Finite Group Databasebeta

← #12129332

Subgroups — #12129332

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
1C5×#2283C211yesmaximal, characteristic, complemented
2C4×#4076C211yesmaximal, characteristic
3C4×C22⋊#168C211yesmaximal, characteristic, complemented
4#10600351C211yesmaximal, characteristic, complemented
5#10600350C211yesmaximal, characteristic, complemented
6#10600335C211yesmaximal, characteristic, complemented
7#10600334C211yesmaximal, characteristic, complemented
8#10600317C211yesmaximal, characteristic
9#10600316C211yesmaximal, characteristic
10#10600313C211yesmaximal, characteristic, complemented
11#10600312C211yesmaximal, characteristic, complemented
12C4×#3939C211yesmaximal, characteristic, complemented
13C4×#3940C211yesmaximal, characteristic, complemented
14C4×#3941C211yesmaximal, characteristic, complemented
15C4×#3941C211yesmaximal, characteristic, complemented
16C22×C42×C5C2211yescharacteristic
17C2×#4076C2211yescharacteristic
18C2×C4×C22⋊D5—21no—
19C2×C4×D20C2211yescharacteristic
20C5×#383—21no—
21C5×#382C2211yescharacteristic
22C5×#382C2211yescharacteristic
23C5×#381—21no—
24C5×#380C2211yescharacteristic
25C5×#380C2211yescharacteristic
26C4×C5×C4⋊C4C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C4×C5×C22⋊C4—21no—
29C5×#376—21no—
30#65502—21no—
31#65501C2211yescharacteristic
32C2×C22⋊#168C2211yescharacteristic
33C2×C22⋊#168C2211yescharacteristic
34C2×#3941C2211yescharacteristic
35C2×#3941C2211yescharacteristic
36C2×#3941C2211yescharacteristic
37C2×#3941C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3940C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42#65229—21no—
43#65228C2211yescharacteristic
44C4×#685—21no—
45C4×C4⋊Dic5C2211yescharacteristic
46#65217C2211yescharacteristic
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
60C23×C4×C5D411yescharacteristic
61C23×C4×C5D411yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C22×C22⋊D5—21no—
64C22×D20C2311yescharacteristic
65C22×C4×D5—21no—
66C2×C5×C4⋊C4C2311yescharacteristic
67C2×C5×C4⋊C4C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C22⋊C4—21no—
71C2×C5×C22⋊C4—21no—
72C2×C42×C5—22no—
73C2×C42×C5—22no—
74C2×C42×C5—21no—
75C2×C42×C5—21no—
76C2×C42×C5D411yescharacteristic
77C2×C42×C5D411yescharacteristic
78C2×C42×C5C2311yescharacteristic
79C2×C42×C5C2311yescharacteristic
80C2×C22⋊Dic5—21no—
81#4076—22no—
82#4076—22no—
83C4×C22⋊D5—44no—
84C2×#685—21no—
85C2×#685—21no—
86C2×#685—21no—
87C2×#685—21no—
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×#683—21no—
92C2×C4×Dic5—21no—
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C4×D20—22no—
98C4×D20—22no—
99C5×#95—21no—
100C5×#95—21no—
101C5×#95—21no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110C22⋊#168—22no—
111C22⋊#168—22no—
112#3941—22no—
113#3941—22no—
114#3941—22no—
115#3941—22no—
116#3940—22no—
117#3940—22no—
118#3939—22no—
119#3939—22no—
120C4×#168—22no—
121C4×#168—22no—
122C4×#121—51no—
123#2283D511yescharacteristic, complemented
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×C5C2×D411yescharacteristic
138C23×D5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—41no—
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2411yescharacteristic
161C2×C22⋊D5—24no—
162C2×C22⋊D5—42no—
163C2×C22⋊D5—42no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C2×D20—21no—
168C2×D20—21no—
169C2×D20—21no—
170C2×D20—21no—
171C2×D20—21no—
172C2×D20#4112yes—
173C2×C4×D5—42no—
174C2×C4×D5—42no—
175C2×C4×D5—42no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C22⋊C4—42no—
185C5×C22⋊C4—42no—
186C42×C5—22no—
187C42×C5—22no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5—42no—
191C42×C5—42no—
192C42×C5#4112yes—
193C42×C5#4112yes—
194C22⋊Dic5—42no—
195#685—24no—
196#685—42no—
197#685—42no—
198#685—42no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5#4112yes—
205#683—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×#121—51no—
220C2×C4×D4—51no—
221C2×C4×D4—101no—
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#390—51no—
236#389—51no—
237#388—101no—
238#386—101no—
239#383—21no—
240#382C2×D511yescharacteristic
241#382C2×D511yescharacteristic
242#381—21no—
243#380—51no—
244#380C2×D511yescharacteristic
245#380C2×D511yescharacteristic
246C4×C4⋊C4—51no—
247C4×C4⋊C4C2×D511yescharacteristic
248C4×C4⋊C4C2×D511yescharacteristic
249C4×C22⋊C4—21no—
250C4×C22⋊C4—101no—
251#376—21no—
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#13512yes—
269C23×C5C22×D411yescharacteristic
270C22×D5—22no—
271C22×D5—41no—
272C22×D5—41no—
273C22×D5—41no—
274C22×D5—41no—
275C22×D5—41no—
276C22×D5—41no—
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—21no—
284C2×C4×C5—21no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—44no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—44no—
294C2×C4×C5—41no—
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—41no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5#12312yes—
307C2×C4×C5#12312yes—
308C2×C4×C5#13512yes—
309C2×C4×C5AGL(1,ℤ/8)12yes—
310C2×C4×C5C2×#4111yescharacteristic
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C22⋊D5—48no—
317C2×Dic5—22no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323C2×Dic5—41no—
324C2×Dic5—41no—
325C2×Dic5—41no—
326D20—22no—
327D20—22no—
328D20—41no—
329D20—41no—
330C4×D5—84no—
331#168—22no—
332#168—22no—
333#168—41no—
334#168—41no—
335C22×D4—51no—
336C22×D4—101no—
337C23×C4—101no—
338C23×C4C22⋊D511yescharacteristic
339C23×C4C22⋊D511yescharacteristic
340C23×C4C22×D511yescharacteristic
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—51no—
345#121—102no—
346#121—102no—
347C4×D4—102no—
348C4×D4—102no—
349C4×D4—204no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4C22×D511yescharacteristic
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D511yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—101no—
361C2×C22⋊C4—101no—
362C2×C22⋊C4—101no—
363C2×C22⋊C4—101no—
364C2×C22⋊C4—101no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—21no—
368C2×C42—21no—
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—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
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×C5C2×#12311yescharacteristic
405C22×C5#52511yescharacteristic
406C22×C5#53211yescharacteristic
407C22×C5C2×#13511yescharacteristic
408C22×C5C2×#13511yescharacteristic
409C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C5#57511yescharacteristic
411C2×D5—42no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—81no—
415C2×D5—81no—
416C2×D5—81no—
417C2×D5—81no—
418C4×C5—22no—
419C4×C5—41no—
420C4×C5—41no—
421C4×C5—41no—
422C4×C5—81no—
423C4×C5—81no—
424C4×C5—81no—
425C4×C5—81no—
426C4×C5#48214yes—
427C4×C5#52911yescharacteristic
428C4×C5#52911yescharacteristic
429C4×C5#52911yescharacteristic
430C4×C5#52911yescharacteristic
431Dic5—42no—
432Dic5—81no—
433Dic5—81no—
434C24—101no—
435C24C2×C22⋊D511yescharacteristic
436C2×D4—52no—
437C2×D4—104no—
438C2×D4—101no—
439C2×D4—101no—
440C2×D4—101no—
441C2×D4—101no—
442C2×D4—101no—
443C2×D4—202no—
444C2×D4—202no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—101no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4—202no—
465C22×C4—202no—
466C22×C4—202no—
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—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—52no—
494C4⋊C4—101no—
495C4⋊C4—101no—
496C4⋊C4—101no—
497C4⋊C4—101no—
498C4⋊C4—101no—
499C4⋊C4—202no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—104no—
503C22⋊C4—202no—
504C22⋊C4—202no—
505C22⋊C4—202no—
506C22⋊C4—202no—
507C42—21no—
508C42—21no—
509C42—22no—
510C42—22no—
511C42—42no—
512C42—42no—
513C42—202no—
514C42#70912yes—
515C42#70912yes—
516C2×C5—42no—
517C2×C5#239511yescharacteristic
518C2×C5C2×#48211yescharacteristic
519C2×C5#309111yescharacteristic
520C2×C5#310211yescharacteristic
521C2×C5#310511yescharacteristic
522C2×C5#316811yescharacteristic
523C2×C5#317111yescharacteristic
524D5—82no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—102no—
532C23—201no—
533C23—201no—
534C23—201no—
535C23—201no—
536C23—201no—
537C23—201no—
538C23#409612yes—
539C23C22×C22⋊D511yescharacteristic
540D4—102no—
541D4—102no—
542D4—208no—
543D4—201no—
544D4—201no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
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—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—102no—
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—404no—
584C2×C4#407512yes—
585C2×C4#407512yes—
586C2×C4#409512yes—
587C2×C4#409612yes—
588C2×C4C2×#70911yescharacteristic
589C2×C4C2×#70911yescharacteristic
590C2×C4D5×#4111yescharacteristic
591C2×C4D5×#4111yescharacteristic
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—202no—
607C22—202no—
608C22—202no—
609C22—401no—
610C22—401no—
611C22—401no—
612C22—401no—
613C22C2×#407511yescharacteristic
614C22C2×#409511yescharacteristic
615C22C2×#409611yescharacteristic
616C22C2×#409611yescharacteristic
617C22#6615611yescharacteristic
618C22#6616211yescharacteristic
619C22#6616611yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—202no—
629C4—401no—
630C4—401no—
631C4#6529214yes—
632C4#6586211yescharacteristic
633C4#6586211yescharacteristic
634C4#6586211yescharacteristic
635C4#6586211yescharacteristic
636C2—42no—
637C2—402no—
638C2C2×#6529211yescharacteristic
639C2#1061394611yescharacteristic
640C2#1061400511yescharacteristic
641C2#1061486511yescharacteristic
642C2#1061486611yescharacteristic
643C2#1061487111yescharacteristic
644C2#1061487211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2283C2
socleC23×C5C22×D4
prime radicalC2×#4076C22
hypercenter#2283D5
hypocenterC5#23758
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
1. C5×#2283C2semidirect
3. C4×C22⋊#168C2semidirect
4. #10600351C2semidirect
5. #10600350C2semidirect
6. #10600335C2semidirect
7. #10600334C2semidirect
10. #10600313C2semidirect
11. #10600312C2semidirect
12. C4×#3939C2semidirect
13. C4×#3940C2semidirect
14. C4×#3941C2semidirect
15. C4×#3941C2semidirect
123. #2283D5semidirect
598. C5#23758semidirect

Maximal subgroups

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

subgroupindex
C5×#22832
C4×#40762
C4×C22⋊#1682
#106003512
#106003502
#106003352
#106003342
#106003172
#106003162
#106003132
#106003122
C4×#39392
C4×#39402
C4×#39412
#237585