Finite Group Databasebeta

← #13034009

Subgroups — #13034009

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65706C211yesmaximal, characteristic
2C2×#65708C211yesmaximal, characteristic
3#10606670C211yesmaximal, characteristic
4#10604316C211yesmaximal, characteristic, complemented
5#10604315C211yesmaximal, characteristic, complemented
6#10604181C211yesmaximal, characteristic, complemented
7C4×#4004C211yesmaximal, characteristic, complemented
8#10603781C211yesmaximal, characteristic, complemented
9#10603779C211yesmaximal, characteristic, complemented
10#10603778C211yesmaximal, characteristic, complemented
11#10603778C211yesmaximal, characteristic, complemented
12#10603777C211yesmaximal, characteristic
13#10603777C211yesmaximal, characteristic
14#10603776C211yesmaximal, characteristic
15#10603775C211yesmaximal, characteristic
16C22×#700C2211yescharacteristic
17C22×D5⋊C8C2211yescharacteristic
18C2×#4038C2211yescharacteristic
19C2×#4004C2211yescharacteristic
20C2×#4004C2211yescharacteristic
21C2×#4004C2211yescharacteristic
22C2×#4003C2211yescharacteristic
23C2×#4003C2211yescharacteristic
24C2×#4002C2211yescharacteristic
25C2×#4002C2211yescharacteristic
26C2×#4002C2211yescharacteristic
27C2×#4002C2211yescharacteristic
28C2×#4002C2211yescharacteristic
29C2×C4⋊#170C2211yescharacteristic
30C2×C4⋊#170C2211yescharacteristic
31C2×C4⋊#170C2211yescharacteristic
32C2×C4×#170C2211yescharacteristic
33C2×C4×#170C2211yescharacteristic
34C2×C4×#170C2211yescharacteristic
35C2×C4×#170C2211yescharacteristic
36C2×C4×#170C2211yescharacteristic
37#65708C418yescomplemented
38#65706C418yescomplemented
39C5×#387C411yescharacteristic
40#65279C411yescharacteristic
41#65270C411yescharacteristic
42C4⋊C4×Dic5C2211yescharacteristic
43#65229C411yescharacteristic
44C42×Dic5C2211yescharacteristic
45#64959C411yescharacteristic
46#64958C411yescharacteristic
47#64955C2211yescharacteristic
48#64955C2211yescharacteristic
49#64943C411yescharacteristic
50#64942C411yescharacteristic
51#64938C2211yescharacteristic
52#64937C2211yescharacteristic
53#64918C2211yescharacteristic
54#64918C2211yescharacteristic
55#64918C2211yescharacteristic
56#64918C2211yescharacteristic
57#64918C2211yescharacteristic
58#64918C2211yescharacteristic
59#64918C2211yescharacteristic
60#64918C2211yescharacteristic
61#20553—51nomaximal, Sylow
62C22×C4×D5C2311yescharacteristic
63C22×#170C2311yescharacteristic
64C22×#170C2311yescharacteristic
65C22×#170C2311yescharacteristic
66C22×#170C2311yescharacteristic
67C22×#170C2311yescharacteristic
68C22×#170C2311yescharacteristic
69C22×#170C2311yescharacteristic
70C22×#170C2311yescharacteristic
71C2×#700—41no—
72C2×#700—41no—
73C2×#700C2×C414yes—
74C2×D5⋊C8—41no—
75C2×D5⋊C8—41no—
76C2×D5⋊C8C2×C414yes—
77C2×C5×C4⋊C4C2×C411yescharacteristic
78C2×C5×C4⋊C4C2×C411yescharacteristic
79C2×C42×C5C2×C411yescharacteristic
80C2×#685C2×C411yescharacteristic
81C2×#685C2×C411yescharacteristic
82C2×#685C2×C411yescharacteristic
83C2×#685C2×C411yescharacteristic
84C2×#685C2×C411yescharacteristic
85C2×#685C2×C411yescharacteristic
86C2×C4⋊Dic5C2×C411yescharacteristic
87C2×C4⋊Dic5C2×C411yescharacteristic
88C2×#683C2×C411yescharacteristic
89C2×#683C2×C411yescharacteristic
90C2×C4×Dic5C2×C411yescharacteristic
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#4038C2×C414yes—
100#4038C2×C414yes—
101#4004C2×C414yes—
102#4004C2×C414yes—
103#4004C2×C414yes—
104#4003C2×C414yes—
105#4003C2×C414yes—
106#4002—41no—
107#4002—41no—
108#4002—41no—
109#4002—41no—
110#4002C2×C414yes—
111C4⋊#170C2×C414yes—
112C4⋊#170C2×C414yes—
113C4⋊#170C2×C414yes—
114C4×#170—41no—
115C4×#170—41no—
116C4×#170—41no—
117C4×#170—41no—
118C4×#170C2×C414yes—
119C5×#95C2×C411yescharacteristic
120C5×#95C2×C411yescharacteristic
121C5×#95C2×C411yescharacteristic
122C5×#95C2×C411yescharacteristic
123#3963C2×C411yescharacteristic
124#3963C2×C411yescharacteristic
125#3963C2×C411yescharacteristic
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131C2×#433—51no—
132C2×#424—51no—
133#2298—51no—
134#1771—51no—
135#1771—51no—
136#1770—51no—
137C8×C4⋊C4—51no—
138#1768—51no—
139#1768—51no—
140#1767—51no—
141C4×C4⋊C8—51no—
142#1753—51no—
143#1753—51no—
144#1752—51no—
145C8×C22⋊C4—51no—
146C23×D5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C22×C411yescharacteristic
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C22×C411yescharacteristic
154C22×Dic5C22×C411yescharacteristic
155C22×Dic5C22×C411yescharacteristic
156C22×Dic5C22×C411yescharacteristic
157C22×Dic5C22×C411yescharacteristic
158C22×Dic5C22×C411yescharacteristic
159C22×Dic5C22×C411yescharacteristic
160C22×Dic5C2411yescharacteristic
161C2×C4×D5—21no—
162C2×C4×D5—21no—
163C2×C4×D5—21no—
164C2×C4×D5—21no—
165C2×C4×D5C22×C412yes—
166C2×C4×D5C22×C412yes—
167C2×#170—21no—
168C2×#170—21no—
169C2×#170—21no—
170C2×#170—21no—
171C2×#170—21no—
172C2×#170—21no—
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×#170C22×C412yes—
184C2×#170C22×C412yes—
185C2×#170C22×C412yes—
186C2×#170C22×C412yes—
187C2×#170C22×C412yes—
188C2×#170C22×C412yes—
189C2×#170C22×C412yes—
190C2×#170C22×C412yes—
191#700—44no—
192D5⋊C8—44no—
193C5×C4⋊C4—41no—
194C5×C4⋊C4C4214yes—
195C42×C5—41no—
196#685—22no—
197#685—22no—
198#685—41no—
199#685—41no—
200#685C4214yes—
201#685C4214yes—
202C4⋊Dic5—41no—
203C4⋊Dic5C4214yes—
204#683—22no—
205#683—22no—
206C4×Dic5—22no—
207C4×Dic5—22no—
208C4×Dic5—21no—
209C4×Dic5—21no—
210C4×Dic5—21no—
211C4×Dic5—21no—
212C4×Dic5—21no—
213C4×Dic5—21no—
214C4×Dic5—21no—
215C4×Dic5—21no—
216C4×Dic5—41no—
217C4×Dic5C22×C412yes—
218C4×Dic5C22×C412yes—
219C4×Dic5C22×C412yes—
220C4×Dic5C22×C412yes—
221C22×M16—51no—
222C23×C8—51no—
223C2×#117—51no—
224#433—58no—
225#424—58no—
226C2×C4⋊C8—51no—
227C2×C4⋊C8—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8—51no—
230C2×C4⋊C8—51no—
231C2×C4⋊C8—51no—
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×#97—51no—
235C2×#97—51no—
236C2×#97—51no—
237C2×#97—51no—
238C2×#97—51no—
239C2×C4×C8—51no—
240C2×C4×C8—51no—
241C2×C4×C8—51no—
242C2×C4×C8—51no—
243C2×C4×C8—51no—
244#388—51no—
245#388—51no—
246#388—51no—
247#388—51no—
248#387—51no—
249#387—51no—
250#387—51no—
251#387AGL(1,𝔽5)11yescharacteristic
252C4×C4⋊C4—51no—
253C4×C4⋊C4—51no—
254C4×C22⋊C4—51no—
255C4×C22⋊C4—51no—
256#376—51no—
257C43—51no—
258#336—51no—
259#336—51no—
260#336—51no—
261#336—51no—
262#336—51no—
263#336—51no—
264#336—51no—
265#336—51no—
266C23×C5C23×C411yescharacteristic
267C22×D5—21no—
268C22×D5—21no—
269C22×D5—21no—
270C22×D5—21no—
271C22×D5—21no—
272C22×D5—21no—
273C22×D5C2×C4212yes—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
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×C5C2×C4212yes—
292C2×C4×C5C2×C4212yes—
293C2×C4×C5C2×C4212yes—
294C2×C4×C5#13112yes—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
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—21no—
308C2×Dic5—21no—
309C2×Dic5—21no—
310C2×Dic5C2×C4212yes—
311C2×Dic5C2×C4212yes—
312C2×Dic5#13112yes—
313C2×Dic5C23×C411yescharacteristic
314C2×Dic5C23×C411yescharacteristic
315C2×Dic5H(5,𝔽2)11yescharacteristic
316C2×Dic5H(5,𝔽2)11yescharacteristic
317C2×Dic52−1+411yescharacteristic
318C2×Dic52−1+411yescharacteristic
319C4×D5—22no—
320C4×D5—22no—
321C4×D5—22no—
322C4×D5—22no—
323#170—22no—
324#170—22no—
325#170—22no—
326#170—22no—
327#170—22no—
328#170—22no—
329#170—22no—
330#170—22no—
331C23×C4—51no—
332C2×M16—54no—
333C2×M16—201no—
334C2×M16—201no—
335C22×C8—51no—
336C22×C8—51no—
337C22×C8—51no—
338C22×C8—51no—
339C22×C8—51no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—51no—
343C22×C8—54no—
344C22×C8—201no—
345C22×C8—201no—
346#117—54no—
347#117—54no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4—51no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
353C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
354C2×C22⋊C4—51no—
355C2×C22⋊C4—51no—
356C2×C22⋊C4—51no—
357C2×C22⋊C4—51no—
358C2×C22⋊C4—51no—
359C2×C22⋊C4—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—51no—
363C2×C42—51no—
364C2×C42—51no—
365C2×C42—51no—
366C2×C42—51no—
367C2×C42—51no—
368C2×C42—51no—
369C2×C42C2×AGL(1,𝔽5)11yescharacteristic
370C4⋊C8—54no—
371C4⋊C8—54no—
372C4⋊C8—54no—
373C4⋊C8—54no—
374C4⋊C8—54no—
375C4⋊C8—54no—
376C22⋊C8—54no—
377C22⋊C8—54no—
378#97—54no—
379#97—201no—
380#97—201no—
381#97—201no—
382#97—201no—
383C4×C8—54no—
384C4×C8—201no—
385C4×C8—201no—
386C4×C8—201no—
387C4×C8—201no—
388#95—51no—
389#95—51no—
390#95—51no—
391#95—51no—
392#95—51no—
393#95—51no—
394#95—51no—
395#95—51no—
396#95C2×AGL(1,𝔽5)11yescharacteristic
397#95C2×AGL(1,𝔽5)11yescharacteristic
398#95C2×AGL(1,𝔽5)11yescharacteristic
399#95C2×AGL(1,𝔽5)11yescharacteristic
400C22×C5C22×C4211yescharacteristic
401C22×C5#52011yescharacteristic
402C22×C5#52011yescharacteristic
403C22×C5C2×#13111yescharacteristic
404C22×C5C2×#13111yescharacteristic
405C22×C5#56811yescharacteristic
406C22×C5#56811yescharacteristic
407C2×D5—22no—
408C2×D5—22no—
409C2×D5—22no—
410C2×D5—41no—
411C2×D5—41no—
412C2×D5—41no—
413C2×D5—41no—
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—41no—
419C4×C5—41no—
420C4×C5—41no—
421Dic5—22no—
422Dic5—22no—
423Dic5—22no—
424Dic5—41no—
425Dic5—41no—
426Dic5—41no—
427Dic5#51811yescharacteristic
428Dic5#51911yescharacteristic
429Dic5#52011yescharacteristic
430Dic5#52011yescharacteristic
431C24—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—51no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4C22×AGL(1,𝔽5)11yescharacteristic
446C22×C4C22×AGL(1,𝔽5)11yescharacteristic
447C22×C4C22×AGL(1,𝔽5)11yescharacteristic
448C22×C4C22×AGL(1,𝔽5)11yescharacteristic
449C22×C4C22×AGL(1,𝔽5)11yescharacteristic
450C22×C4C22×AGL(1,𝔽5)11yescharacteristic
451C22×C4C22×AGL(1,𝔽5)11yescharacteristic
452M16—204no—
453C2×C8—52no—
454C2×C8—52no—
455C2×C8—52no—
456C2×C8—52no—
457C2×C8—52no—
458C2×C8—52no—
459C2×C8—52no—
460C2×C8—52no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8—101no—
465C2×C8—101no—
466C2×C8—101no—
467C2×C8—101no—
468C2×C8—101no—
469C2×C8—101no—
470C2×C8—101no—
471C2×C8—101no—
472C2×C8—101no—
473C2×C8—101no—
474C2×C8—101no—
475C2×C8—101no—
476C2×C8—101no—
477C2×C8—204no—
478C4⋊C4—41no—
479C4⋊C4—54no—
480C4⋊C4—102no—
481C4⋊C4—102no—
482C4⋊C4—201no—
483C4⋊C4C4×AGL(1,𝔽5)14yes—
484C22⋊C4—54no—
485C22⋊C4—54no—
486C22⋊C4—102no—
487C22⋊C4—102no—
488C22⋊C4—201no—
489C22⋊C4—201no—
490C42—41no—
491C42—52no—
492C42—52no—
493C42—52no—
494C42—52no—
495C42—101no—
496C42—101no—
497C42—101no—
498C42—101no—
499C42—101no—
500C42—102no—
501C42—101no—
502C42—101no—
503C42—101no—
504C42—102no—
505C42—201no—
506C2×C5#227411yescharacteristic
507C2×C5C4×#13111yescharacteristic
508C2×C5#287511yescharacteristic
509C2×C5#299211yescharacteristic
510C2×C5#299211yescharacteristic
511C2×C5#299311yescharacteristic
512C2×C5#299311yescharacteristic
513D5—42no—
514C23—52no—
515C23—101no—
516C23—101no—
517C23—101no—
518C23—101no—
519C23—101no—
520C23—101no—
521C23C23×AGL(1,𝔽5)11yescharacteristic
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—51no—
540C2×C4—51no—
541C2×C4—51no—
542C2×C4—51no—
543C2×C4—51no—
544C2×C4—51no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—101no—
556C2×C4—101no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—101no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—101no—
565C2×C4—101no—
566C2×C4—101no—
567C2×C4C2×C4×AGL(1,𝔽5)12yes—
568C2×C4C2×C4×AGL(1,𝔽5)12yes—
569C2×C4C2×C4×AGL(1,𝔽5)12yes—
570C2×C4#413312yes—
571C8—102no—
572C8—102no—
573C8—102no—
574C8—102no—
575C8—102no—
576C8—102no—
577C8—102no—
578C8—102no—
579C5#2055311yescharacteristic, complemented, Sylow
580C22—102no—
581C22—102no—
582C22—102no—
583C22—201no—
584C22—201no—
585C22—201no—
586C22—201no—
587C22C22×C4×AGL(1,𝔽5)11yescharacteristic
588C22#6625611yescharacteristic
589C22C2×#413311yescharacteristic
590C22D5⋊#13111yescharacteristic
591C22#6626411yescharacteristic
592C22#6626611yescharacteristic
593C22#6626611yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—51no—
602C4—51no—
603C4—51no—
604C4—51no—
605C4—102no—
606C4—102no—
607C4—102no—
608C4—201no—
609C4—201no—
610C4—201no—
611C2—202no—
612C2#1061712711yescharacteristic
613C2#1061713611yescharacteristic
614C2C4×#413311yescharacteristic
615C2#1061727711yescharacteristic
616C2#1061730011yescharacteristic
617C2#1061734011yescharacteristic
618C2#1061735311yescharacteristic
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#387C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#387AGL(1,𝔽5)
hypocenterC5#20553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #10604316C2semidirect
5. #10604315C2semidirect
6. #10604181C2semidirect
7. C4×#4004C2semidirect
8. #10603781C2semidirect
9. #10603779C2semidirect
10. #10603778C2semidirect
11. #10603778C2semidirect
37. #65708C4semidirect
38. #65706C4semidirect
579. C5#20553semidirect

Maximal subgroups

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

subgroupindex
C2×#657062
C2×#657082
#106066702
#106043162
#106043152
#106041812
C4×#40042
#106037812
#106037792
#106037782
#106037772
#106037762
#106037752
#205535