Finite Group Databasebeta

← #12171981

Subgroups — #12171981

Order 1280.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2361C211yesmaximal, characteristic
2#10605244C211yesmaximal, characteristic, complemented
3#10602473C211yesmaximal, characteristic
4#10602473C211yesmaximal, characteristic
5C4×#3964C211yesmaximal, characteristic, complemented
6#10602400C211yesmaximal, characteristic, complemented
7#10602349C211yesmaximal, characteristic, complemented
8#10602346C211yesmaximal, characteristic, complemented
9#10600445C211yesmaximal, characteristic, complemented
10#10600433C211yesmaximal, characteristic, complemented
11#10600411C211yesmaximal, characteristic, complemented
12#10600394C211yesmaximal, characteristic, complemented
13#10600260C211yesmaximal, characteristic, complemented
14#10600253C211yesmaximal, characteristic, complemented
15#10600244C211yesmaximal, characteristic, complemented
16C2×C5×#121C2211yescharacteristic
17C2×C4×C5×D4—21no—
18C2×C4×C5×D4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C5×#390C2211yescharacteristic
21C5×#389C2211yescharacteristic
22C5×#388—21no—
23C5×#386—21no—
24C5×#385—21no—
25C4×C5×C4⋊C4C2211yescharacteristic
26C4×C5×C22⋊C4C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28C2×#3964C2211yescharacteristic
29C2×#3964C2211yescharacteristic
30C2×#3964C2211yescharacteristic
31#65501C2211yescharacteristic
32#65501C2211yescharacteristic
33C2×C22⋊#168C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39#65240—21no—
40#65237—21no—
41#65224C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43#65217C2211yescharacteristic
44#65217C2211yescharacteristic
45C2×C4⋊#168C2211yescharacteristic
46C2×C4×#168C2211yescharacteristic
47#64949—21no—
48#64944—21no—
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#27032—51nomaximal, Sylow
60C22×C5×D4—21no—
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5—21no—
64C23×C4×C5C2311yescharacteristic
65C5×#121—22no—
66C5×#121—22no—
67C4×C5×D4—22no—
68C4×C5×D4—41no—
69C4×C5×D4—44no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—41no—
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C4⋊C4C2311yescharacteristic
77C2×C5×C22⋊C4—21no—
78C2×C5×C22⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4D411yescharacteristic
82C2×C5×C22⋊C4D411yescharacteristic
83C2×C42×C5—21no—
84C2×C42×C5C2311yescharacteristic
85C2×C42×C5C2311yescharacteristic
86C2×C22⋊Dic5—21no—
87C2×C22⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2311yescharacteristic
94C2×#683—21no—
95C2×#683—21no—
96C2×C4×Dic5—21no—
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C5×#95—21no—
102C5×#95—21no—
103C5×#95D411yescharacteristic
104C5×#95D411yescharacteristic
105#3964—22no—
106#3964—22no—
107#3964—22no—
108#3964—41no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114C22⋊#168—22no—
115C22⋊#168—41no—
116#3940—22no—
117#3940—22no—
118#3940—22no—
119#3940—41no—
120C4⋊#168—22no—
121C4×#168—41no—
122#2497—51no—
123#2361D511yescharacteristic
124#2071—51no—
125#2065—51no—
126#2034—51no—
127#2034—51no—
128#1948—51no—
129#1941—51no—
130#1923—51no—
131#1920—51no—
132#1919—51no—
133#1864—51no—
134#1853—51no—
135#1823—51no—
136C4×#102—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—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—42no—
158C22×C4×C5—42no—
159C22×C4×C5—42no—
160C22×C4×C5—42no—
161C22×C4×C5—81no—
162C22×C4×C5—81no—
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2411yescharacteristic
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—42no—
178C5×C4⋊C4—42no—
179C5×C4⋊C4#4112yes—
180C5×C4⋊C4#4112yes—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—41no—
183C5×C22⋊C4—42no—
184C5×C22⋊C4—42no—
185C5×C22⋊C4—81no—
186C5×C22⋊C4SD1614yes—
187C42×C5—21no—
188C42×C5—21no—
189C42×C5—21no—
190C42×C5—21no—
191C42×C5—42no—
192C22⋊Dic5—81no—
193C22⋊Dic5—81no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—81no—
203C4⋊Dic5—81no—
204#683—42no—
205#683—81no—
206C4×Dic5—81no—
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—21no—
218C2×#168#4112yes—
219C2×#121C2×D511yescharacteristic
220C2×C4×D4—21no—
221C2×C4×D4C2×D511yescharacteristic
222C22×C4⋊C4C2×D511yescharacteristic
223C2×#106—51no—
224C2×#106—51no—
225C2×#106—51no—
226C2×#106—51no—
227C2×C4⋊C8—51no—
228C2×#102—51no—
229C2×#102—51no—
230C2×#102—51no—
231C2×#102—51no—
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×C4×C8—51no—
235#400—101no—
236#396—101no—
237#390C2×D511yescharacteristic
238#389—51no—
239#389—51no—
240#389C2×D511yescharacteristic
241#388—21no—
242#388—101no—
243#387—101no—
244#386—21no—
245#385—21no—
246#384—51no—
247#380—51no—
248#380—51no—
249C4×C4⋊C4—51no—
250C4×C4⋊C4C2×D511yescharacteristic
251C4×C22⋊C4C2×D511yescharacteristic
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×C5C2×SD1612yes—
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—22no—
288C2×C4×C5—21no—
289C2×C4×C5—22no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
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—41no—
307C2×C4×C5—41no—
308C2×C4×C5—84no—
309C2×C4×C5—84no—
310C2×C4×C5C2×SD1612yes—
311C2×C4×C5C2×SD1612yes—
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5C2×#4111yescharacteristic
316C2×C4×C5H(5,𝔽2)11yescharacteristic
317C2×C4×C52−1+411yescharacteristic
318C2×Dic5—41no—
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—
330#168—22no—
331#168—41no—
332#168—41no—
333#168—41no—
334C22×D4—21no—
335C22×D4C22×D511yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4C22×D511yescharacteristic
339C22×C8—51no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—51no—
343#121—22no—
344#121—22no—
345C4×D4—22no—
346C4×D4—41no—
347C4×D4—44no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—51no—
353C2×C4⋊C4—51no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—101no—
357C2×C4⋊C4—101no—
358C2×C4⋊C4—101no—
359C2×C4⋊C4—101no—
360C2×C4⋊C4C22×D511yescharacteristic
361C2×C4⋊C4C22×D511yescharacteristic
362C2×C4⋊C4C22×D511yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—101no—
368C2×C22⋊C4—101no—
369C2×C22⋊C4C22⋊D511yescharacteristic
370C2×C22⋊C4C22⋊D511yescharacteristic
371C2×C42—21no—
372C2×C42—101no—
373C2×C42C22×D511yescharacteristic
374C2×C42C22×D511yescharacteristic
375#106—102no—
376#106—102no—
377#106—102no—
378#106—201no—
379C4⋊C8—102no—
380#102—102no—
381#102—102no—
382#102—102no—
383#102—201no—
384C22⋊C8—102no—
385C22⋊C8—201no—
386C4×C8—201no—
387#95—21no—
388#95—21no—
389#95—101no—
390#95—101no—
391#95—101no—
392#95—101no—
393#95—101no—
394#95C22⋊D511yescharacteristic
395#95C22⋊D511yescharacteristic
396C22×C5—22no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—41no—
402C22×C5—41no—
403C22×C5—42no—
404C22×C5—42no—
405C22×C5—42no—
406C22×C5—81no—
407C22×C5—81no—
408C22×C5—81no—
409C22×C5—81no—
410C22×C5#52511yescharacteristic
411C22×C5#54611yescharacteristic
412C22×C5#54711yescharacteristic
413C22×C5C22×SD1611yescharacteristic
414C22×C5#57511yescharacteristic
415C22×C5#57611yescharacteristic
416C22×C5#57711yescharacteristic
417C4×C5—22no—
418C4×C5—22no—
419C4×C5—41no—
420C4×C5—42no—
421C4×C5—41no—
422C4×C5—42no—
423C4×C5—41no—
424C4×C5—81no—
425C4×C5#52911yescharacteristic
426C4×C5#53911yescharacteristic
427C4×C5#55311yescharacteristic
428C4×C5#55611yescharacteristic
429Dic5—81no—
430Dic5—81no—
431Dic5—81no—
432Dic5—81no—
433C24—21no—
434C24C2×C22⋊D511yescharacteristic
435C2×D4—24no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4#70912yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4—101no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—101no—
463C22×C4C2×C22⋊D511yescharacteristic
464C22×C4C2×C22⋊D511yescharacteristic
465C22×C4C2×C22⋊D511yescharacteristic
466C22×C4C2×C22⋊D511yescharacteristic
467C22×C4C2×C22⋊D511yescharacteristic
468C22×C4C23×D511yescharacteristic
469C2×C8—52no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—101no—
478C2×C8—101no—
479C2×C8—101no—
480C2×C8—101no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—101no—
488C4⋊C4—101no—
489C4⋊C4—101no—
490C4⋊C4—101no—
491C4⋊C4—101no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—101no—
495C4⋊C4—202no—
496C4⋊C4—401no—
497C4⋊C4—401no—
498C4⋊C4—401no—
499C4⋊C4#70912yes—
500C4⋊C4#71112yes—
501C22⋊C4—24no—
502C22⋊C4—41no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—401no—
507C22⋊C4—401no—
508C22⋊C4#68714yes—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—401no—
515C2×C5—42no—
516C2×C5—82no—
517C2×C5#246611yescharacteristic
518C2×C5#310111yescharacteristic
519C2×C5#311911yescharacteristic
520C2×C5#329511yescharacteristic
521C2×C5#332111yescharacteristic
522C2×C5#333511yescharacteristic
523C2×C5#335511yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23C2×#68712yes—
538C23C22×C22⋊D511yescharacteristic
539D4—22no—
540D4—22no—
541D4—48no—
542D4—41no—
543D4—41no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
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—84no—
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×C4C2×#68712yes—
585C2×C4C2×#68712yes—
586C2×C4C2×#70911yescharacteristic
587C2×C4C2×#70911yescharacteristic
588C2×C4C2×#71111yescharacteristic
589C2×C4#414411yescharacteristic
590C2×C4D5×#4111yescharacteristic
591C2×C4#415011yescharacteristic
592C8—102no—
593C8—201no—
594C8—201no—
595C8—201no—
596C5#2703211yescharacteristic, complemented, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#6612511yescharacteristic
612C22C22×#68711yescharacteristic
613C22#6614011yescharacteristic
614C22#6615611yescharacteristic
615C22#6615811yescharacteristic
616C22#6616911yescharacteristic
617C22#6617111yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—81no—
626C4—401no—
627C4—401no—
628C4—401no—
629C4—401no—
630C4#6587211yescharacteristic
631C4#6587611yescharacteristic
632C4#6589211yescharacteristic
633C4#6589811yescharacteristic
634C2—42no—
635C2—82no—
636C2#1061404511yescharacteristic
637C2#1061410011yescharacteristic
638C2#1061429911yescharacteristic
639C2#1061521411yescharacteristic
640C2#1061524811yescharacteristic
641C2#1061527011yescharacteristic
642C2#1061534411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2361C2
socleC23×C5C22×D4
prime radicalC2×C5×#121C22
hypercenter#2361D5
hypocenterC5#27032
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #10605244C2semidirect
5. C4×#3964C2semidirect
6. #10602400C2semidirect
7. #10602349C2semidirect
8. #10602346C2semidirect
9. #10600445C2semidirect
10. #10600433C2semidirect
11. #10600411C2semidirect
12. #10600394C2semidirect
13. #10600260C2semidirect
14. #10600253C2semidirect
15. #10600244C2semidirect
596. C5#27032semidirect

Maximal subgroups

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

subgroupindex
C5×#23612
#106052442
#106024732
C4×#39642
#106024002
#106023492
#106023462
#106004452
#106004332
#106004112
#106003942
#106002602
#106002532
#106002442
#270325