Finite Group Databasebeta

← #12129334

Subgroups — #12129334

Order 1280.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#121C211yesmaximal, characteristic
2#10613791C211yesmaximal, characteristic, complemented
3#10602473C211yesmaximal, characteristic
4#10602472C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic, complemented
6C4×#3964C211yesmaximal, characteristic, complemented
7C4×C22⋊#168C211yesmaximal, characteristic, complemented
8#10600447C211yesmaximal, characteristic, complemented
9#10600434C211yesmaximal, characteristic, complemented
10#10600406C211yesmaximal, characteristic, complemented
11#10600402C211yesmaximal, characteristic, complemented
12#10600312C211yesmaximal, characteristic, complemented
13#10600300C211yesmaximal, characteristic, complemented
14C4×#3939C211yesmaximal, characteristic, complemented
15C4×#3940C211yesmaximal, characteristic, complemented
16C2×C5×#121C2211yescharacteristic
17C2×C4×C5×D4—21no—
18C2×C4×C5×D4C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C5×#390C2211yescharacteristic
21C5×#389C2211yescharacteristic
22C5×#388—21no—
23C5×#386—21no—
24C5×#380C2211yescharacteristic
25C4×C5×C4⋊C4C2211yescharacteristic
26C4×C5×C22⋊C4—21no—
27C2×#3964C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31#65501C2211yescharacteristic
32#65501C2211yescharacteristic
33#65500—21no—
34C4×C22⋊Dic5—21no—
35C2×C22⋊#168C2211yescharacteristic
36C2×C22⋊#168C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41#65226—21no—
42#65225C2211yescharacteristic
43#65225C2211yescharacteristic
44C4×C4⋊Dic5C2211yescharacteristic
45C4×C4⋊Dic5C2211yescharacteristic
46#65221—21no—
47C2×C4×#168C2211yescharacteristic
48C2×C4×#168C2211yescharacteristic
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#23758—51nomaximal, Sylow
60C22×C5×D4—21no—
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5D411yescharacteristic
64C23×C4×C5D411yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C5×#121—22no—
67C5×#121—22no—
68C4×C5×D4—22no—
69C4×C5×D4—22no—
70C4×C5×D4—44no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4—21no—
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C42×C5—22no—
81C2×C42×C5—22no—
82C2×C42×C5—21no—
83C2×C42×C5D411yescharacteristic
84C2×C42×C5D411yescharacteristic
85C2×C42×C5C2311yescharacteristic
86C2×C42×C5C2311yescharacteristic
87C2×C22⋊Dic5—21no—
88C2×C22⋊Dic5—21no—
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C5×#95—21no—
100C5×#95—21no—
101C5×#95—21no—
102#3964—22no—
103#3964—22no—
104#3964—22no—
105#3964—22no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114C22⋊#168—22no—
115C22⋊#168—22no—
116#3940—22no—
117#3940—22no—
118#3939—22no—
119#3939—22no—
120C4×#168—22no—
121C4×#168—22no—
122C4×#121D511yescharacteristic
123#2283—51no—
124#2101—51no—
125#2092—51no—
126#2085—51no—
127#2077—51no—
128#2076—51no—
129#2073—51no—
130#2034—51no—
131#2033—51no—
132C4×#107—51no—
133C4×#106—51no—
134C4×#102—51no—
135C4×#102—51no—
136C4×C22⋊C8—51no—
137C24×C5—21no—
138C24×C5C2×D411yescharacteristic
139C2×C5×D4—24no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—42no—
146C2×C5×D4—42no—
147C2×C5×D4#4112yes—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—41no—
163C22×C4×C5—42no—
164C22×C4×C5—42no—
165C22×C4×C5—42no—
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×D411yescharacteristic
171C22×C4×C5C2411yescharacteristic
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—42no—
182C5×C4⋊C4#4112yes—
183C5×C22⋊C4—24no—
184C5×C22⋊C4—42no—
185C5×C22⋊C4—42no—
186C5×C22⋊C4—42no—
187C5×C22⋊C4—42no—
188C42×C5—22no—
189C42×C5—22no—
190C42×C5—21no—
191C42×C5—21no—
192C42×C5—42no—
193C42×C5#4112yes—
194C42×C5#4112yes—
195C22⋊Dic5—42no—
196C22⋊Dic5—42no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—21no—
205C4×Dic5—42no—
206C4×Dic5—42no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168#4112yes—
218C2×#168#4112yes—
219C2×#121C2×D511yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2×D511yescharacteristic
222C22×C42C2×D511yescharacteristic
223C2×#107—51no—
224C2×#107—51no—
225C2×#106—51no—
226C2×#106—51no—
227C2×#102—51no—
228C2×#102—51no—
229C2×#102—51no—
230C2×#102—51no—
231C2×C22⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×C4×C8—51no—
234C2×C4×C8—51no—
235#390C2×D511yescharacteristic
236#389C2×D511yescharacteristic
237#388—21no—
238#386—21no—
239#383—101no—
240#382—51no—
241#382—51no—
242#381—101no—
243#380—51no—
244#380—51no—
245#380C2×D511yescharacteristic
246C4×C4⋊C4—51no—
247C4×C4⋊C4—51no—
248C4×C4⋊C4C2×D511yescharacteristic
249C4×C22⋊C4—21no—
250C4×C22⋊C4—101no—
251#376—101no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#336—51no—
261#336—51no—
262C23×C5—21no—
263C23×C5—21no—
264C23×C5—21no—
265C23×C5—21no—
266C23×C5—21no—
267C23×C5—21no—
268C23×C5—22no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5#13512yes—
276C23×C5C22×D411yescharacteristic
277C5×D4—22no—
278C5×D4—22no—
279C5×D4—48no—
280C5×D4—41no—
281C5×D4—41no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—22no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—44no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—44no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—84no—
309C2×C4×C5#12312yes—
310C2×C4×C5#12312yes—
311C2×C4×C5#13512yes—
312C2×C4×C5AGL(1,ℤ/8)12yes—
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C2×C4×C5C2×#4111yescharacteristic
317C2×C4×C5C2×#4111yescharacteristic
318C2×C4×C5C2×#4111yescharacteristic
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—41no—
326C2×Dic5—41no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—41no—
331#168—22no—
332#168—22no—
333#168—41no—
334#168—41no—
335C22×D4—21no—
336C22×D4C22×D511yescharacteristic
337C23×C4—21no—
338C23×C4C22⋊D511yescharacteristic
339C23×C4C22⋊D511yescharacteristic
340C23×C4C22×D511yescharacteristic
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—51no—
345#121—22no—
346#121—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—44no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—101no—
364C2×C22⋊C4—101no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—21no—
368C2×C42—101no—
369C2×C42—101no—
370C2×C42C22⋊D511yescharacteristic
371C2×C42C22⋊D511yescharacteristic
372C2×C42C22×D511yescharacteristic
373C2×C42C22×D511yescharacteristic
374#107—102no—
375#107—102no—
376#106—102no—
377#106—102no—
378#102—102no—
379#102—102no—
380#102—102no—
381#102—102no—
382C22⋊C8—102no—
383C22⋊C8—102no—
384C4×C8—102no—
385C4×C8—102no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—101no—
390#95—101no—
391#95—101no—
392#95—101no—
393#95—101no—
394#95—101no—
395#95—101no—
396#95—101no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—41no—
404C22×C5—42no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—81no—
408C22×C5—81no—
409C22×C5—81no—
410C22×C5—81no—
411C22×C5C2×#12311yescharacteristic
412C22×C5#52511yescharacteristic
413C22×C5#53211yescharacteristic
414C22×C5C2×#13511yescharacteristic
415C22×C5C2×#13511yescharacteristic
416C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C5#57511yescharacteristic
418C4×C5—22no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—42no—
422C4×C5—41no—
423C4×C5—81no—
424C4×C5—81no—
425C4×C5#48214yes—
426C4×C5#52911yescharacteristic
427C4×C5#52911yescharacteristic
428C4×C5#52911yescharacteristic
429C4×C5#52911yescharacteristic
430Dic5—81no—
431Dic5—81no—
432Dic5—81no—
433Dic5—81no—
434C24—21no—
435C24C2×C22⋊D511yescharacteristic
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4#70912yes—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—41no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—101no—
467C22×C4C2×C22⋊D511yescharacteristic
468C22×C4C2×C22⋊D511yescharacteristic
469C22×C4C2×C22⋊D511yescharacteristic
470C22×C4C2×C22⋊D511yescharacteristic
471C22×C4C2×C22⋊D511yescharacteristic
472C22×C4C23×D511yescharacteristic
473C2×C8—52no—
474C2×C8—52no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—101no—
480C2×C8—101no—
481C2×C8—101no—
482C2×C8—101no—
483C2×C8—101no—
484C2×C8—101no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4—101no—
498C4⋊C4—101no—
499C4⋊C4#70912yes—
500C22⋊C4—24no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—202no—
506C22⋊C4—202no—
507C42—21no—
508C42—21no—
509C42—22no—
510C42—22no—
511C42—42no—
512C42—202no—
513C42—202no—
514C42#71112yes—
515C42#71112yes—
516C2×C5—42no—
517C2×C5—82no—
518C2×C5#239511yescharacteristic
519C2×C5C2×#48211yescharacteristic
520C2×C5#309111yescharacteristic
521C2×C5#310211yescharacteristic
522C2×C5#310511yescharacteristic
523C2×C5#316811yescharacteristic
524C2×C5#317111yescharacteristic
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23#409612yes—
539C23C22×C22⋊D511yescharacteristic
540D4—22no—
541D4—22no—
542D4—48no—
543D4—41no—
544D4—41no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—44no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—84no—
572C2×C4—201no—
573C2×C4—201no—
574C2×C4—201no—
575C2×C4—201no—
576C2×C4—201no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—201no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4#407812yes—
585C2×C4#408112yes—
586C2×C4#408112yes—
587C2×C4#409612yes—
588C2×C4C2×#70911yescharacteristic
589C2×C4C2×#70911yescharacteristic
590C2×C4C2×#71111yescharacteristic
591C2×C4C2×#71111yescharacteristic
592C2×C4D5×#4111yescharacteristic
593C2×C4D5×#4111yescharacteristic
594C8—102no—
595C8—102no—
596C8—201no—
597C8—201no—
598C5#2375811yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#6612511yescharacteristic
614C22C2×#407811yescharacteristic
615C22C2×#408111yescharacteristic
616C22C2×#409611yescharacteristic
617C22C2×#409611yescharacteristic
618C22#6615611yescharacteristic
619C22#6616611yescharacteristic
620C4—22no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—401no—
628C4—401no—
629C4—401no—
630C4—401no—
631C4#6532414yes—
632C4#6587211yescharacteristic
633C4#6587211yescharacteristic
634C4#6589111yescharacteristic
635C4#6589111yescharacteristic
636C2—42no—
637C2—82no—
638C2#1061404011yescharacteristic
639C2#1061407711yescharacteristic
640C2#1061425911yescharacteristic
641C2C2×#6532411yescharacteristic
642C2#1061464411yescharacteristic
643C2#1061486511yescharacteristic
644C2#1061502311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC4×C5×#121C2
socleC23×C5C22×D4
prime radicalC2×C5×#121C22
hypercenterC4×#121D5
hypocenterC5#23758
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #10613791C2semidirect
5. C4×#3964C2semidirect
6. C4×#3964C2semidirect
7. C4×C22⋊#168C2semidirect
8. #10600447C2semidirect
9. #10600434C2semidirect
10. #10600406C2semidirect
11. #10600402C2semidirect
12. #10600312C2semidirect
13. #10600300C2semidirect
14. C4×#3939C2semidirect
15. C4×#3940C2semidirect
598. C5#23758semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1212
#106137912
#106024732
#106024722
C4×#39642
C4×C22⋊#1682
#106004472
#106004342
#106004062
#106004022
#106003122
#106003002
C4×#39392
C4×#39402
#237585