Finite Group Databasebeta

← #13036407

Subgroups — #13036407

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65773C211yesmaximal, characteristic
2C2×C4×#704C211yesmaximal, characteristic, complemented
3Dic5×#123C211yesmaximal, characteristic
4#10604947C211yesmaximal, characteristic
5#10604902C211yesmaximal, characteristic, complemented
6#10604324C211yesmaximal, characteristic, complemented
7#10604322C211yesmaximal, characteristic, complemented
8#10604316C211yesmaximal, characteristic, complemented
9#10604315C211yesmaximal, characteristic, complemented
10#10604239C211yesmaximal, characteristic, complemented
11#10604237C211yesmaximal, characteristic, complemented
12#10604232C211yesmaximal, characteristic, complemented
13#10604227C211yesmaximal, characteristic, complemented
14#10604226C211yesmaximal, characteristic, complemented
15C22⋊C4×#170C211yesmaximal, characteristic, complemented
16C22×#704C2211yescharacteristic
17C22×#704C2211yescharacteristic
18C23×#170C2211yescharacteristic
19C2×C5×#123C411yescharacteristic
20C2×D4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C2×C22⋊#170C2211yescharacteristic
23C2×C22⋊#170C2211yescharacteristic
24C2×C22⋊#170C2211yescharacteristic
25C2×C22⋊#170C2211yescharacteristic
26C2×C22⋊#170C2211yescharacteristic
27#65773—24no—
28C2×#4004C2211yescharacteristic
29C2×#4004C2211yescharacteristic
30C4×#704—24no—
31C2×#4002C2211yescharacteristic
32C2×#4002C2211yescharacteristic
33C2×#4002C2211yescharacteristic
34C2×#4002C2211yescharacteristic
35C2×C4⋊#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37C2×C4×#170C2211yescharacteristic
38C2×C4×#170C2211yescharacteristic
39#65509C411yescharacteristic
40#65500C411yescharacteristic
41#65270C411yescharacteristic
42#65270C411yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C4⋊C4×Dic5C2211yescharacteristic
45#65240C411yescharacteristic
46#65240C411yescharacteristic
47#65239C411yescharacteristic
48C22⋊C4×Dic5C2211yescharacteristic
49C22⋊C4×Dic5C2211yescharacteristic
50C22⋊C4×Dic5C2211yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#21562—51nomaximal, Sylow
62C22×C5×D4C2×C411yescharacteristic
63C23×C4×C5C2×C411yescharacteristic
64C23×Dic5C2×C411yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C2×#704—22no—
68C2×#704—22no—
69C2×#704—22no—
70C2×#704—22no—
71C2×#704—22no—
72C2×#704D414yes—
73C22×#170—22no—
74C22×#170—22no—
75C22×#170—22no—
76C22×#170C2311yescharacteristic
77C22×#170C2311yescharacteristic
78C22×#170C2311yescharacteristic
79C22×#170C2311yescharacteristic
80C22×#170C2311yescharacteristic
81C22×#170C2311yescharacteristic
82C22×#170C2311yescharacteristic
83C22×#170C2311yescharacteristic
84C5×#123—24no—
85C2×C5×C4⋊C4C2×C411yescharacteristic
86C2×C5×C4⋊C4C2×C411yescharacteristic
87C2×C5×C22⋊C4C2×C411yescharacteristic
88C2×C5×C22⋊C4C2×C411yescharacteristic
89C2×C5×C22⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic5C2×C411yescharacteristic
91C2×C22⋊Dic5C2×C411yescharacteristic
92C2×C22⋊Dic5C2×C411yescharacteristic
93C2×C22⋊Dic5C2×C411yescharacteristic
94C2×C22⋊Dic5C2×C411yescharacteristic
95D4×Dic5—22no—
96D4×Dic5—22no—
97C2×C4⋊Dic5C2×C411yescharacteristic
98C2×C4⋊Dic5C2×C411yescharacteristic
99C2×C4⋊Dic5C2×C411yescharacteristic
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5C2×C411yescharacteristic
103C2×C4×Dic5C2×C411yescharacteristic
104C2×C4×Dic5C2311yescharacteristic
105C2×C4×Dic5C2311yescharacteristic
106C2×C4×Dic5C2311yescharacteristic
107C2×C4×Dic5C2311yescharacteristic
108C2×C4×Dic5C2311yescharacteristic
109C22⋊#170—22no—
110C22⋊#170—22no—
111C22⋊#170—22no—
112C22⋊#170—22no—
113C22⋊#170—22no—
114#4004—22no—
115#4004—22no—
116#4002—22no—
117#4002—22no—
118#4002—22no—
119#4002—22no—
120C4⋊#170—22no—
121C4×#170—22no—
122C4×#170—22no—
123C4×#170—22no—
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131#3963C2×C411yescharacteristic
132#3963C2×C411yescharacteristic
133#3963C2×C411yescharacteristic
134C2×#435—51no—
135C2×C4×M16—51no—
136C4×#123—51no—
137#1924—51no—
138#1923—51no—
139#1917—51no—
140#1916—51no—
141#1870—51no—
142#1851—51no—
143#1817—51no—
144#1771—51no—
145#1770—51no—
146#1753—51no—
147#1752—51no—
148C8×C22⋊C4—51no—
149C24×C5C22×C411yescharacteristic
150C24×C5C22×C411yescharacteristic
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—41no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—41no—
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C22×C411yescharacteristic
159C22×C4×C5C22×C411yescharacteristic
160C22×C4×C5C22×C411yescharacteristic
161C22×C4×C5C22×C411yescharacteristic
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—41no—
175C22×Dic5C22×C411yescharacteristic
176C22×Dic5C22×C411yescharacteristic
177C22×Dic5C22×C411yescharacteristic
178C22×Dic5C22×C411yescharacteristic
179C22×Dic5C22×C411yescharacteristic
180C22×Dic5C22×C411yescharacteristic
181C22×Dic5C22×C411yescharacteristic
182C22×Dic5C2×D412yes—
183C22×Dic5#4112yes—
184C22×Dic5C2411yescharacteristic
185#704—28no—
186#704—28no—
187C2×#170—21no—
188C2×#170—21no—
189C2×#170—21no—
190C2×#170—21no—
191C2×#170—21no—
192C2×#170—21no—
193C2×#170—21no—
194C2×#170—21no—
195C2×#170—21no—
196C2×#170—21no—
197C2×#170—21no—
198C2×#170—21no—
199C2×#170—21no—
200C2×#170—21no—
201C2×#170—21no—
202C2×#170—21no—
203C2×#170—21no—
204C2×#170—21no—
205C2×#170—44no—
206C2×#170C2×D412yes—
207C2×#170C2×D412yes—
208C2×#170#4112yes—
209C2×#170#4112yes—
210C2×#170#4112yes—
211C2×#170#4112yes—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C22⋊C4—22no—
215C5×C22⋊C4—22no—
216C5×C22⋊C4M1614yescomplemented
217C22⋊Dic5—22no—
218C22⋊Dic5—22no—
219C22⋊Dic5—22no—
220C22⋊Dic5—41no—
221C22⋊Dic5—41no—
222C4⋊Dic5—22no—
223C4⋊Dic5—22no—
224C4⋊Dic5—41no—
225C4×Dic5—22no—
226C4×Dic5—22no—
227C4×Dic5—21no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5—21no—
234C4×Dic5—21no—
235C4×Dic5—21no—
236C4×Dic5—21no—
237C22×M16—51no—
238C22×M16—51no—
239C23×C8—51no—
240C2×#123AGL(1,𝔽5)11yescharacteristic
241C2×C4×D4—51no—
242C22×C42—51no—
243#435—104no—
244C2×C4⋊C8—51no—
245C2×C4⋊C8—51no—
246C2×C4⋊C8—51no—
247C2×C22⋊C8—51no—
248C2×C22⋊C8—51no—
249C2×C22⋊C8—51no—
250C2×C22⋊C8—51no—
251C2×C22⋊C8—51no—
252C4×M16—104no—
253C2×#97—51no—
254C2×#97—51no—
255C2×#97—51no—
256C2×#97—51no—
257C2×C4×C8—51no—
258C2×C4×C8—51no—
259C2×C4×C8—51no—
260#388—51no—
261#388—51no—
262#387—51no—
263#387—51no—
264#386—51no—
265#385—51no—
266#381—51no—
267C4×C4⋊C4—51no—
268C4×C4⋊C4—51no—
269C4×C22⋊C4—51no—
270C4×C22⋊C4—51no—
271C4×C22⋊C4—51no—
272#336—51no—
273#336—51no—
274#336—51no—
275#336—51no—
276#336—51no—
277#336—51no—
278#336—51no—
279#336—51no—
280#336—51no—
281#336—51no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5C4×D412yes—
295C23×C5C2×M1612yes—
296C23×C5C23×C411yescharacteristic
297C5×D4—44no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—44no—
312C2×C4×C5C2×M1612yes—
313C2×C4×C5C2×M1612yes—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—21no—
329C2×Dic5—21no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—21no—
333C2×Dic5—21no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—21no—
337C2×Dic5—44no—
338C2×Dic5—41no—
339C2×Dic5—41no—
340C2×Dic5—41no—
341C2×Dic5—41no—
342C2×Dic5C4×D412yes—
343C2×Dic5#13112yes—
344C2×Dic5C22×D411yescharacteristic
345C2×Dic5C2×#4111yescharacteristic
346C2×Dic5C2×#4111yescharacteristic
347C2×Dic5C2×#4111yescharacteristic
348C2×Dic5C2×#4111yescharacteristic
349C2×Dic5C2×#4111yescharacteristic
350#170—22no—
351#170—22no—
352#170—22no—
353#170—41no—
354#170—41no—
355#170—41no—
356#170—41no—
357#170#12314yescomplemented
358C22×D4C2×AGL(1,𝔽5)11yescharacteristic
359C23×C4—51no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4C2×AGL(1,𝔽5)11yescharacteristic
363C2×M16—54no—
364C2×M16—102no—
365C2×M16—102no—
366C2×M16—102no—
367C2×M16—102no—
368C2×M16—102no—
369C22×C8—51no—
370C22×C8—51no—
371C22×C8—51no—
372C22×C8—51no—
373C22×C8—51no—
374C22×C8—51no—
375C22×C8—51no—
376C22×C8—51no—
377C22×C8—102no—
378C22×C8—102no—
379C22×C8—102no—
380#123—24no—
381C4×D4—102no—
382C4×D4—102no—
383C2×C4⋊C4—51no—
384C2×C4⋊C4—51no—
385C2×C4⋊C4—51no—
386C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
387C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
388C2×C22⋊C4—51no—
389C2×C22⋊C4—51no—
390C2×C22⋊C4—51no—
391C2×C22⋊C4—51no—
392C2×C22⋊C4—51no—
393C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
394C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
395C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
396C2×C42—51no—
397C2×C42—51no—
398C2×C42—51no—
399C2×C42—51no—
400C2×C42—51no—
401C2×C42—51no—
402C2×C42—51no—
403C2×C42—102no—
404C2×C42—102no—
405C4⋊C8—102no—
406C4⋊C8—102no—
407C4⋊C8—102no—
408C22⋊C8—102no—
409C22⋊C8—102no—
410C22⋊C8—102no—
411C22⋊C8—102no—
412C22⋊C8—102no—
413#97—102no—
414#97—102no—
415#97—102no—
416#97—102no—
417C4×C8—102no—
418C4×C8—102no—
419C4×C8—102no—
420#95—51no—
421#95—51no—
422#95—51no—
423#95—51no—
424#95—51no—
425#95—51no—
426#95—51no—
427#95—51no—
428#95—51no—
429#95—51no—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—22no—
434C22×C5—22no—
435C22×C5—22no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5C2×C4×D411yescharacteristic
445C22×C5C4×#4111yescharacteristic
446C22×C5C4×#4111yescharacteristic
447C22×C5C22×M1611yescharacteristic
448C22×C5C2×#13111yescharacteristic
449C22×C5#56811yescharacteristic
450C22×C5#56811yescharacteristic
451C4×C5—22no—
452C4×C5—22no—
453C4×C5—41no—
454C4×C5—41no—
455C4×C5—41no—
456Dic5—22no—
457Dic5—22no—
458Dic5—41no—
459Dic5—41no—
460Dic5—41no—
461Dic5—41no—
462Dic5—41no—
463Dic5C2×#12311yescharacteristic
464Dic5#52511yescharacteristic
465Dic5#52911yescharacteristic
466Dic5#52911yescharacteristic
467C24C22×AGL(1,𝔽5)11yescharacteristic
468C24C22×AGL(1,𝔽5)11yescharacteristic
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—41no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—51no—
476C22×C4—52no—
477C22×C4—52no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—51no—
481C22×C4—51no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—51no—
485C22×C4—101no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—101no—
492C22×C4—101no—
493C22×C4—101no—
494C22×C4—101no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—201no—
498C22×C4C22×AGL(1,𝔽5)11yescharacteristic
499C22×C4C22×AGL(1,𝔽5)11yescharacteristic
500C22×C4C22×AGL(1,𝔽5)11yescharacteristic
501C22×C4C22×AGL(1,𝔽5)11yescharacteristic
502C22×C4C22×AGL(1,𝔽5)11yescharacteristic
503M16—108no—
504M16—108no—
505C2×C8—52no—
506C2×C8—52no—
507C2×C8—52no—
508C2×C8—52no—
509C2×C8—52no—
510C2×C8—52no—
511C2×C8—101no—
512C2×C8—101no—
513C2×C8—101no—
514C2×C8—101no—
515C2×C8—101no—
516C2×C8—101no—
517C2×C8—101no—
518C2×C8—101no—
519C2×C8—101no—
520C2×C8—101no—
521C2×C8—101no—
522C2×C8—101no—
523C2×C8—101no—
524C2×C8—101no—
525C2×C8—101no—
526C2×C8—101no—
527C2×C8—101no—
528C2×C8—101no—
529C2×C8—204no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—102no—
533C4⋊C4—102no—
534C4⋊C4—201no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—102no—
538C22⋊C4—102no—
539C22⋊C4—102no—
540C22⋊C4—201no—
541C22⋊C4—201no—
542C22⋊C4#70414yescomplemented
543C42—101no—
544C42—101no—
545C42—101no—
546C42—101no—
547C42—101no—
548C42—101no—
549C42—101no—
550C42—101no—
551C42—102no—
552C42—101no—
553C42—102no—
554C42—101no—
555C2×C5—42no—
556C2×C5—42no—
557C2×C5C4×#12311yescharacteristic
558C2×C5#293311yescharacteristic
559C2×C5D4×M1611yescharacteristic
560C2×C5#296511yescharacteristic
561C2×C5#296711yescharacteristic
562C2×C5#296911yescharacteristic
563C2×C5#297011yescharacteristic
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23D4×AGL(1,𝔽5)12yes—
577C23C2×#70412yes—
578C23C23×AGL(1,𝔽5)11yescharacteristic
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—44no—
594C2×C4—51no—
595C2×C4—51no—
596C2×C4—51no—
597C2×C4—51no—
598C2×C4—51no—
599C2×C4—51no—
600C2×C4—52no—
601C2×C4—52no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—101no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—101no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—101no—
619C2×C4—101no—
620C2×C4—101no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—201no—
626C2×C4—201no—
627C2×C4—201no—
628C2×C4—201no—
629C2×C4—204no—
630C2×C4C2×#70412yes—
631C2×C4C2×#70412yes—
632C8—54no—
633C8—102no—
634C8—102no—
635C8—102no—
636C8—201no—
637C8—201no—
638C8—201no—
639C8—201no—
640C5#2156211yescharacteristic, complemented, Sylow
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22#6625611yescharacteristic
656C22C2×D4×AGL(1,𝔽5)11yescharacteristic
657C22D5⋊#13111yescharacteristic
658C22#6626411yescharacteristic
659C22#41×AGL(1,𝔽5)11yescharacteristic
660C22#41×AGL(1,𝔽5)11yescharacteristic
661C22C22×#70411yescharacteristic
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—51no—
668C4—51no—
669C4—51no—
670C4—51no—
671C4—102no—
672C4—102no—
673C4—201no—
674C4—201no—
675C4—201no—
676C4—201no—
677C4—201no—
678C2—42no—
679C2—42no—
680C2#1061729111yescharacteristic
681C2#1061729311yescharacteristic
682C2#1061729511yescharacteristic
683C2AGL(1,𝔽5)×#12311yescharacteristic
684C2D4×#70411yescharacteristic
685C2#1061754511yescharacteristic
686C2#1061754611yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutator, socleC23×C5C23×C4
FittingC2×C5×#123C4
prime radicalC22×C5×D4C2×C4
cosocleC22×Dic5C24
hypercenterC2×#123AGL(1,𝔽5)
hypocenterC5#21562
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×C4×#704C2semidirect
5. #10604902C2semidirect
6. #10604324C2semidirect
7. #10604322C2semidirect
8. #10604316C2semidirect
9. #10604315C2semidirect
10. #10604239C2semidirect
11. #10604237C2semidirect
12. #10604232C2semidirect
13. #10604227C2semidirect
14. #10604226C2semidirect
15. C22⋊C4×#170C2semidirect
216. C5×C22⋊C4M16semidirect
357. #170#123semidirect
542. C22⋊C4#704semidirect
640. C5#21562semidirect

Maximal subgroups

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

subgroupindex
C2×#657732
C2×C4×#7042
Dic5×#1232
#106049472
#106049022
#106043242
#106043222
#106043162
#106043152
#106042392
#106042372
#106042322
#106042272
#106042262
C22⋊C4×#1702
#215625