Finite Group Databasebeta

← #13034071

Subgroups — #13034071

Order 1280.

974 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65694C211yesmaximal, characteristic
2C2×#65693C211yesmaximal, characteristic
3#10607181C211yesmaximal, characteristic
4#10604313C211yesmaximal, characteristic, complemented
5#10604312C211yesmaximal, characteristic, complemented
6#10604227C211yesmaximal, characteristic, complemented
7C22⋊C4×#170C211yesmaximal, characteristic, complemented
8#10604224C211yesmaximal, characteristic, complemented
9#10604223C211yesmaximal, characteristic, complemented
10C4×C4⋊#170C211yesmaximal, characteristic, complemented
11#10604175C211yesmaximal, characteristic, complemented
12#10603781C211yesmaximal, characteristic, complemented
13#10603781C211yesmaximal, characteristic, complemented
14#10603777C211yesmaximal, characteristic, complemented
15#10603775C211yesmaximal, characteristic, complemented
16C22×#704C2211yescharacteristic
17C23×#170C2211yescharacteristic
18C22×#700C2211yescharacteristic
19C22×D5⋊C8C2211yescharacteristic
20C2×#4038C2211yescharacteristic
21C2×#4027C2211yescharacteristic
22C2×#4023C2211yescharacteristic
23C2×C22⋊#170C2211yescharacteristic
24C2×C22⋊#170C2211yescharacteristic
25C2×#4003C2211yescharacteristic
26C2×#4003C2211yescharacteristic
27C2×#4002C2211yescharacteristic
28C2×#4002C2211yescharacteristic
29C2×#4002C2211yescharacteristic
30C2×#4002C2211yescharacteristic
31C2×C4⋊#170C2211yescharacteristic
32C2×C4⋊#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65694C418yescomplemented
38#65693C418yescomplemented
39C5×#388C411yescharacteristic
40#65261C411yescharacteristic
41#65246C411yescharacteristic
42#65246C411yescharacteristic
43#65240C411yescharacteristic
44C22⋊C4×Dic5C2211yescharacteristic
45#65229C411yescharacteristic
46C42×Dic5C2211yescharacteristic
47#64958C411yescharacteristic
48#64955C2211yescharacteristic
49#64938C2211yescharacteristic
50#64936C411yescharacteristic
51#64918C2211yescharacteristic
52#64918C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#20566—51nomaximal, Sylow
62C22×C22⋊D5C2×C411yescharacteristic
63C23×Dic5C2311yescharacteristic
64C22×C4×D5C2311yescharacteristic
65C2×#704—41no—
66C2×#704—41no—
67C2×#704C2×C414yes—
68C22×#170—41no—
69C22×#170—41no—
70C22×#170C2×C414yes—
71C22×#170C2311yescharacteristic
72C22×#170C2311yescharacteristic
73C22×#170C2311yescharacteristic
74C22×#170C2311yescharacteristic
75C22×#170C2311yescharacteristic
76C22×#170C2311yescharacteristic
77C22×#170C2311yescharacteristic
78C22×#170C2311yescharacteristic
79C2×#700—41no—
80C2×#700—41no—
81C2×#700C2×C414yes—
82C2×D5⋊C8—41no—
83C2×D5⋊C8—41no—
84C2×D5⋊C8C2×C414yes—
85C2×C5×C4⋊C4C2×C411yescharacteristic
86C2×C5×C22⋊C4C2×C411yescharacteristic
87C2×C5×C22⋊C4C2×C411yescharacteristic
88C2×C5×C22⋊C4C2×C411yescharacteristic
89C2×C42×C5C2×C411yescharacteristic
90C2×C22⋊Dic5C2×C411yescharacteristic
91C2×C22⋊Dic5C2×C411yescharacteristic
92C2×#685C2×C411yescharacteristic
93C2×#685C2×C411yescharacteristic
94C2×#685C2×C411yescharacteristic
95C2×#685C2×C411yescharacteristic
96C2×#685C2×C411yescharacteristic
97C2×C4⋊Dic5C2×C411yescharacteristic
98C2×#683C2×C411yescharacteristic
99C2×#683C2×C411yescharacteristic
100C2×#683C2×C411yescharacteristic
101C2×#683C2×C411yescharacteristic
102C2×#683C2×C411yescharacteristic
103C2×C4×Dic5C2×C411yescharacteristic
104C2×C4×Dic5C2×C411yescharacteristic
105C2×C4×Dic5C2×C411yescharacteristic
106C2×C4×Dic5C2311yescharacteristic
107C2×C4×Dic5C2311yescharacteristic
108C2×C4×Dic5C2311yescharacteristic
109C2×C4×Dic5C2311yescharacteristic
110C2×C4×Dic5C2311yescharacteristic
111#4038—41no—
112#4038—41no—
113#4027C2×C414yes—
114#4027C2×C414yes—
115#4023—41no—
116#4023—41no—
117C22⋊#170C2×C414yes—
118C22⋊#170C2×C414yes—
119#4003C2×C414yes—
120#4003C2×C414yes—
121#4002—41no—
122#4002—41no—
123#4002C2×C414yes—
124#4002C2×C414yes—
125C4⋊#170C2×C414yes—
126C4⋊#170C2×C414yes—
127C4×#170—41no—
128C4×#170—41no—
129C4×#170—41no—
130C4×#170—41no—
131C5×#95C2×C411yescharacteristic
132C5×#95C2×C411yescharacteristic
133#3963C2×C411yescharacteristic
134#3963C2×C411yescharacteristic
135#3963C2×C411yescharacteristic
136#3963C2×C411yescharacteristic
137C2×#435—51no—
138C2×#435—51no—
139#2293—51no—
140#1771—51no—
141#1771—51no—
142C4×C4⋊C8—51no—
143#1753—51no—
144#1753—51no—
145C8×C22⋊C4—51no—
146C8×C22⋊C4—51no—
147#1750—51no—
148#1750—51no—
149#1745—51no—
150#1729—51no—
151#1729—51no—
152C24×C5C22×C411yescharacteristic
153C23×D5C22×C411yescharacteristic
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C22×C411yescharacteristic
156C22×C4×C5C22×C411yescharacteristic
157C22×C4×C5C22×C411yescharacteristic
158C22×C4×C5C22×C411yescharacteristic
159C22×C4×C5C22×C411yescharacteristic
160C2×C22⋊D5—41no—
161C2×C22⋊D5—41no—
162C2×C22⋊D5C4214yes—
163C22×Dic5—21no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5C22×C411yescharacteristic
168C22×Dic5C22×C411yescharacteristic
169C22×Dic5C22×C411yescharacteristic
170C22×Dic5C22×C411yescharacteristic
171C22×Dic5C22×C411yescharacteristic
172C22×Dic5C22×C412yes—
173C22×Dic5C22×C412yes—
174C22×Dic5C22×C411yescharacteristic
175C22×Dic5C2411yescharacteristic
176C2×C4×D5—21no—
177C2×C4×D5—21no—
178C2×C4×D5—21no—
179C2×C4×D5—21no—
180C2×C4×D5C22×C412yes—
181C2×C4×D5C22×C412yes—
182#704—44no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—21no—
186C2×#170—21no—
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—44no—
200C2×#170C22×C412yes—
201C2×#170C22×C412yes—
202C2×#170C22×C412yes—
203C2×#170C22×C412yes—
204C2×#170C22×C412yes—
205C2×#170C22×C412yes—
206C2×#170C22×C412yes—
207C2×#170C22×C412yes—
208#700—44no—
209D5⋊C8—44no—
210C5×C4⋊C4—41no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—41no—
213C5×C22⋊C4C4214yes—
214C42×C5—22no—
215C22⋊Dic5—22no—
216C22⋊Dic5—41no—
217#685—22no—
218#685—22no—
219#685—41no—
220#685—41no—
221#685C4214yes—
222C4⋊Dic5—41no—
223#683—41no—
224#683—41no—
225#683—41no—
226#683—41no—
227#683C4214yes—
228C4×Dic5—22no—
229C4×Dic5—21no—
230C4×Dic5—21no—
231C4×Dic5—21no—
232C4×Dic5—21no—
233C4×Dic5—21no—
234C4×Dic5—21no—
235C4×Dic5—21no—
236C4×Dic5—21no—
237C4×Dic5—41no—
238C4×Dic5—41no—
239C4×Dic5C22×C412yes—
240C4×Dic5C22×C412yes—
241C22×M16—51no—
242C22×M16—51no—
243C23×C8—51no—
244C23×C8—51no—
245C2×C4×D4—51no—
246C2×#117—51no—
247C2×#117—51no—
248#435—58no—
249#435—58no—
250C2×C4⋊C8—51no—
251C2×C4⋊C8—51no—
252C2×C22⋊C8—51no—
253C2×C22⋊C8—51no—
254C2×C22⋊C8—51no—
255C2×C22⋊C8—51no—
256C2×#97—51no—
257C2×#97—51no—
258C2×#97—51no—
259C2×#97—51no—
260C2×C4×C8—51no—
261C2×C4×C8—51no—
262C2×C4×C8—51no—
263C2×C4×C8—51no—
264#390—51no—
265#390—51no—
266#389—51no—
267#389—51no—
268#388—51no—
269#388—51no—
270#388—51no—
271#388AGL(1,𝔽5)11yescharacteristic
272C4×C4⋊C4—51no—
273C4×C22⋊C4—51no—
274C4×C22⋊C4—51no—
275C43—51no—
276#336—51no—
277#336—51no—
278#336—51no—
279#336—51no—
280#336—51no—
281#336—51no—
282#336—51no—
283#336—51no—
284#336—51no—
285#336—51no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5C2×C4212yes—
293C23×C5C23×C411yescharacteristic
294C22×D5—21no—
295C22×D5—21no—
296C22×D5—21no—
297C22×D5—21no—
298C22×D5—21no—
299C22×D5—21no—
300C22×D5C2×C4212yes—
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—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5C2×C4212yes—
317C2×C4×C5C2×C4212yes—
318C2×C4×C5#13112yes—
319C22⋊D5—44no—
320C2×Dic5—21no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—21no—
331C2×Dic5—21no—
332C2×Dic5—21no—
333C2×Dic5—21no—
334C2×Dic5—21no—
335C2×Dic5—21no—
336C2×Dic5—21no—
337C2×Dic5—21no—
338C2×Dic5—21no—
339C2×Dic5C2×C4212yes—
340C2×Dic5C2×C4212yes—
341C2×Dic5#13112yes—
342C2×Dic5C23×C411yescharacteristic
343C2×Dic5C23×C411yescharacteristic
344C2×Dic5H(5,𝔽2)11yescharacteristic
345C2×Dic5H(5,𝔽2)11yescharacteristic
346C2×Dic5H(5,𝔽2)11yescharacteristic
347C2×Dic52−1+411yescharacteristic
348C4×D5—22no—
349C4×D5—22no—
350C4×D5—22no—
351C4×D5—22no—
352#170—22no—
353#170—22no—
354#170—22no—
355#170—22no—
356#170—22no—
357#170—22no—
358#170—22no—
359#170—22no—
360C22×D4—51no—
361C23×C4—51no—
362C23×C4—51no—
363C2×M16—54no—
364C2×M16—54no—
365C2×M16—201no—
366C2×M16—201no—
367C2×M16—201no—
368C2×M16—201no—
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—54no—
378C22×C8—54no—
379C22×C8—201no—
380C22×C8—201no—
381C22×C8—201no—
382C22×C8—201no—
383C4×D4—54no—
384C4×D4—54no—
385#117—201no—
386#117—201no—
387#117—201no—
388#117—201no—
389C2×C4⋊C4—51no—
390C2×C4⋊C4—51no—
391C2×C4⋊C4—51no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—51no—
395C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
396C2×C22⋊C4—51no—
397C2×C22⋊C4—51no—
398C2×C22⋊C4—51no—
399C2×C22⋊C4—51no—
400C2×C22⋊C4—51no—
401C2×C22⋊C4—51no—
402C2×C22⋊C4—51no—
403C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
404C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
405C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
406C2×C42—51no—
407C2×C42—51no—
408C2×C42—51no—
409C2×C42—51no—
410C2×C42—51no—
411C2×C42—51no—
412C2×C42—51no—
413C2×C42—51no—
414C2×C42C2×AGL(1,𝔽5)11yescharacteristic
415C4⋊C8—54no—
416C4⋊C8—54no—
417C22⋊C8—54no—
418C22⋊C8—54no—
419C22⋊C8—54no—
420C22⋊C8—54no—
421#97—54no—
422#97—54no—
423#97—201no—
424#97—201no—
425C4×C8—201no—
426C4×C8—201no—
427C4×C8—201no—
428C4×C8—201no—
429#95—51no—
430#95—51no—
431#95—51no—
432#95—51no—
433#95C2×AGL(1,𝔽5)11yescharacteristic
434#95C2×AGL(1,𝔽5)11yescharacteristic
435C22×C5—22no—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5C22×C4211yescharacteristic
443C22×C5#51811yescharacteristic
444C22×C5#52011yescharacteristic
445C22×C5C2×#13111yescharacteristic
446C22×C5C2×#13111yescharacteristic
447C22×C5#56811yescharacteristic
448C22×C5#56811yescharacteristic
449C2×D5—22no—
450C2×D5—22no—
451C2×D5—22no—
452C2×D5—41no—
453C2×D5—41no—
454C2×D5—41no—
455C2×D5—41no—
456C4×C5—22no—
457C4×C5—22no—
458C4×C5—22no—
459C4×C5—41no—
460C4×C5—41no—
461C4×C5—41no—
462Dic5—22no—
463Dic5—22no—
464Dic5—22no—
465Dic5—41no—
466Dic5—41no—
467Dic5—41no—
468Dic5#51811yescharacteristic
469Dic5#51811yescharacteristic
470Dic5#52011yescharacteristic
471Dic5#52011yescharacteristic
472C24—51no—
473C24C22×AGL(1,𝔽5)11yescharacteristic
474C2×D4—54no—
475C2×D4—201no—
476C2×D4—201no—
477C22×C4—51no—
478C22×C4—52no—
479C22×C4—52no—
480C22×C4—51no—
481C22×C4—51no—
482C22×C4—51no—
483C22×C4—52no—
484C22×C4—52no—
485C22×C4—51no—
486C22×C4—51no—
487C22×C4—51no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—101no—
491C22×C4—101no—
492C22×C4—101no—
493C22×C4—101no—
494C22×C4—101no—
495C22×C4—101no—
496C22×C4C22×AGL(1,𝔽5)11yescharacteristic
497C22×C4C22×AGL(1,𝔽5)11yescharacteristic
498C22×C4C22×AGL(1,𝔽5)11yescharacteristic
499C22×C4C22×AGL(1,𝔽5)11yescharacteristic
500C22×C4C22×AGL(1,𝔽5)11yescharacteristic
501C22×C4C22×AGL(1,𝔽5)11yescharacteristic
502M16—204no—
503M16—204no—
504C2×C8—52no—
505C2×C8—52no—
506C2×C8—52no—
507C2×C8—52no—
508C2×C8—52no—
509C2×C8—52no—
510C2×C8—52no—
511C2×C8—52no—
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—204no—
529C2×C8—204no—
530C4⋊C4—41no—
531C4⋊C4—54no—
532C4⋊C4—201no—
533C4⋊C4—201no—
534C4⋊C4—201no—
535C4⋊C4—201no—
536C4⋊C4—201no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—54no—
540C22⋊C4—102no—
541C22⋊C4—102no—
542C22⋊C4—102no—
543C22⋊C4—201no—
544C22⋊C4—201no—
545C22⋊C4—201no—
546C22⋊C4C4×AGL(1,𝔽5)14yes—
547C42—22no—
548C42—52no—
549C42—52no—
550C42—101no—
551C42—101no—
552C42—101no—
553C42—101no—
554C42—101no—
555C42—101no—
556C42—101no—
557C42—102no—
558C42—101no—
559C42—201no—
560C42—201no—
561C2×C5—42no—
562C2×C5#227511yescharacteristic
563C2×C5#287311yescharacteristic
564C2×C5C4×#13111yescharacteristic
565C2×C5#298111yescharacteristic
566C2×C5#298111yescharacteristic
567C2×C5#299211yescharacteristic
568C2×C5#299211yescharacteristic
569D5—42no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—52no—
577C23—101no—
578C23—101no—
579C23—101no—
580C23—101no—
581C23—101no—
582C23—101no—
583C23C2×C4×AGL(1,𝔽5)12yes—
584C23C23×AGL(1,𝔽5)11yescharacteristic
585D4—204no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—51no—
602C2×C4—51no—
603C2×C4—51no—
604C2×C4—51no—
605C2×C4—51no—
606C2×C4—51no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—52no—
610C2×C4—102no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—102no—
615C2×C4—102no—
616C2×C4—102no—
617C2×C4—102no—
618C2×C4—101no—
619C2×C4—101no—
620C2×C4—101no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—101no—
626C2×C4—101no—
627C2×C4—101no—
628C2×C4—101no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—101no—
633C2×C4C2×C4×AGL(1,𝔽5)12yes—
634C2×C4C2×C4×AGL(1,𝔽5)12yes—
635C2×C4#413112yes—
636C8—102no—
637C8—102no—
638C8—102no—
639C8—102no—
640C8—102no—
641C8—102no—
642C8—102no—
643C8—102no—
644C5#2056611yescharacteristic, complemented, Sylow
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—102no—
653C22—102no—
654C22—102no—
655C22—201no—
656C22—201no—
657C22—201no—
658C22—201no—
659C22C22×C4×AGL(1,𝔽5)11yescharacteristic
660C22C2×#413111yescharacteristic
661C22#6625811yescharacteristic
662C22D5⋊#13111yescharacteristic
663C22#6626411yescharacteristic
664C22#6626411yescharacteristic
665C22#6626611yescharacteristic
666C4—22no—
667C4—22no—
668C4—22no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—51no—
673C4—51no—
674C4—51no—
675C4—51no—
676C4—102no—
677C4—102no—
678C4—102no—
679C4—201no—
680C4—201no—
681C4—201no—
682C2—42no—
683C2—202no—
684C2#1061710611yescharacteristic
685C2C4×#413111yescharacteristic
686C2#1061717211yescharacteristic
687C2#1061724411yescharacteristic
688C2#1061729911yescharacteristic
689C2#1061731811yescharacteristic
690C2#1061735311yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#388C4
socleC23×C5C23×C4
prime radicalC22×C22⋊D5C2×C4
cosocleC22×Dic5C24
hypercenter#388AGL(1,𝔽5)
hypocenterC5#20566
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #10604313C2semidirect
5. #10604312C2semidirect
6. #10604227C2semidirect
7. C22⋊C4×#170C2semidirect
8. #10604224C2semidirect
9. #10604223C2semidirect
10. C4×C4⋊#170C2semidirect
11. #10604175C2semidirect
12. #10603781C2semidirect
13. #10603781C2semidirect
14. #10603777C2semidirect
15. #10603775C2semidirect
37. #65694C4semidirect
38. #65693C4semidirect
644. C5#20566semidirect

Maximal subgroups

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

subgroupindex
C2×#656942
C2×#656932
#106071812
#106043132
#106043122
#106042272
C22⋊C4×#1702
#106042242
#106042232
C4×C4⋊#1702
#106041752
#106037812
#106037772
#106037752
#205665