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#390C211yesmaximal, characteristic, complemented
2C2×#65506C211yesmaximal, characteristic
3C4×#4076C211yesmaximal, characteristic, complemented
4#10602921C211yesmaximal, characteristic, complemented
5#10602353C211yesmaximal, characteristic, complemented
6#10602348C211yesmaximal, characteristic, complemented
7C4×C22⋊#168C211yesmaximal, characteristic, complemented
8#10600450C212yesmaximal, complemented
9#10600440C212yesmaximal, complemented
10#10600437C212yesmaximal, complemented
11#10600429C212yesmaximal, complemented
12C23×C5×D4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4—21no—
15C22×C5×C22⋊C4—21no—
16C22×C42×C5C2211yescharacteristic
17C22×#686C2212yes—
18C2×#4076C2211yescharacteristic
19C2×C4×C22⋊D5—21no—
20C2×C4×D20C2211yescharacteristic, complemented
21C5×#390—21no—
22C5×#390—21no—
23C5×#390C2212yes—
24C5×#390C2212yes—
25#65506C418yescomplemented
26C2×#3964C2212yes—
27C2×#3964C2212yes—
28C2×#3964C2212yes—
29#65502—21no—
30#65501C2211yescharacteristic
31C2×C22⋊#168C2211yescharacteristic
32C2×C22⋊#168C2211yescharacteristic
33C2×#3941C2212yescomplemented
34C2×#3939C2212yescomplemented
35#65229—21no—
36#65228C2211yescharacteristic, complemented
37C4×#685—21no—
38C4×C4⋊Dic5C2211yescharacteristic, complemented
39#65217C2211yescharacteristic, complemented
40C2×C4×#168C2212yescomplemented
41#64749C2212yescomplemented
42#64749C2212yescomplemented
43#64744C2212yescomplemented
44#22040—51nomaximal, Sylow
45C25×C5—21no—
46C22×C5×D4—21no—
47C22×C5×D4—22no—
48C22×C5×D4—42no—
49C22×C5×D4—42no—
50C22×C5×D4C2×C414yescomplemented
51C22×C5×D4C2312yes—
52C23×C4×C5—21no—
53C23×C4×C5D411yescharacteristic
54C23×C4×C5D411yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C22×C22⋊D5—21no—
57C22×D20C2311yescharacteristic
58C22×C4×D5—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—42no—
61C2×C5×C4⋊C4C2312yes—
62C2×C5×C22⋊C4—22no—
63C2×C5×C22⋊C4—22no—
64C2×C5×C22⋊C4—22no—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—44no—
67C2×C5×C22⋊C4—44no—
68C2×C42×C5—42no—
69C2×C42×C5D411yescharacteristic
70C2×C42×C5D411yescharacteristic
71C2×C42×C5C2311yescharacteristic
72C2×C42×C5C2311yescharacteristic
73C2×C22⋊Dic5—21no—
74C2×#686—42no—
75C2×#686—42no—
76C2×#686C2×C418yescomplemented
77#4076—22no—
78#4076C2×C414yes—
79C4×C22⋊D5—44no—
80C2×#685—21no—
81C2×#685—21no—
82C2×#685—21no—
83C2×#685—21no—
84C2×C4⋊Dic5C2311yescharacteristic
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×#683—21no—
88C2×C4×Dic5—21no—
89C22×#168C2312yes—
90C22×#168C2312yes—
91C4×D20—42no—
92#3964—42no—
93#3964—42no—
94#3964C2×C418yescomplemented
95#3963—21no—
96#3963—21no—
97#3963—21no—
98C22⋊#168—22no—
99C22⋊#168C2×C414yescomplemented
100#3941—42no—
101#3939—42no—
102C4×#168—42no—
103C2×#447—51no—
104C4×#121—51no—
105C2×#390D511yescharacteristic, complemented
106#1970—52no—
107#1934—52no—
108#1925—52no—
109#1879—52no—
110#1874—51no—
111#1852—51no—
112#1786—51no—
113C4×C22⋊C8—51no—
114C24×C5—24no—
115C24×C5—22no—
116C24×C5—42no—
117C24×C5—42no—
118C24×C5—42no—
119C24×C5—42no—
120C24×C5—42no—
121C24×C5—42no—
122C24×C5C2×D411yescharacteristic
123C23×D5—21no—
124C2×C5×D4—24no—
125C2×C5×D4—22no—
126C2×C5×D4—22no—
127C2×C5×D4—22no—
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—48no—
131C2×C5×D4—42no—
132C2×C5×D4—42no—
133C2×C5×D4—48no—
134C2×C5×D4C22×C414yes—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—41no—
141C22×C4×C5—41no—
142C22×C4×C5—41no—
143C22×C4×C5—42no—
144C22×C4×C5—42no—
145C22×C4×C5—42no—
146C22×C4×C5D814yescomplemented
147C22×C4×C5C22×C412yes—
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5#4112yes—
154C22×C4×C5C2411yescharacteristic
155C2×C22⋊D5—24no—
156C2×C22⋊D5—42no—
157C2×C22⋊D5—42no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C2×D20—22no—
162C2×D20—22no—
163C2×D20—21no—
164C2×D20C22×C412yes—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C5×C4⋊C4—22no—
169C5×C4⋊C4—22no—
170C5×C4⋊C4—42no—
171C5×C22⋊C4—44no—
172C5×C22⋊C4—44no—
173C5×C22⋊C4—44no—
174C5×C22⋊C4—44no—
175C42×C5—22no—
176C42×C5—22no—
177C42×C5—41no—
178C42×C5—41no—
179C22⋊Dic5—42no—
180#686—48no—
181#685—24no—
182#685—42no—
183#685—42no—
184#685—42no—
185C4⋊Dic5—21no—
186C4⋊Dic5—22no—
187C4⋊Dic5—22no—
188C4⋊Dic5C22×C412yes—
189#683—42no—
190C4×Dic5—42no—
191C2×#168—22no—
192C2×#168—22no—
193C2×#168—22no—
194C2×#168—22no—
195C2×#168—22no—
196C2×#168C22×C414yes—
197C23×D4C2×D511yescharacteristic
198C22×D8—52no—
199C2×#121—51no—
200C2×C4×D4—51no—
201C2×C4×D4—101no—
202C22×C4⋊C4C2×D511yescharacteristic
203C22×C22⋊C4—21no—
204C22×C22⋊C4—21no—
205C22×C42C2×D511yescharacteristic
206#447—58no—
207C2×#107—52no—
208C2×#102—52no—
209C2×#102—52no—
210C2×#102—52no—
211C2×#102—52no—
212C2×C22⋊C8—51no—
213C2×C22⋊C8—51no—
214C2×C4×C8—52no—
215#390—21no—
216#390—21no—
217#390—51no—
218#390C2×D512yes—
219#390C2×D512yes—
220#389—51no—
221#388—101no—
222#386—101no—
223#380—51no—
224C4×C4⋊C4—51no—
225C4×C22⋊C4—101no—
226#340—52no—
227#340—52no—
228#336—52no—
229C23×C5—21no—
230C23×C5—21no—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—24no—
234C23×C5—48no—
235C23×C5—48no—
236C23×C5—42no—
237C23×C5—42no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5—48no—
243C23×C5—84no—
244C23×C5—84no—
245C23×C5—84no—
246C23×C5—84no—
247C23×C5C4×D412yes—
248C23×C5C2×D812yes—
249C23×C5#13512yes—
250C23×C5C22×D411yescharacteristic
251C22×D5—22no—
252C22×D5—41no—
253C22×D5—41no—
254C22×D5—41no—
255C22×D5—41no—
256C22×D5—41no—
257C22×D5—41no—
258C5×D4—24no—
259C5×D4—24no—
260C5×D4—48no—
261C5×D4—42no—
262C5×D4—42no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—24no—
272C2×C4×C5—24no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—44no—
277C2×C4×C5—44no—
278C2×C4×C5—42no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—84no—
282C2×C4×C5C4×D412yes—
283C2×C4×C5C2×D812yes—
284C2×C4×C5C2×D812yes—
285C2×C4×C5AGL(1,ℤ/8)12yes—
286C2×C4×C5C23×C411yescharacteristic
287C2×C4×C5C2×#4111yescharacteristic
288C2×C4×C5H(5,𝔽2)12yes—
289C2×C4×C5H(5,𝔽2)12yes—
290C22⋊D5—48no—
291C2×Dic5—22no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300D20—24no—
301D20—42no—
302C4×D5—84no—
303#168—24no—
304#168—42no—
305C25—21no—
306C22×D4—22no—
307C22×D4—21no—
308C22×D4—42no—
309C22×D4—42no—
310C22×D4—51no—
311C22×D4—101no—
312C22×D4C4×D514yescomplemented
313C22×D4C22×D512yes—
314C23×C4—21no—
315C23×C4—101no—
316C23×C4C22⋊D511yescharacteristic
317C23×C4C22⋊D511yescharacteristic
318C23×C4C22×D511yescharacteristic
319C2×D8—58no—
320C2×D8—202no—
321C2×D8—202no—
322C22×C8—52no—
323C22×C8—52no—
324#121—54no—
325#121—102no—
326C4×D4—202no—
327C4×D4—204no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—101no—
334C2×C4⋊C4C22×D512yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—101no—
342C2×C22⋊C4—101no—
343C2×C22⋊C4—101no—
344C2×C22⋊C4—101no—
345C2×C22⋊C4—101no—
346C2×C42—42no—
347C2×C42—101no—
348C2×C42C22⋊D511yescharacteristic
349C2×C42C22⋊D511yescharacteristic
350C2×C42C22×D511yescharacteristic
351C2×C42C22×D511yescharacteristic
352#107—202no—
353#102—58no—
354#102—202no—
355#102—202no—
356#102—202no—
357C22⋊C8—54no—
358C22⋊C8—102no—
359C4×C8—202no—
360#95—101no—
361#95—101no—
362#95—101no—
363C22×C5—22no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5—22no—
367C22×C5—22no—
368C22×C5—22no—
369C22×C5—44no—
370C22×C5—44no—
371C22×C5—44no—
372C22×C5—816no—
373C22×C5—82no—
374C22×C5—82no—
375C22×C5—82no—
376C22×C5—82no—
377C22×C5C4×D814yes—
378C22×C5C2×C4×D411yescharacteristic
379C22×C5#53411yescharacteristic
380C22×C5#53511yescharacteristic
381C22×C5C22×D811yescharacteristic
382C22×C5C2×#13511yescharacteristic
383C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C5#57511yescharacteristic
385C2×D5—42no—
386C2×D5—42no—
387C2×D5—42no—
388C2×D5—81no—
389C2×D5—81no—
390C2×D5—81no—
391C2×D5—81no—
392C4×C5—22no—
393C4×C5—22no—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—41no—
397C4×C5—82no—
398C4×C5#51812yes—
399C4×C5#53812yes—
400Dic5—42no—
401Dic5—81no—
402Dic5—81no—
403C24—22no—
404C24—24no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—101no—
412C24C2×C22⋊D511yescharacteristic
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—48no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—48no—
423C2×D4—52no—
424C2×D4—104no—
425C2×D4—101no—
426C2×D4—102no—
427C2×D4—102no—
428C2×D4—202no—
429C2×D4—202no—
430C2×D4C2×C4×D514yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—202no—
446C22×C4—202no—
447C22×C4—202no—
448C22×C4#68614yescomplemented
449C22×C4C2×C4×D512yes—
450C22×C4#70912yes—
451C22×C4C2×C22⋊D511yescharacteristic
452C22×C4C2×C22⋊D511yescharacteristic
453C22×C4C2×C22⋊D511yescharacteristic
454C22×C4C2×C22⋊D511yescharacteristic
455C22×C4C2×C22⋊D511yescharacteristic
456C22×C4C23×D511yescharacteristic
457D8—208no—
458C2×C8—54no—
459C2×C8—102no—
460C2×C8—102no—
461C2×C8—102no—
462C2×C8—102no—
463C2×C8—102no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—42no—
467C4⋊C4—52no—
468C4⋊C4—101no—
469C4⋊C4—102no—
470C4⋊C4—102no—
471C4⋊C4—202no—
472C22⋊C4—44no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—104no—
477C22⋊C4—202no—
478C22⋊C4—202no—
479C22⋊C4—202no—
480C22⋊C4—202no—
481C42—22no—
482C42—22no—
483C42—41no—
484C42—41no—
485C42—202no—
486C2×C5—24no—
487C2×C5—84no—
488C2×C5#232111yescharacteristic
489C2×C5C2×C4×D811yescharacteristic
490C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
491C2×C5#318611yescharacteristic
492C2×C5#318811yescharacteristic
493C2×C5#320511yescharacteristic
494C2×C5#321111yescharacteristic
495D5—82no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—24no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—84no—
511C23—84no—
512C23—84no—
513C23—84no—
514C23—102no—
515C23—201no—
516C23—201no—
517C23—201no—
518C23—201no—
519C23—201no—
520C23—201no—
521C23C4×C22⋊D512yes—
522C23C2×#68612yes—
523C23#409612yes—
524C23C22×C22⋊D511yescharacteristic
525D4—24no—
526D4—24no—
527D4—48no—
528D4—42no—
529D4—42no—
530D4—104no—
531D4—208no—
532D4—202no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—102no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4—201no—
560C2×C4—201no—
561C2×C4—404no—
562C2×C4C4×C22⋊D512yes—
563C2×C4C2×#68612yes—
564C2×C4C2×#68612yes—
565C2×C4#407812yes—
566C2×C4C22×C4×D511yescharacteristic
567C2×C4C2×#70911yescharacteristic
568C2×C4#414412yes—
569C2×C4#414412yes—
570C8—104no—
571C8—202no—
572C5#2204011yescharacteristic, complemented, Sylow
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—816no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—82no—
587C22—202no—
588C22—202no—
589C22—202no—
590C22—401no—
591C22—401no—
592C22—401no—
593C22—401no—
594C22C4×#68614yes—
595C22C2×C4×C22⋊D511yescharacteristic
596C22C22×#68611yescharacteristic
597C22C2×#407811yescharacteristic
598C22#6613811yescharacteristic
599C22#6613911yescharacteristic
600C22C2×#409611yescharacteristic
601C22#6615611yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—41no—
607C4—82no—
608C4—202no—
609C4—401no—
610C4—401no—
611C4#6582012yes—
612C4#6582812yes—
613C2—24no—
614C2—84no—
615C2—402no—
616C2#1061382711yescharacteristic
617C2C2×C4×#68611yescharacteristic
618C2C4×#407811yescharacteristic
619C2#1061435611yescharacteristic
620C2#1061435711yescharacteristic
621C2#1061467711yescharacteristic
622C2#1061489711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#390C2
socleC23×C5C22×D4
prime radicalC2×#65506C2
cosocleC22×C4×C5C24
hypercenterC2×#390D5
hypocenterC5#22040
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×C5×#390C2semidirect
3. C4×#4076C2semidirect
4. #10602921C2semidirect
5. #10602353C2semidirect
6. #10602348C2semidirect
7. C4×C22⋊#168C2semidirect
8. #10600450C2semidirect
9. #10600440C2semidirect
10. #10600437C2semidirect
11. #10600429C2semidirect
20. C2×C4×D20C22semidirect
25. #65506C4semidirect
33. C2×#3941C22semidirect
34. C2×#3939C22semidirect
36. #65228C22semidirect
38. C4×C4⋊Dic5C22semidirect
39. #65217C22semidirect
40. C2×C4×#168C22semidirect
41. #64749C22semidirect
42. #64749C22semidirect
43. #64744C22semidirect
50. C22×C5×D4C2×C4semidirect
76. C2×#686C2×C4semidirect
94. #3964C2×C4semidirect
99. C22⋊#168C2×C4semidirect
105. C2×#390D5semidirect
146. C22×C4×C5D8semidirect
312. C22×D4C4×D5semidirect
448. C22×C4#686semidirect
572. C5#22040semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3902
C2×#655062
C4×#40762
#106029212
#106023532
#106023482
C4×C22⋊#1682
#106004502
#106004402
#106004372
#106004292
#220405