Finite Group Databasebeta

← #13033940

Subgroups — #13033940

Order 1280.

886 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65697C211yesmaximal, characteristic
2C2×#65697C211yesmaximal, characteristic
3#10606109C211yesmaximal, characteristic
4#10604897C211yesmaximal, characteristic
5C4×C22⋊#170C211yesmaximal, characteristic
6#10604316C211yesmaximal, characteristic, complemented
7#10604316C211yesmaximal, characteristic, complemented
8#10604315C211yesmaximal, characteristic, complemented
9C4⋊C4×#170C211yesmaximal, characteristic, complemented
10#10604224C211yesmaximal, characteristic
11#10604224C211yesmaximal, characteristic
12#10603781C211yesmaximal, characteristic, complemented
13#10603781C211yesmaximal, characteristic, complemented
14#10603780C211yesmaximal, characteristic, complemented
15#10603779C211yesmaximal, characteristic, complemented
16C22×C4×Dic5C2211yescharacteristic
17C2×#4023C2211yescharacteristic
18C2×#4023C2211yescharacteristic
19C2×C22⋊#170C2211yescharacteristic
20C2×C22⋊#170C2211yescharacteristic
21C2×C22⋊#170C2211yescharacteristic
22C2×C22⋊#170C2211yescharacteristic
23C2×#4004C2211yescharacteristic
24C2×#4004C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
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
37C2×C4×#170C2211yescharacteristic
38C2×C4×#170C2211yescharacteristic
39#65697C418yescomplemented
40#65697C418yescomplemented
41C5×#385C411yescharacteristic
42#65499C411yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C4⋊C4×Dic5C2211yescharacteristic
45#65261C411yescharacteristic
46#65261C411yescharacteristic
47#65239C411yescharacteristic
48#65235C411yescharacteristic
49#64938C2211yescharacteristic
50#64938C2211yescharacteristic
51#64936C411yescharacteristic
52#64936C411yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#20541—51nomaximal, Sylow
62C23×C4×C5C2×C411yescharacteristic
63C23×Dic5C2×C411yescharacteristic
64C23×Dic5C2311yescharacteristic
65C22×#170C2311yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C22×#170C2311yescharacteristic
72C22×#170C2311yescharacteristic
73C2×C5×C4⋊C4C2×C411yescharacteristic
74C2×C5×C4⋊C4C2×C411yescharacteristic
75C2×C5×C22⋊C4C2×C411yescharacteristic
76C2×C5×C22⋊C4C2×C411yescharacteristic
77C2×C22⋊Dic5C2×C411yescharacteristic
78C2×C22⋊Dic5C2×C411yescharacteristic
79C2×C4⋊Dic5C2×C411yescharacteristic
80C2×C4⋊Dic5C2×C411yescharacteristic
81C2×#683C2×C411yescharacteristic
82C2×#683C2×C411yescharacteristic
83C2×#683C2×C411yescharacteristic
84C2×#683C2×C411yescharacteristic
85C2×#683C2×C411yescharacteristic
86C2×#683C2×C411yescharacteristic
87C2×#683C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×C4×Dic5—41no—
90C2×C4×Dic5—41no—
91C2×C4×Dic5C2×C411yescharacteristic
92C2×C4×Dic5C2×C411yescharacteristic
93C2×C4×Dic5C2311yescharacteristic
94C2×C4×Dic5C2311yescharacteristic
95C2×C4×Dic5C2311yescharacteristic
96C2×C4×Dic5C2311yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99#4023—41no—
100#4023—41no—
101#4023C2×C414yes—
102#4023C2×C414yes—
103C22⋊#170C2×C414yes—
104C22⋊#170C2×C414yes—
105C22⋊#170C2×C414yes—
106C22⋊#170C2×C414yes—
107#4004C2×C414yescomplemented
108#4004C2×C414yescomplemented
109#4002—41no—
110#4002—41no—
111#4002—41no—
112#4002—41no—
113#4002C2×C414yescomplemented
114#4002C2×C414yescomplemented
115C4⋊#170C2×C414yescomplemented
116C4⋊#170C2×C414yescomplemented
117C4×#170—41no—
118C4×#170—41no—
119C4×#170—41no—
120C4×#170—41no—
121C4×#170C2×C414yescomplemented
122C4×#170C2×C414yescomplemented
123C5×#95C2×C411yescharacteristic
124C5×#95C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131C2×#433—51no—
132C2×#433—51no—
133#2296—51no—
134#1771—51no—
135#1771—51no—
136#1771—51no—
137#1771—51no—
138#1770—51no—
139#1770—51no—
140C8×C4⋊C4—51no—
141C8×C4⋊C4—51no—
142#1750—51no—
143#1750—51no—
144#1749—51no—
145C4×C22⋊C8—51no—
146C24×C5C22×C411yescharacteristic
147C22×C4×C5—22no—
148C22×C4×C5—41no—
149C22×C4×C5—41no—
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C22×C411yescharacteristic
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C22×C411yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—22no—
161C22×Dic5—41no—
162C22×Dic5—41no—
163C22×Dic5C22×C411yescharacteristic
164C22×Dic5C22×C411yescharacteristic
165C22×Dic5C22×C411yescharacteristic
166C22×Dic5C22×C411yescharacteristic
167C22×Dic5C22×C411yescharacteristic
168C22×Dic5C22×C411yescharacteristic
169C22×Dic5C22×C412yes—
170C22×Dic5C22×C412yes—
171C22×Dic5C22×C411yescharacteristic
172C22×Dic5C2411yescharacteristic
173C2×#170—21no—
174C2×#170—21no—
175C2×#170—21no—
176C2×#170—21no—
177C2×#170—21no—
178C2×#170—21no—
179C2×#170—21no—
180C2×#170—21no—
181C2×#170—21no—
182C2×#170—21no—
183C2×#170—21no—
184C2×#170—21no—
185C2×#170—21no—
186C2×#170—21no—
187C2×#170—21no—
188C2×#170—21no—
189C2×#170C22×C412yes—
190C2×#170C22×C412yes—
191C2×#170C22×C412yes—
192C2×#170C22×C412yes—
193C2×#170C22×C412yes—
194C2×#170C22×C412yes—
195C2×#170C22×C412yes—
196C2×#170C22×C412yes—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—41no—
199C5×C22⋊C4—41no—
200C5×C22⋊C4C4214yes—
201C22⋊Dic5—41no—
202C22⋊Dic5C4214yes—
203C4⋊Dic5—22no—
204C4⋊Dic5—41no—
205#683—22no—
206#683—22no—
207#683—41no—
208#683—41no—
209#683—41no—
210#683—41no—
211#683C4214yes—
212#683C4214yes—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—21no—
217C4×Dic5—21no—
218C4×Dic5—21no—
219C4×Dic5—21no—
220C4×Dic5—21no—
221C4×Dic5—41no—
222C4×Dic5—41no—
223C4×Dic5C22×C412yes—
224C4×Dic5C22×C412yes—
225C4×Dic5C22×C412yes—
226C4×Dic5C22×C412yes—
227C2×#117—51no—
228C2×#117—51no—
229C22×C42—51no—
230#433—58no—
231#433—58no—
232C2×C4⋊C8—51no—
233C2×C4⋊C8—51no—
234C2×C4⋊C8—51no—
235C2×C4⋊C8—51no—
236C2×C22⋊C8—51no—
237C2×C22⋊C8—51no—
238C2×C22⋊C8—51no—
239C2×C22⋊C8—51no—
240C2×#97—51no—
241C2×#97—51no—
242C2×#97—51no—
243C2×#97—51no—
244C2×#97—51no—
245C2×#97—51no—
246C2×C4×C8—51no—
247C2×C4×C8—51no—
248C2×C4×C8—51no—
249C2×C4×C8—51no—
250C2×C4×C8—51no—
251C2×C4×C8—51no—
252#389—51no—
253#389—51no—
254#389—51no—
255#389—51no—
256#385—51no—
257#385—51no—
258#385—51no—
259#385AGL(1,𝔽5)11yescharacteristic
260C4×C4⋊C4—51no—
261C4×C4⋊C4—51no—
262C4×C4⋊C4—51no—
263C4×C4⋊C4—51no—
264#336—51no—
265#336—51no—
266#336—51no—
267#336—51no—
268#336—51no—
269#336—51no—
270#336—51no—
271#336—51no—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5C2×C4212yes—
279C23×C5C23×C411yescharacteristic
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—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—44no—
296C2×C4×C5C2×C4212yes—
297C2×C4×C5C2×C4212yes—
298C2×C4×C5#13112yes—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—22no—
310C2×Dic5—22no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5—44no—
321C2×Dic5C2×C4212yes—
322C2×Dic5C2×C4212yes—
323C2×Dic5C2×C4212yes—
324C2×Dic5#13112yes—
325C2×Dic5C23×C411yescharacteristic
326C2×Dic5C23×C411yescharacteristic
327C2×Dic5H(5,𝔽2)11yescharacteristic
328C2×Dic5H(5,𝔽2)11yescharacteristic
329C2×Dic52−1+411yescharacteristic
330C2×Dic52−1+411yescharacteristic
331#170—22no—
332#170—22no—
333#170—22no—
334#170—22no—
335#170—22no—
336#170—22no—
337#170—22no—
338#170—22no—
339C23×C4—51no—
340C23×C4—51no—
341C23×C4C2×AGL(1,𝔽5)11yescharacteristic
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—51no—
345C22×C8—51no—
346C22×C8—51no—
347C22×C8—51no—
348C22×C8—51no—
349C22×C8—51no—
350#117—54no—
351#117—54no—
352#117—201no—
353#117—201no—
354C2×C4⋊C4—51no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—51no—
358C2×C4⋊C4—51no—
359C2×C4⋊C4—51no—
360C2×C4⋊C4—51no—
361C2×C4⋊C4—51no—
362C2×C4⋊C4—51no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
365C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
366C2×C22⋊C4—51no—
367C2×C22⋊C4—51no—
368C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
369C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
370C2×C42—51no—
371C2×C42—51no—
372C2×C42—51no—
373C2×C42—51no—
374C2×C42—51no—
375C2×C42—51no—
376C2×C42—51no—
377C2×C42—51no—
378C2×C42—201no—
379C2×C42—201no—
380C4⋊C8—54no—
381C4⋊C8—54no—
382C4⋊C8—54no—
383C4⋊C8—54no—
384C22⋊C8—54no—
385C22⋊C8—54no—
386C22⋊C8—54no—
387C22⋊C8—54no—
388#97—54no—
389#97—54no—
390#97—201no—
391#97—201no—
392#97—201no—
393#97—201no—
394C4×C8—54no—
395C4×C8—54no—
396C4×C8—201no—
397C4×C8—201no—
398C4×C8—201no—
399C4×C8—201no—
400#95—51no—
401#95—51no—
402#95—51no—
403#95—51no—
404#95—51no—
405#95—51no—
406#95C2×AGL(1,𝔽5)11yescharacteristic
407#95C2×AGL(1,𝔽5)11yescharacteristic
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—41no—
414C22×C5—41no—
415C22×C5C22×C4211yescharacteristic
416C22×C5#51811yescharacteristic
417C22×C5#51911yescharacteristic
418C22×C5C2×#13111yescharacteristic
419C22×C5C2×#13111yescharacteristic
420C22×C5#56811yescharacteristic
421C22×C5#56811yescharacteristic
422C4×C5—22no—
423C4×C5—22no—
424C4×C5—22no—
425C4×C5—41no—
426C4×C5—41no—
427C4×C5—41no—
428Dic5—22no—
429Dic5—22no—
430Dic5—22no—
431Dic5—22no—
432Dic5—41no—
433Dic5—41no—
434Dic5—41no—
435Dic5#52011yescharacteristic
436Dic5#52011yescharacteristic
437Dic5#52011yescharacteristic
438Dic5#52011yescharacteristic
439C24C22×AGL(1,𝔽5)11yescharacteristic
440C22×C4—22no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—51no—
444C22×C4—52no—
445C22×C4—52no—
446C22×C4—51no—
447C22×C4—51no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—101no—
454C22×C4—101no—
455C22×C4—101no—
456C22×C4—101no—
457C22×C4—102no—
458C22×C4—201no—
459C22×C4—201no—
460C22×C4C22×AGL(1,𝔽5)11yescharacteristic
461C22×C4C22×AGL(1,𝔽5)11yescharacteristic
462C22×C4C22×AGL(1,𝔽5)11yescharacteristic
463C22×C4C22×AGL(1,𝔽5)11yescharacteristic
464C22×C4C22×AGL(1,𝔽5)11yescharacteristic
465C22×C4C22×AGL(1,𝔽5)11yescharacteristic
466C2×C8—52no—
467C2×C8—52no—
468C2×C8—52no—
469C2×C8—52no—
470C2×C8—52no—
471C2×C8—52no—
472C2×C8—52no—
473C2×C8—52no—
474C2×C8—101no—
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—
485C2×C8—101no—
486C2×C8—101no—
487C2×C8—101no—
488C2×C8—101no—
489C2×C8—101no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—54no—
493C4⋊C4—54no—
494C4⋊C4—102no—
495C4⋊C4—102no—
496C4⋊C4—102no—
497C4⋊C4—201no—
498C4⋊C4—201no—
499C4⋊C4—201no—
500C4⋊C4—201no—
501C4⋊C4—201no—
502C22⋊C4—41no—
503C22⋊C4—54no—
504C22⋊C4—201no—
505C22⋊C4C4×AGL(1,𝔽5)14yes—
506C42—52no—
507C42—52no—
508C42—52no—
509C42—52no—
510C42—101no—
511C42—101no—
512C42—101no—
513C42—101no—
514C42—101no—
515C42—101no—
516C42—101no—
517C42—101no—
518C42—201no—
519C42—201no—
520C2×C5—42no—
521C2×C5#227411yescharacteristic
522C2×C5C4×#13111yescharacteristic
523C2×C5#287511yescharacteristic
524C2×C5#297611yescharacteristic
525C2×C5#297611yescharacteristic
526C2×C5#298511yescharacteristic
527C2×C5#298511yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23C2×C4×AGL(1,𝔽5)12yes—
535C23C23×AGL(1,𝔽5)11yescharacteristic
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—44no—
552C2×C4—51no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—51no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—52no—
561C2×C4—52no—
562C2×C4—102no—
563C2×C4—102no—
564C2×C4—102no—
565C2×C4—102no—
566C2×C4—101no—
567C2×C4—101no—
568C2×C4—101no—
569C2×C4—101no—
570C2×C4—101no—
571C2×C4—101no—
572C2×C4—101no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—101no—
580C2×C4—101no—
581C2×C4—101no—
582C2×C4—101no—
583C2×C4—204no—
584C2×C4C2×C4×AGL(1,𝔽5)12yes—
585C2×C4C2×C4×AGL(1,𝔽5)12yes—
586C2×C4#413112yes—
587C8—102no—
588C8—102no—
589C8—102no—
590C8—102no—
591C8—102no—
592C8—102no—
593C8—102no—
594C8—102no—
595C5#2054111yescharacteristic, complemented, Sylow
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C22×C4×AGL(1,𝔽5)11yescharacteristic
604C22C2×#413111yescharacteristic
605C22#6625611yescharacteristic
606C22#6625811yescharacteristic
607C22#6626211yescharacteristic
608C22D5⋊#13111yescharacteristic
609C22#6626411yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—51no—
617C4—51no—
618C4—51no—
619C4—51no—
620C4—102no—
621C4—102no—
622C4—102no—
623C4—102no—
624C4—201no—
625C4—201no—
626C4—201no—
627C2—42no—
628C2#1061709811yescharacteristic
629C2C4×#413111yescharacteristic
630C2#1061713611yescharacteristic
631C2#1061721811yescharacteristic
632C2#1061727311yescharacteristic
633C2#1061727411yescharacteristic
634C2#1061729611yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#385C4
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenter#385AGL(1,𝔽5)
hypocenterC5#20541
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
6. #10604316C2semidirect
7. #10604316C2semidirect
8. #10604315C2semidirect
9. C4⋊C4×#170C2semidirect
12. #10603781C2semidirect
13. #10603781C2semidirect
14. #10603780C2semidirect
15. #10603779C2semidirect
39. #65697C4semidirect
40. #65697C4semidirect
107. #4004C2×C4semidirect
108. #4004C2×C4semidirect
113. #4002C2×C4semidirect
114. #4002C2×C4semidirect
115. C4⋊#170C2×C4semidirect
116. C4⋊#170C2×C4semidirect
121. C4×#170C2×C4semidirect
122. C4×#170C2×C4semidirect
595. C5#20541semidirect

Maximal subgroups

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

subgroupindex
C2×#656972
#106061092
#106048972
C4×C22⋊#1702
#106043162
#106043152
C4⋊C4×#1702
#106042242
#106037812
#106037802
#106037792
#205415