Finite Group Databasebeta

← #12167417

Subgroups — #12167417

Order 1280.

764 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2492C211yesmaximal, characteristic
2#10605196C211yesmaximal, characteristic
3#10602587C211yesmaximal, characteristic, complemented
4#10602572C211yesmaximal, characteristic, complemented
5#10602493C211yesmaximal, characteristic
6#10602485C211yesmaximal, characteristic
7#10600483C211yesmaximal, characteristic, complemented
8#10600474C211yesmaximal, characteristic, complemented
9#10600467C211yesmaximal, characteristic, complemented
10#10600460C211yesmaximal, characteristic, complemented
11#10600320C211yesmaximal, characteristic
12#10600295C211yesmaximal, characteristic
13C4×#3942C211yesmaximal, characteristic, complemented
14#10600254C211yesmaximal, characteristic, complemented
15#10600244C211yesmaximal, characteristic
16C2×C5×C4⋊Q8C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C22×#689C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C2×#4070C2211yescharacteristic
21C2×C4×Dic10C2211yescharacteristic
22C5×#400—21no—
23C5×#393—21no—
24C5×#391—21no—
25C5×#391C2211yescharacteristic
26C5×#391C2211yescharacteristic
27C5×#388—21no—
28C5×#380C2211yescharacteristic
29C4×C5×C4⋊C4C2211yescharacteristic
30C4×C5×C22⋊C4C2211yescharacteristic
31C2×#3967C2211yescharacteristic
32C2×#3967C2211yescharacteristic
33C2×#3967C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35C2×C22⋊#168C2211yescharacteristic
36C2×#3942C2211yescharacteristic
37C2×#3942C2211yescharacteristic
38C2×#3942C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40#65235—21no—
41C22⋊C4×Dic5—21no—
42C4×C4⋊Dic5C2211yescharacteristic
43#65218C2211yescharacteristic
44#65217C2211yescharacteristic
45C2×C4⋊#168C2211yescharacteristic
46C2×C4×#168C2211yescharacteristic
47#64944—21no—
48#64936—21no—
49#64749C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64744C2211yescharacteristic
58#64744C2211yescharacteristic
59#26726—51nomaximal, Sylow
60C22×C5×Q8—21no—
61C22×C5×Q8C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×Dic5—21no—
64C22×Dic10C2311yescharacteristic
65C5×C4⋊Q8—22no—
66C5×C4⋊Q8—41no—
67C5×C22⋊Q8—22no—
68C5×C22⋊Q8—41no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4—21no—
76C2×C5×C22⋊C4D411yescharacteristic
77C2×C5×C22⋊C4D411yescharacteristic
78C2×C42×C5—21no—
79C2×C42×C5C2311yescharacteristic
80C2×C42×C5C2311yescharacteristic
81C2×C22⋊Dic5—21no—
82C2×#689—22no—
83C2×#689—41no—
84C2×#689—41no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—41no—
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91#4070—22no—
92#4070—22no—
93C2×#683—21no—
94C2×#683—21no—
95C2×#683—21no—
96C2×C4×Dic5—21no—
97C2×C4×Dic5—21no—
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C22×#168C2311yescharacteristic
102C4×Dic10—22no—
103C4×Dic10—41no—
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110C5×#95D411yescharacteristic
111C5×#95D411yescharacteristic
112#3967—22no—
113#3967—22no—
114#3967—41no—
115#3963—21no—
116#3963—21no—
117#3963—21no—
118#3963—21no—
119C22⋊#168—41no—
120C22⋊#168—41no—
121#3942—22no—
122#3942—22no—
123#3942—41no—
124#3939—22no—
125C4⋊#168—41no—
126C4×#168—41no—
127#2492D511yescharacteristic
128#2360—51no—
129#2056—51no—
130#2036—51no—
131#2024—51no—
132#2001—51no—
133#1987—51no—
134#1933—51no—
135#1928—51no—
136#1923—51no—
137#1921—51no—
138#1878—51no—
139#1872—51no—
140#1824—51no—
141C4×#103—51no—
142C24×C5C2×D411yescharacteristic
143C2×C5×Q8—21no—
144C2×C5×Q8—21no—
145C2×C5×Q8—21no—
146C2×C5×Q8—21no—
147C2×C5×Q8—21no—
148C2×C5×Q8—21no—
149C2×C5×Q8—42no—
150C2×C5×Q8—42no—
151C2×C5×Q8—81no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
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×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2411yescharacteristic
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—42no—
173C22×Dic5—42no—
174C22×Dic5—81no—
175C2×Dic10—21no—
176C2×Dic10—21no—
177C2×Dic10—21no—
178C2×Dic10—21no—
179C2×Dic10—21no—
180C2×Dic10#4112yes—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4—21no—
186C5×C4⋊C4—42no—
187C5×C4⋊C4—42no—
188C5×C4⋊C4#4112yes—
189C5×C22⋊C4—41no—
190C5×C22⋊C4—42no—
191C5×C22⋊C4—81no—
192C5×C22⋊C4Q1614yescomplemented
193C42×C5—21no—
194C42×C5—21no—
195C42×C5—21no—
196C42×C5—21no—
197C42×C5—81no—
198C22⋊Dic5—24no—
199#689—44no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—21no—
204C4⋊Dic5—42no—
205C4⋊Dic5#4112yes—
206C4⋊Dic5#4112yes—
207#683—24no—
208#683—42no—
209#683—81no—
210C4×Dic5—42no—
211C4×Dic5—81no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168—21no—
217C2×#168—21no—
218C2×#168—21no—
219C2×#168—21no—
220C2×#168—21no—
221C2×#168—21no—
222C2×#168—21no—
223C2×#168—21no—
224C22×Q16—51no—
225C2×C4⋊Q8C2×D511yescharacteristic
226C2×C22⋊Q8—51no—
227C2×C22⋊Q8C2×D511yescharacteristic
228C2×C4×Q8—51no—
229C22×C4⋊C4—51no—
230C2×#107—51no—
231C2×C4⋊C8—51no—
232C2×#103—51no—
233C2×#103—51no—
234C2×#103—51no—
235C2×#103—51no—
236C2×#103—51no—
237C2×#103—51no—
238C2×C22⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×C4×C8—51no—
241#400—21no—
242#393—21no—
243#391—21no—
244#391—51no—
245#391C2×D511yescharacteristic
246#391C2×D511yescharacteristic
247#389—51no—
248#389—101no—
249#388—21no—
250#387—101no—
251#385—101no—
252#380C2×D511yescharacteristic
253C4×C4⋊C4—51no—
254C4×C4⋊C4C2×D511yescharacteristic
255C4×C22⋊C4—101no—
256C4×C22⋊C4C2×D511yescharacteristic
257#340—51no—
258#340—51no—
259#340—51no—
260#340—51no—
261#340—51no—
262#340—51no—
263#340—51no—
264#340—51no—
265#336—51no—
266#336—51no—
267C23×C5—21no—
268C23×C5—21no—
269C23×C5—21no—
270C23×C5—21no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5C2×Q1612yes—
274C23×C5C22×D411yescharacteristic
275C5×Q8—41no—
276C5×Q8—41no—
277C5×Q8—41no—
278C5×Q8—41no—
279C5×Q8—84no—
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—22no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
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—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5C2×Q1612yes—
310C2×C4×C5C2×Q1612yes—
311C2×C4×C5C2×#4111yescharacteristic
312C2×C4×C5C2×#4111yescharacteristic
313C2×C4×C5C2×#4111yescharacteristic
314C2×C4×C5C2×#4111yescharacteristic
315C2×C4×C5H(5,𝔽2)11yescharacteristic
316C2×C4×C5H(5,𝔽2)11yescharacteristic
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
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—84no—
330Dic10—22no—
331Dic10—22no—
332Dic10—41no—
333Dic10—41no—
334#168—41no—
335#168—41no—
336#168—41no—
337#168—41no—
338C22×Q8—21no—
339C22×Q8—51no—
340C22×Q8C22×D511yescharacteristic
341C23×C4—101no—
342C23×C4C22×D511yescharacteristic
343C2×Q16—102no—
344C2×Q16—201no—
345C2×Q16—201no—
346C22×C8—51no—
347C22×C8—51no—
348C22×C8—51no—
349C22×C8—51no—
350C4⋊Q8—22no—
351C4⋊Q8—41no—
352C22⋊Q8—22no—
353C22⋊Q8—41no—
354C22⋊Q8—102no—
355C22⋊Q8—102no—
356C4×Q8—102no—
357C4×Q8—201no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—102no—
364C2×C4⋊C4—101no—
365C2×C4⋊C4—101no—
366C2×C4⋊C4—101no—
367C2×C4⋊C4—101no—
368C2×C4⋊C4—201no—
369C2×C4⋊C4C22×D511yescharacteristic
370C2×C4⋊C4C22×D511yescharacteristic
371C2×C4⋊C4C22×D511yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—101no—
375C2×C22⋊C4C22⋊D511yescharacteristic
376C2×C22⋊C4C22⋊D511yescharacteristic
377C2×C42—21no—
378C2×C42—101no—
379C2×C42—101no—
380C2×C42C22×D511yescharacteristic
381C2×C42C22×D511yescharacteristic
382#107—102no—
383C4⋊C8—201no—
384#103—102no—
385#103—102no—
386#103—102no—
387#103—102no—
388#103—201no—
389#103—201no—
390C22⋊C8—201no—
391C22⋊C8—201no—
392C4×C8—201no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—101no—
400#95—101no—
401#95—101no—
402#95—101no—
403#95C22⋊D511yescharacteristic
404#95C22⋊D511yescharacteristic
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5#52511yescharacteristic
413C22×C5#54611yescharacteristic
414C22×C5#54611yescharacteristic
415C22×C5C22×Q1611yescharacteristic
416C22×C5#57511yescharacteristic
417C22×C5#57711yescharacteristic
418C22×C5#57711yescharacteristic
419C4×C5—22no—
420C4×C5—22no—
421C4×C5—41no—
422C4×C5—41no—
423C4×C5—41no—
424C4×C5—42no—
425C4×C5—81no—
426C4×C5—81no—
427C4×C5—81no—
428C4×C5#52911yescharacteristic
429C4×C5#53811yescharacteristic
430C4×C5#55511yescharacteristic
431C4×C5#55911yescharacteristic
432Dic5—42no—
433Dic5—42no—
434Dic5—42no—
435Dic5—81no—
436C24C2×C22⋊D511yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—42no—
444C2×Q8—42no—
445C2×Q8—52no—
446C2×Q8—81no—
447C2×Q8—101no—
448C2×Q8—101no—
449C2×Q8—101no—
450C2×Q8—101no—
451C2×Q8—101no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—101no—
463C22×C4—101no—
464C22×C4—101no—
465C22×C4—101no—
466C22×C4—202no—
467C22×C4—202no—
468C22×C4—401no—
469C22×C4C2×C22⋊D511yescharacteristic
470C22×C4C2×C22⋊D511yescharacteristic
471C22×C4C2×C22⋊D511yescharacteristic
472C22×C4C2×C22⋊D511yescharacteristic
473C22×C4C2×C22⋊D511yescharacteristic
474C22×C4C23×D511yescharacteristic
475Q16—204no—
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—
485C2×C8—101no—
486C2×C8—101no—
487C2×C8—101no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—52no—
496C4⋊C4—52no—
497C4⋊C4—104no—
498C4⋊C4—101no—
499C4⋊C4—101no—
500C4⋊C4—101no—
501C4⋊C4—101no—
502C4⋊C4—202no—
503C4⋊C4—202no—
504C4⋊C4—401no—
505C4⋊C4#71112yes—
506C22⋊C4—41no—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—104no—
510C22⋊C4#68914yescomplemented
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—81no—
516C42—202no—
517C42—401no—
518C2×C5—42no—
519C2×C5#245911yescharacteristic
520C2×C5#310411yescharacteristic
521C2×C5#312511yescharacteristic
522C2×C5#329911yescharacteristic
523C2×C5#329911yescharacteristic
524C2×C5#331111yescharacteristic
525C2×C5#332311yescharacteristic
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23C2×#68912yes—
533C23C22×C22⋊D511yescharacteristic
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—84no—
539Q8—102no—
540Q8—102no—
541Q8—201no—
542Q8—201no—
543C2×C4—21no—
544C2×C4—21no—
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—41no—
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—102no—
573C2×C4—102no—
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—201no—
584C2×C4—404no—
585C2×C4C2×#68912yes—
586C2×C4C2×#68912yes—
587C2×C4C2×#71111yescharacteristic
588C2×C4#414411yescharacteristic
589C2×C4D5×#4111yescharacteristic
590C2×C4D5×#4111yescharacteristic
591C2×C4D5×#4111yescharacteristic
592C2×C4#414911yescharacteristic
593C8—201no—
594C8—201no—
595C8—201no—
596C8—201no—
597C5#2672611yescharacteristic, complemented, Sylow
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#6614011yescharacteristic
606C22C22×#68911yescharacteristic
607C22#6615611yescharacteristic
608C22#6616211yescharacteristic
609C22#6616311yescharacteristic
610C22#6617011yescharacteristic
611C22#6617111yescharacteristic
612C4—22no—
613C4—22no—
614C4—41no—
615C4—41no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—202no—
622C4—202no—
623C4—202no—
624C4—401no—
625C4#6600411yescharacteristic
626C4#6601211yescharacteristic
627C4#6601411yescharacteristic
628C4#6601511yescharacteristic
629C2—42no—
630C2#1061472811yescharacteristic
631C2#1061509911yescharacteristic
632C2#1061519311yescharacteristic
633C2#1061523211yescharacteristic
634C2#1061528211yescharacteristic
635C2#1061537111yescharacteristic
636C2#1061539611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC5×#2492C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
hypercenter#2492D5
hypocenterC5#26726
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2492

Complements

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

NH ≅ G/Ntype
3. #10602587C2semidirect
4. #10602572C2semidirect
7. #10600483C2semidirect
8. #10600474C2semidirect
9. #10600467C2semidirect
10. #10600460C2semidirect
13. C4×#3942C2semidirect
14. #10600254C2semidirect
192. C5×C22⋊C4Q16semidirect
510. C22⋊C4#689semidirect
597. C5#26726semidirect

Maximal subgroups

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

subgroupindex
C5×#24922
#106051962
#106025872
#106025722
#106024932
#106024852
#106004832
#106004742
#106004672
#106004602
#106003202
#106002952
C4×#39422
#106002542
#106002442
#267265